ML20207S119
| ML20207S119 | |
| Person / Time | |
|---|---|
| Site: | Comanche Peak  |
| Issue date: | 09/30/1986 |
| From: | ROBERT L. CLOUD ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML20207S118 | List: |
| References | |
| NUDOCS 8703190005 | |
| Download: ML20207S119 (158) | |
Text
{{#Wiki_filter:) O Robert L. Cloud and Associates, Inc.
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O RLG O o CINCHED, SINGLE-STRUT U-BOLT SUPPORTS t O Design Review, Application Procedure and Acceptance Criteria Rev. 0 O l l i
- n RLCA/P142/01-86/004 l
f September, 1986 l iC ( l 50 I Robert L. Cloud Associates, Inc. i 125 University Avenue 20 Main Street Berkeley, California 94710 Cotuit, Massachusetts 02635 0 - t 'C 0703190005 061204 5 PDR ADOCK 0500 i
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N 10 g) TABLE OF CONTENTS
. Lase List of Figures lii O
List of Tables vii Nomenclature viii
;g Executive Summary ,
xii 1.0 Introduction 1 2.0 Previous Tests and Analyses by Westinghouse 3
!O 3.0 Supplementary Finite Element Analyses 6 I 3.1 Base Model for Stability and Stress 8
- Evaluation (Model 1) .
f 3.1.1 Description of Model 8 l 3.1.2 Load Case Analyses 11 'O, 3.1.3 Pipe Stress Distributions 17 ( l 3.2 Refined Elasto-Plastic Model fo'r Stress 21 Evaluation (Model 2) { lO 3.2.1 Description of Model 21 j 3.2.2 Load Case Analyses 22 j 3.2.3 Pipe Stress Distributions 22 3.3 Temperature Dependent Elastc -Plastic 23 Model for Thermal Cycling Evaluation () (Model 3) ! 3.3.1 Description of Model 23 l 3.3.2 Load Case Analyses 24 3.3.3 U-Bolt Tension Effects 24 3.3.4 Fatigue Evaluation 25 j [ 'O 4.0 Design Procedure 27 i j 4.1 Rotational Resistance of U-bolt Assembly 27
-(stability)
, '4.1.1 Equilibrium Conditions 27 4.1.2 Rotational Stability Conditions 29
'O 4.1.3 Empi rical Friction Factors and 30 4.1.4 Tensile Strut Load 33 j' - -i-L.. "O ,
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~;;^; ;;;~~' D _ . , , . _ - . : L. _ _ L . _ _ _ _ _ _ , . _ - . - _ _ _ . - _ - _ . _ .
c 0 ' I i s T BLE OF CONTENTS (con't) O E. age c 4.2 Load Distribution and Stiffness Properties 34 4.2.1 Mathematical Model of Pipe and U-Bolt Assembly 34 O. 4.2.2 Distribution of External Strut [ Load Between Pipe and U-bolt 35 4.2.3 Stiffness of Pipe (Kp) 37 4.2.4 Stiffness of U-Bolt Assembly (Kcl) 39 4.3 Internal Pressure and Thermal Expansion 41 C) Effects 4.4 Stress Calculations 43 4.4.1 U-Bolt Stresses 43 4.4.2 Cross Piece Stresses 44 4.4.3 Pipe Stress Evaluation 45 g 4.5 Prediction of Preload Losses 48 4 4.6 Validation of Design Procedure 53
- 4.6.1 Rotational Slippage Resistance 53 '
i 4.6.2 Friction Factors 53 jO 4.6.3 Distribution of Strut Load Between 54
- Pipe and U-Bolt i
; 5.0 Design Criteria 55 5.1 Stability Criteria 55 !g 5.2. U-bolt Component Stress Criteria 55
- 5.3 Local Pipe Acceptability 57 ll 5.3.1 Overview of Applicable Code 57 '
! Requirements - -
l 5.3.2 Implementation for Concentrated 59
! Radial Line Load O 5.3.2.1 Plastic Analyses for 59 Determination of Collapse Load '
5.3.2.2 Implementation for Cinched 63 l'j U-Bolt Supports lO l
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- 6.0 Conclusions 65 j 7.0 References 66 6
jg Tables Figures j , io
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O iO List of Fiqures 1.1 Typical Configuration of a Single-Strut, Cinched U-Bolt Assembly O 3.1 Test Configuration Represented by FEA [1] 3.2 FEA Model 1; Overview of Primary Model and Substructures O 3.3 FEA Model 1; Detailed Model Portion 3.4 FEA Model 1; Distribution of Gap / Friction Elements 3.5 Gap / Friction Element Behavior j 3.6 FEA Models 1 and 2; U-Bolt Force During Cinching l 3.7 FEA Model 1; U-Bolt / Pipe Form Distribution During ,
! Cinching O 3.8 FEA Model 1; Rotational Capacity for a Lateral Load 4 3.9 FEA Model 1; U-Bolt / Pipe Force Distribution during j Lateral Load l' 3.10 FEA Model 1; Predicted Failure Loads Compared JG to Friction Test Results , ; 3.11 FEA Model 1; U-Bolt / Pipe Force Distribution During ;
j Compressive Strut Load i 3.12 FEA Model 1; U-Bolt Tension as a Function of ; a} O Compressive Strut Load from Tests [1] and Analysis i 1 a I 10 :' 1 i lo - j -lii-
,D i
l . . _ . _ _ _ _ . _ _ . . . .. - . i [
O l () 3.13 FEA Model 1; U-Bolt / Pipe Force Distribution during Inclined Compressive Strut Load 3.14 FEA Model 1; Rotational Resistance Capacity Under Inclined Compressive Strut Load LO 3.15 FEA Model 1; Normal Force Distribution Resulting t from Internal Pressure 3.16 FEA Model 1; Circumferential Flexural and Membrane . Stresses Due to Preload of 4,140 lbs at z = 0.5 in. O 3.17 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 5,300 lbs at z = 0.5 in. l I 3.18 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs at z = 1.5 in. [ ! O 3.19 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs at z = 2.5 in. 3.20 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs at Z = 4 in. O 3.21. FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs and Compressive Load of 10 kips at z = 0.5 in. 3.22 FEA Model 1; Circumferential Flexural and Membrane
! Stresses Due to Preload of 4,140 lbs and Pressure of 600 psi at z - 0.5 in.
I' O J 3.23 FEA Model 1; Longitudinal Membrane Stress in the j Pipe / Cross Piece Contact Area Due to a Preload of j 5,300 lbs. $0 3.24 FEA Model 1; Longitudinal Flexural Stress in the Pipe / l' Cross Piece Contact Area Due to a Preload of 5,300 lbs. j! 3.25 Comparison of Pipe Stress Results between FEAs and Tests j for Outside Pipe Surface 30 i ' 3.26 FEA Model 2; Refined, Elasto-Plastic Model Detailed Portion 3 3.27 FEA Model 2; Refined, Elasto-Plastic Model Substructure O 3.28 FEA Model 2; Circumferential Flexural, Membrane, and
; Equivalent Stresses at z = 0.5 Due to Preload of 5425 lbs.
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O l 3.29 ~Comparision of Equivalent Stress Distributions
) Between Model 1 and Model 2 3.30 FEA Model 3; Overview of Primary Model and Substructures O 3.31 Stress-Strain Relationship Used for SA312, TP304 Stainless Steel 3.32 Parameter Study for Validation Study of Through Thickness Mesh Refinement [26]
3.33 U-bolt Tension Histogram During Thermal C.ycling O Analysis [29] I 3.34 Contact Force versus Pipe Diameter Reduction l for Thermal Cycling Analysis [29] 4.1 Idealized U-Bolt Model for Design Application
;g 4.2 Mathematical Model of U-Bolt / Pipe Assembly 4.3 Simplified U-Bolt / Pipe Model
? O 4.4 Change in Cross Piece / Pipe Contact Force Due to External Load )i 4.5 Schematic Representation of Change in U-bolt Tension Variation with External Strut Load 1 4.6 U-Bolt / Pipe Assembly with Shim Plate for Thermal
' 9' Expansion Evaluation 4.7 U-Bolt Assembly Idealization for Stress i Calculations l
5 p' 4.8 Load Distribution and Stress Location for Local
;' Pipe Stress Evaluation [28]
l 4.9 Characteristic shape of Circumferential Bending and Membrane Stress Distributions i 4.10 Comparison of Maximum Slip Force between Test Results
!g [1] and Design Procedure (Section 4) for 4" Schedule
- 160 pipe.
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O () 4.11 Comparision of Maximum Slip Force between Test Results [1] and Design Procedure (Section 4) for 10" Schedule 40 S.S. pipe. 4.12 Comparison of Maximum Slip Force between Test Results [1] and Design Procedure (Section 4) for 10" Schedule O 80 C.S. pipe. 4.13 Comparison of Maximum Slip Force between Test Results [1] and Design Procedure (Section 4) for 32" M.S. Pipe. O 4.14 Comparison of U-bolt Leg Force under the Effect of Tensile Strut Load between Test Results [1] and Design Procedure (Section 4) for 10" Schedule 40 S.S. pipe. 4.15 Comparison of U-bolt Leg Force Under the Effect of Compressive Strut Load between Test Results [1] and O Design Procedure (Section 4) for 10" Schedule 40 l S.S. Pipe, i 4.16 Comparison of Circumferential Pipe Stresses from i FEA (Model 1 in Sectin 3), " BEARING" [27], and FEA [27] program used for verification of " BEARING". LO 4.17 Comparison of Longitudinal Pipe Stresses from FEA (Model 1 in Section 3), " BEARING" [27], and FEA [27] program used for verification of " BEARING". 5.1 Support Reaction (R) vs. Diameter Reduction Curve - C Case 1 5.2 Support Reaction (R) vs. Diameter Reduction Curve - Case 2 , 5.3 Support Reaction (R) vs. Diameter Reduction Curve -
- O Case 3 5.4 Support Reaction (R) vs. Diameter Reduction Curve -
Case 4
- 5.5 Support Reaction (R) vs. Diameter Reduction Curve -
- O Case 5 4
5.6 Load Cycling Behavior of 12" SCH 80S Pipe Between , 1G Load and 2/3 x Pc.
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i i O i O List of Tables 2.1 Matrix of Westinghouse Tests t 2.2 Matrix of Existing (Westinghouse) Finite Element EO Analyses 3.1 Representative Maximum Elastic Stresses from FEA 3.2 Comparison of Temperature Dependent Properties of Pipe Materials i O l 4.1 U-Bolt Stresses Before, During and Afte'r Thermal Cycling and Creep Tests [1] / 4.2 Comparison of U-bolt tension and Pipe Stresses i Between Design Procedure (Section 4) and FEA [2] o for 4" Schedule 160 pipe. 4.3 Comparison of U-bolt Tension and Pipe Stresses , Between Design Procedure (Section 4) and FEA[2] i for 10" Schedule 40 S.S. Pipe. ! o 4.4 Comparison of U-bolt Tension and Pipe Stresses Between Design Procedure (Section 4) and FEA[2] for 10" Schedule 80 C.S. Pipe. f 4.5 Comparison of U-bolt Tension and Pipe Stresses l
, Between Design Procedure (Section 4) and FEA[2] !O for 32" M.S. pipe.
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! 4.6 Minimum and average value of friction factor, , 1 i based on test results [1] ll ! 5.1 Dimensional Parameters Used for Plastic Collapse Load Analyses [12]
(Q L , I { t .I IO 1 n -vil-h 4 O l
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'O O Nomenclature:
A Distance between pipe / cross piece contact point and center of pin in cross piece connecting the strut (inches) .O a Change in contact force between pipe and cross piece due to external strut load P (1bs) 2 , au Cross section area of U-bolt (inches ) 12 b Change in contact force between pipe and U-bolt due to external strut load P (1bs) bc Cross piece width (inches) C Constant in collapse load equation Cg Factor accounting for preload losses in t U-bolt I D Nominal pipe diameter (inches)
- O D, Pipe outer diameter (inches) d U-bolt diameter (inches) ;
I dm mean pipe diameter (inches) { !O E Young's moddlus (psi) f Exponent in collapse load equation . 4 ftb U-bolt tensile stress (ksi) O Fu U-bolt tension (1bs) i 4 F.S. Factor of safety j Fp Force between cross peice and pipe (lbs) l, f
- O g Exponent in collapse load equation {
I h Height of cross-piece I Moment of inertia of cross-section of cross-piece (in+) 30
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O O I E Moment of inertia of cross section of cross-piece (in+) Ec Cross-piece stiffness (lbs/ inch) K,eg Combined stiffness of cross-piece and
- O U-bolt (1bs/ inch)
Kp Pipe stiffness based on unit change in pipe diameter (lbs/ inch) Ku p-bolt stiffness (1bs/ inch) Kt Proportionality factor of U-bolt torquing L, Half the difference in length between cross-piece and bracket (inches) O Lg Half the length of bracket in cross-piece , assembly (inches) Ng Force between cross-piece and pipe (1bs) Ng Force between U-bolt and pipe (lbs) t O P External strut load, +ve for compression, L
-ve for tension (1bs) l l
Pc Collapse load (lbs) l 0 PT Tangential strut load (lbs) , i p Internal pressure of pipe (psi) - l R Pipe outer radius (inches) O Rt Pipe inner radius (inches) Rm Pipe mean radius (inches) r l r U-bolt radius (inches) ,
,O tp Pipe thickness (inches) l ! I t'
[ Shim plate thickness (inches)
\ , T Torque required to produce a U-bolt i tension, Uo, which equals lO (u.
- Kt.d)/12 (ft/lbs) o
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- g Tt Torque required to ensure rotational stability against inclined external strut load (ft-lbs)
Tg Torque required to ensure U-bolt remains in tension upon loading of compressive 40 strut load (f t-Ibs) T3 Torque required to ensure contact between pipe and cross-piece upon loading of tensile strut load (f t-lbs) !O U Average U-bolt tension between leg 1 and leg 2 (1bs)
- U, U-bolt initial tension due to preload (1bs) o Uy t U U-bolt tension in leg 1, leg 2, respectively, (1bs)
A. Equivalent coefficient of friction between pipe and cross-piece, U-bolt j {g g Angle of inclination of external strut load (degrees) i N[ Factors for distribution of external strut load between the U-bolt / pipe ,
- contact and cross-piece / pipe contact
- O AUr Increase of U-bolt tension due to pressure effect AUs Difference in U-bolt tension between leg 1 and leg 2 (1bs) i('
\ \ AUr Increase in U-bolt tension due to j differential thermal expansion ; i air'ATs,ATu changes in temperature in pipe, shim . l plate, and U-bolt, respectively ( F) l
- 'O o(p, 4' 4 Coefficients of thermal expansion of pipe, shim plate, and U-bolt respectively, (in/in/ F)
- 7 Poisson's ratio f Differential expansion between U-bolt and i the pipe (inches) i i
i -x-l0 _ _ _ . . _ _ _ _ _ . _ _ . _ . , _ _ _ _ _ _ _ . _ . , _ , . _ _ _ . . . . _ _ _ _ _ _ _ _ _ _ _ . . . , _ . _ . . , _ _ . ~ , . _ _ . _ - _ _ _ _ _
I O l O 4 Pipe and shim plate expansion (inches) f Thermal expansion of U-bolt without cross-piece constraint (inches) O [O b I ! O s vO t
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- O I
j C> EXECUTIVE
SUMMARY
This report describes a comprehensive design review performed by RLCA of the cinched U-bolt pipe support clamps used at the Comanche Peak Steam Electric
- O station. The design review consisted of: (1) review of existing tests and analyses; (2) performance of complementary, confirmatory analyses; (3) development of conservative design procedure; and (4) definition of j acceptance criteria consistent with applicable Code requirements.
lO As shown in Figure 1.1, the cinched U-bolt assembly consists of a U-shaped, threaded rod, a structural cross piece member and a bracket for strut attachment. The assembly is completed by tightening the nuts on the U-bolt to a predetermined torque !O level to achieve the appropriate clamping action on i the pipe. This operation, which is referred to as j cinching the U-bolt, is required to prevent slippage between the U-bolt and the pipe. A conservative design procedure has been developed }O
- (section 4.0), which has been validated against full
! scale tests as well as detailed finite element analyses. The design procedure takes into account the following i design and functionality aspects of the cinched U-bolts: i ! o U-bolt torque (preload) required to assure IO rotational stability of the U-bolt assembly, ! when subjected to inclined, compressive or
- tensile strut loading.
I
- o Potential for loss of preload due to thermal
- cycling or other time dependent effects.
!O l o Prediction of force and stress variations in U-bolt components and locally in the pipe ( under the combined effects of preload, thermal i cycling, pressure cycling and external strut ! reaction. !O 3 o Code compliance of U-bolt components and the
- pipe under worst case of the combined effects
- from preload, thermal cycling, pressure cycling,
{ and support reactions transmitted through the
- strut.
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O g Executive Summarv (Continued) Full Scale Tests fil l A series of full scale tests were performed in 1984 by Westinghouse [1] to investigate the O characteristic behavior of cinched U-bolts under , enveloping service conditions in terms of slippage potential and resulting maximum stresses in the U-bolt components and locally in the pipe. A total of four configurations were tested, ranging in pipe size from 4 inch to 32 inch. The following tests were )O Performed (see also test matrix overview in Table 2.1): ! a. Bolt torque versus bolt tension test for all , four configurations with U-bolt sizes ranging l from 0.5 inch to 2.75 inch. The results from l g this test showed an approximately linear ! relationship between applied torque and resulting tension.
- b. Friction tests for all four configurations, where the rotational load capacity was O determined as a function of bolt torque (preload) and dimensional parameters. The results showed a linear relationship between preload and rotational friction c~apacity.
I
- c. Load distribution tests for 10 inch configuration. The variation of U-bolt tension lO with strut load was determined for different l initial preload levels.
I d. Thermal cycling tests. Three of the configurations were subjected to series of 10 lO complete sequential cycles between room temperature and design temperature. The l applicable design temperatures were 560 F for the 4 inch and 32 inch configuration, and 250
> F for the 10 inch configuration.
l l e. Short term relaxation tests. The three configurations subjected to thermal cycling lC tests were held at the design temperature for 24 I hours while strain measurements were recorded. The U-bolt strain variations (i.e., the l change in preload) were negligible in all { cases confirming the absence of short term
- g. O relaxation effects after the initial thermal j cycles.
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- , . ,. . ... .. , - . ~ . - - . - . . . - . . . - . . . ~ . . - ;O l C) Executive summarv (Continued)
- f. Normal vibration and seismic simulation tests :
were performed on a 10 inch configuration by introducing forcing functions to the U-bolt assembly through an inclinded strut attached 0- to the cross piece bracket. During the early phase of the vibration test a slight
- repositioning (friction redistribution) took place which resulted in a small preload
! reduction. No perceptible rotational slippage occurred, and the axial repositioning that ,O was observed was consistently self-stabilizing j towards a reduction in strut angle. Westinghouse FEA [2] Westinghouse performed finite element analyses lO (FEA) of U-bolt / pipe configurations corresponding to 3 the tested configurations (2]. Analyses were performed to evaluate variations in U-bolt leg tension and stresses in U-bolt components as well as the pipe i under the following load combinations: !O a. Preload only i l b. Preload and thermal expansion
- c. Preload and thermal expansion and internal
! pressure 10 l d. Preload and thermal expansion and internal i pressure and compressive strut load. . F ) It was concluded [2] from these analyses that: 1 l L7 o The stability of the U-bolt support can be l assured by cinching. , i [ o For cinching torque values used in the analyses, j the stresses in the U-bolt components and the pipe will be acceptable.
- O 3 RLCA Finite Element Analyses (Section 3.0) i Additional FEAs, supplementing those performed by i Westinghouse, have been performed by Robert L. Cloud Associates (RLCA) in order to support a general design iO procedure for cinched U-bolts. The specific objectives
! for these additional analyses were as follows:
i l -xiv-e0
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10 JO Executive summarv (continued)
, a. Confirm the ability of the analytical model ;
to reproduce the slippage failure mode 1
- demonstrated during the friction tests.
lO b. Confirm the adequacy of the FEA mesh refinement used.
- c. Demonstrate that the variation in U-bolt tension observed in the load distribution tests can be analytically reproduced. ;
.O
- d. Demonstrate a detailed understanding of the development of friction forces under different service conditions and their effect on rotational stability.
JO e. Evaluate the margin to slippage failure under i enveloping design conditions with inclined strut load and without the stabilizing effects ; of thermal expansion and internal pressure. i
, f. Evaluate the potential for preload losses
10 caused by local pipe plasticity during thermal cycling. j l g. Determine the maximum acceptable, local l
- compressive load effect on the pipe based on 3
comprehensive elasto-plastic collapse load li jO evaluations. l l h. Determine the potential for local fatigue damage
- or incremental deformation in the pipe wall as a
! result of cyclic loading. !O The results from these analyses are summarized
- briefly in the following paragraphs.
i l . The majority of the analyses (items a,c,d,e 1:
't
- above) were performed on an elastic model representing E the 10 inch Sch. 40s configuration that had been lC subjected to a full range of tests [1]. A refined
- model using elasto-plastic elements was used to
! confirm the adequacy and reliability of results from ,.
- the base model (item b, above). A detailed, double symmetric model with temperature-dependent, elasto-plastic element properties was used for the 4
.O ? thermal cycling evaluation (item f, above). i
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O C) Executive Summarv (Continued) The analyses successful demonstrated the analytical reproducibility of rotational slippage failures observed in the tests. The analysis of the enveloping design condition with an inclined (5 degrees)
,O compressive strut load demonstrated that the ultimate slippage failure could be approached in a predictable, stable fashion.
Thermal cycling analyses were performed for conservative, enveloping combinations of those design O parameters that would tend to maximize the potential for resulting loss of preload, namely o Stainless steel pipe material with a high coefficient of thermal expansion, and a
, significant reduction in (Code-specified) yield ' C) strength at increasing temperatures.
o High temperature l o Large diameter, thin-walled pipe l l C) o High initial preload l l The resulting, maximum preload loss under this L extreme scenario was found to be 184. The bounding value for these losses under less extreme conditions is ;< estimated at 10-124 based on the analyses. It is O further estimated that less than 5% of the cinched , U-bolts at CPSES are associated with design parameters 4 that could make the preload losses approach the higher (; percentage given. Preload losses due to initial friction ' redistribution are estimated not to exceed 2-5%. The . lO loss of preload would take place during the first full ! thermal cycle with no additional losses in subsequent cycles. These thermal cycling analyses were also used ( to demonstrate that neither fatigue nor ratcheting under sustained internal pressure will goven the design. O Subsection NC of ASME III addresses the local ) pipe effects at supports only in qualitative terms. ;; It states, for example, that " damage", " buckling",
" collapse", and " flattening" of the pipe shall be ;
prevented. Due to the absence of code-specified local I jo i 4 -xvi-1 3 o 3 _ __ _ _ -. ._ _ . , _ _ , . . _ . . _ _ . _ - - . - . _ _ . _ , _ . _ _ _ . . _ _ _ . _ _ _ _ _ _ . . . . , . . . - - ~ . _ , _ . , _ . . -
i r Executive Summary (Continued) f C) l pipe stress limitations at support contact regions, it was decided to explicitly evaluate the potential for damage, collapse and flattening of the pipe by means of detailed, plastic collapse load analyses. In this , O analyses, the term " collapse load" is consistently used ' in accordance with the conservative, relative deformation-based definition used in ASME Section III.
