ML20207D776

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Rev 0 to Richmond Insert/Structural Tube Steel Connection, Design Interation Equation for Bolt/Threaded Rods
ML20207D776
Person / Time
Site: Comanche Peak Luminant icon.png
Issue date: 09/10/1986
From:
ROBERT L. CLOUD ASSOCIATES, INC.
To:
Shared Package
ML20207D684 List:
References
NUDOCS 8612310196
Download: ML20207D776 (20)
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RICHMOND INSERT / STRUCTURAL TUBE STEEL CONNECTION

' DESIGN INTERATION EQUATIOM FOR BOLT / THREADED RODS I

RLCA/P142/01-86/008 REVISION 0 9/10/86 Prepared by:

Robert L. Cloud Associates, Inc.

125 University Avenue 20 Main Street Berkeley, CA 94710 Cotuit, MA 02635 Y

__ _ , . _ _ _ ~ . _ . . . _ _ _ _ . . ..._.,.__ - _

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1.0 INTRODUCTION

This report, prepared by Robert L. Cloud Associates, Inc. (RLCA) for the Texas Utilities Generating Company (TUGCO), describes the interaction

. equation to be used for the design of threaded rods / bolts

  • subjected to combined shear, tension, and bending loads at the Comanche Peak Seam Electric Station (CPSES), Units 1 and 2. This study is a part of RLCA's continuing effort in support of TUGCO's licensing for CPSES.

Bolts and threaded parts fastening individual structural members together are designed conventionally -

to carry shear, tension, or a combination of the two.

Both AISC Code (Ref. 1) and ASME,Section III Code (Ref. 2) pr ride the design requirements for these fasteners.

At CPSES, threaded rods / bolts are used to secure structural tubing in pipe supports to Richmond Inserts embedded into the building concrete. Consequently, these ,

j rods / bolts are subjected to bending as well as shear and

! tension. The AISC Code does not specifically address

.such load combinations for the fasteners. Although Subsection NF, " Component Supports," of the ASME Code is also silent in the design of the fasteners under .

combined shear, tension and bending loads, NB-3232.2 addresses bolts in tension plus bending and the corresponding allowable stress for use in Class 1 pressure retaining components.

This report establishes an interaction equation for j threaded rods / bolts under combined shear, tension and I bending loads at CPSES. This interaction equation was

! derived in a manner consistent with that used by both

- AISC and ASME Codes in establishing the interaction equation for combined shear and tension.

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  • Terms of threaded rod and bolt are used l

interchangeably for CPSES applications in this report.

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4

, 2.0 REVIEW OF APPLICABLE CODES .

Both AISC and ASME Codes specifically address the .

design requirements for bolts under combined shear and tension. Subsection 1.6.3 of " Specification and Code" of the AISC Code (herein referred to as the "AISC

, . Specification") gives three linear equations as the requirements. NF-3324 of the ASME Code adopts an elliptical equation as the design requirements for the bearing type joints. The threaded rods / bolts of interest at CPSES are under this classification.

Figure 2.1 shows a comparison between the interaction relationships of the two codes. As noted in the commentary on the AISC Specification, the ellipse is also allowed for use as an interaction equation. The AISC interaction relationship is a simplified representation of the elliptical equation which'is based on test results.

High-strength bolts tested in combined shear and tension are reported by Chesson, et al (ASCE Journal-Ref. 3). The test results are shown in Figure 2.2.

The tensile stress used is based on the stress area, whereas the shear stress depends on the location of the

. shear plane: in threads or shank. As seen from Figure 2.2, the following elliptical interaction curve was identified to approximate the test results:

f f vu .2 (1)

(Feu)2+(0.62xFvu)ru "1 where f eu = tensile stress at failure f vu = shear stress at failure F

ru = with ultimate tensile strength no shear stresses present Although the elliptical interaction curve was obtained for high-strength bolts, the similar elliptical

[

representation was reported to have been derived for other types of fasteners (" Guide to Design Criteria for Bolted and Riveted Joints"-Ref. 4). The elliptical equation, therefore, was employed as a basis for the design of bolts and threaded parts in the AISC and ASME Codes.

, By applying a factor of safety to each of the terms of Eq. (1), the following design interaction equation shown in Figure 2.1 is obtained: .

f t\

2 (fyg 2 . (2)

(Fe/ \Fy/

where f t

= tensile stress fy = shear stress Ft = allowable tensile stress in absence of shear .