! A series of elasto-plastic collapse load analyses were performed for pipe sizes ranging from 12 inch to 30 O,
inches (12]. Based on the results from these analyses, a generalized formula was derived which defines the collapse load as a function of pipe size, wall thickness, support width and yield strength. The 3 allowable compressive load effect on the pipe due to l preload and all other loading conditions is then i O_ determined as a two-thirds of the collapse load, consistent with the design philosophy of ASME Section r III. l Desian Procedure RLCA has developed a general design procedure f() (Section 4.0) for cinched U-bolts, which has been validated against results from tests as well as detailed l finite element analyses. The design procedure covers I all relevant aspects of the U-bolt design in terms of Code compliance as well as the demonstrated ability to ( '_- perform its intended function as summarized below: o slippage Resistance. A methodology has been
- developed to determine the minimum required
; U-bolt preload (bolt torque) for assurance of rotational stability. This methodology was lU ; theoretically derived and then validated ; against results from tests and FEA. The , method accounts for the reduction in U-bolt tension that takes place when the assembly is subjected to compressive strut reactions. It further accounts for strut load magnitude and
- C) angle of inclination as well as dimensional
- parameters such as pin / bracket eccentricity, pipe size, wall thickness, cross piece width and thickness, and U-bolt size. The minimum
- required torque value is increased by a safety factor of 1.5 consistent with Code O requirements for stabilty considerations.
-xvil-0 i
O I IC? Executive Summary (Continued) i ! O Allowance for conservatively predicted preload I losses is made by a factor which increases l initial bolt torque. i o Effects from partially restrained pipe expansion i due to temperature and pressure. The increases in U-bolt tension, cross piece bending and pipe compression due to temperature and pressure are determined as part of the design C, procedure. 1 o strut reaction distribution between pipe and U-bolt. The maximum U-bolt tension increase under tensile strut load as well as maximum pipe compression under compressive strut load 4 O are quantified. This load distribution between pipe and U-bolt is dependent on the relative stiffness between the U-bolt and the , pipe and has been validated against tests and j FEA. ; i O o U-bolt component acceptance criteria. The maximum load effects on the U-bolt and the : cross piece due to worst case combination of preload, thermal expansion, internal pressure, and tensile strut reactions are determined and limited to allowables defined by ASME J3 III/NF. These maximum total component stresses are further limited to the yield stress at temperature in order to prevent preload losses due to permanent deformation.
! o Pipe acceptability. The maximum compressive 'O force on the pipe caused by the combined ; effects of preload, restrained thermal , expansion, restrained pressure expansion, and compressive strut reactions is determined and compared to allowable values derived from detailed elasto-plastic collapse load analyses.
O The potential for fatigue.pamage or incremental deformation under sustaingd' internal pressure
, and thermal cycling has been demonstrated to be '
negligible.
-xviii-f a .
i
O
.O Executive summarv (Continued)
Conclusions Based on the evaluations presented in this report, it is concluded that cinched U-bolts designed
.O and preloaded in accordance with the design procedure defined by section 4, while satisfying the acceptance criteria in section 5, have been demonstrated to have i the ability to perform their intended functions and to meet all applicable Code requirements.
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1.0 INTRODUCTION
f L As part of the current reevaluation of all piping and pipe supports at Comanche Peak Steam Electric Station (CPSES), a design verification effort has been performed for the support category that employs C} cinched U-bolts with a single strut or snubber. (A typical U-bolt configuration with a definition of the terms used in this report is shown in Figure 1.1). The U-bolt clamp assembly (Figure 1.1) is associated I with characteristic load transfer mechanisms that, in most respects, are comparable an6 similar to those of a lO " standard pipe clamp". Most importantly, it is recognized that both types of clamps rely on friction forces between the pipe and the clamp to prevent rotation around the pipe axis when the clamp is subjected to inclined strut loads. These friction O forces are in both cases assured by pre-torquing the bolts that hold the clamp assemblies together. The j standard pipe clamp has been more commonly used than the j U-bolt clamp and has therefore accumulated a larger ,
; experience-based performance record. This is one of the reasons for the detailed evaluations that have been i]O ;
performed for the cinched U-bolt clamp as reported herein. The engineering aspects that have been d addressed in the evaluations have focused primarily on the following topics: o structural stability, i.e., assurance of O adequate rotational resistance to prevent a 1 3-hinge mechanism between the clamp and the -i strut. . e I t 1 o Potential for time-dependent preload losses.
\
19 ' o Acceptability of stresses and strains introduced by the cinched U-bolt locally in the pipe wall as well as in the U-bolt assembly itself under d all internally and externally generated loads. 1 I The current design verification of cinched L ]O U-bolts consists of four parts: (1) review of b q) existing tests and analyses, (2) performance of j additional, complementary analyses, (3) derivation of a 3 l0 1 i 'l 0
]
30 ,
,-,+,.--e
_.,,m- ,_.-,,,,,,7 r,,4.._,,y.,-o, , - , , ,..w,___,-,---,------.-,-y--~.,_,_,y__,, ,my,,,- -.,o,-__ ---..._,__.w. - - - -
,,,,-..._,,w.,,,_--,_,_-,- ~
'O lO design procedure with validation against tests and analyses, and (4) definition of acceptance criteria.
This report provides a generic design procedure for determination of minimum required preload on cinched U-bolts. It further provides the analytical and iO empirical basis for this procedure, as well as identification of applicable acceptance criteria in accordance with ASME Section III. The results presented in the report demonstrate that the cinched U-bolt design procedures defined in SWEC document CPPP-7, Attachment 4-12, conservat,1vely satisfy all applicable Code iO requirements. iO l l i .! O O iO i i 2 a O I f l i 0 iO l
.O O 2.0 PREVIOUS TESTS AND ANALYSES BY WESTINGHOUSE Westinghouse Electric Corporation performed on TUGCO's request in early 1984, a series of full scale tests and finite element analyses on four single-strut cinched U-bolt supports. The purpose of these tests
- O and analyses was to investigate the ability of the U-bolt assemblies to resist rotation around the pipe when subjected to eccentric loading, and to investigate the local stress state in the pipe as influenced by the l presence of the cinched U-bolt. The results from these q tests and analyses were reported in [1] and [2],
(O respectively.
- A total of four configurations were included in the test program ranging in pipe size from 4 inch to 32 inch. The following tests were performed (see also test O
matrix overview in Table 2.1):
- a. Bolt torque versus bolt tension test for all four configurations with U-bolt sizes ranging from 0.5 inch to 2.75 inch. The results from this test showed an approximately linear relationship between applied torque and O resulting tension,
- b. Friction tests for all four configurations, where the rotational load capacity was determined as a function of bolt torque (preload) and dimensional parameters. The V results showed a linear relationship between preload and rotational friction capacity.
- c. Load distribution tests for 10 inch configuration. The variation of U-bolt tension as a function of strut load magnitude was O determined for different initial preload levels.
- d. Thermal cycling tests. Three of the configurations were subjected to series of 10 complete sequential cycles between room temperature and design temperature. The O. applicable design temperatures were 560 F for the 4 inch and 32 inch configuration, and 250 F for the 10 inch configuration.
O it) _ . _ . , _ . . . _ . . , ,, . . ~ . . . . ,.
O O e. Short term relaxation tests. The three configurations subjected to thermal cycling tests were held at the design temperature for 24 hours while strain measurements were recorded. The U-bolt strain variations (i.e., the change in preload) were negligible in all cases O indicating the absence of short term relaxation effects after the initial thermal cycles.
- f. Normal vibration and seismic simultation tests were performed on a 10 inch configuration by introducing forcing functions to the U-bolt O assembly through an inclined strut attached to the cross piece bracket. During the early phase of the vibration test a slight repositioning (friction redistribution) took place which resulted in a small preload reduction. No perceptible rotational slippage occurred, and C the axial repositioning that was observed was consistently self-stabilizing towards a reduction in strut angle.
The Westinghouse finite element analyses [2] corresponded to the test configurations reported in [1]. O These analyses were performed to evaluate variations in U-bolt leg tension and stresses in U-bolt components as well as the pipe under the following load combinations (see also FEA matrix overview in Table 2.2):
- a. Preload only
- b. Preload and thermal expansion 1
l c. Preload and thermal expansion and internal pressure O d. Preload and thermal expansion and internal pressure and compressive strut load. It was concluded [2] from these analyses that o The stability of the U-bolt support can be l0 assured by cinching. o For the preload torque values that were used 4 in the analyses, the stresses in the U-bolt components and the pipe were shown to be acceptable. O _ m mm . . . s , -o.sw s - - - ,w w s n. , e e .q
O O The results from the tests as reported in [1], have been used extensively in the current design verification effort for purposes of bench-marking and validating additional analytical behavior predictions as well as a simplified design application methodology. T3 Relevant parts of the test results are referenced and discussed in applicable sections of the report. For more detailed information about the Westinghouse testa and analyses related to cinched U-bolts, see References [1] and [2]. O IO l 1 1 0 , O t O O l 1 O l l
>O j
O O 3.0 SUPPLEMENTARY FINITE ELEMENT ANALYSES Based on the review of existing analyses and tests (section 2), it was determined that. complementary finite element analyses (FEA) would be performed for the objective of confirming:
- a. Analytical reproducibility of slippage failure mode demonstrated during the friction tests reported in [1].
- b. Analytical reproducibility of the load O distribution tests reported in [1]. -
- c. Distribution of normal forces and friction forces between pipe and U-bolt assembly, and redistribution of these forces under various load conditions.
,O
- d. Failure prediction (slippage) under enveloping design conditions, i.e., 5 degree inclined strut load, with no thermal or pressure effects. l
- e. Adequacy of simplified working model to
!O conservatively predict U-bolt behavior for design purposes. ,
- f. Predictability of preload losses due to local l pipe plasticity during thermal cycling. t
') 9. Potential for pipe wall fatigue damage or incremental deformation (shakedown to elastic !
action). These analyses are not meant to replace any of the l existing Westinghouse analyses, but rather to supplement ; O them and provide more detailed information as listed above. Particular emphasis in these supplementary , analyses has been placed on the analytical representation ' of distributed, variable friction forces and the ability ' of the finite element model to reproduce the actual slippage failure mode. In addition, the temperature- I O dependent elasto-plastic properties of the pipe material were taken into account for thermal cycling evaluations. These considerations were not addressed in (2]. . The base configuration chosen for the supplementary analyses was the 10 inch schedule 40 stainless steel O (88) pipe with a 3/4" U-bolt as tested [1;. This selection was based on the following consnderations. O
O O o This configuration was subjected to the widest range of testing conditions (see Table 2.1) and therefore provides the best basis for verification of an analytical design procedure. O o The relatively thin-walled pipe provides a relevant basis for conclusions regarding local pipe stresses. o The combination of thin-walled pipe and stainless steel provides a basis for bounding conclusions O regarding preload losses during initial thermal cycling. This is due to the characteristic properties of stainless steel such as high thermal expansion coefficient and rapid reduction in yield strength at increased temperatures in this configuration. A limited set of analyses (cinching load case) was also performed on a configuration that was similar to the base configuration in all respects except for the pipe wall thickness which was changed from schedule 40 to schedule 80. This dimensional parameter change 'O provides information related to variation in the relative pipe /U-bolt stiffness, which has a significant effect on the internal load distribution within the pipe /U-bolt assembly. For cost / benefit reasons, three separate finite
; element models were generated with character 1ctic l, properties specifically tailored to different analysis requirements: ,
Model it 0 This is an electic r.odel with a mesh size approximately the same as that used for the analyses reported in [2]. The majority of the analyses related to stability and friction development were performed using this model as described in Section 3.1 below. O
').
l 0 l j
O O Model 2: This model is a refinement of Model 1 with elasto-plastic pipe shell elements in the vicinity of the U-bolt and cross piece that are one-half the size of the corresponding O elastic elements in Model 1. This model was used for a limited number of analyses to confirm the adequacy of the mesh refinement of Model 1. These analyses are described in section 3.2. O Model 3: This model was used exclusively for predictios. of worst case preload losses due to thermal cycling. The model takes advantage of the double symmetry that is possible with this type of loading. The 0
- element mesh is a further refinement of Model 2 and takes into account the temperature dependent elasto-plastic material properties. The thermal cycling analyses performed with this model are described in Section 3.3.
0 3.1 PASE MODEL FOR STABILITY AND STRESS EVALUATION Model I was generated using the ANSYS Code [3] on the RLCA VAX 11/750 computer. The model was made consistent with the as-tested configuration of the 10 Q inch Schedule 40 pipe /U-bolt as reported in [1] and is shown in Figure 3.1. The details of the model generation, the load case analyses performed, and the results obtained are discussed below in Subsections 3.1.1, 3.1.2 and 3.1.3, respectively. O 3.1.1 Description of Model The analytical model represents a 10 foot section of pipe welded to fixed end plates with the U-bolt located at midspan as indicated in Figure 3.1. Recognizing symmetry at the plane of the U-bolt reduces O the analytical model to that shown in Figure 3.2. This figure shows the primary analytical model and the i substructures used to represent the distant pipe sections and boundary end condition. Figure 3.3 shows only the primary model of the U-bolt on the pipe. O O p
. -- - - _ - - __ . - .= - - - _ . - - - - . - _ - - . -
s io
!O The size of the pipe elements in the contact region :
between the pipe and the U-bolt clamp is similar to that { used in the previous analyses [2] for the corresponding
; configuration. The main criterion for the choice of i mesh size for this particular model was its ability j to accurately represent deformations and friction to phenomena. Detailed stress representation was ; ) secondary, since the more refined models (#2 and 93) ( ) would be used for confirmatory elasto-plastic stress,_ t }
comparisons. l The circumference of the pipe at the U-bolt plane jo of symmetry was divided into 36 equal elements of 10 4
- degrees each (0.91 inch) . Five " rings" of 36 elements each made up the pipe section of the primary model as
} shown in Figure 3.3. The three rings closest to the j
U-bolt have a longitudinal dimension of 1.0" while the long. The outer 2.0" ring connects to outer two are 2.0 lC the first substructure. The mesh size in the - , substructed segments was increased by a factor of two in *
- the first segment and was then kept constant in the 1
) remaining three segments as shown in Figure 3.2. The l
! end of the 4th substructure model was fully restrained '
i consistent with the test condition. The eJements used iO to represent the pipe wall were quadrilateral shell j elements, ANSYS type STIF63. The U-bolt was modeled as a sequence of beam l i' elements representing a solid circular rod. Over the curved 180 degree region of potential contact with !
- o the pipe, the U-bolt nodal points were placed directly N i opposite the corresponding pipe nodal points at 10
( degree intervals. Each connection of the U-bolt leg
- portion to the cross piece was modeled as being ,
i pinned at mid-depth. The last 1/2 inch length of l each U-bolt leg, before the cross piece connection, hj was modeled as a special element having mechanical 1 ! properties identical to the rest of the U-bolt, but I with fictitious thermal expansion properties. These two elements were used for introduction of U-bolt preload through application of a thermal contraction. The coefficient of thermal expansion for these elemente ! l0 was defined as -0.2 in/in/ F. This meant that an applied temperature difference of 1 F resulted in a p t ti corresponding shortening of the U-bolt leg of 0.1 inch / li' ' which represents one complete turn of the nut with 10 threads per inch. The elements used for the U-bolt were j ANSYS type STIF4. !! O i lI 4 II [o h 4 a y--.~.....-.-.-.--
~
f .I, - r
~
70& , :n
/ - ,/
9-:O The contact between the U-bolt and the pipe was represented by gap / friction elements (AESYS type STIF52) 1 j'^ connecting each U-bolt node with its pipe counterpart at
" - every 10 degrees over the 180 degree region as shown in
'~
Figure 3.4. Tne initial gap sizes were based on an _~ _ - C assumed inside U-bolt bend radius that was 1/16* 1arger
- .O than the outside pipe. radius, centered 1/16" from the pipe center and wsth a point contact at the top of the assembly.. This corresponds to a nonlinear increase in
. gap from 0" (closed) at the top to 1/16" at 90 degrees away from the top on uither side.
JO The behavior of the gap / friction elements is illustrated in Figure 3.5a. The frictional force developed in this element is a function of the normal fored, N, the shear force in the plane of contact, s,
. . and the coefficent'of friction, . As Figure 3.5b indicates, the applied shear force is resisted by an IO equal f riction' force up to the limit of N. At ahear
' forces greater than this limit, an unbalanced ahear force ( = S-AN) develops. For the simple model shown in
- Figure 3.5 (a), the unbalanced shear force would result
- in motion as characterized by Figure 3.5c. In the 1 U-bolt scuel the unbalanced shear force in a single gap 30 element would preclude convergence and force the
' analysis into another iteration. The subsequent
- iteration would have a slightly different force
- / distribution dephndent on the unbalanced shear force as l well as a small relative displacement of the gap element i releasing the shear force. The magnitudes of
!O displacements (slippage) and force redistributions are l ' determined iterat.tvely until equilibrium and
- compatibility have been achieved.
! The cross piece, which for the tested configuration i consisted of a structural steel plate 1-1/4" thick by 4" !O wide, was modeled by quadrilateral shell elements (STIF l 63). A combination of plate elements in the shape of a i "Y" was used to represent the offset strut load i application point, or bracket, as shown in Figure 3.3. 1 10 f I O k C
.. . _ - . = .. . - _ - -- .- . . . .
O 13 The initial line of contact between the pipe and the cross piece, along the width of the cross piece, was modeled with initially closed gaps at each node. A line of potential contact was modeled with geometrically consistent gap openings on either side of the initial contact line. A friction coefficient of 0.16 was specirted for all gap / friction elements at.the cross piece an, well as
- the U-bolt contact with the pipe surface. This value was selected as being representative of the results from the friction tests [1]. For a further discussion hD about the interpretation of the friction test results for determination of friction coefficient values, see ,
Section 4.1.3. i l Boundary conditions prohibiting out of plane l displacements were specified for all pipe, U-bolt, lO ! and cross piece nodal points located in the plane of
- h. symmetry passing through the center of the U-bolt
- ' assembly. Consistent with the consideration of
- symmetry, only half the widtb<of the U-bolt and cross l piece were modeled. Similarly, all applied strut loads j and all resulting forces in the plane of symmetry j O represent only one-half of the actual quantities.
l 3.1.2 Load Case Analyses a (" Model 1, as described in 3.1.1 above, was subjected to the following load case analyses:
- 0 I, a. U-bolt cinching (preload) of Schedule 40
) < as well as Schedule 80 pipe ? > b. Preload plus tangential (90 cegrees) strut loao i (friction test) for Schedule 40 pipe
- r. O
! c. Preload plus straight (0 degree) compressive I strut loads for Schedule 40 pipe
- d. Preload plus inclined (5 degrees) compressive strut load for Schedule 40 pipe
, e. Preload plus internal pressure for Schedule j 40 pipe sO J 1 jo
-_m,.-._._.__ , - - _ _ . - - - - - . . -
O i O The results from these 6 load case analyses are discussed in the following paragraphs:
- a. U-bolt cinchina (preload) k The cinching of the U-bolt to a conforming fit
'O around approximately one half of the pipe circumference I
is accomplished in the field by gradually tightening the i U-bolt nuts in an alternating fashion to obtain as i uniform a tension in the two legs as possible. This l operation was represented in the finite element model by l gradually subjecting the short U-bolt elements at the - l, 0 crosa piece (see section 3.1.1) to a thermal. contraction in steps corresponding to approximately 1/10 turn of the U-bolt nuts. This rate of " torquing" the U-bolts corresponds to a relative displacement between the U-bolt and the cross piece of 0.01" per step. O The graph in Figure 3.6 shows the build-up of U-bolt tension force as a function of the number of turns of the nut. This graph illustrates the gradual
, closing of the gaps (cinching) during the early stage of j the torquing operation. The low U-bolt stiffness, i.e.,
a slow build-up of U-bolt tension, during this stage 10 represents primarily the bending of the U-bolt required to reach a conforming fit with the pipe. When this } conformance approaches 150 degrees the stiffness
; increases rapidly and changes from nonlinear to linear characteristics. This linear stiffness corresponds to an essentially fully cinched condition and represents l
O the combined elastic deformation characteristics of the U-bolt, cross piece and pipe. The effect of relative
- pipe stiffness on cinching behavior is shown in Figure 3.6 by the curves for Schedule 40 and Schedule 80 pipes.
[ During the cinching operation and throughout the h continued tensioning of the U-bolt, the radial pressure lO between the pipe and the U-bolt components, as l represented by the normal force across the gap elements L in the model, is steadily increasing and redistributing h along the lines of contact. In the absence of any 4 external strut loads, the contact force between the pipe ?O, and the cross piece is always equal to the sum of the 1 tension in the two U-bolt shanks as dictated by j equilibrium requirements. The magnitude of the total i normal (radial) force between the pipe and the O l l
O 4 [O conforming U-bolt is, however, less obvious to determine from equilibrium criteria, since the vertical components of the normal forces as well as those of the developed
, friction forces contribute to vertical equilibrium of the U-bolt taken as a free body. .' O The distribution of normal forces acting on the cinched part of the U-bolt, and equally on the pipe, is shown in Figure 3.7a for four bolt torque levels during the cinching operation. As can be seen from these distributions, the normal forces are consistently lowest at the centerline of the U-bolt and reach their O maximum closer to the straight leg portions. This is due to the simultaneous build-up of friction forces which tend to resist the bolt tension introduced at the cross piece level and therefore prevent some of the increasing U-bolt strain (and stress) from reaching the center of the curved portion. As further illustrations O of these phenomena, Figure 3.7b shows the distribution ! of friction forces developed during the torquing ,,
operation and Figure 3.7c shows the corresponding distribution of tension in the U-bolt.
- b. Prgload plus tancential strut load O
I This load case corresponds to.the friction tests j reported in [1]. The analysis for this cese was performed in order to evaluate the ability of the model ,l to reproduce the slippage failure mode. L iO The analyses are performed for two different j levels of initial preload, namely 2040 lbs and 4140 l lbs tension (per U-bolt leg). , P2 These preload levels correspond to torque values of j approximately 46 ft-lbs and 83 ft-lbs, respectively, as 10 per the test results, [1]. For each of these preload 1 cases, an external load was applied at the strut pin } location in a direction parallel to the cross piece and L then increased in discrete load steps until slippage failure occurred. I! O This type of slippage failure occurs when the 4 overturning moment about the pipe centerline exceeds the
. resisting moment generated by the friction forces between the pipe and the U-bolt / cross-piece contact h areas. The maximum potential resisting friction force 1 h at any given load level is limited by the total normal i. ,0 l'
i r .
!O li
.O s o (radial) force across the contact surfaces multiplied by i the friction coefficient. For the U-bolt tension level of 4140 lbs, Figure 3.8 indicates how this total normal force increases with increasing external load, i.e., the
- moment resisting capacity increases with increasing externally applied moment. Figure 3.9a shows the JO redistribution of normal forces across the U-bolt contact surface as a function of external moment, and
] Figure 3.9b shows the corresponding redistribution j of developed friction forces. (Note that a distinction has to be made between potential friction forces, which are fully defingd by the product of normal force and C friction coefficient, and developed friction forces which also depend on external or other forces perpendicular to the normal forces. The potential friction force is therefore the upper bound for the { friction force that can be developed). O Actual slippage failure represents a numerically
; unstable situation for the finite element model since l equilibrium cannot be achieved when the externally l
applied loading exceeds the resicting friction capacity. l The failure load therefore has to be determined i approximately by trial and error in small load steps.
!O The failure loads for the two " friction test analyses" I performed are plotted in Figure 3.10 together with l the test results obtained from [1]. The analytically
- determined failure loads correlate closely with the test a
results. jO c. Preload plus straight (0 decree), compressive [ strut load 4 P' This analysis case corresponds to the load distribution tests reported in [1], and was performed in order to evaluate the predictability of load
'O distribution between U-bolt and pipe from compressive j strut loads. The analysis was performed with an
- initial preload of 4140 lbs per U-bolt leg.
Of primary interest for this load case is the
; change in U-holt tension since this is the force that j0 develops the normal force between the U-bolt and pipe.
p The total normal force on the pipe dictates the ability b of the U-bolt assembly to resist rotational slippage. j Therefore, this net force must be quantified to [ demonstrate.that stability is maintained. l 1 'O _ ~ . . _ ,
- O
.c The analysis was conducted by gradually increasing the load to a maximum of 15 kips. To circumvent any 4
potential side effects from the simplified bracket model, the load was applied directly to the cross piece. 7 10 Figure 3.11a shows how the normal force distribution between the U-bolt and pipe changes as the load is increased. Figure 3.11b shows the friction force distribution. It is noted that the angle of i conformity as well as the total normal force diminish, l as expected, with increasing strut load. i O A comparison of analysis results with corresponding results from the load distribution tests [1] is shown i in Figure 3.12 in terms of U-bolt tension as a function of compressive strut load. The tests shown in this figure were performed for initial preloads that were 1 o different from those used in the analysis. For an approximately fully cinched condition, however, the load
, transfer is linear and independent of preload. A meaningful comparison of results should, therefore, , address the slope of the curves rather than the absolute i
values on the preload axis. O
- d. Preload plus inclined, compressive strut load This load case is identical to the load .
distribution analysis (straight strut load) discussed C above, with the exception that the strut load is , inclined 5 degrees, which represents the maximum i allowable strut / snubber angle as per the CPSES design l criteria. This load case is therefore particularly i relevant since it represents a design condition. i i l0 The inclined strut load case can also be viewed as a superposition of the tangential load case (item l "b" above) and the straight strut load case (item "c" above). Due to the small load angle, and thereby relatively small tangential load component, the ,
! behavior of the straight strut load is expected to i l0 dominate. !
5-h l0 i e
! to
O. 1 0- Figure 3.13a shows the normal force distributions between the U-bolt and pipe for different I magnitudes of the inclined, compressive strut load. f Figure 3.13b shows the friction force distribution. 1 As expected, these distributions are similar to those ] for the straight strut load (Figure 3.11) with JO superimposed redistributions caused by the tangential t load component. I J Figure 3.14 shows, as functions of increasing i strut load, the change in overturning uoment, j represented by the total circumferential force on the
;O pipe developed by the applied strut load and the
} corresponding resisting moment capacity, represented i by " potential" friction forces. (Note that the potential friction force is the product of the total normal force and the friction coefficient at any i given load step.) 10 l As indicated by the solid lines in Figure 3.14, the analysis was performed in gradual load steps to a ], maximum strut load of 13 kips. In lieu of continuing i the analysis by trial and error to the actual failure load, the available margin to the slippage failure O was estimated from the ratio between the overturning and resisting force curves. This results in a predicted i failure load exceeding 16 kips. In comparison, the j simplified design procedure (Section 4.1) applied to this configuration and load condition results in an j allowable load of 10.6 kips, which implies a predicted O failure load of 15.9 kips with consideration of the j required safety factor of 1.5. l The shape of the two curves in Figure 3.14 e illustrate some significant aspects about the behavior
- of a cinched U-bolt subjected to a compressive, inclined 4
!O strut loading. The top curve which represents the potential resisting force remains relatively constant over the load range examined. The gradual drop of this curve for strut loads up to about 11 kips is a result of j the initial loss of the lateral confining U-bolt 1 pressure and its contribution to the total normal force.
j () When the strut load is increased beyond this range, the ' elastic loss of U-bolt tension occurs at a slower rate
; than the increase in normal force between the pipe and the cross piece, which accounts for the positive slope
?; of the resisting force curve beyond a strut load of 4 1o
;O P
6
- . . . _ . . . = '*-
- 6-
O f i
- O approximately 11 kips. This phenomenon is caused by the
.t increase in U-bolt flexibility that occurs when the 1 degree of cinching is reduced as a result of reduced } U-bolt tension. The slope of the resisting force curve j will gradually approach 45 degrees when the U-bolt j tension goes to zero. 1 The design procedure described in Section 4 conservatively assumes a constant rate of reduction in j U-bolt tension corresponding to the upper bound U-bolt j stiffness. This design approach, as shown schematically in Figure 4.5, consistently leads to an under jO prediction of available U-bolt tension. This under l prediction widens with increasing strut load and I provides for additional margin against slippage failure I which, conservatively, is ignored in the design j procedure. ]O The increased slope of the applied load curve in i Figure 3.14 accounts for second order effects. As a i result of increasing inclined strut loads and j simultaneously increasing difference in U-bolt leg ; i tension, the cross piece tends to pivot, or " roll", - j slightly on its line of contact with the pipe. This
]O means that the strut load acts on the U-bolt with a
- slowly increasing eccentricity. These effects are j artificially amplified in the finite element analysis
, due to the discretization of gap elements. In reality a ,
l continuous resistance against the cross piece roll is i
; provided by the curved pipe surface, which cannot be .O fully represented in the FEA even with an extremely fine , ! discretization.
j e. Preload Plus Internal Pressure , f !
- ! This load case evaluates the effects of internal [
]O pressure on the pretensioned U-bolt assembly. Figure J 3.15 shows how the normal forces between the pipe and i U-bolt are affected. This load case is very similar to a an increase in U-bolt preload, the main difference being a that the active pressure loading is applied on the t inside rather than the outside of the pipe. L
;O i !
1 3.1.3 Pipe Stress Distributions S Representative stress plots obtained from the finite element analysis (Model 1, elastic) are provided j in Figure 3.16 through 3.24 for various load cases "O and locations as described below:
': :o
- i ['
t t
- - - , - - - - - n.,, ,- , e- n.. - ,- 7.--.-r--,-r , - . - - - - - - - . - . - - - - - - , . , - - - - - - . , _ , . , . - - , , , - - , - . , , - - - - - - - - _ , . - - - - - - - - , - - - . . - , . _ _ _ _ _ _ _ - _ _ - -
'O O. Figure 3.16:
Circumferential bending and membrane stresses 0.5 inch from U-bolt center line ( 2 = 0.5) for preload (only) of 4,140 lbs/ leg.
,O Figure 3.17:
Same as Figure 3.16 but with preload increased to 5,425 lbs/ leg Figure 3.18: i 'C Circumferential bending and membrane stresses e at 2 = 1.5; i.e, 0.5 inch inside the i cross-piece contact edge, for preload of
;- 4,140 lbs/ leg O Figure 3.19:
Same as Figure 3.18 but at Z = 2.5 in., i.e, 0.5 inch outside the cross-piece contact edge Figure 3.20: O
! Same as 3.19 but at 2 = 4.0 inches l
Figure 3.21: Circumferential bending and membrane stresses O at Z = 0.5 for preload of 4,140 lbs and compressive, straight strut load of 10,000 lbs. Figure 3.22: 1 40 Circumferential bending and membrane stresses 7 at E = 0.5 in for preload of 4,140 lbs and internal pressure of 600 psi Figure 3.23: I 10 Longitudinal membrane stress in the cross-j piece contact area; preload only (5,300 lbs) p Figure 3.24: Longitudinal bending stress in the cross-l! O piece contact region; preload only (5,300 lbs) l I 0 4
~ ~ , = . - . . p
, - - _ - . - _ . . . _ _ , , _ . _ _ . _ _ . . _ , _ . . _ _ . _ _ _ . . , _ _ . _ _ , , _ . , . . . . _ _ . , _ _ _ _ , _ , . _ . . _ _ r . _ _. __,, _ _ . . _ _ _ . _. , __- __ _ _ _ ,,
I
. O.
1. l O As can be seen from Figures 3.16 through 3.22, the distribution of circumferential membrane and bending stresses are very similar in shape for different load cases such as preload, preload plus compressive j strut load, and preload plus internal pressure. This is due to the fact that all these load effects are
;0 , introduced into the pipe locally at the U-bolt assembly through the same basic load transfer mechanism, namely through concentrated compressive forces between
{ the cross piece and the pipe along a narrow contact 4 strip across the width of the cross piece. These j similarities between stress distributions will exist qO provided the U-bolt remains essentially cinched, i.e., y the strut load is not sufficient to reduce the U-bolt j tension to zero. I f one notable exception to these similarities 5 between load cases is the circumferential membrane 10 stress distribution due to internal pressure. These ] tensile membrane stresses, which are typical for any
; unconstrained pipe,'are only partially suppressed and
{ redistributed by the presence of the constraining ! ] U-bolt assembly. [ i
'O The typical circumferential bending stress distribution close to the center of the U-bolt assembly can be divided into three main regions with distinct ; characteristics around the half symmetric pipe ;
j perimeter. The first region, in the immediate vicinity i i of the cross piece line of contact, is characterized L J, 0 by steep gradient bending stresses that reach a i i maximum immediately below the cross piece line load. lj These maximum stresses are highly localized and . diminish rapidly in the longitudinal direction well as i the circumferential direction (Figures 3.18, 3.19, j 3.20).
- ! O j The second region of interest is the portion of ;
the " unconfined" pipe perimeter between the cross . [i
- j piece and the first U-bolt contact point, that is bounded by inflection points. This region is 1
1 characterized by low membrane stresses and relatively 1 40 uniform bending stresses of moderate magnitude. These [
; bending stresses are relatively localized in the i g longitudinal pipe direction and the longitudinal J gradient is less pronounced than that in the first j region.
lO 1 a i N 2 jO 3 . 4 +
--.se,. ,.. , , _ _- . - - - . ,n_,., , , . . , , .,,-w, -.a , n -. - --..,-- ,,,_ _.--. - ,-n-
!O
- () The third region is the portion of the circumference that is in contact with the cinched U-bolt. By virtue of the " confinement" of the pipe wall provided by the U-bolt, the circumferential bending stresses in this region are relatively smoothly distributed and of low magnitude. The circumferential
;O membrane stresses (compressive) are higher in this region than elsewhere around the pipe perimeter in the vicinity of the U-bolt. They are still low, though, and serve mainly to reduce the corresponding tensile stresses caused by internal pressure. In
- general the cirpumferential stresses in this confined tO region are of little consequence.
The longitudinal membrane and bending pipe stress distributions are most significant in the vicinity of the cross piece contact. These stresses, , which have significantly lower magnitudes and gradients
;O than the circumferential stresses, are plotted in
- Figures 3.23 and 3.24 for a preload of 5,300 lbs.
For the load case of U-bolt preloading (cinching), pipe stress results have been compared between tests [1] and FEA. Figure 3.25 shows this comparision for
- O 4 outside surface pipe stresses in three main characteristic regions, namely
- (1) the unconfined
, region (points A, B, C in Figure 3.25); (2) the vicinity of cross piece contact (points C, D, E); and (3) the region of U-bolt contact (points G, B, I, J). With ! few exceptions, the stress results from the two FEA's !O and the tests compare very well with each other. In l- seven of the nine locations examined, the RLCA FEA j results exceed the test results. The main reason for differences in results between the three stress sources l is the sensitivity to exact location due to the steep i stress gradients in the vicinity of contact between the 10 0-bolt components and the pipe. The locations of the } strain gauges used in the tests are only approximately
- known, as is the longitudinal dimension of the elements j in the Westinghouse FEA [2]. The high stress value frcm
- the test for location "B", is further likely to have
- been affected by localized surface imperfections in the i C) line of contact, since the longitudinal stress variation
- between points H and J would'not be expected to be as
- Jarge as indicated. i O
;O i
I _ _ _ , . . _ . . .., -
O i co Representative, elastic stress values for different i l load cases are summarized in Table 3.1 for the pipe element closest to the center of the cross piece. j 3.2 REFINED ELASTO-PLASTIC MODEL FOR STRESS l EVALUATION (MODEL 2) 'O A refined finite element model used to verify the base model and provide information on the elasto-plastic behavior was run on a CRAY computer. Like the base model, this model was generated and analyzed using the ANSYS Code [3] . The refined model o was developed on the RLCA VAX computer and transmitted to the CRAY for the load case analyses. l 3.2.1 Description of Model ! The primary differences between the base and , o refined model are (1) size of elements throughout the model, (2) inclusion of elasto-plastic elements (ANSYS type STIF48) in the areas of pipe where yielding may occur, and (3) level of detail in modeling the cross piece bracket. Figures 3.26 and 3.27 show computer plots of the detailed and substructured Jo portions of the model, respectively. The substructure element used in the refined model was generated in a single pass and maintains the level of circumferential refinement (10 degrees) seen in the last layer of the detailed portion of the model. The yield strength used for this model was based on an estimated actual strength
. exceeding the minimum specified value at room
]O temperature by 20%. For SA312 TP304 material this ? results in a yield stress of 36 ksi. It should be noted ) that, since the analysis results from this model are not j used to justify the acceptability of a specific maximum g pipe stress value, the choice of yield strength is gg essentially arbitrary and only governed by an attempt to 3 simulate the tested configurations as realistically as
- possible.
1 The cross piece and bracket were modeled using h 3-D isoparametric solid elements, ANSYS type STIF45. a jo The gap / friction elements are used in the same l way as in the base model. Since the circumferential I node spacing is 5 degrees, there are 37 gap elements [ used along the curved portion of the U-bolt. Rows of y gap elements located at +/-5 degrees and +/-10 degrees 4o are used at the cross piece contact area. li o j . o i ._. -
'O f I lo 3.2.2 Load Case Analysis The elasto-plastic model was analyzed for the < load case corresponding to U-bolt preload. Figure , 3.6 shows how the preload curve compared to that of Model 1. 40 The normal, friction, and axial force distributions developed by the U-bolt preload corresponded well , with the results from the elastic model. Differences
- were due to the presence of more closely spaced gap elements. This refinement allowed the conforming jo process to proceed in a more continuous manner than with the coarser elastic model.
3.2.3 Pipe Stress Distributions { , As discussed, the elastic model showed that the l critical stresses were located in the region where lo the pipe contacts the cross piece. These stresses ! are governed primarily by the normal force between the pipe and cross piece. As a result, the stresses
- in this region from a compressive support load can be l represented by continuing the cinch load until the
!() desired normal force has been reached. l The cinch load was continued to a U-bolt prelead
- of 6,525 lbs which corresponds to a normal force at 8
the cross piece of 13,050 lbs. This normal force is , l equivalent to a preload of 4140 lbs with a 10 kip ig compressive strut load.
- l l Figure 3.28 shows the circumferential bending .
, and membrane stresses at a preload of 5,425 lbs. i These curves, which can be compared with those in l Figure 3.17 for the elastic model, show that while !
- O the flexural stresses are essentially the same at 5 1 degrees off the line of contact, the equivalent stresses
- are smaller and level off at 36 kai. The equivalent stresses, which dictate plastic behavior, take the tri-axial stress state into consideration and therefore
- are a better means of judging the extent of plasticity i IO than a total or flexural stress in the circumferential }
! direction. ,
- O.
i
; O t'
i f- _n- . - . n,.-~. -,, ,. _ _ - . - - _ _ = . . . . . - _ , . _ _ , . - _ _ . . _ - _ , . . - . _ . . _ . _ _ . _ _ . . . , _ .- . - , - , _ . _ _ . . - _ - . _ .. _ .,.,,_ _ __ _ _ _ _ - _ ___ _._____ _ . _ _._-_ __ __
O l O. Figure 3.29 compares the equivalent strees j z distribution at the outside surface of the two FEA , l models used. The loading condition represented is that I of cinching due to 0.7 turns of the nut (approximately l 4140 lbs, 83 f t. Ibs of torque) . The contours of the i two models are very similar which indicates that the
'O mesh refinement of Model 1 is sufficient and that the ! resulting elastic stress distributions are 1 representative. The only area where differences are i seen is where the cross piece contacts the pipe. In ! this area the elastic stresses are slightly greater than f yield whereas the elasto-plastic stresses remain l C) essentially at yield.
l 3 3.3 TEMPERATURE DEPENDENT ELASTO-PLASTIC MODEL FOR j THERMAL CYCLING EVALUATION (MODEL 3) 6 1 A third FEA model, Model 3, was developed to IC) examine the effects of local pipe plasticity during
; thermal cycling and sustained internal pressure. The ,, , configuration modeled is the same as that for Models 1 1 and 2 shown in Figure 3.1. This model was generated and analyzed on the RLCA VAX computer.
lO 3.3.1 Description of Model I
, Figure 3,30 illustrates the portion of the model l near the U-bolt. As this figure indicates, the primary . model was reduced to a small part of the pipe, the U-bolt and the contact with the cross piece. The .C. remainder of the pipe and the cross piece were represented by substructures. Figure 3.32 shows the results from a parameter study [26] comparing models
,, with one layer versus 3 layers of STIF45 elements b through the wall thickness. The results from this 1 parameter study demonstrate that the plastic force-10 deformation behavior of the pipe under concentrated loading can be adequately represented by one element layer through the thickness, as used in Model 3. The temperature dependence of the pipe material
! yield stress, as defined in ASME Section III, Table . C) I-2.2, was incorporated in the model. For the stainless ! steel used (SA 312, TP304), the yield stress drops from ! 30 kai at 70 degrees F to 20.7 ksi at 400 degrees F as ! indicated in Figure 3.31. The strain hardening slopes were determined from test results [Refs. 8 & 25]. The . constraining action of the U-bolt on the pipe during lO i i
4 i [ i
_ _ ~ _ . O heat-up was modeled through an equivalent coefficient of l C) expansion term. This term considers the differences in l expansion coefficients between pipe and U-bolt materials as well as the assumption that the temperature rise in the U-bolt is one half of that in the pipe. This temperature distribution between pipe and U-bolt is Im based on a review of test results [1] and is consistent
!" with SWEC Procedure CPPP-7, Attachment 4-12. The gap j elements in Model 3 were assumed to be frictionless, i ; 3.3.2 Load Case Analysis
{ p' Model 3 was subjected to a load sequence of l initial cinching and application of an internal pressure
> of 400 psi followed by a thermal cycle in the pipe of 70 degrees F to 400 degrees F and back to 70 degrees F. ! The cinching was accomplished in the manner described i previously for Models 1 and 2. The internal pressure
- O was applied uniformly to the primary model and substructure in 50 psi increments. The thermal cycle was carried out by increasing and decreasing the temperature in increments of 33 degrees F.
j 3.3.3 U-Bolt Tension Effects l The initial cinching to 0.70 turns of the nut resulted in 3870 lbs. of tension in the shank of the
! U-bolt. The 6% difference in tension between this model and the two previous models was a result of neglecting friction between the U-bolt and pipe. As .g expected, the frictionless condition resulted in j~ lower tension forces due to a longer " effective ! length" of the U-bolt. The U-bolt tension increased to 4100 lbs with the presence of a 400 psi internal pressure. The U-bolt tension increased to 5898 lbs.
t when the temperature was increased to 400 degrees F and
;g decreased to 3,362 lbs when the temperature was returned - to 70 degrees F. This corresponds to a preload loss of 18%. Analyses for subsequent thermal cycles did not result in any additional loss of preload. The U-bolt tension force changes through this load cycling sequence is shown as a histogram in Figure 3.33. The
- c
; '3 force-deformation graph in Figure 3.34 shows the contact force between pipe and cross-piece through the load sequence.
The parameters in terms of dimensions, temperature
. range, and material (SS) for this analysis were I
selected to maximize preload losses due to thermal
!)C cycling. The pipe wall thickness affects the preload t
40 eee, - -, ,,, . - - , - . - - - - -c.- -,
I jo () loss since it determines the maximum local strain in 1 the pipe wall under a given loading. The temperature affects the preload loss in two ways: (1) by the amount of restrained thermal expansion, i.e., the force acting on the pipe; and (2) by the amount of j yield stress reduction. The presence of internal i C) pressure affects the preload loss by increasing the 3 contact force between the pipe and cross-piece i throughout the thermal cycling and, thereby, the
! amount of localized, permanent pipe wall deformation.
I The material type affects the preload loss by the i same mechanisms as the temperature since both the
- O thermal expansion coefficient and the yield stress i temperature dependence are different for different j materials. Table 3.2 shows a comparison of these j parameters at different temperatures for carbon steel (SA106, Grade B) and stainless steel (SA312 TP304).
j t As the table indicates, the expansion coefficient and
!O the rate of yield stress reduction for SA312 exceed those for SA106 by approximately 30% and 100%, ! respectively, in the temperature range of interest. ;
For approximate comparision purposes the susceptability to preload losses due to thermal cycling can therefore i be expected to be at least twice as great for l; l() configurations with stainless steel pipe than for
; carbon steel pipe.
i 1 In summary, it is concluded from these analyses ;. l that for cinched U-bolt configurations comprising: (1) 1:
; stainless steel pipe, and (2) high operating temperature L iO (T 1 300 degrees F), and (3) thin-walled pipe (D/t 1 ! ; 25), allowance should be made in the design for preload J losses due to thermal cycling of up to 18%. Other ~
1 configurations, i.e., stainless steel pipe applications that do not exceed the temperature and D/t limitations [ t above, and all carbon steel applications are expected O based on the analysis results, to experience maximum j t losses due to thermal cycling of no more than 10-12%. suggested allowances in the design procedure for these [p i and other potential causes for preload losses are !
, presented in Section 4.5.
j () 3.3.4 Fatique Evaluation ll The results from the Model 3 analyses were also i used to evaluate the fatigue behavior of the pipe due to
; cyclical thermal loadings with internal pressure. This ; evaluation examined the maximum range of principal , C) strain in the circumferential direction for comparison to ASME Section III criteria.
iO " o . l! t _. ._ _ . 4
. O i
The strains provided by ANSYS for the elements used O are global component strains at the element's integration points. Since the integration points are
, not located at the element's surface, the surface i
strains are extrapolated from strains at the integration points. This extrapolation provides surface component strains while the ASME Code fatigue criteria are based l O on principal strains. Since the maximum strains occur ( along the line of contact of the pipe, the global [ cartesian component values are very close to those in a 1 cylindrical system. Further, a determination of l principal strains at this location indicates that the O circumferential* surface strains are within 15% of the l maximum principal strains. I Using the maximum range of circumferential surface strains, the maximum alternating stress is 12 kai
! conservatively based on an elastic modulus at 70 degrees F. Based on ASME Code Section III, Figure I-9.2.1, this alternating stress level corresponds to
{O one million cycles. If a more realistic number of 20,000 cycles are considered, the maximum allowable alternating stress is 55 kai. The difference between the expected alternating stress (12 ksi) and the all wable (55 ksi) indicates that fatigue will not be a O Concern. O i
- O 4
4 i L
- O C
I lO t 'l
O f L 10 4.0 DESIGN PROCEDURE r I The tests and detailed analyses described in the foregoing sections for a limited number of configurations have served to verify the load transfer capabilities of cinched U-bolts and the predictability of their behavior under a full range of operating lO conditions. For general design applications, however, I a less costly and cumbersome methodology is required. This section, therefore, describes the derivation of closed-form design equations and procedures based on O simplifying but conservative assumptions. These equations serve to relate the dimensional and preload
! related U-bolt parameters to stability conditions as well as stress states in the U-bolt assembly and the pipe. Several aspects of the simplified models described in the following subsections are based on a O detailed review and partial modification of work reported in [4]. The basis for the design procedure i described in this Section is documented in RLCA calculation files, [16] through [22].