Fy = allowable shear stress in absence of tension To determine the factor of safety imposed on Eq.

(1) in the AISC and ASME Codes, A36 threaded rods in 1-inch and 1 1/2-inch diameter were examined since this is-the material used most commonly for tube steel and Richmond Insert connections at CPSES.

. Table 1.5.2.1 of the AISC Specification shows 0.6 and 0.3 of the yield strength for the tensile and shear allowables, respectively. Thess give .

Fe = 0.6 x 36 = 21.6 kai (based on tensile stress area)

Fy = 0.3 x 36 = 10.8 kai (based on gross area)

When the minimum ultimate tensile strength is taken to be 58 ksi, the factors of safety become 58/21.6 = 2.69 for tension (0.62x58xAK)/(10.8xAD) = 2.34 for shear (1" diameter)

= 2.43 for shear (1 1/2" diameter) where AK = root area AD = gross area Note that a value of 0.62 for shear is based on test results on high-strength bolts.

i

Since the principal method of the AISC Specification is the working stress design, the corresponding factors of safety against the yield.

4 strength are also calculated below:

1/0.6 = 1.67 for tension 1/ JT/0.3 x(AK/AD) = 1.35* for shear (1" diameter)

= 1.40* for shear (1 1/2" diameter)

The AISC Specification uses a factor of safety of 1.67 as the basic value for the working stress method (see Section 1.9 of " Steel Structures"-Ref. 5).

NF-3324 of the ASME Code specifies the following .

allowables: -

Fu =Fru /2 for tension Fv = 0.62 Fru /3 for shear It is apparent that the factor of safety against the ultimate strength is 2 and 3 for tension and shear, respectively.

. Bolts subjected to bending are addressed in neither the AISC Specification nor Subsection NF, " Component i Support," of the ASME Code. However, Subsection NB,

" Class 1 Components," states, in NB-3232.2, that the maximum value of service stress due to direct tension plus bending, neglecting stress concentrations, shall not exceed three times the stress values of Table I-1.3.

Since the stress values are one third of the yield

, strength of bolting materials, the resulting allowables l for combined tension and bending are the yield strength.

l The tensile stress is limited to two times the above

! stress values in accordance with NB-3232.1.

This corresponds to a factor of safety against the yield strength as follows,

, 1/(2/3) = 1.5 in tension alone 1x1.7/1 = 1.7 in bending alone Note that a factor of 1.7 used above results from the ratio of plastic section modulus to elastic section

! modulus for a circular section.

I

  • The shear yield stress varies between one-half and five-eights of the tension yield stress. See

" Commentary on AISC Specification."

The review of the AISC and ASME Codes applicable to the design of bolts and threaded parts has shown that the factor of safety for bolts and threided parts varies widely because it depends primarily on the interpretation of past theoretical and experimental studies. Section 5.4.2 of " Guide to Design Criteria" 7

(Ref. 4) states that a minimum factor of rr.fety of 2.0 against failure has been satisfactory according to past practice.

The results of the re' view in this section are used to derive a design interaction equation for bolts and threaded rods subjected to combined snear, tension and bending as described in the following two sections. e e

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3.0 INTERACTION EQUATION FOR FAILURE This section describes and evaluates the interaction equation proposed by RLCA for use in developing a design interaction equation for threaded rods and bolts under combined shear, tension and bending.

Although tests have been performed to study the strength and behavior of bolts and rivets subjected to various combinations of shear and tension, no tests appear to have been conducted on those. fasteners under combined shear, tension and bending. This is because, as noted in section 1.0, the fasteners are not conventionally designed to carry bending. As a result,.

no interaction equation which represents the failure mechanism of the fasteners under such loading condition has been developed experimentally.

The AISC Specification lists, in the commentary section, references which provide a design basis fo.r the development of the specification. Section 2.8,

" Connections", references "ASCE, Manual and Reports on .

Engineering Practice, No. 41" (Ref. 6) which presents an interaction equation derived theoretically (referred to

,as the ASCE interaction equation). The equation which was developed for a rectangular section subjected, to combined shear, axial, and bending loads, establishes the mechanism of plastic hinge formation based on the elastic and perfectly plastic material behavior.