4.1 ROTATIONAL RESISTANCE OF U-BOLT ASSEMBLY (STABILITY) , O . 4.1.1 Eauilibrium Conditions ! I An idealized U-bolt model used for the determination of load transfer characteristics and
. rotational stability conditions is shown in Figure 4.1. !O The forces acting on the U-bolt and cross piece under l the effects of preload and external strut load are shown on the free body diagrams in the figure.
The main idealization made in this model is } associated with the representation of the resultant 10 forces acting on the cinched, or conformed, part of the 4' U-bolt. As discussed in Section 3.1, the distributions of normal and friction forces acting along the i pipe /U-bolt contact surface are complex and highly
, variable with respect to both shape and magnitude under e varying load conditions. Since a significant taction !O of the total normal force, N2, acts on the sio s of the i U-bolt (i.e., in the regions close to the U-bolt legs as demonstrated by the finite element analyses), the !
1 magnitude of N2 is dependent on equilibrium conditions ' J as well as deformation compatibility between the pipe i and the U-bolt. This means that the normal force on lO ! the U-bolt cannot be quantified based on simple, I l l' 4
i: O vertical force equilibrium with the U-bolt tension O (see Figure 4.1). Nevertheless, the total normal force on the curved portion of the U-bolt is closely related to the U-bolt leg tension forces. The resultant normal force acting on the curved l j C) U-bolt portion can be shown to always exceed the total i U-bolt tensile force for the types of cinched U-bolt assemblies that are of interest at CPSES. This is also i confirmed by the results from the finite element t analyses [15]. j For design purposes, the resultant of the
.O distributed normal force acting on the U-bolt is conservatively assumed to equal the sum of the U-bolt I tension in the two legs, i.e.,
i. 6 Q N2 = U1 + U2 = 2 Uo - b 10 (1) -j Where: b = elastic reduction in U-bolt tension j due to external strut load, P. (See 4.2.2). , O Uo = initial preload per U-bolt leg N2, 01, U2 = as defined in Figure 4.1 It should be noted that the orientation of N2, as defined by the angle O' in Figure 4.1, will always be HO such that equilibrium with the external load, P, is 1 assured in the horizontal direction. The resistance i against rotation provided by friction is independent of this angle and no attempt will therefore be made to j quantify it. H-
!O vertical equilibrium of forces acting on the cross i; piece requires that:
P cose + U1 + U2 - N1 = 0 (2a) Moment equilibirum of the cross piece requires
!' s (2b>
A u = Us - Uz = Psme< D, + ^d i [O I . 1
~ -
w e n e- -a. w w- m- ..e.o- .~w ~ - e--+ -n . ~ y
10 Also, based on Figure 4.1: 10 N1 = 2Uo + a (3) 2 Uo = initial, total preload a = increase in cross piece / pipe contact force due O to external load, P P = a + b = Total strut load, positive for (4) compression, negative for tension O In this expression, the approximation has been made that for small angles, 8, cose al. 4.1.2 Rotational Stability Conditions The condition for stability can now be defined as:
- O (Externally applied moment) < (Internal Resisting Moment) or !
i O P sin 0 * (A+R) < (N1
- N2) */,k* R (5) ,
After reduction, equations (1) through '.5) yield: '
~
Uo > P sin 0 [A + 1 + 1 -a 2 ,2 \R (6) 2 p. 1 O I s Equation (6) defines the minimum required preload per - I U-bolt leg for rotational stability of the U-bolt assembly.
;O For use of Equation (6) in actual design applications, the following reformulation is made: ;
l 3'
- 1) > (FS) *C*i Km d P sin 0[A + 1}+ 1 -1 (7) l i;
{ 24 2u (R / g[ Ke+ li 2 r i O ( Rcu / - where: ld = minimum design bolt torque required j (FS) = factor of safety (see Section 5.1) jo i i 1
;O n i
i
.r-.. , - - . . - . - , . -- - . . . ~ . . - . . . - .
1 IO E e I Kt = empirical constant relating bolt torque to [O bolt tension (see section 4.1.3) ' j/A = friction factor relating rotational friction resistance to U-bolt tension (see section 4.1.3) O Ci = Factor (>1) providing allowance for preload losses (see section 4.5) d = U-bolt diameter I ~
'O 1 =1-a ; (8)
Nkd O This latter term describes the distribution of external strut load, P, between increased
} pipe / cross piece force (=a), and reduced j U-bolt tension (= P-a). The derivation ,
3 and definition of these terms is described I l in section 4.2. ; i I C) Equation (7) is only valid if the average U-bolt i I tension is not reduced to zero as a result of the vertical component of the compressive strut load. i
} This requirement of maintaining a non-zero preload i i
i can be expressed as a secondary minimum torque I criterion:
+0 1
j;
! 1[g> (FS) *C*i Kt
- d
- P__
- 1 (9) l
] 2+ 0([ g, i, \ ket jO with terms defined as before. li l Both equation (7) and (9) have to be satisfied l for stability to be assured. o i 4.1.3 Empirical Friction Factors /k m and Et 1 0 < The values for the friction factor,jk, and the constant, Kt , the latter of which relates U-bolt torque to leg tension, are both determined from tests s
!O l !o
- i
~ , _ . _ , . . . .
3
- O reported in [1]. The friction tests, as previously )
O referred to in connection with FEA correlations in Section 3.1.2.b, consisted of applying a tangential load at the strut pin on preloaded U-bolt assemblies ! in increments until rotational slippage occurred. , These tests were performed for a range of preload levels on each of the four test specimens. The L O I friction factors were determined from the test results b as follows: l l j AA = P7(A+R) = Pv(A+R) K, d (10) 4 e U.
- R 48
- R* t O where Er = tangential load at slippage failure The results from the friction tests, in terms of failure load and friction factors, were reported in
[1] as functions of bolt torque. Since the governing Parameter is bolt tension rather than bolt torque, a
'O proper interpretation of the results requires knowledge about the tension / torque relationship.
l Equation (10) shows that the definition of the l two factors,jk and Kt , are not independent of each O other. The two constants should, therefore, be determined consistently from the same tests in order to 1 avoid arbitrary and unjustified conservatism. In order ; l to arrive at appropriately conservative values for both I
! Kg and j/A the following approach has been used:
i
- O o For each preload (torque) level considered in j
} the friction test of a particular test specimen, i l determine the associated values of Kt andj4 .
(Note that the torque versus preload is g provided for each individual test in [1], Appendix III). 3 O o For each set of Kr andj4 values, determine l the ratio of j/s/K t .
) ! ! o The lowest of these ratios for a given test j specimen represents the most conservative set 10 of values that can be obtained from the j tests. . - l' ?
I
;o I
i O I i l . _ . . _ . _ . . - _ _ _ , _ .. .
.O O Based on this approach, the following values of the factors were determined: Pipe Size : 4" 10" 32" U-bolt size : 1/2" 3/4" 2-3/4" Kt : 0.25 0.27 0.21 p : 0.12 0.16 0.22 lo i A summary of friction factor values obtained from tests [1] are provided in Table 4.6. This table is
- based on data points extracted from Figures 13 through i g' 16 of [1]. Each data point represents the tangential
- ' slippage load for a particular pipe size and U-bolt torque value. The summary in Table 4.6 provides a measure of the level of conservatism in the I interpretation of the friction tests. The lower bound values of the friction factors that are selected for O design purposes are consistently lower, and in some cases significantly lower, than the mean values minus one standard deviation of the test results for each pipe size. >
For design purposes, the friction and bolt torque O factors obtained from tests are generalized to a full range of pipe and U-bolt sizes as follows:
- 1. Bolt torque factor, Kt ;
Theoretically, this parameter should I lO vary with bolt diameter and pitch only, with ! a slight trend towards lower values for l increasing bolt diameter. The value of this I factor is therefore conservatively set to
; 0.27 for bolt sizes from 1/2" through 1-3/4" ;.
- and to 0.21 for bolt sizes larger than 1-3/4". ;.
O 2. Friction factor j This factor, as determined from the tests is !' not a constant as traditionally assumed for ; friction coefficients. The reason for this 1 g' apparent anomaly is that the friction factor { as determined here is not a local friction coefficient, but rather a global factor relating the overall resisting moment to the
; external load at failure. This factor thereby incorporates the effects from variations in jo , *O
_____ . _ . _ ~ - - _ . I
- l D l l "O total normal forces between the contact i surfaces, as well as size-related effects. A l given surface imperfection size (lack of l perfect conformity) would for example have a
- more severe effect on a small pipe than on a e large one. The variation in the friction 1
0 factor observed in the tests is therefore not i unexpected. Based on the current review of the friction test results [1], the following values , of the friction factor are suggested for ,o design purposes: a Pipe size less than or equal : = 0.12
- to 6" i
f Pipe sizes from 8" to 22" : = 0.16 3O ? Pipe sizes greater than or j equal to 24" = 0.22 i 4.1.4 Tensile Strut Load
,0 At a certain magnitude of tensile strut load, the cross piece may separate from the pipe suprface. The mechanism then required to provide resistance against rotation relies on the developed shear in the U-bolt ! legs. To be consistent with the design of the U-bolt as a O Pure tension member, it is necessary to assure that a sufficiently high friction force exists between pipe and cross-piece to balance the horizontal component of the j strut load. To satisfy this criterion, the required 3 torque is:
3 l0 7' ) (- p.cos e)
- tk .cl , %e y _ 1 g3o,)
2+ ,A g_
.y.r_
,y/
P= External strut load, positive for compression, j negative for tension. 50 1 Since this criterion is not related to stability of the g assembly, but is rather an assurance against exceedence
, of design stress conditions under service loading
,; o conditions, the resulting required torque value does not incorporate any safety factor in addition to what is implied in allowable stresses. ( o l l
--,r~---- ,e-+~v-- - - -
,m , ,.,--,,--,...-r- - - - - . . - ,--a,.. - - . - . , - - - --,- - -- - - , - , - , - - - . - . , - - - - - - - -
O
.o 4.2 LOAD DISTRIBUTION AND STIFFNESS PROPERTIES 4.2.1 Mathematical Model of Pipe and U-bolt Assemb1v The spring model of the pipe U-bolt assembly proposed in [4] has been reviewed and found
'O appropriate. The model is shown in Figure 4.2. The spring Ke represents the cross piece stiffness and the spring Ku represents the U-bolt stiffr ess. The pipe is modeled by two springs in series,o(kr and /kr . The spring M Kr represents the stiffness of the upper, laterally h
- g unconfined, portion of the pipe while pKr represents the stiffness of the lower portion where the U-bolt and the pipe are in contact and a distributed contact force exists. Since dke and g>Kr in series represent the total pipe stiffness, o( and /
must satisfy the following relationship.
;O i 1 + 1 =1 (11) ,
- M /
In other words, ol or f can never be less than one. .o In the circumferential direction, the upper portion of the pipe is subjected primarily to bending ! , stresses, while the lower portion is subj,ected primarily l to membrane stresses. The upper portion, which is repre-
- sented by D(K r , is expected to deform more than the
! lower portion. In other words, M is always less lg than 2 and p is always greater than 2. Thus, we have i the following condition: j 1 < o( < 2 (12) f The location of the dividing line between the pipe
- g portion represented by p( and g is dependent on the amount
! of lateral confining pressure provided by the U-bolt. l As shown by the FEA in Section 3 (Figures 3.5 and 3.6) F the increasing stiffening effect provided by the tensioned U-bolt stabilizes to a constant value as soon as the preload exceeds a relatively low threshold IO values. This threshold preload corresponds to a , U-bolt / pipe contact length over approximately 100 to 120 degrees, which can be expected to be exceeded for practical design applications. ; N 10 - L O '- h
0 1 'O
- It is therefore appropriate to select a constant based on FEA results. The value for described analyses the parameter in Sect c( ion 3 result in an O( - value of approximately 1.4. Since the value foro(, based on expressions for " unconfined" and " confined" pipe
, stiffness, is relatively insensitive to pipe dimensions, .!O the same value can be applied to all pipe sizes. The mathematical model shown in Figure 4.2 can
- be simplified by using an equivalent spring Kct to represent the U-bolt assembly. The simplified model is shown in Figure 4.3.
O The stiffness of the U-bolt assembly Kcc , which l consists of Kc and Ku in series, can be expressed as follows: h Kc *Ku 0g K ct = (13) i Ec + Ku 4.2.2 Distribution of External Strut Load Between Pipe and U-Bolt A U-bolt asssembly model subjected to a compressive (O strut load is shown in Figure 4.3, where Kctand Kp
! represent the stiffness of the U-bolt assembly and the ! pipe, respectively. Prior to application of the strut ,
I load, P, the U-bolt is assumed to have been preloaded to ! a tension of U. in each leg. In the following
!'O derivation it is further assumed that the preload is i' ! sufficient to maintain contact between the pipe and the
- I cross piece as well as the U-bolt (see Equations (9) and l
(14a)). Using this spring model it can be shown that the j force between the pipe and the cross piece is: O _ _ 1 (14)
! F7 = E U. + P* 1-
*( fdu + N.
L
}g 4
where the strut load, P, is positive for compression. l:
} Equation (14) is valid only if contact is i maintained between the pipe and the cross piece, i.e.,
j for positive values of Fp . In addition to equations
- O i
, lO t .
.. - . - . . _ . - . - = --
lC f i (6) and (9), this leads to the following, third lq3 requirement on minimum ;; reload: U, ) P i
, (14 ,)
0(( - + 1.)_ i I Equation (14a) is of interest for the determination O
- of support stiffness to be used in the piping analysis.
This stiffness typically is determined from the a individual stiffness values of support components l between the pipe wall and the point of attachment to the ! supporting structural element. Since the U-bolt cross ! piece remains in contact with the pipe wall under all O conditions, the only flexibility contribution from the l cinched U-bolt assembly is the through-thickness ! flexibility of the cross piece. This flexibility can be
- considered negligible and, therefore, the cinched U-bolt
! components do not affect the support stiffness. The average force between the two U-bolt legs can be j expressed as: U = U, - P 1 (15)
,o((Ken + 1)
,C 2 Kr , I c As shown by equations (14) and (15) , the U-bolt tension decreases due to a compressive strut load, l p# while the contact force between pipe and cross piece ( increases. The parameter, o( , and the stiffness ratio of the pipe to the U-bolt assembly are the main
- parameters determining the distribution of the external
, load between the pipe and the U-bolt. Figure 4.4 l- shows the distribution of the external load between
- C) the U-bolt and the pipe as a function of these parameters.
Figure 4.5 shows schematically how the U-bolt tension is affected by tensile or compressive strut loads. O O
_ _ . . , _.~ . . _ _ _ _ _ _ . _
' ~ .O 7' 4
4.2.3 Stiffness of Pipe (Ko) 0 The stiffness of the pipe is defined as the force required to produce a unit diameter reduction , i along the line connecting the points of contact , with the cross piece and with the apex of the U-bolt. , O As described previously, the pipe is subjected to 4" i concentrated compressive force from the cross piece and . to a distributed, radial force from the U-bolt. The pipe stiffness is the inverse of the pipe displacement due to one unit of force. The pipe displacement is estimated by addition of two displacements which can be O calculated analytically. The two displacements are ~ described in the following"
- a. Displacement of Djoe at the contact point with the cross piece.
O This displacement is determined based on the solution for a pipe subjected to a pair of concentrated radial pinching loads. .The displacement is determined at one of the loading points. The equation to estimate this displacement is as follows for a unit force [7): o' sh ons i L (16) A = 6. % E a t "4 (.Ent},, 1 ( Rm r 4. p Where E = Young's modulus of pipe material
'O tp = Thickness of pipe wall Rm = Mean radius of pipe
- L = Characteristic length of pipe The limitations to this equation, as stated in [7]
j are: t l
- O 1
f i< ( it (17a) Em [ i "" tg > 10 (17b)
- O 6
y l0 , Ii 1 U , s
y .. . - 7.,
~p: mp , l- /
I )(O 4/;s i< [
/. -
- N ,
j g- -The parameter L/Ryndescribes the influence of free
., end conditions. The stiffness, or the inverse of the
,' X . displacement, increases asymptotically with increasing length to a point where end conditions do not affect the
, local stiffness. For the current application, where no i ; ,
free pipe ends exist in the vicinity of the U-bolts, the l c.' 7, ' maximum ratio of 18 for L/Rngds used. Length increases l beyond 18Rogare assumed not,to affect the solution. It is recognized that the assumption of concentrated point forces, as opposed to short line loads along the cross piece width, may lead to a slight underestimate of pipe i stiffness. This inaccuracy, however, is corrected for (,1 by the value of alpha, which is benchmarked against FEA (section 4.2.1). Following substitution of L/Ryn= 18, we have the following simplified expression for the pipe [' displacement due to unit pinching loads: O ' l.5 21 : 0slil- *[ R"I (18)
/
e +.y \ tr / (3, b. Pipe displacement at the apex of U-bolt / pipe
~
. gentact -
The pipo displacement associated with the distributed contact force between the U-bolt and the 4 pipe, is based on the solution for a pipe subjected to a uniformly distributed, radial, ring load around (g' the pipe. , [ The magnitude of the uniform ring load is so chosen i [ that the vertical resultant of half the ring load equals F , one. The magnitude of the ring load is as follows: , (3- 1 y = 2Rm (19) The radiul displadement under the load around the pipe ;
,. , is defined by the following equation [7]. !
t - o.25
'. g _~. Rm , 3(l - F )- (20) 2 4E4 . Rd < pt ' .
o G
- .:~ ~;: ~. L . . - . . - - . ~:--_----.-._.-..-_ . -. .-- --I
- C ?4 i
O where F'is Poisson's' ratio. For steel, the Poisson's ratio can.be taken to be 0.3. Therefore, Eq. 20 is simplified as=follows:
/ Rn \
A 1_ E* t,n321, \ tg 1 (21) "O:
"The pipe stiffness Kp is then estimated by g,p v144 N-(o.sziqte)*5 Rm (22)
_ E, tp tr Enty i C) 4 14.2.4 Stiffness =of U-Bolt Assemb1v (Kc1) The stiffness of the U-bolt assembly consists of the combined stiffncsses of the cross piece and the U-bolt.
- O
The cross piece stiffness is defined as two times the U-bolt leg force required to induce a unit relative
! vertical displacement between the U-bolt hole location and the center of the cross piece. 'O The stiffness can be written as:
, -i 6<
K,= ,,1+ , g, + g, [ +. ( , (23) !O , where Li is half of the distance between the'two U-bolt ; < 1egs minus half of the length of the bracketi; L 2 is j i ., half the length of the bracket; and It and I2 are the t l moments of inertia of the cross piece and the cross j to Piece with bracket, respectively (See Figure 4.7.b). i ! The U-bolt stiffness, Ku ,C is defined as the force ,
- required to induce a unit displacement of the U-bolt ;
- apex relative to the U-bolt nuts. The U-bolt stiffness
! ,is dependent on the degree of cinching (See Figure 3.5) lI .g and is therefore determined below in terms of upper and i (' lower bounds. I' i i O P i ,
O t 3 i O
- a. Up er B und (Fully Cinched)
The U-bolt is treated as a frictionless cable with axial force only. l ,, Thus, the upper bound of the U-bolt stiffness is [ O ', k, - ausE _ (24) l + (R + h)*o5 i
- O i
where h is the height of the cross piece and a v is the cross section area of the U-bolt. Unless the threaded length of the U-bolt below the nut is negligible, the area Qu should be determined as the length-weighted ,l'O average f threaded and nominal areas in equation (24).
- b. Lower Bound (Uncinched)
The lower bound of the U-bolt stiffness is i
, calculated by assuming that the U-bolt deformation is '
Primarily due to bending. The flexibility of the 0 U-bolt is the deflection of the U-bolt apex due to a unit concentrated load, perpendicular to the cross piece at the nut locations. By using the minimum energy theorem considering t-g both axial and bending effects, the deflection at the tip relative to the nuts can be determined. The - stiffness of the U-bolt can then be obtained by i inverting the flexibility. I Thus, the lower bound stiffness is : l i
'O a ueE (25) ,
l g""=1.is,(r 4 os (g +b) ;
- {
0 : i where r is the radius of the U-bolt cross section. l io t 1
- O l
1 _ . _ .-_.. . - . . .
O
'O Based on comparisons with FEA (see Figure 3.5), the upper bound U-bolt stiffness as defined by equation (24) is a good approximation already at relatively low levels of preload. The upper bound estimate should therefore be used in design applications. .O 4.3 INTERNAL PRE'SSURE AND THERMAL EXPANSION EFFECTS
- a. Pressure Effects Since the U-bolt assemblies are installed at
- <3 ambient temperature on unpressurized pipes, the temperature increase and fluid pressure under operating conditions will affect the U-bolt preload.
If the internal pressure is greater than the atmospheric pressure, the U-bolt tension will increase 33 due to the restraining effect the U-bolt has on pipe expansion. The change in U-bolt tension can be expressed by the following equation [6].
- O AUg ={K 4( DRt (26)
Et
- R ) (2-Y) p Where 13 Ri = Inside radius of pipe R = Outside radius of pipe E = Young's modulus of pipe material '
tp = Thickness of pipe wall y = Poisson's ratio p = Gage pressure of the fluid in the pipe lO K = Equivalent stiffness Similarly, the compressive force, Fp , between the pipe and cross piece will increase by an amount equal to twice the increase in U-bolt leg tension. !g The parameter K in Eq. (26) is the equivalent stiffness representing the pipe and U-bolt system, and is defined as follows: Ket
- K g i K= (27) ,
iO K eg + Kp , i i i !O 1 !_ - m _ .. .. _ _.. _ . _ ._. - ... .
.g
O O where K and K are the stiffness values of the
'U-bolt assembly and the pipe, respectively, as determined by equations (22) and (13).
- b. Temperature Effect lO Similar to the internal pressure effect, the i U-bolt preload is also affected by the differential thermal expansion between the U-bolt assembly and the
. P ipe. If the U-bolt assembly and the pipe had a uniform temperature rise and a uniform coefficient of thermal expansion, there would be no change in U-bolt tension due to thermal transients. I Figure 4.6 shows the dimensions of a U-bolt / pipe i assembly that are pertinent to the evaluation of the , restrained thermal expansion effects. An optional shim !
- plate or spread plate between the U-bolt and the pipe is l g also shown. Point A is the contact point between the 4 cross piece and pipe and Point B is the contact point j between the shim plate and the U-bolt at the apex of the
) U-bolt. I
- To determine the thermal expansion effect on U-bolt tension, the differential thermal expansion O between U-bolt and pipe needs to be determined.
The change in preload is the force required to close the hypothetical gap from this differential thermal i expansion. lO By allowing the U-bolt, the cross piece, the
- shim plate, and the pipe to expand freely due to j temperature change, we can calculate the differential j expansion between pipe and U-bolt. There are two .
expansions to considers fg 1. Thermal expansion of the pipe and the spread plate (li), I f 2. Thermal expansion of U-bolt without the l: constraint of the cross piece (di), ? l! O The equations to calculate the two thermal expansion quantities are described in the following: 2 1 1!O 1 [r
- g i h
i _ -. _ . . _ - _, ..
.O , g) 1. Pipe and shim plate expansion, di :
4 = d er ATp4 D, + 4 x 4T 3
- f (28)
( where dr, ds are the thermal expansion O coefficients of pipe and spread plate materials, respectively; 4Tp , 4Ts are the temperature changes from ambient to operation in pipe and spread plate, respectively.
- 2. Thermal expansion of U-bolt without the
- c) cross piece constraint, dl
T2 = Ol#4Iu e (D,+ t') (29) , where clu , ATu are the thermal expansion
- coefficient and the temperature change in 50 0-bolt, respectively.
i The differential expansion (J) between the U-bolt and the
- pipe can thus be calculated by the following equations
- # = .G - di (30) lO l The increase in U-bolt tension due to this l differential expansion is as follows
l = I .O [* (31) ! where K is determined by Eq. (27). A negative value represents a decrease in the U-bolt tension. Similarly, the compressive force, FF , between the pipe l
' g~ and the cross piece will change by an amount equal to twice the change in U-bolt leg tension.
4.4 STRESS CALCULATIONS
- This subsection describes simplified expressions g for determination of relevant stresses in the U-bolt j assembly components and locally in the pipe to be used i in the design process. Corresponding acceptance
- allowable stresses and other acceptance criteria are defined in Section 5.2 and 5.3.
.O 4.4.1 U-B lt Stresses
.O
lO The U-bolt can be treated as a structural member
- CL subjected to pure tension. The compatibility controlled bending stresses that occur during the cinching process ;
have no net effect on the load carrying capability of the U-bolt and can be neglected. No prying effects are present at the nut / cross piece contact. The governing U-bolt stress can therefore be determined from: O 4 fg = P_ (32) au Where: . -} = average tensile stress ftb U = U-bolt force representing the load . condition of interest (see Section 5.2) !
- O = U-bolt net tensile area au 4.4.2 Cross Piece Stresses
' The cross piece can be treated as a symmetric, O double cantilever as shown in Figure 4.7b. The cantilever length'is the distance from the center of a U-bolt leg to the critical section of the cross piece for bending and shear stresses. The loading on the cantilever consists of the maximum U-bolt tensile force, U, corresponding to the load / operating condition of O 1 interest (see Section 5.2). Depending on the structural i detailing of the cross piece and the bracket, the critical section is either at the center of the cross piece (maximum bending moment) or at the edge of the i bracket (minimum cross section). l0 The weld between bracket and cross piece needs to be checked against: o Direct tension perpendicular to the cross piece due to maximum tensile strut force i) o Shear parallel to the cross piece due to tangential component of inclined strut load L o Horizontal shear due to bending moment acting on composite cross section consisting of cross O Piece and bracket F O
r !O lg3 4.4.3 PiDe Stress Evaluation A complete evaluation of the stress / deformation state in the pipe, locally at the U-bolt, needs to consider the global effects due to pipe moments and internal pressure as well as the purely local effects O induced by the cinched U-bolt. The global effects due to moments and internal pressure are limited in terms of general membrane stresses by equations 8, 9, 10 and 11 of NC-3650. These limitations are checked routinely in the normal course
.O of Piping analysis.
The local effects on the pipe such as those due to concentrated support reactions are not addressed in
- subsection NC in terms of specific stress limitations. !
It is, however, stated in Nc3613.3 under " Mechanical 'O Strength" that the pipe wall thickness shall be ! increased "when necessary to prevent damage, collapse or i buckling of pipe due to superimposed loads from supports or other causes." In the absence of code-specified local stress lO limitations, the requirements of NC-3613.3 are shown to be satisfied by means of detailed elasto-plastic ( collapse load analyses, which provide accurate ! representations of the true stress / deformation behavior of the pipe. By including a full representative pipe span in the models for these analyses, a comprehensive f g- evaluation of the combined global and local effects on ! the pipe is performed at the support points. A ! The derivation of the allowable compressive forces ! applied locally to the pipe based on the collapse load
- analyses is addressed in Section 5 under " Acceptance l g~ Criteria". The information in Section 5.3 on this topic l is a summary of results from [12], which describes
[ the collapse load analyses in detail. The remainder of this subsection will address an
- alternate, optional method of local pipe evaluation based L
on equivalent elastic, local pipe stresses in the support / pipe contact region. i The development of allowable compressive local i pipe reactions based on collapse load analyses has been limited to pipe sizes greater than 10 inch, since it is (O
.O i
)
4
- O i
i
!O primarily for these larger pipe sizes that local evaluations based on elastic stress criteria tend to be excessively conservative and therefore would warrant a more detailed evaluation. The elastic stress calculation methods described in the following paragraphs are therefore intended primarily for conservative application to pipe sizes smaller than 10 lC inch. The methodology is, however, applicable to all pipe sizes.
The primary location of interest for pipe stress evaluation is the vicinity of the cross piece contact jo with the pipe which is identified as location "A"
- in Figure 4.9. The stresses in this region, as discussed in Section 3.1.3, are consistently higher than
- elsewhere in the cross section, including the contact region between the U-bolt and the pipe. The pipe stress i gradients in the vicinity of the cross piece are 10 dependent on the contact load distribution along the
, initial contact line. This longitudinal load distribution is in turn a function of relative stiffness , between pipe and cross piece as well as the total load i I magnitude. As an example, a stiff cross piece member on . a relatively flexible pipe wall will tend to concentrate l, !O more of the contact force towards the edges of the cross ; i piece. In addition, an increase in total contact force l i magnitude further amplifies this concentration towards ! the edges. For design purposes, of course, a detailed ! case-by-case evaluation of this load and stiffness
- dependent distribution is not feasible. Based on 10 findings from the finite element analyses described in
- Section 3, a tapered line load distribution has been adopted with maximum intensities at the cross piece j edges and zero at the center line.
I In the lateral (circumferential) direction the lo initial contact line load is broadened under increasing load from a idealized line to a narrow strip of surface i ' area as a result of a very localized pipe wall deformation. This " seating" of the two initially disasimilar surfaces of pipe and cross-piece is a physical necessity since contact stresses under a line 6o load would have approached infinity. The local l plasticity in the immediate vicinity of the idealized j line load is thereby a self-stabilizing process which I i starts at very low load levels. These phenomena have ' i been evaluated in detail in connection with the collapse [ load analysec [12]. tO ( 46-O !
.wy,. ,,s.-m--..y _m3-%--
LO ;
- 1 4
The maximum circumferential pipe stresses generally [ C) occur on the line of initial contact just inside the i, edges of the cross piece. Recognizing the localized i self-stabilizing yielding in the immediate vicinity of i the line load, the location of the relevant reference j stress values has been selected at 5 degrees away from the initial line load, directly below the cross piece C) edge. This location is identified by an "X" in Figure 4.8, which also shows the selected tapered line load i distribution. A computer program " BEARING", developed by RLCA for
,0 determination of lo:a1 pipe stresses caused by radial line loads, have been used to determine local pipe j stresses at the location identified in Figure 4.8 )
i for a wide range of pipe sizes / schedules and cross-piece widths under a unit load of 1 kip. These stress calculations have been documented in [28], which also f contains a tabulation of all results. The validity of lO the program BEARING has been verified [27] against finite
; element analysis results. Figures 4.16 and 4.17 show a
} comparison of stress profiles predicted by BEARING and by FEA as extracted from [27]. The stress profiles in i Figures 4.16 and 4.17 represent a longitudinal slice
! through the pipe wall 5 degrees away from the line 10 load. The comparison in Figures 4.16 and 4.17 show I
I very close correlation between BEARING and FEA and is representative for other comparisons in [27] for a l total of four different configurations. Figures 4.16 and 4.17 also include stress profiles obtained from 10 the Model 1 FEA described in Section 3.1.3. These FEA results were extracted from the cinching load
- case normalized to a cross piece force of 1 kip.
- since Model 1 incorporated a realistic representation -
, of the cross piece, and thereby a realistic contact j
i force distribution, these results give an indication of the conservatism inherent in the tapered load
!O distribution used in the BEARING analyses. The i stresses calculated from " BEARING" were also compared 1 with FEA result [2] in Tables 4.2 to 4.5 which also show good correlation.
s O As stated above and in Section 3.1.3, the stresses ]O in the region of cross piece contact are governing over a those in the region of circumferential contact with the U-bolt. For reasons of completeness and comparison, a 4, set of simplified stress equations from [20] are ] provided below for this latter region. i ]O,
.O i
~ - _ _ _ _ _ _ _
-O
- Stresses in confined Region C-D (Figure 4.9)
- C) (Based on [7], page 463, case 15)
Circumferential bending: !O *. -i.s 65e essmwor = 0.5
- Rm +5t e w F.
(36) Circumferential membrane
~
I O
-e.5 -t.5
%, ,g = s.M
- R,. .e t, e Fo (37)
Longitudinal bending: O -e.s -i.5 (, - i.2
- R m -* t r .e Fu (38)
Where Rm = pipe mean radius [ inches] l t = pipe wall thickness [ inches] p O y = tensile force in U-bolt for load u condition under consideration [1bs] The stresses determined above are those caused locally by the U-bolt only. For a complete evaluation of the stress state in the pipe wall, stresses due to JO internal pressure (unconfined by U-bolt) and global piping moments shall also be taken into consideration. 4.5 PREDICTION OF PRELOAD LOSSES I g- The reliance on U-bolt tension forces to provide frictional resistance against rotation necessitates i the consideration of potential reduction in U-bolt i preload as a function of time. The possible causes for time-dependent preload losses fall into three categories, namely (1) mechanically related g redistributions of tensile strains along the U-bolt [ due to friction redistribution and local repositioning;
; (2) permanent deformation due to gross yielding in
( U-bolt, cross piece, or pipe; and (3) relaxation phenomena due to prolonged state of high stress and high temperature. i
- 4) :
j O i
O O (1) Losses related to friction redistribution During the initial cinching operation (torque, or preload), the friction between the pipe and the U-bolt tends to resist the stretching of the conforming portion of the U-bolt. This means that the U-bolt o strain distribution is non-uniform with a maximum in the straight shank portion and a minimum at the center of the curved portion. During subsequent load application the friction force distribution will change as discussed in Section 3, accompanied by a corresponding change in U-bolt strain distribution. This strain redistribution 70 will lead to a small reduction in U-bolt shank stress.
- Conservative estimates of this shank stress loss can be
, made by assuming that the redistribution leads to a ( state of constant strain and that the elastic deformation of pipe and cross piece remain unchanged during the redistribution. Losses have thus been (O estimated to range from approximately 24, based on i finite element analyses [15], to 64 based on L conservative hand calculations [22]. l (2) Losses due to gross yielding A Permanent loss of preload would be expected if [O significant plastic deformation were to occur in the U-bolt or the cross piece as a result of initial preload, thermal expansion or tensile strut load. This situation is prevented by predicting and limiting f, the U-bolt and cross piece stresses to values at or lO below the yield strength as defined in Section 5. $ The potential for preload losses resulting from } localized permanent stains in the pipe wall at the cross j piece contact zone due to thermal cycling has been the j subject of detailed analyses as described in Section 3.3. These analyses, which were based on an estimated Io worst case combination of pipe material (SS), high 4 initial preload, thin pipe wall'(D/te= 29), and high temperature (400 F), resulted in a predicted upper bound
; of thermal cycling-related preload losses of 16%. Based l on these analyses, it was also estimated that for j (3 configurations satisfying any one of the following q criteria, an upper bound of 12% losses can be 9 conservatively assumed:
1 10
,0 1
- = =2- -
0 All carbon steel pipe applications 0 stainless steel pipe applications for which: (a) D/tp i 25 (b) T 1 300 F (c) Initial preload compression effect on O the pipe is less than 50% of allowable (see section 5.3). (3) Losses related to relaxation phenomena p' The temperature in the U-bolt / cross piece assembly l' is not expected to exceed 350 F, and the pipe wall in U-bolt assemblies is not expected to exceed a mean
- temperature of approximately 550 F. At these temperature levels, creep phenomena are usually negligible. This was further illustrated by the thermal O cycling and " creep" tests performed by Westinghouse for three different pipe /U-bolt configurations [1]. The i test specimen of particular interest was the 4 inch Schedule 160 configuration, which from a potential l relaxation standpoint, was subjected to extreme stress i
and temperature conditions. l O Table 4.1 contains a summary of equivalent elastic U-bolt stresses before, during and after the thermal cycling and " creep" tests. These stresses have been determined from U-bolt force information provided in [1] with U-bolt cross-sectional area of 0.142 sq. in. and 0.196 sq. in. the threaded region and in the shank
'O region, respectively. It is apparent from the stresses shown in the table that significant yielding must have a taken place in the threaded region of the U-bolt. The j calculated stress in the threaded region of leg 1 j changed from an initial pre-test value (at ambient q temperature) of 41.6 ksi to 53.9 kai at the end of the i first cycle, and to 48.6 kai at the end of cycle 10.
- The corresponding stress values in the shank region were d
30.1 kai, 39.1 kai and 35.2 kai. The U-bolt material F. (SA36) has a specified minimum yield strength of 36 ksi
; at 70 F and 30.0 kai at 450 F. It is therefore likely
- g that some yielding in the threaded bolt area took place during the torquing operation even prior to the heat-up
! of the pipe.
a } 1 i . i
;O 1
i
~
- _- :::LL: X:L . - _ . _ . - - . . _ _ _ _ _ - _ _
O
~13 During the thermal cycling, temperatures of 450 F and 560 F in the U-bolt and pipe, respectively, were maintained for one hour prior to data recording.
Shakedown to elastic cycling of the U-bolt forces took place during the first 4-5 cycles after which very little change was observed between cycles. .O When the 24-hour " creep" test was commenced immediately following the last thermal cycle the stress in the U-bolt was, therefore, essentially at the yield point. At ambient conditions following the 24-hour test period, during which the temperature was maintained at
.O 445 F (U-bolt) and 560 F (pipe), the U-bolt forces were
- 4854 lbs and 4398 lbs as compared to 4871 lbs and 4410 lbs at ambient prior to the creep test. Thus, no change
, in ambient condition preload took place during the test { despite the extreme stress and temperature conditions, iO Thus, the only preload losses that were detected during the thermal cycling tests and the subsequent 24 hour holding period at temperature, were those that ' would be predicted due to gross yielding of the I effective U-bolt cross-sectional area in the threaded region. This category of losses is prevented by iO provisions in the proposed design procedure by limiting the stress in the U-bolt to the yield stress under worst case combination of the effects due to preload, thermal j expansion, internal pressure and strut load.
- Relaxation in connections involving threaded parts can be divided into short-term and long-term effects.
lO 3 Short-term relaxation, which occurs in minutes or hours j is the result of localized contact loading on the threads near or past the yield stress. Uneven contact
, surfaces may, for example, result in localized contact j stresses approaching or exceeding yield. The 40 Westinghouse " creep" tests, which were monitored for a 24-hour period would have identified these short-term I relaxation effects if they had been of any significance.
i h The potential for long term relaxation effects in 4 the U-bolt is currently being addressed by SWEC in the p (3 form of direct, tensile relaxation texts performed for a 1 full range of applicable stress and temperature values. j The specification for these tests in contained in [30] . i
- o l
6 L O h 7~~Til:2Zj ' ._ il.E_ __ _ _ [_.11_ _ _ _ _i_ ___ _ _ . ___ _ _ _ _ _ _ _ _ . _ _ .
'O ~() In summary, with regard to all potential causes of preload losses it can thus be concluded that: 1 I'
o Preload losses are likely to occur as a result of friction redistribution and U-bolt repositioning over surface imperfections g that may have created temporary binding during initial torquing. Based on tests and analyses, a conservative upper bound loss of approximately 54 has been established for these phenomena. o Preload losses may occur following high
- . C) temperature thermal cycling as a result of i permanent strains in a localized pipe wall
. region. Under extreme conditions these losses have been estimated at 18%. o Losses due to gross plastic deformation of
; U-bolt components are prevented by limiting
- C) the maximum predicted stresses due to all causes in these components to the minimum specified
} yield stress at temperature. i o Losses due to short-term relaxation phenomena are negligible. i) C For design purposes, the total estimated preload loss can be conservatively accounted for by increasing l the required torque value (Section 4.1) by the following l amounts: i ls' (a) 304 for stainless steel pipe applications l with: .f o Maximum operating temperature exceeding i 300 F, and i g) o D/t ratio exceeding 25, and i o Initial preload compression effect on s the pipe exceeding 50% of allowable l value at temperature as per Section L 5.3. O (b) 204 for all other applications. o l' 1 jo 4 t O i
' ' ~
~
, [_ _2_~$ __,_
______._.-._____,_.[,. . _ _ ._ _ [ _ __ 5_ _ _
- O l
4.6 VALIDATION OF DESIGN PROCEDURE l
;O The validity and conservatism of the design procedure defined in section 4 has been verified by comparison with results from tests and detailed finite element analyses. The following subsections describes some of the more significant aspects of these
- (D comparisons.
4.6.1 Rotational Slippace Resistance (Section 4.1) 7 The purpose of this aspect of the design procedure 10 is to determine the minimum U-bolt torque (preload) required to prevent rotational slippage under inclined or eccentric compressive strut loading. Equation (7), ' section 4.1.2, which defines this minimum torque, can be reformulated to provide a maximum allowable strut load for a given bolt torque value. Applying this reformulated equation to the 10 inch U-bolt i C) configuration that was analyzed for inclined strut loading (Section 3.1.2.d, Figure 3.14) results in an l allowable compressive strut load of 10.6 kips with a
- safety factor of 1.5. The rotational capacity at this !'
i ' load level as determined by FEA exceeds the applied ,O loading by a factor of 1.64, which means that the actual
- safety factor exceeds the design factor. The design j equation is therefore conservative.
! 4.6.2 Friction Factors 10 The two empirically determined friction factors, which relate U-bolt torque to tension and characterize i the friction resistance between pipe and U-bolt are discussed in section 4.1.3. Using the values * [ recommended in the text for these friction factors in j the simplified design procedure model (Figure 4.1) ?O results in predicted slippage failure loads as shown by the broken lines in Figures 4.10 through 4.13. The
- solid curves in these four figures shows the slippage ,,
failure loads for different initial torque values that l i were obtained from the friction tests [1] under tangential loading. A comparison of the test curves and
- O the design procedure curves in the figures shows that i the design procedure, with few and small exceptions, l
[ significantly under predicts the slippage failure load. f L C F t u O F Y -- -_::: -~ r DL_T_ i- - - , _ _ _
'O ,
4.6.3 Distribution of strut Load Between Pipe and U-Bolt O-When a strut load is applied to the U-bolt assembly, a certain fraction of the load is transmitted to the U-bolt legs and the remainder is transmitted directl , piece. yThis to the pipe via the contact with the cross ' schematically in Figure 4.5 for tensile as wellisasshown distribution of the strut reaction () compressive strut loads. The relative distribution between U-bolt tension and pipe compression is a function of assembly andthe therelative pipe. stiffness between the U-bolt
!O This load distribution is of significance for the following aspects of the design process. .
o Prediction of normal force distribution and thereby rotational resistance.
'O o Prediction of maximum U-bolt tension for comparison with acceptance criteria.
o Prediction of maximum pipe compression for ' j comparision with acceptance criteria. :
! C) Figures 4.14 (tensile strut load) and 4.15 i (compressive strut load) show how the design procedure t
- predicts the load distribution in terms of U-bolt ,
i tension variations in comparison with test results [1]. :, t I, O ; i t i l ! I.
- o a
O O O l! l _::2:: :L ::L : ~ ~
~'
O O 5.0 DESIGN CRITERIA This section describes the proposed design acceptance criteria in terms of required margin to failure and maximum stress limits for the cinched U-bolt assembly and associated local force / deformation effects g on the pipe. 5.1 STABILITY CRITERIA stability failure for the U-bolt assembly is defined as rotational slippage around the pipe when the g' U-bolt is subjected to an inclined, compressive strut load. A conservative methodology for the determination of minimum bolt torque required to prevent this type of failure for a given configuration and load condition is described in Section 4.1. O This methodology explicitly takes into account all predictable factors of any significance that affect the stability condition, including allowance for time-dependent preload losses. A safety factor of 1.5 will be applied to the O minimum torque determined in accordance with Section 4.1. This value is consistent with the requirement in Subsection NF of the ASME Code [9] for Service l Levels A, B and C that loadings shall not exceed 2/3 of the critical buckling load. g 5.2 U-Bolt component stress criteria This subsection addresses the two main components of the U-bolt assembly, i.e., the U-bolt and the cross piece. Both of these fall under the jurisdiction I of Subsection NF of the Code. O The U-bolt is treated as a general tensile, structural member for Code compliance purposes. Thus, O . U 6 0. 6
- Sy f (41) c tb Gu l .
'O r -.-..n..-. - -
- O
, C) Where f = U-bolt tensile stress tb , U = maximum U-bolt leg force due to preload and external, tensile strut load
- O au = minimum U-bolt cross sectional stress area S = minimum specified yield stress y
0 In addition to the above Code stress limit, gross yielding of the U-bolt in tension has to be prevented, as discussed in Section 4.5, in order to maintain intended preload. Therefore, the maximum U-bolt leg , tension due to all load effects shall not exceed the yield strength of the material (20]:
- 3) ,
=
U us) 4 37 (42) k (FAxiMu M) 3 Where: U (max) = Maximum U-bolt leg force due to preload, restrained pressure / thermal expansion, and tensile strut load, calculated as per - Section 4.4 O Stresses in the cross piece member, calculated as described in Section 4.4, shall be subjected to stress limitations consistent with those described above for the U-bolt.
- g Thus, as per NF-3322.1, stretaes in the cross piece caused by maximum tensile strut loadc shall be limited to:
Nominal shear : 0.40 Sy
. Bending : 0.66 Sy (compact section)
)
,0.75 Sy (solid plate) lO i l
R3 ! w_ - - , ,+ - .= *e
l \
- O l
l The cross piece has a function identical to that of l iO the U-bolt in elastica 11y maintaining the preload forces ' t in the assembly. The total maximum cross piece bending stresses due to all simultaneous load effects, therefore, shall be limited to the yield strength, consistent with the corresponding limitation on the U-bolt tensile stress. Code limits provided above for stresses caused
- by strut loads are applicable to design and Service l Level A loads. Code stress limits applicable to l Service Levels B, C and D strut loads are defined by 4r) the stress limit factors in Table NF-3623(b)-1 in the Code. The increase factor for shear stresses shall not exceed 1.5, however. The stress limit factors are such that the functionality criterion of limiting total
- maximum stresses to the yield strength generally will govern the design rather than the Code stress limits.
!O 5.3 LOCAL PIPE ACCEPTABILITY l 5.3.1 Overview of Applicable Code Recuirements i Subarticle NC-3000 of the ASME Code [9] provides the stress criteria for Class 2 piping. These criteria lO are applicable to stresses caused by global bending and
, torsional moments acting over pipe cross sections.
Local effects in regions of concentrated contact forces
- l. between pipe wall and support hardware are addressed
. only briefly and qualitatively in this Subarticle. Code paragraphs that are pertinent to the discussion of these
[JO local support contact effects can be found under NC-3112.4, NC-3613.3, and NC-3645: Paragraph NC-3112.4 states under " Design Allowable Stress Values" that general membrane , stresses for NC-components shall be limited to !C allowable values. A footnote comments further on i this criterion: "It is recognized that high l localized and secondary stresses may exist in
- components designed and fabricated in accordance l with the rules of this Subsection; however, insofar i as practical, design rules for details have been
,0 written to hold such stresses at a safe level j consistent with experience". I t , i b L !
tO Paragraph NC-3613.3 states under " Mechanical
- 13 Strength" that the pipe wall thickness shall be increased "when necessary to prevent damage, collapse or buckling of pipe due to superimposed loads from supports or other causes."
- Paragraph NC-3645 states under " Attachments"
- O that external and internal attachments to piping shall be designed in a manner that prevents excessive localized bending stresses and flattening
. of the pipe as well as harmful thermal gradients in l the pipe wall. The paragraph also points out that such attachments be designed to minimize stress
- 3 3 concentrations in applications where the number of stress cycles is relatively large for the expected life of the component.
As the above three paragraphs indicate, subsection
- g NC recognizes and accepts the existence of high i localized bending and secondary stresses but does not provide explicit limits on these stresses. The phenomena of " pipe flattening", " collapse", " damage" and
" buckling" that are mentioned in paragraphs NC-3613.3 and NC-3645 can not be accurately represented by linear elasti analysis techniques. This is due to the
' C> inevitable local yielding at the idealized contact line
, and the associated nonlinear changes in contact area and i contact pressure distribution under increasing loads. .
Due to the absence of specific limitations in i Subsection NC of the Code with regard to localized ,
- O pipe / support contact effects, it was decided to perform :
detailed, rational analyses for the evaluation of the local pipe effects and for the determination of acceptance criteria consistent with the design philosophy of ASME Section III. These analyses, which '.g' are reported in detail in [12], take into account the ' simultaneous effect locally in the pipe from: (1)
- global effects from internal pressure and overall pipe l moments, as well as (2) purely local effects due to the
- contact pressure between the pipe and the support .
j member. j U The basis for the local code-acceptability of the , pipe is then based on the local collapse load determined l by detailed plastic analysis of the pipe / support
- configuration. The definition of " collapse load" for 10 i
l i 0
,u _ _ , _ , . . _ _ . ._, _ .
- 9
.._..._-_.---._.._--_-,.___...,_--.__-~__
O-qg purposes of the evaluations in this report corresponds to the definition used in ASME Section III (II-1430 as referenced from NB-3228). This definition of collapse load is very conservative for application to pipe / support contact effects as can be seen from the results presented in following paragraphs. The pipe has a significant capacity to withstand support contact i
;O loads in excess of the " collapse load" as defined here.
Consistent with the design philosophy of ASME Section III [9], the allowable compressive bearing load is then established as two-thirds of the determined 11 apse load. The increase in this collapse load
;O fraction allowed by [9] for Emergency and Faulted Conditions is, conservatively, not taken credit for in the current application.
5.3.2 Implementation for concentrated, Radial Line Loads '. { C) As demonstrated by tests [1], finite element
- analyses (Section 3), and the pipe stress evaluations described in Section 4.0, the governing stresses and deformations for the pipe are in the region of contact with the cross piece. The stresses in the opposite half
',3 of the pipe in the U-bolt contact region are consistently lower due to the confining effect of the U-bolt, which tends to reduce the circumferential bending deformations. ! The acceptability of the pipe can be expressed in terms of a maximum compressive force along the line of
- O
- - contact between the cross piece and the pipe. The local l effect on the pipe due to this compressive force in the
. cinched U-bolt application is similar to that occurring - l in the general. case of a pipe supported by a straight ! structural member such as in a box frame or trapeze
- 0 3
support. A maximum allowable value for this compressive force can be defined based on the collapse load as l determined by detailed plastic analysis, g 5.3.2.1 Plastic Analyses for Determination of Collapse , Load t E) A series of detailed, elasto-plastic finite element analyses have been performed to determine the local plastic collapse load of pipe sections under line load contact with support members. These analyses are
- described in detail in [12] and will be described only in summary f rm in the following paragraphs.
0 1 i i
- I l !
10 L i w ,, _ _ n . -.n.- , , , - . - - . - . . - , . - . . . -- . . - . , . . .
.__ .- - = -. - -
- O
'0 In order to achieve a conservative, comprehensive representation of the local pipe behavior at support points, a complete pipe span was modeled for each dimensional configuration. This ensured that the local effects due to the radial support reaction as well as .o- the longitudinal membrane stresses due to pipe bending
- moments are incorporated in the analyses.
A total of five pipe configurations were evaluated j with dimensional parameters as listed in Table 5.1. The uniform loading on the pipe spans was gradually hg increased in discrete steps until the collapse load had been reached. As mentioned earlier, the collapse load was defined, consistent with ASME Section III, as the support reaction for which the corresponding pipe deformation (diameter reduction at the support) was twice the equivalent elastic deformation. !O The results from the analyses in terms of
- force / deformation curves (i.e., support reaction versus i
diameter reduction) are presented in Figures 5.1 through 5.5 for the five analysis configurations listed in Table 5.1. !O The force / deformation curves at increasing loads are characterized by: (1) a " material softening effect" due to the localized yielding in the contact region, and (2) a " geometric hardening effect" due to the gradual increase in contact area that takes place when
- o the curved pipe surface accommodates itself to the flat support surface. This local deformation {
in the contact region has a beneficial, stabilizing : effect on the distribution of contact pressure on the l l pipe under increasing load. l jo Due to the nodal discretization of the gap elements in the analysis model [12), this increase in contact area shows up as a slight wave form in the force / deformation curves. In reality this phenomenon is continuous, which can be represented in the analytical i force / deflection curve by drawing a smooth curve through- , !o the upper bound of the wave form. ; This refinement has been conservatively ignored in i determining the collapse loads in Figures 5.1 through 5.5. The analysis for Case 5 (30" Std) was terminated at !O 4 i jo i 1 ,
. = % ,, ,.... - , w . _ . . . . . m, , . . . . . . . . .
10' l 4 a total load of 65 kips without having reached the ! O collapse load. This analysis demonstrates that for this l configuration (high D/t - ratio) the geometric : hardening effect is sufficient to compensate for the material softening effect in the load range of 20 to 65 kips. The conclusion from this analysis case is that the limit load is at least greater than 65 kips. O In order to demonstrate the local behavior of the pipe under cyclical reaction loads, three of the , analysis models (Cases 1, 2 and 3) were subjected to complete unload / reload cycles from initial levels of 24.8 and 35.3 kips, respectively, which correspond i) L approximately to the allowable load of two-thirds of the collapse load. One of these load cycling analyses (Case e 1), was also subjected to sustained internal pressure of 400 psi during the thermal cycling for evaluation of ratcheting potential. These load cycle analyses g demonstrate that: 1 i (1) Essentially all permanent deformation j takes place during the first half load cycle up to j , the maximum load. The incremental deformations at j l the second load cycle to maximum load, following. i uni ading, were 0.3%, 0.2%, and 1.5% for cases ! O 1, 2 and 3, respectively. The presence of i sustained internal pressure (Case 1) does not perceptively change the second cycle relative deformation.
, g- In evaluating these load cycling results from the standpoint of elastic shakedown, it is important to recognize the highly localized nature in this application of those cyclical bending 3
stresses that are of such magnitude that they < potentially could lead to progressive deformation 11 they had been distributed around the O circumference of the pipe. The small amount of incremental strain that may occur in the most r highly strained points in the contact zone during L the first few cycles will lead to a self-J stabilizing redistribution of hoop stresses away a) g from the center of this zone. For comparison purposes, it is noted that t the classical ratcheting case of axisymmetric i high cyclical bending stresses acting in
- conjunction with internal pressure does not have this redistribution potential, which is the very
]l's reason that ratcheting is a potential concern for that case. t J b j;
O i 10 It is concluded from the load cycling analysis ' that shakedown to elastic action takes place in the first few (5-10) cycles and that any incremental deformation following the initial loading are i negligible. ^o
. (2) The maximum cyclic circumferential strain range obtained from these analyses was 0.00337 in/in, which corresponds to an alternating stress of 48.5 kai. This alternating stress corresponds to approximately 6,000 allowble full load cycles in Figure I-9.1 of [29]. A " full lO load cycle" as used here represents loading to maximum allowable design load followed by complete unloading. This is obviously a very conservative load cycling definition for cinched U-bolts since a significant preload is present at all times. A more realistic fatigue evaluation to specifically for cinched U-bolt applications is described in Section 3.3.4.
The parameters that determine the collapse load are ! C) Material yield strength (at temperature), Sy (T) (ksi) Pipe mean diameter, dm (inches) Pipe wall thickness, tp (inches)
- O support member width, be (inches)
I Based in part on work published by Amdahl, 1980 ([14] as referred in [13]) it has been determined that s the radial line load capacity of pipes can be expressed {0 in the form ! 2 f g
* (43)
P,c = C
- S (T)
- t p y de) tp
- dbc) m
{0 iG i. (O j . _ _ _ . _ . . . , _ ..
, - - . . - _ _ _ _ - _ . _ . _ - - - - , _ . - . . _ _ _ . - _ . - ~ ~ _ _ _ . _ - - - _ . . - _ - - - -
O g where C is an empirical constant. Pc is collapse load (kips) Using this expression in conjunction with the definition of collapse load for the current application, the constant, C, and exponents, f and g, were determined
' O by curve fitting with the results from the current analyses. This resulted in the following final expression for the " collapse load":
- O 2 0.73 0.3 Pc = 0.84 *Sy(T)
- t, ( dm i ( be i ' (44)
- \ tr / Wm/
5.3.2.2 Implementation for Cinched U-Bolt Supports 1 L g Based on the analysis results presented in [12), as summarized in the previous subsections, and consistent I with the requirements of NC-3613.3, the acceptance j criterion for the local pipe condition at the cinched U-bolt is defined by equation (45) below. I !) C The compressive reaction between pipe and cross piece, Fp, should not exceed: i f 1 Fp1(2/3)*Pc (45) I
- o h-i j Where
1 0 g . Pc = collapse load determined from equation (44), 1 (kips) 1 P' Fp = Compressive force between pipe and cross piece, including the maximum combined contributions from U-bolt preload (torque), restrained thermal expansion, restrained f (.) pressure expansion, and compressive strut j load (see Section 4.0). i [' In addition to safety factors required by Code, the l limitation imposed by equation (45) is conservative in the following respects: 30 , 4
; 'O *
- O t
- O a. The limit load defined by equation (44) is
- based on unconfined pipe sections subjected to
- concentrated support reactions. The true limit load for a cinched U-bolt application is expected to be significantly higher due to the lateral 4
confining effect of the preloaded U-bolt. !O b. The code requirements that form the basis i for equation (44) are intended to satisfy primary j load limitations. For reasons of procedural simplification in the current application, the secondary loads due to restrained pressure and thermal expansion are conservatively included with
- 0' the primary load from strut reactions. This is
! clearly conservative since the secondary load
- effects cannot contribute to collapse of the pipe
- section.
?
!O
! CP t 'O
!O l l0, r [O I I -
a jO ;
6.0 CONCLUSION
S l O. < When designed and preloaded in accordance with the i procedure in section 4 of this report, whili. satisfying the acceptance criteria defined in section 5, the cinched U-bolt support has been demonstrated to perform q3 its intended function and to satisfy all applicable Code , Criteria. A combination of full scale tests and detailed finite element analyses have been used to , verify the conservatism inherent in the design l procedure. SPecifically, the design procedure assures that {O (1) Rotational stability of the U-Bolt' assembly will be maintained under worst case conditions of inclined compressive strut loading with safety margins consistent with
- AsME, section III/NF.
!O (2) Minimum U-bolt preload required for rotational ;
stability will be maintained through all operational cycles. q (3) Stress levels in the U-bolt components are , i) such that all applicable Code criteria will be satisfied and the support will"be able to perform its intended function under all ! specified operating conditions. l i 'g
; (4) The local load effects on the pipe caused by the presence of the cinched U-bolt will be maintained within acceptable limits defined by the Code. ,
- O t
O i [O i t I ;O 6
/
-+,_-.~.e _ , . . . - + - . . - . . - . , . . - . f
-- .. . . _ _ _._._._. . _ ._ _ __ , _ _,-. _ ,.. .-._.__._....._.__..._s._,,__._.__--.~.__.___.
4 {Q ; r ,
^
s -
;s t
t
? '
i O
7.0 REFERENCES
- 1. WCAP-10620 Comanche Peak Steam Electric Station i U-Bolt Support'/ Pipe Test. Westinghouse Electric Corporation, July 1, 1984.
l
- 2. WCAP-10627 Comanche Peak Steam Electric Station
.O 's
,U-Bdit Finite Element Analysis. Westinghouse Electric Corporation, July 26, 1984.
- 3. ANSYS, Swanson Analysis Systems, Inc., Version 3 4.1.B (CRAY) and 4.1.C (VAX).
' O 4. "U-Bolt Cinching, comanche Peak Unit 1," EBASCO, File No. 3717 (1.2C)/3QE15, Calculation No. 001, i Rev. 1, 1995. s
- 5. S. TimontenMo and S. Wainowsky-Krieger," Theory g of Plates and Shells," 2nd Edition, McGraw-Hill Book Company, 1959.
- 6. S. Timoshenko, " Strength of Materials," Part II, .
1 .. 3rd Edition, McGraw-Hill Book Company, 1956. l ' g 7. R.J. Roark and W.C. Young, " Formulas for Stress and Strain," 5th Edition, McGraw-Hill Book : Company, 1975. i
' I
- 8. Letter .to attcridees for " Leak-Before-Break !.
International Policies and Supporting Research" from i Wilkowski, G.M., Battelle's Columbus Laboratories, ! IU Columbus, Ohio, October 20-30, 1985. i L
- 9. ASME Boiler and Pressure Vessel Code Section III, 1974 Edition.
!g k
- 10. L.S.D. Morley, "The Thin-Walled Circular cylinder Subjected to Concentrated Radial Loads", Quarterly
. Journal of Mechanics and Applied Mathematics,
, volume XIII, Part 1, 1960.
n l 11. RLCA Calctlation P-142-1-514-Oll, Rev. O,
- g " Theoretical Basis for Probram " BEARING", July 1986 j 12. RLCA Calculation P142-1-514-012, 1986, " Local Plstic
! . Collapse Load analysos of Pipe at Concentrated Support Reactions", Rev. O, August, 1986 l
- o i
66-O ,
O q) 13. M. Jones, T. Wiczbicki, " Structural Crashworthiness". Butterworth & Co. (Publications) Ltd, 1984.
- 14. Amdahl, J., Impacts and Collisions offshore, Progress Report No. 10, Impact Capacity of Steel Platforms and Tests on Large Deformations of Tubes under Transverse Loading, Det Norske Veritas, Report O No. 80-0036 (1980).
, 15. RLCACakculationNo.P-142-1-514-001,Rev.O, 1986, " Finite Element Analysis of Cinch U-Bolt on ,/
A 10" Pipe". C 16. RLCA Calculation No. P-142-1-514-002, Rev. O, 1986, "CPSES, U-Bolt Cinching: Derivation of Stability Criteria due to the Effect of Inclined External Load".
- 17. RLCA Calculation No. P-142-1-514-003, Rev. O,
'O 1986, "CPSES U-Bolt Cinching: Derivation of U-Bolt Stiffness, Cross-Piece Stiffness, and Pipe Stiffness".
- 18. RLCA Calculation No. P-142-1-514-004, Rev. O,
'() 1986" CPSES, U-Bolt Cinching: Distribution of j.
External Load Between Pipe and U-Bolt, Derivation i of Coefficients and .
- 19. RLCA Calculation No. P-142-1-514-005, Rev. O, 1986, "CPSES, U-Bolt Cinching: Pressure and
;g Temperature Effect on U-Bolt / Pipe Clamp Assembly".
1 20. RLCA Calculation No. P-142-1-514-006, Rev. O, 1986, "CPSES, U-Bolt Cinching: Calculation of Cross-Piece Stresses, U-Bolt Stresses, and Pipe Stresses". O 21. RLCA Calculation No. P-142-1-514-007, Rev. O, 1986, "CPSES, U-Bolt Cinching: Summary of Equations
- for Design Verification of CPSES Single i Strut / Snubber, Cinched U-Bolt Supports".
'g 22. RLCA Calculation No. P-142-1-514-008, Rev. O, , 1986, "CPSES, U-Bolt Cinching: Technical Discussion , on U-Bolt / Pipe Assembly Behavior Concerning Change in U-Bolt Force due to Friction i l Redistribution or Friction Lost". !O l
- o o
- _ . _ _ _ _ _ _ _ . _ . . . , . .~ ._. -
q
l l O i i O 23. RLCA Calculation No. P-142-1-514-009, Rev. O, ! 1986, "CPSES U-Bolt Cinching Finite Element Analysis of Eccentric, Compressive Strut Load on a Single Strut / Snubber Cinched U-Bolt Support. ,
- 24. RLCA Calculation No. P-142-1-514-010, Rev. O, 1986, "CPSES, U-Bolt Cinching: Finite Element O Analysis of Cinched U-Bolt for Prediction of Preload Losses".
- 25. " Elastic-Plastic Methodology to Establish R-Curves and Instability Criteria", J.D. Landes, D.E.,
McCabe, American welding Institute, February 1986. O
- 26. RLCA Calculation No. P-142-1-514-014, Rev. O, 1986,
" Study on Adequacy of Modeling a Pipe Using One Layer of Solid Elements for Elasto-Plastic Analysis".
O 27. RLCA Calculation No. P142-1-514-016, Rev. 1, 1986,
- " Verification of RLCA Program BEARING for Local Pipe ;
Stress Calculations in the Vicinity of support j Contact", August, 1986. ! l; !g 28. RLCA Calculation No. P142-1-512-004, Rev. 2, 1986, ! t
" Application of Program BEARING to a Selection of ,
i Pipe Sizes and Thicknesses: Calculation of Local j-Pipe Stresses in Region of Pipe / Support Contact". j-
- 29. RLCA Calculation No. P-142-1-514-015, Rev. O, 1986, g "U-Bolt Thermal Cycling Fatigue Analysis with j Internal Pressure".
- 30. " Engineering Scope of Work for Stress Relaxation Testing", 15454-N022K, 8/19/86.
;O l
l i
!o ;
j'" !
!o
! i I
.. . - - _ . - _ - _ - - _ - -_-_-_-_---.-_-.-..-.-..--.Il
_ . _ _ _ J '
.O O Table 2.1 Test Matrix [1] 'O Test Specimen (size / material): 4" Sch. 160 10" Sch. 40 10" Sch. 80 32" SS SS CS Main Steam Test Category
- O -
Bolt torque versus X X X X bolt tension 'O Friction test X X X X Load distribution X test
- O Thermal cycling X X X test Short term relaxation X X X O
Normal vibration X . simulation test
- 0 Seismic load X simulation test X = test performed '
O O
'O
.~.-. .- -,.....-. ,.. . - . . . . - - . . . .-- --.
O O Table 2.2 Matrix of Previous Finite Element Analyses [2] O Pipe Size 4" Sch. 160 10" Sch 40 10" Sch 80 32" MS U-bolt size 1/2" 3/4" 3/4" 2-3/4"
- 1. Preload X X X X (60 ft-lbs) (100 ft-lbs) (100 ft-lbs) (240 ft-lbs)
O 2. Preload & X X X X Thermal
- 3. Preload, X X X X Thermal & Pressure
() 4. Preload, --- --- --- X Thermal, Pressure
& Straight Strut i Load l S. Preload, X X X X
- O Thermal, (2,000 lbs) (10,000 lbs) (10,000 lbs) (100,000 lbs) i
~
Pressure & i Inclined Strut . Load . 6. Minimum X X X --- iO t Preload (9 ft-lbs) (46 ft-lbs) (11 ft-lbs) l 7. Minimum X X X --- Preload, Thermal, ! Pressure & i Inclined Strut jo e l X = analysis case :- l l, l O l-
.O O
Table 3.1 Representative Maximun Elastic Stresses at Centroid of Element 11 (5 decrees and 0.5 inch from cross piece center line) g Circumferential Longitudinal Stress (ksi) Stress (ksi) Load Case Medrane Bending Mee rane Bending O Preload 1 - 2.53 -29.01 - 5.43 - 9.46 (4,140 lbs) Preload 2 - 3.24 -36.91 - 6.84 -12.04
.O (5,300 lbs)
Preload 1 + - 3.69 -41.50 -12.25* -13.67 Comp. Strut Load (10 kips)
- O Preload 1 + 5.70 -31.29 - 5.53 -10.18 Internal Pressure (600 psi)
- This value includes -5 ksi from global bending of the pipe.
O i i 1 4 0 . O
- O
,g Table 3.2 Comparison of Temperature Dependent Properties of Pipe Materials 0 Temperature Thermal Expansion Yield Stress
[ degrees F] Coefficient [9] [9] [in/in/ degrees [ksi) F x E6] SA106 SA312 SA106 SA312 .O Grade B TP304 Grade B TP304 70 35.0 30.0 g 100 6.50 8.55 35.0 30.0 . 200 6.67 8.79 31.9 25.0 300 6.87 9.00 31.0 22.5 g 400 7.07 9.19 30.0 20.7 500 7.25 9.37 28.3 19.4 4 O Note: The material properties listed above were obtained from ASME Section III 1983 Edition, including Addenda through W 84. This Edition, which is later than the Code of Record, was chosen since it contains significantly refined and more accurate data for these material behavior parameters. P I l !O ?b ' t _,, _ _ , . _ _ . . _ . _
O Table 4.1 O U-Bolt Stresses Before, During and After Thermal Cycling and " Creep" Tests (From [1]) 4" Sch. 160 specimen Leg 1 (ksi) Leg 2 (ksi) 13 Thread Shank Thread Shank Region Region Prior to thermal 41.6 30.1 44.3 32.1 cycling test (ambient) (60 ft-lbs torque)
)
End of cycle 1 (hot) 53.9 39.1 52.0 37.7 g End of cycle 10 (hot) 48.6 35.2 45.1 32.7 i Prior to " creep" test 34.3 24.9 31.1 22.5 ' (ambient) 33 After " creep" test 34.2 24.8 31.0 22.5 (ambient)
- O iO l
O l O , O :
~
O Table 4.2 O Comparison of U-Bolt Tension and Pipe Stresses Between Desion Procedure (Section 4) and FEA [2] for 4" Sch. 160 Pipe Pipe Stresses (ksi) i Predicted U-Bolt O Force (kips) Design Procedure FEA (Ref. [2]) Design Case Procedure FEA [2] BEARING Procram Illi g Circumf. Longit. Circumf. Longit. a 5.41 5.41 19.04 11.69 16.85 7.27 b 8.86 8.31 31.19 19.14 25.14 10.64 c 9.21 8.58 32.39 19.88 32.84 10.90 d 9.12 8.33 35.18 21.59 34.29 16.64
- O Pipe Size: 4" Sch. 160, t=0.531" U-bolt: 1/2" Load Case: a. Preload of 5400 lbs per U-bolt leg O b. Preload + Thermal (pipe temperature of 559 degree F)
- c. Preload + Thermal + Pressure (2485 psi)
- d. Preload + Thermal + Pressure + Compressive Strut L ad (2000 lbs at 5 degree)
O 4 Stress Location: Outside pipe wall surface under the edge of the ! cross-piece, 5 degrees away from the initial l contact line. FEA results are interpolated between centroids on either side of the cross jg piece edge. l .O lo s
-- ., , - . . . . . . . . . _ . . . . - - . ...p- .
!o Table 4.3 'g Comparison of U-Bolt Tension and Pipe Stresses Between Design Procedure (Section 4) and FEA [2] for 10" Sch 40 SS Pipe Pipe Stresses (ksi) Predicted U-Bolt
- g Force (kips) Design Procedure FEA (Ref. [2])
Design Case Procedure FEA [2] BEARING Program [111 Circumf. Longit. Circumf. Longit. 10 - a 5.62 5.63 42.15 28.21 41.88 23.70 b 6.86 6.92 51.46 34.44 50.94 28.29 iO c 7.10 7.23 53.26 35.64 53.08 29.55 f d 4.82 4.78 70.80 47.38 65.80 43.01 O Pipe Size: 10" Sch. 40 SS, t=0.365" ! U-bolt: 3/4" Load Case: a. Preload of 5620 lbs per U-bolt leg i
,0 b. Preload + Thermal (pipe temperature of 210 degree F) ,
- c. Preload + Thermal + Pressure (600 psi)
- d. Preload + Thermal + Pressure + Compressive Strut ,
, Load (10,000 lbs at 5 degree) !O Outside pipe wall surface under the edge of the
( Stress Location: cross-piece, 5 degrees away from the initial contact line. FEA results are interpolated between centroids on either side of the cross-piece edge. !
'O f
jo i
;O
iO Table 4.4 O Comparison of U-Bolt Tension and Pipe Stresses Between Design Procedure (Section 4) and FEA (21 for 10" Sch. 80 C.S. Pipe Pipe Stresses (ksi) Predicted U-Bolt O Force (kips) Design Procedure FEA (Ref. [2]) Design Case Procedure FEA [2] BEARING Program [111 Circumf. Longit. Circumf. Longit. .g a 7.53 7.53 24.55 16.26 23.08 12.21 b 9.48 8.91 30.92 20.49 26.22 13.75 O c 9.77 9.19 31.87 21.12 27.99 14.20 d 8.50 8.11 42.81 28.36 36.86 22.90
- O Pipe Size
- 10" Sch. 80 C.S., tp = 0.594" l U-bolt: 3/4" Load Case: a. Preload of 7530 lbs per U-bolt leg O b. Preload + Thermal (pipe temperature of 210 degree F)
- c. Preload + Thermal + Pressure (600 psi) .
L d. Preload + Thermal + Pressure + Compressive Strut a 0,000 lbs at 5 degree) lO ( Stress Location: Outside pipe wall surface under the edge of the cross-piece, 5 degrees away from the initial contact line. FEA results are interpolated between centroids on either side of the cross pie e edge. lO O ', i
;e l a
i O l ! Table 4.5 l LO Comparison of U-Bolt Tension and Pipe Stresses Between Design l l Procedure (Section 4) and FEA [2] for 32" M.S. Pipe i Pipe Stresses (ksi) Predicted U-Bolt
.O Force (kips) Design Procedure FEA i (Ref. [2])
Design f Case Procedure FEA [2] BEARING Program [111 ________
. Circumf. Longit. Circumf. Longit.
- O i
!, a 6.05 6.05 3.99 2.90 4.52 2.99 Y l b 32.95 27.45 21.74 15.81 19.74 12.89 'O c 39.22 37.15 25.87 18.82 33.20 17.28 d 19.54 16.23 42.67 31.03 45.23 27.15 f O Pipe Size: 32" M.S., tp = 1.45" t U-bolt: 2-3/4" Load Case: a. Preload of 6050 lbs per U-bolt leg O b. Preload + Thermal (pipe temperature of 557 degree F) f
- c. Preload + Thermal + Pressure (1285 psi)
- d. Preload + Thermal + Pressure + Compressive Strut Load (100,000 lbs at 5 degree)
! Stress Location: Outside pipe wall surface under the edge of the cross-piece, 5 degrees away from the initial contact line. FEA results are interpolated
- between centroids on either side of the cross-
! piece edge. iO i 9 0 0 6 O 1 . - . .
O Table 4.6 i
- O Minimum and averace value of friction factor, based on test results Ill Value of Standard avg jR avg A Test Number of Average Minimum deviation y ~1 - 5.1 Spec. data pts. Aavg Amin Fn-1 (excluding 2 extreme
.O values) 4" Sch. 5 0.17 0.12 0.029 0.14 0.16 160 10" Sch. 13 0.19 0.16 0.018 0.17 0.17 *._ 40, S.S.
10" Sch. 16 0.23 0.18 0.034 0.19 0.20 80, C.S. 32" M.S. 5 0.37 0.22 0.011 0.27 0.33
;O 4
O i f i !o i r l I IO i I I f I O e b
- O
_ _ _ _ _ . . _ . _ . . , _ ~ . _ . _ . . l ,
- O Table 5.1 O
Dimensional Parameters Used for Plastic Collapse Load Analyses [12] .O Analysis Nominal Pipe Wall Support Span Case No. Diameter Thickness Width Length (in) (in) (in) (ft) k 1 12 0.375 4 23 0 2 12 0.5 4 23 . 3 18 0.375 2 28 1 4 18 0.375 4 28 O 5 30 0.375 4 35 l. iO .i i 8 i. 1 lo 1 ,1 s 4 11
!0 1
4O P 0 _ _,_ _n---- , . - ~ , . - - - - . - - - . . - . . - . . . , , . , . . - - - . . - . . - . , , - . .-, - - . , . -
O
////////////
O O . Strut or Snubber O Bracket C 3 O p Washer U-Bolt Cross Piece Shank (Plate, TS, Channel, etc.) O . v u-sole
~
r Pipe : U-Bolt
'O Contact Portion ,
I I i : I l 1O Figure 1.1 Typical Configuration of a Single-Strut, cinched j U-Bolt Assembly
- O h
i t jO I. $ 4 i0 1 l: I l: s i 6 _ - - , - . . - - - . . . ~ . _ . - - . - . . - - -. -,. , -. -- . - _ . -
- O.
*I
_ end plate (typ.) _
/
/
I
/ /
/ h
;O'
/
6_
+
1 Pipe : 10" Sch 40 O ss , t = 0.365'? o 5 i .C' cross piece S 6 _,b , (h O 3/4" U-Bolt i I section I-I O fG i h
'1 a i ! Figure 3.1 1
I Test Configuration Represented by FEA [1] s
;O j
i i
;O .
1 i -- -- - - . _ ..... _ __.....__.._._.. , _ __,, _ _ , _ ,, _ _ _ _ , , , _ , , , , I-
.O O
.0 7
/
O ,' 4th substructure
/
\
3rd substructure o \ nd 2 substructure
\ st1 substructure l O
k Primary nodel ; 9 i, 'O s0 4 i' i,0 l Figure 3.2 O HM Mxlel 1; Overview of Primary Model and Substructures i jO
) i 1 - . . . _ . - - . . _ , . _ . . . . _ . . _ . _ _ . . . . . _ . . _ . _ _ , _ . , _ _ _ , _ . . _ _ _ , _
_,1
t 10 O 10 - i-r l l- - l'O y r / IO [
/
V'
// ,.
l. lo / N \,.
\ '
O I
/
O
\
i 0 EO Model y. Detagged Model yOrtion 3 Ei8ure 3'3 - I e i k
)O .
i i
;O i
i - ----. .. '"' mg , um 1'wy '~~~..u. ?' e ~*Myw, , Ms ., w,. * - ~%D.,,
2 o I 0-y\\ N \ N f N 7 o /
- x. /
/
O-T z/ N
~
0-N
\ ! O I
s ;.
- -O 1 i
l 1 LO
; Figure 3.4 FEA Model 1: Distribution of Gap / Friction Elements i
l l C 0 ev e -
O N O
'r 0 (a) s
~
F O F a pN - - - - - - 0 (b) 1 1
=
S O b 'O (c) 0 - s yN B
. O'
' Figure 3.5 ,
'O t
f Gap / Friction Element Behavior O !
. _ _ . . _ ._ _ , _ .,__.,t
[ _
O O'
'O 10 --
.O 8--
/
O
/ /
6-- O n
~<
x o. t
/ /
/
/
v j / m4e
- / /
/ Sch 40
* / /
W
/ Model 1 i.O " ,
- - - Model 2 u
c4 o2-- Sch 80 m
$ / - - - Model 1 l0
- O ; ; ; ; ; ;
J 0.25 0.50 0.75 1.0 1.25 O Turns of the Nut (1 turn = 0.1" Shortening of U-Bolt) Figure 3.6 FEA Models 1 and 2; U-Bolt Force During Cinching l lO B l t r 0 l i
E
.O Normal Force aoo (lb/ degree)
.D + conpression 15e (a) D
= 'O l 3 .
J A O so so N O
... 3, e
. 4-. .
O Friction Force (lb/ degree)
+ clockwise Y force on P iPe
- O
.so .so g g
.io (b)
.O .,, ,
,, s, ;
C = o.8 - "" D . 3o o - 1.o y .. .e Axial Force P O (c) .
+ tension X g 2
~ A -
0 e
.,, 3, 3, ,o
\. O t t r Figure 3.7
- O FEA Model 1; U-Bolt / Pipe Force Distribution during Cinching O
1 f
. . - - . . . . . . - - . . ~ - . - - , . - . , . . - . , . - - . . - - . - - , - - - - ~ - . ~ , . - . , .
- O-a
- O 3.5 -
Potential . (=EN p) ,' g resisting i force /
/
/
3.0 /
~ /
lO /
/
-- 4y U g n
E, 2.5 -- ,' ( = assumed resisting capacity in design j ' procedure, Section 4) v
- O e /
u e ' t 2. 0' -- / o i m f C / O 3u / .. o /
/ !
t W
- 1. 5 -
/ l
/ ,
U, 6 O
- f Applied, external loading .
u ' d 1. 0 " I m i e / l
!O O e \
/
@ 0.5 -- / ;
o }
/
j i
/
- O 0 /
0 0.5 1.0 1.5 2.0 Lateral Load (kips) lC l FiRure 3.8 i ,' FEA Model 1; Rotational Capacity for a Lateral Load l 9 !O P
~e ~~--e*-**-merswm,,.e.,,xp,.m.,-..~, w_.,, ,. . . _ , _ , _ _ _ , , _ , , _ , _ __ _ _ _ _ _
4
;O - +
Normal Force
>0. (1b/ degree)
O P f + carpression 150 20
.O-A -
A B B (a) O e: . 3 g g e
" 3o A- o tbs. .
O' E - t$$ *ti. Friction Force o - 2000 ids. a (lb/ degree)
+ clockwise force on pipe 10
- e. -
e
^
>0 (f J// "- D (b) ,; g
-so
- . 0 i
l C Figure 3.9 I: FEA Model 1; U-Bolt / Pipe Force Distribution jo during Lateral Load O
~ ~ ' ~
O O O O. O O .O O ' O' O O ,
- j
.j 4.0 4
^l 'l n 3.0 vs 6 ~
S 2.0 M l Analysis Results l. E e
- / Test Results l $
i 4
- y 1.0
. m b $
i
.J 70 80 90 100 110 120 130 0 10 20 30 40 50 60
! Bolt Torque (ft.lbs.)
r Figure 3.10 F FEA Model 1; Predicted Failure Loads Compared to Friction Test Results i 4 I M .,,,s.+,.se - n. - - + .
O . e
. M .-
tw Normal Force O (lb/ degree)
+ cmpression ,
-Q/- .
p soo O
^
i 3 B A (a) C ., O l "" E
..a .= so .o 'Q A=
s-0 kips 3 C= 6 D= priCtion Force r - 15
.ao (lb/ degree)
A + clockwise force on pipe
- .0 C ~a u/
g x-
,o , &
- g ..io AC S A (b) 2o G
f I ?O I Figure 3.11 O FEA Model 1; U-Bolt / Pipe Force Distribution during Compressive Strut Load 6 10 I b . . . - . . . . - - . . - . - - - - . - ..
...7-.....-~..--.--
O O O O O O O O O O O 9.0 - 8.0 l .. 7.0 3-n
} } .h6.0 1 6 -
100 ft.lbs. (Test) c 5.0 1
.S I
l 67 ft.lbs. (Test)
! u 30 j .3 Analysis ! N 2.0 1 o t m 1.0 7 33 ft.lbs. (Test) 1 e -
-i 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Compressive Strut Load (kips) f 1 1 Figure 3.12
, FEA Model li U-Bolt Tension as a Function of Compressive ,
i j Strut Load from Tests [1] and Analysis
~i 4
4 .. . . . _ . . - . - - _ _
m ~.
- O ,,
'6 150 ,
O ^ 840 -
- + g 130 -
W ' ao O I J f N sto- .y 100 -. < A H 90 - v g 80 - ~ Y GO U e4 'O ~ i
- O / gg so - -
3 j s* Ag 50 - 40 - e4 C. } P eE 30 - EO WU 20 - O Z+ 10 - 0 0 ' l
, , , , , 1 7- :i 90 -
6 -90 -70 -50 -30 -10 10 30 50 70 ., i O Ok + 4k e 6k & Sk .n 10k g (a) . 0 30 m oo
- a G Q. .'
D k e4 oo c. 20 G oa ' NO
,o 10 - '
c4 W s vu W \ cO o - s3 ! -+N
.,4 i c3 '
03 4o 4J O os Q. +o , u N+ -30 , , , . . , , , , . . . . . , ,
-70 -50 -30 -10 10 30 50 70 90 O -90 O Ok . su . sk a iOk t
( ! O (b) I, Figure 3.13 FEA Model 1: U-Bolt / Pipe Force Distribution lO o during' Inclined Compressive Strut Load I
$0 1
I - .-- _ ...___ .,_ _ _ _ . _ _ , . . . . .. ,, _ _ , _ _ _ _ . _ . _ . _ i
N O 'C C O '
C O O O O O t
.5 Allowable Lond-as per i Friction Force Design Proceduto (Section 4.1.2) at Pipe O.D. (kips)
I i L s
,3 ~
' /
Potential Friction
'- Capacity 7 :
II / _. _ I I / s
. 7 2
9 r l
. ! l .
~,
,l
' +
1 i .., .
~ . .t
' \
Developed Friction g due to Applied Ioad 1 )FailureLeadas
' [ l
! I per Design Procedure
( Section 4.1.2) l 2 4 6 8 10 12 14 16 Applied Conpressive s Strut load (kips) Figure 3.14 FEA Model 1; RotationalResistance Capacity Under Inclined Compressive Strut Load
)
~3 _. - . __ . . . . _ _ . .
.na... ._
=~: - ;- .~ -
O O O. O O. ;O ' a O 0; O O O
)
N s; - s _ Normal Force /
-l Circumferential .7egree 8
; : (lbs.) . ! .
~
l \. - 1
% 'J-2 i ,
120 V '
+ !- j -.
2 t i 600 psi - 1 -
-- 80 j 600 psi 3 ! 300 psi
-J ' 300 psi
~t \
0 psi 0 psi
. . -40 ',
t a
-80 -70 -60 -50 -40 -30 -20 -10 10 20 30 40 50 60 70 80 4
! I
. ,t j Figure 3.15 FEA Model 1; Normal Force Distribution Resulting from
; Internal Pressure i
t i j ,
- W _ _.
._.._.. . .. _.._., ..__ ; _o._._._.._._.. , _ _ _ ,
45 45 44 al 44 4% %I 45 Ei ii 45
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O
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k' , ;. i g,, gg'k b g 1,-[.
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=%hj!%g$$fj;p$_,}$. h?\\ ii
=s w m gEi!5f sg % wegigN %m
, 4L in M1 4= m m+ . im millMw=1 : _
{ W .[s '.I .
$hhh$Mk.*ph k :_:
9 iP@ 'dS-5 m" 6,L g 4 $ 3/ Q Circumferential Stresses
':, ~-
I4 *# g
@*i) i - D? ,- , ,gs'j :.<, ,g j '
5%
'f ,4Vf/ ) Membrane s 4
[ -
/r I '
- - - - - - Flexural Preload - 4140.lbs.
y*
*,,,~~ ' "" # "
Q$)k} \ ,
.O.; ,. ' l ' *
t.'z .
\
54 is 44 %4 54 44 %% 55 Ei %% E4 Figure 3.16 FEA Model 1; Circumferential Flexural and Membrane Stresses
' Due to Preload of 4,140 lbs. at z = 0.5 inch M . . . . . . . - ~
C C G O O O O O O O O 45 - 45 44 45 44 45 %% 5% Es %% 55 g gt ' ~ ' hg 7 -[!. lR5 , '\ y 'I:',If
' 'i'*'j ~. ? g ' Q 1~
go,. - _ '~,6 '?*: ; ~ 1 . [Q j'bE ' l '. ;p'. .( \ i ;, h'S, 0 l A .
, yp " #
~
T Q : Y' . "
- j. 3 .. , , .,-j i jj
.[ rf .
u L J /g g g 4#]M ; ud4g $ s]; g , - N$ l f ig20h= y .gkh gi f - _
~
h . If +
%s '
hjj , , -- inn $f 5% g h, . y, gl J
\ - - - - - - Flexural -
- % ^h -
/ j;! .ki'.\, \\g\ 1 ..[+ % Preload - 3300 lbs. l
~-
f " g .
, Ikf f 9 A
4.,,,,, l k " 'J 7;{ ', 2" - ' N'J
\ e-g[ ..*2 / [
^
e '\ \ \ -@ 54 is 44 44 54 Et 5% %5 5% 5% 55
- Figure 3.17 FEA Model 1; Circumferential Flexural and Membrane Stresses
' Due to Preload of 5,300 lbs. at z = 0.5 inch
O O 5 O O b O O C O O. as 44 e a e a su as sa as as l \ ;gh ,
., /g/, / ',
'd
,( -l
- .' f
~
N
,' '{
, h .N; .
' i- ,.
~
+ v Y~tf" W- _h h
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4 $Nk
- gig VMr t:E fff5 NNk p*r e
'3 g ;gg/c4 ,y: 53 / gfqfggiggg 4
,. +gg M.o.s- g w. -
/
af Circumferential Stresses u, M,,^ g (q- 3 , (ksi) , g -
+f,7fi i -
Membrane
$p .
/ ,
x
\ ~ - - - - Flexural Preload - 4140 lbs.
~
W- -'}
- - . S.
~- -
s 44 pgpf .
~',.8 j \S idi = - 2 5" lit
^ ^
.. ,', y,, ll .h. l
^ '
x
^
Oh .
. ? , 54 54 4% 44 E4 E4 4% Ei Ii 5% 56 ' Figure 3.18 FEA Model 1; Circumferential Flexural and Membrane Stresses
- Due to Prelaod of 4,140 lbs. at z = 1.5 inches 4
l J ..
O O O G O O O O O O O ik hk Bh th Bh kh kh hh th kh th
~ '
I ,I x.
~ . . . I ,- ,} .-
h
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t h*
. ~ q%
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*Fif ettg'y' ..!$,$' ~?9:.;f.% gi >{f'Q;[ WWh Ey hk
*k i
%Ql QQ(~ fq. - (T. Rhh q Q-1 Ohit jy['Eingdh@
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% . sy 1 y Ti .b..4 g
1 - _ . . n- y _
\ :
___~[
~~~~
Circumferential Stresses i +, Y - g, git - g, g.-
. . , - 'ph
.# (ksi)
; I$ -
+
M ' Membrane kh
> ys - - - - - Flexural
#' I /. If{ '*%
f ( Preload = 4140 lbs. z - 2.5" s p - f" <
.[/ /
Lg \. g
$f ', } i
%/;&llkll
[ 4$ / -
, , ,f . ) ??f % '
II M , /[ BB hh h)
/f RB O)fRb Rh n$iQ@'g(h k de Rh hk 5
ik hb Figure 3.19 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs. at z = 2.5 inches a M . -.-.- , . . , . .
. ~ _ . . _ ._ _ _ - - - - -_- - _ _ ~- - 1 .- - s 45 Mi 44 al 44 44 ii% EE is qq gy Yd
. , \h \ l ' f
/ /,f/ V ' 5 {'
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. ,. K l t- !
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y
. .bf; '
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! [h!N k, p .
Circumferential Stresses i 49 .
;< (ksi) -
' ^
/,if f '
Membrane j
'/ ' \ ~ ~ ~ ~ ~ - - Flexural
.., ! Preload - 4140 lbs.
% %[ #g -;@@hA, 49 % ' - ,, j yL . As : z = 4.0" ~-
- ) -
, , l )
A ' I .b 'f,h~{
>{f^ / / 1 \ u.
A hi * -
/ l \ . .- k. .
t
' 44 44 44 34 %4 04 44 54 55 Rj y(
Figure 3.20 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs. at z = 4.0 inches
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!I 5 5 M
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. p- -w 4.' Circumferential Stresses
=---
hu j (ksi) 1 .'. . : .
; gg.
M7 ' [ .
/'
ay
- - - - - - Flexural Hembrane
-{
,9 Cy.[i ,k 1 '' 3 y Preload = 4140 lbs.
//
4 g[f 4 ,' ';- [ [.-<
,k .. ,.
/- -
s'];y] Pressure - 600 psi, g
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' O/!!llgy411 @H
'pp k ',%q
':, V! ? g' 'oil t '~I e
,y, y . I!
\,ibbp..
. ;,qs, f N t d' i _g \ \% \% #S lg .v4s,f f
' 8,f 1,1 ! W}l,;ll .
54 54 44 44 %4 54 %4 44 44 %i %4 Figure 3.22 FEA Model 1; Circumferential Flexural and Membrane Stresses Due to Preload of 4,140 lbs. and Pressure of 600 psi at z = 0.5 inch T
~ ~ ~
O O o O O O O O O ;O i l j Stress (ksi) JL I 5 - i ; i lary,itudinal , distance l g
; l f) -10 .
H edge of cr ss piece offset angle I i v i
- d:
c - 25'
! A I
- B l C l
N (C wB 1 I ,NA, i 1 3 4 5 6 Imgitudinal Distance fran U-Bolt (inches) a j j Figure 3.23 FEA Model 1; Longitudinal Membrane Stress in the Pipe / Cross Piece Contact Area Due to Preload of 5300 lbs. 4 J
G O O O O O- O O O .O O' lI Stress i t (ksi) A 20 -- i
, , edge of h , , ,
cross piece i tomeituainst g distance 15 -- A
~ offset angle
% A= 5' n = 15+
I 1 C = 25'
- ' 10 --
- I-a .
B i
- 5-- .
i C - l 7 1 1 l 3 4 5 6 Iongitudinal Distance frcm U-Bolt (inches) 4 5 Figure 3.24 FEA Model 1; Longitudinal Flexural Stress in the Pipe / Cross Piece Contact Area Due to Preload of 5300 lbs. i k, t i i
O O
/
/ll O , /
O '
- J O ,
i O m st @ me f j Location FEA FEA l orientation Tests 2114 2410 2413 A ciretmferential " 2049 2007 B 2417 O " -2790 -3560 -3386 C -3932 longitudinal -1343 -3652 D " -1323 -1400 E -50 l' -1368 -1814 -2132 G circunferential -2431 -1657 H longitudinal -3407 149 -1153 -1430 circunferential lO I J longitudinal 348 -1566 -1116 Stress (psi] Normalized to 1 kip U-Bolt Tension O Figure 3.25 l 0 Comparison of Pipe Stress Results between FEAs and Tests 1 j for Outside Pipe Surface
,3 i i , . - - . . . . _ _ _ , . . _ _ _ _ __ t n= Wp&6
iO l
- O l
/ .
- O V
~,
'Q
/
ll
$/
\
'l
/ x /
,y?{ /\
1 1 1 t '
\[
\/ /
'l / fI
/ /
N h ,9 /
&& i ~Yb 10
\b N N s' Ns
\
N s,> Af'-[
- O N g,J'
\/'
\s,/
f Figure 3.26 FEA Model 2; Refined, Elasto-Plastic Model Detailed Portion
- O
-- ]
a lO l JO O r /:
~M t,
~**-
/I
'9 O mw,.' . F 4 I,l" 9 : ,~
~'V f
) < w o _g .
.i .
'o
. /
,o .
/
/ .
',,y.-. ..
, ,; _.y ,. :, ",
/
e W~ ,,~ ' ' . , p-M n ,,;+ ', 3 [- ." m 'h,. . + . .. <:
/ . 9, ', -/
i yt ..
/ / /
tjff-
.+n~ m haM.g -ijw . gd ,g Q;;< x
/o i
;WplWW j.E./
r m &' ._,, l 8O 1 i Figure 3.27 O FEA Model 2; Refined, Elasto-Plastic Model Substructure l i I IO I I I ,i 'i te p l!O i!
- s. . _ _ . _ . _ . . , _ . . . . . . . . . . . - . _ . -- . , .
.7
-. ~ , .
O G G O O O O O O O O 44 44 44 al 44 44 4% is is 44 44 f 44 (4
"I Mi 5%
ik kN I
= 5=-:
f : -:::::- _ ;- .:.m
~/ ':::
oA Circumferential Stresses (kii) . 55 4 ' yg - , Membrane
\ s x - . qNv (
'K' Preload - 5425 lbs.
k5 ,;,
. .g $, z = 0.5" $%
\ \ J
...\ ,
is $ J' ' (i
$ \, a 'sk)$ W<
t o\\\\\\ , y l\'&R?r.
\:4 * .
+
44 is 44 44 44 44 %i %i Ii %i %% Figure 3.28 Model 2; Circumferential Flexural, P.embrane, and Equivalent Stresses at z = 0.5 inch due to Preload of 5425 lbs,
!O
- o \
. Model 1 - Elastic CO' *
- O M '/
O 3 0 1 f H> del 2 - Elasto-Plastic i o O A3 Note A= s (lowest contour)
; 2500 pst increments M
O Figure 3.29 O Caparison of Equivalent Stress Distributions Between Model 1 and Model 2 i O
. , __ - ~. . _.- ,._ . _ .- -. _ . .. _.. . . . - _ . . . . , - , . .
, g-- 9 9 9 G 9 9 9 9 9 -9 I
I 'l Primary model
^j
.i Pipe extension
' substructure
#/
's s
s
' s
,, / _
s s- , i s : s-s, , 1 hh i i Cross piece i , substructure i Figure 3.30 FEA Model 3; Overview of Primary Model and Substructures a - _ . . - . . . .
-O.
- O O
5. lo g d h l 40 - !O l l l
- 70' !00' F 30 -
30.0 11%g
- O
< t g,,.g g.7 25.o , -
- Soo*F 22.5 { E 4oo*F To.7 ' S.9 E $.o*g/
20 - O i l 10 3 iO E 27.4 x 10 !. 1 0 ; ; . = 0 0 0.001 0.002 0,003 0.004 0.005 0.006 Strain (in/in) i ,O Fig. 3-31 Stress-Strain Relationship Used for SA312, TP304 Stainless Steel (8,25] i i l iO Io
- - - - . , - .~-.rn-------,_-.---,-------..----.--.-,---__.--.-.- . . - _ - - - . _ , - - , - , - - - _ _ . _ , - - - - - , - ,
P " p . ,,. l
# l Lf2=4.5 inch 20
/
~
I R = 5.375 inches
/ -
t = 0.365 inches R j t ~~. 0
/
\ /
N, j '
.o (a) Schematic of Model Used in [26]
l 2000 .-
.O .-
e' 2500 . B (.O 2000 f" e w , i ,
=
h1$00 ,
= x . 1 layer I' ,
l 1000 . Q d
- a L .
- 3 2 500 .
l O O O
~
0.05 0.1 0.15 0'. 2 0.'25 Displacement at point of Load (inches) (b) Force-Displacement Comparison Re'sults[26] , O r Figure 3.32 : - Parameter Study for Validation Study of O Through Thickness Mesh Refinement [26] h O 4 l 1 I
.O i , _ . . . _ . _ . . -. . . _ . _ . , . _ ._ -
.-O
.O.
PRELOAD PRELOAD U-BOLT 7000 - 8 8 TENSION PRESSURE PRESSURE O ""4 7"d88"' (LBS.) 6000 - I5****lb') I5"94 1b*)
- 20s:
PRELOAD
' 0:0::
5000 - PRESSURE PRELOAD PRELOAD PRE WAD, y,70 ey. :.:. .; g g O t=70*r (4300 3ygy y;g;jh,';yhpS:;;;;.jjjii8 PRESSURE ;.: -
- PkESSURE j r=70*r r=70*r 4000 - (3s70 ibs) gj;j;m .!
h"
;g<;g "
~
es:.: sg:.s (3362 lbs) > intii
~-
i 13360 lbs) 3000 - 3...'.".'" sses; U$U .... 88j$ j hhh $$$$$
,.4 [;{ {fjj V8iff s:gs g;ss:. ;iipii 2000 - i: is:sii ~.: sis:
'<;4. :' - "'
. s 2:sss U* :::!;j$j:ji $:y8
""' i;E5*
1000 -:! riss: vss. vY + L 0 LOADINGS l0 { l Figure 3.33 : - U-bolt Tension Histogram During Thermal Cycling Analysis [29] 9 9 i
- D I
.O
...,q
10 O 12 - CONTACT FORCE (kips) O to - THERMAL CYCLING a- P RESSURE [ 6 - PELOM 4 - O 2 - o
/ , , ,
0.02 0.03 0.04 0.05 0.06 O o 0.01 CHANGE IN PIPE DIAMETER (in.) . F ! ,, - . ,.,. . . c--,-.-,,,....... f r Thermal Cycling Analysis (29] O [ 'O : i
- 0 !
h I~ - - .. -. . _ , _ - , . - . . . _ _ . , ,, . , _ _ , , , , , , * * * * "w= -**- < e. . g .z 9 , , , ,
. O O P O
P l e l I I - o . 1 .I
.I O
A . l l l l . . Nixy i l R U2 <r "U1
.I N1 O a._.- --.- _ 4 i
^ g1 U2 f..O I .
! e' H. N2 O i
, N2x4 O I ? i 1 j0 Figure 4.1 Idealized U-Bolt Model for Design Application
!o j b
O ! t
. - - . ~ , - - . - . . . , , . .
i O .' O O O' O O O O O .O
}
Strut Load E
////// / ///////////
Cross Piece l [ K c =K E c l 7 P 7 Tube Steel /U " U K Loa Point K 1 6K 2 2 P 2 U-Bolt # Pipe Figure 4.2 Mathematical Model of the U-Bolt / Pipe Assembly
r-
- .O .
O' O O-
\N\\\\\
i P O ag cl Equivalent loading Point- - l i O 8Yp O Zero Gap G O Figure 4.3 t Sinplified U-Bolt / Pipe Model
-O l
0 I
l 1
- 1. 00 - -
a=2 0.75 -- 1. 1.2 m
' 0.50 -- 1.0 AF /P = fraction of external load, P, o- p g transfered directly to compression between cross piece and pipe 0.25 "
0 ; 0 1 2 3 4 5 6 g/Kel Figure 4.4 Change in Cross Piece / Pipe Contact Force Due to Extemal Ioad. Strut load distribution as function of relative stiffness parameters; Eqn (14).
O O
'O O
U-bolt Tension i l
,O-U-U+g+g o
)O . 1 ,
' Lpoint at which ;
o
' loss of contact ;
2d( + 1) / ,',' between pipe and-t
, cross-piece occurs
,g- ,
!= 1 z' ,
s / s# t / l 7
. . . . 4
< 0.0 >
(Compression) l (Tension) O max External Strut Load P i I Figure 4.5 i l0 Schematic Representation of U-bolt Tension Variation with
, External Strut Load 10 ,
1
;O l i
-e==-wp-.*,me..-,%.~,..,. 7.._.._,.,-,,._._..
i .O O Do + d + 2s O n A , ,h a d* *~~ O
~
R. t tp, R D o O Fm i t O B " l
- >/ !
s Shim Plate ' l : 0 1 O i Figure 4.6 i O U-Bolt / Pipe Assembly with Shim Plate j ip-for Thermal Expansion Evaluation r iO
'k I
O , ( of bracket 9 . 1 I (,ofU-Bolt q , , l 1-i E jdt N , , F h[lii
- NEl ,
.+.-.h , C 'LE '.t 1
O a Tu I .. .i (a) (b) , t
,O A- b -N P
1 1
~
D ' j f Fu .
! A-Section A-A P"4'.
(c) l I I F
) --
l
\b n
6 lO (d) l '$ 1 i ~ ' i Figure 4.7 (a,b,c,d) ( >t j . O i U-Bolt Assembly Idealizations for Stress Calculations l I j.
'o e I:
, ,l
i
# -e O ,
1 It
+
0 Pipel B l I
..g t i 0; . . . 4 t
1 f J' ' o 5 f f. N / g A y gj y Au ,, Tap red contact load ! distribution used for ' Cross-Piece SECTION B - B stress calculation i ,O' I
~
i c F l o i --Location for stress calculation f h I g' w:,5 --L9 J. s l 1 0 l ! ~ k I.O 4 1 5 ] , SEC':' ION A - A ju Figure 4.8 : - Load Distribution and Stress Location f .. for Local Pipe Stress Evaluation [28] 4 1 9
! i I i 1
lO
O [O t O l a
- r i,
B t
; O '
I A I b
'4 O -
- E:
.--q-. . . . .- gf. - . _
C p .
- O Circumferential Circumferential
( membrane stresses bending stresses l , g Note : Each stress category is for clarity shown in one symmetric half only s 't O Figure 4.9 e Characteristic Shape of Circunferential i ' Bending and Menbrane Stress Distributions 1 iO e l
'O
- ' '!;! I ,
4 1 ' , i jija j .. j l 1 !ij !1.. il !
! i.1 1 'l ., s i.$ 4 i ji O =-
=
=
O' ;
<> < m3 a. ueg9i$a,Ee3S8 O.- -
PC ro om . . . . ~ . . . - 1 1 cp 1 2 3 4 5 6 7 8 9 0 1 ea . dr 0 ~ ui rs eo n O-( So - ef c 5. - tM ia ox ni m 4u
)m fS ol 1
0 O-ri 4
"F p
o B O L
~ -
T Sr cc T 1 / -
.- .h e O 5 1b F
i R D Te O 6e 0t w g u r Q U E
/ e s
i s t - pe e - g ie pn 4 F O 2 0
/ n P su R
e ~
.e eT O r 7
1 o
~
T l s 0 c t
'g P e s t
O d O
,V R
e s N D S 2 5
/ u r
c - u s l t s
/
= , . [ a 1
] 3 0
O e e a n d
/
w v s i D e 3
/
N g 5 w e n / O.
=
O.
.e O
2.;-====___-.. . - -. O O O O O C O O O O O 4.0
) ! e Test Results
, ; 8 - Design Procedure jl t
- 4 0 il 5 3. 0 --
t 2
/
.' b /
M / 2 / z i
! S 2.0 - ./
13
/
t
' 2 u.
i S / vi x E 1.0
/
/
1
/ *
/
' r .
i 110 120 130 20 30 40 50 60 70 80 90 100 0 10 BOLT TORQUE - FOOT POUNOS Figure 4.11 .
' Comparison of Maxirpum Slip Force between Test Results [1]Jand Design ' '
Procedure (Section 4) for 10" Sch 40 S.S. pipe. .
' g k e f
0 0 0 0 0 T O O 'O~ O O 5.0 t Test Results i- - - Design Proc.edure
'I o g . t 4.0 . -
I C
+
, i g
.I z j> 8 a.
3.0
! w /
/
. i / j b / C; 2.0 / 1 E
/
.} /
\ $
/' -
g 1.0 y
/
1 . 1 x -
; / .
/
i 4 l 0 10 20 30 40 50 60 70 00 90 100 110 120 130 140 150 160 i BOLT TORQUE - FOOT POUNDS - Figure 4.12 Comparison of Max'imum Slip Force between Test Results (l'] and Design j i j Procedure (Section 4) for 10" Sch.80 C.S. pipe. I i - N .- .
11.0 -l
} -
-l 10.0 Test Results s l* -- Design Procedure ; ~l 9,o '
! o '
! 8 8.0 l C i
$ l -
5 7.0 . e " u 5 6.O v-5.0 I 5 l C 4.0
' u '
E ' ' w b S 3.0 vi ,, y 2.0 - 1.0 V' j 200 250 300 700 1200 i DOLT T0itQUE - FOOT POUNDS . Figure 4.13
- Comparison of Maximum Slip Force between Test Results [1] and' Design Procedure (Section 4) for 32" M.S.' pip,. e l
w . . . . . . - ..a - - _ .. - - -
O' O L Test Results
--- Design Procedure O
9.0 -
.l.
>- e.o- - i- 0 100 Ft-# Preloads ,- .O .!!-
.x #
[ 7.0 - p s k S 67 Ft-# Preloads d 6.0 - } Ei n. O g 5.0 - l S g J 8 4.0-33 Ft-# Preloads -
$ 3.0 - p#
O. ,' 2.0- # l l 1.0 - 10 ( 0.o , , . , 5.0 6.0 7.0 8.0 1.0 2.O 3.0 40
! 0.0 VERTICAL STRUT LOAD (kips) !
{ O Figure 4.14 Comparison of U-bolt Leg Force under the Effect of Tensile Stnit Load between Test Results [1] and Design Procedure (Section 4) for 10" Sch.40 S.S. pipe. O i LO u ( . - ~ - - . . . . . . . . _ _- -
O O Te.st Results
-- Design Procedure O
9.0-80-0 3.4 7.0-5 g ,,o _ , M R-# Preloah ,
~
a '- ,' e E 5 o- '------ O
~ _ ~ 67 - Ft-# Preloads 4,0 -
b ~~~_- --- 8 . 3.0 o JO 2.0-s 33 Ft-# Preloads
~ _ _ - - - -o 0.0 . . . . -
50 6.0 7.'0 8.'0 1.0 2.0 3.0 4.0 O.0 YERTICAL STRUT LOAD (kipsl 'O Figure 4.15 Comparison of U-bolt Leg Force under the Effect of Compressive Stnit Load between Test Results [1] and Design Procedure (Section 4) for 10" Sch 40 S.S. oipe. O a
- O e
n ! !o e, % 9 m
- w m-%*~r,..,e.
WWtr"
-f
O CIRCUMFERENTIAL STRESSES OF 10" Sch.40 Total Land - 1 lip O 5 40 + 0, 4- 0 4 O ! e
- s-g 1
I O O !c . 2-O O i . i a f ', o 2 4 6 i dd a** "* *-a* C-L cloa9 P P8 3 (ia) l O 0 FEA(note 1) + EEAmHG o FEA(note 2) I ? Note 1 - FEA results from [27]; load distribution was based on l io
+
tapered loading with maximum at edge of cross-piece and zero at center of cross-piece. Stress values are j measured on pipe outside surface 5 away from initial line j of loading (same load distribution and stress location as in " BEARING" [27)) . Note 2 - FEA results from Model 1 (section 3.1); load distribution was based on Model 1 which relied on the relative stiffness E between cross-piece and pipe. Stress values are measured O on Pi Pe outside surface 5 away from initial line of loading. W Figure 4.16 : - Comparison of Circumferential Pipe Stresses from i FEA(Model 1 in Section 3), " BEARING"(27), and 1 FEA[27) program used for verification of " BEARING". j 0-k t 4
!O ll 3
-- ., .__.m
,_.- . - - - - - - - . - _ . . . -._ -. _ _ - - = - - - ---
O LONGITUDINAL PIPE STRESSES,10" Sch.40 Total Lead - 1 kb 3.5 - 3- +
- O v 2.5 - +
3 g 6
+
1 2-- o E o D Q o j 1.5 -
?
i
- 1- 0
- O <>
O.5 - O , . . . . 2 4 6 O iO etone.*om x-pcc-t. % p;p.On)
+ EEARING o FEA(note 2)
O FEA(note 1) l Note 1 - FEA results from [27]; load distribution was based on l tapered loading with maximum at edge of cross-piece and l O zero at center of cross-piece. Stress values are l measured on pipe outside surface 5 away fron. initial line
. of loading (same load distribution and stress location as in " BEARING" [273).
.O Note 2 - FEA results from Model 1 (section 3.1); load distribution , d was based on Model I which relied on the relative stiffness between cross-piece and pipe. Stress values are measured ! on pipe outside surface 5 away from initial line of loading. f G i 4 Figure 4.17 : - Comparison of Longitudinal Pipe Stresses from FEA(Model 1 in Section 3), " BEARING"[27], and FEA[27] program used for verification of " BEARING".
- O 8
a jO i I
, :x.-...--=.... . . :. .......-- -.--.-. ...-..a.-....--..-.._..--. 10 O . ELASTIC, 2xELASTIC 50 i
'O 8 /
8 R f 8 (kips) I I i 40 - 1
/ .
O I - 37 kips
-P c I
-/
I I
/
30 - / *N I
.O i /
I i 1' s --
, 3 HbH
,, / /
20 - t t I
!O i 11 111111 11111
^
i I n' R
, L
/
10 - I
~
g / cp= 0.375 in.
/ L = 23 ft.
bc = 4 in. f
~
A/D . O O 0.01 0.02 0.03 0.04 i
- t' I
j Figure 5.1 Support Reaction vs. Diameter i Reduction Curve - Case 1 00 a,
,O I
i ii io - i i t
- ~ _;_....___.__. _ __.. . .____.__ . _ ._ . _.._ ..__- m. ..._....._._.___-...m._.,_.__ .
O s O - ELASTIC 2xELASTIC
- O I / ,
R I '/ (kips). P = 54.5 kips j c i I
/
50 - I
.:0 'l /
I I f
/ -
l I 40 - I I
/
I
- O / e I ,
s I / I / $ ~" 3 0 -- I / 'y ' ' jO
/ I*-**
I I ! / / 41 1 111111 t} ag
/ ,.
L
/
20 . , 0 j
/
/
} ! / 10 - f ' tp= O.5 in. g f L = 23 ft. I be, - 4 in.
/
l i i i i 0 0 0.005 0.0010 0.015 0.020 A/D Figure 5.2 Support Reaction vs. Diameter l Reduction Curve - Case 2 O i I I I f .I
- O i
- - ---.- s.~ . - . .__.-, . . , . , . . _ _ . . , . ._ ,,. _ _ ,_
-_- _.m., _ . _ ~ . . _ _ _ . . _ _ . _ _ _ . . . _ . - - _ _ . . . - . _ . . _ . _ . _ _ . . . . . _ _ _ _ _ _
r-l l O O . ELASTIC f
/ 2xELASTIC O
R I / 1 / (kips) f f 1 I 40 -
. ; /
'O I ~P - 36.5 kips y
/ c .
/
I , t 30 - /
- I f
.0 I i
! /
s l --- i i 3 I / Hb-+\ 20 - f / I ' 44 12 1111;4 '. O , f _
/ R" 'R I
j
- 1-f 10 - f O
/ t,, - 0.375 in.
j / L = 28 ft.
/ be = 2 in.
/
i 1 1 I I I 0 0.010 0.020 0.030 dD fG Figure 5.3 Support Reaction vs. Diameter f- Reduction Curve - Case 3 l 0 i l 1 0
y .- .u. .--. .:.~ a v . - - O O - EIASTIC 2xELASTIC 50 - y
/
O R /
-P = 44.5 kips
/ "
(kips) / l / ) 40 - / f I / C / / l
/ /e .
30 - I ;'
~~~
O I ,' '3
/ f
}.- h -.1
- . I j 20 - I / 11 111111111 11
- l
/ ,,
R R '
/ L Q
l c / ' /
/
j 10 - f
/ cp= 0.375 in. !
L = 28 ft. , O / bc = 4 in. j
/
/
1 i i i i i i 0.01 0.02 n.03 0.04 a /D O Figure 5.4 Support Reaction vs. Diameter f Reduction Curve - Case 4 I O !
}
} i
!O 50 1
j !
n . . . . . . . - . ~ . . . . . . . _ . . - . . - . . . I ELASTIC 2xELASTIC 100 - / R / / 90 - f / (kips) /
/
/
SO - I /
/ /
l / 70 - / j
/ /
60 - / /
/ /
50 - / / 4 f
/ t
/ F-bH f I 40 - p 1 ,
/
,14 111111 1111 1 a I R" 'R
' 30 - / L -
/
/
I / 20 - /
/
/
te= 0.375 in. L = 35 ft. t 30 ~ / bc= 4 in.
/
i i i 6 i 0.01 0.03 0.05 A/D 0 0.02 0.04 0.06 s l. Figure 5.5 Support Reaction vs. Diameter { Reduction Curve - Case 5 4 1 4
, __ . , _ _ ., _ ._. .. . ..._.. . . . _ _ _.-- _ . ~ . _ . ~.._, , . _ . . ,,
n
,n 50 -
O R (kips) 40 -
.O~
pg 2/3xPc = 35.3 kips 30 -
!j/ ,
c' w" REIDAD 4 1' _ 20 - f um tj,
- fL LL LLLLLLLLL
' I R R
*-L :
10 -
/j r t = 0.5 in. - L = 23 ft.
b = 4 in. 1 G Ioad = 2.6 kips i i 0 0.1 0.2
~
A (in.) Figure 5.6 Ioad Cycling Behavior of 12" S T 80S Pipe Eetween 1 G Ioad and 2/3xPc ,s M l
m, a ,
. ,, - ~~~~~ m. . ; y :e. nr ,..,I; - - m " ~ ' 7 ,m .
~
-- W v .: '- ":
n.
- ~~~;".;.".~~~*'*"~~~'"
'V'.*%- .
egk. i
. [. . '
i ; *k + ' ,;f
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n .. ,
- c. - . - , .
nw& 1 Q f,') ,.';l.)*$ f ) L A?
' ^
*a. , , ,; . * ' a. "& 1. * . ;.c L
v g.g";
- y. "V; & - p*n m ' : ~ , n '~
- ' ~ y x kn k*c.m v :gdC ?s .st $.,5 v 7:TkA d ~ ,
S ~ !; ; e
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., p , .,)
[ %. ay'i,. b: e!
; f;; o
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.s
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+ ,H (( a,'
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- I'
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