The ASCE interaction equation is given as follows, V 4 M P Ep

+ -1 (3)

(M ) + (y P )2 2

p y, P l

Py where M = bending moment

- P = axial force

! V = shear force M p = full plastic moment P

y = axial yielding load V = full shear yielding load p

i

~, - _ . . - - ~ . _ _ _ . _ _ _ _ _ _ . _ _ - . . _ _ _ _ . _ _ _ _ . _ _ _ _ _ _ _ . . _ . . _ _ _ . - . _ _ _ _._.-______._ _ ,_ - _ _ . _ _ _ . . - _ . . _ _ ~ _ . _ .

Although the equation was derived for a rectangular section, RLCA demonstrated its applicability to a circular section and suggested it as a basis,for establishing a design interaction equation for threaded rods / bolts under combined shear, tension, and bending loads at CPSES (RLCA Calc.-Ref. 7).

When M is set to be zero, Eq. (3) becomes

( )+( )=1 (4)

Eq. (4) is an elliptical equation which agrees with Eq. (1) which is confirmed by test results. .

The difference between the two equations results from the material behavior observed in the test specimens and assumed in the theoretical model where no strain-hardening was considered.

When V is absent, Eq. (3) reduces to M

f y 52-)=1 (Mp )2+

Vp (5)

Figure 3.1 shows a comparison of Eq. (5) and the exact solution for a circular section. The curves agree very well. Although no test results are available to RLCA on bolts and threaded parts subjected to combined tension and moment, results of tests on short 3-foot wide-flange members, W12x36, are documented 9 in "The Welding Journal" (Ref. 8) for various combinations of axial compression and bending. Figure 3.2 shows that an elliptical equation adequately represents the test results. The initial yield curve computed from o

y = (P/A) + (M/S) (6) i also adequately represents the behavior of the tests

specimens as shown in Figure 3.2.

' The ASCE interaction equation (i.e., Eq. (3)) was also verified theoretically by Stone & Webster Engineering Corporation (SWEC), who independently derived an interaction equation for a circular section based on the generalized stress concept and variational principle (CPSES Technical Report-Ref. 9).

i

_ - - - - - . . . . - . . _ _ , . . _ . . _ . . , . _ . .--_-,__....-,,,___..____.-.-,__.__,_,,,__,.,_.-..,-_____7 . . _ - ,__-

9

,. Figure 3.3 shows the comparison between the two interaction equations theoretically defining the strength of a. circular section: ASCE and SWEC equations. The equations agree very well when a ratio of shear force to full shear yielding load does not exceed 0.5. The ASCE equation becomes increasingly conservative as the ratio exceeds 0.5. Although the SWEC equation is more accurate than the ASCE equation for a circular section, the former is not a closed form solution and, consequently, is not practical for use in the development of a design interaction equation.

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f

, 4.0 PROPOSED DESIGN INTERACTION EQUATION Section 3.0 has demonstrated that Eq. (3) is a good representation of the strength of, bolts and threaded rods subjected to combined shear, tension and bending loads.

The equation, when moment is absent, reduces to an elliptical equation which represented test results and provided a basis for the design interaction equation for

. those fasteners under combined shear and tension loads.

In this case, therefore, Py and Vp in Eq. (3) are replaced simply by the corresponding tensile and shear allowables specified in the AISC or ASME Code applicable to threaded rods and bolts at CPSES. .

When shear is absent, Eq. (3) reduces to Eq. (5).

A factor of safety of 1.67 specified for tension in the AISC Specification is applied to the bending term of Eq.

(5). This yields the following bending allowable for a circular section:

Mp /1.67 = 1.70/1.67xa yxS i

= (1.02xoy)xS

. where S = elastic section modulus Here the stress at the outmost fiber of the section is allowed to reach the yield stress. This agrees with the stress limit specified in NB-3232, which is basically the yield stress. However the effect of strain-hardening on the bending strength is not as significant as on the tensile strength. Therefore the bending allowable specified by the AISC for a solid circular section, 0.75 times the yield stress, is adopted for the design interaction equation.

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,o After reviewing the AISC and ASME Codes and other documents referenced in this report, RLCA has recommended the following interaction equation to be used for the design of threaded rods / bolts at CPSES subjected to combined shear, tension, and bending loads:

I 4

(V y, "1 (7)

(M)+(T)2

- - - +

Ta 1_

T Ta )2 Ma _

- where M = bending moment T = tensile force V = shear force Ma = moment allowable Ta = tensile allowable v,= shear allowable l

I r

5.0 CONCLUSION

AND RECOMMENDATION Since bolts and threaded parts are not .

conventionally designed for use in carrying combined 4 shear, tension, and bending loads, no design requirements are specified in either the AISC or the ASME Code.

After reviewing both codes, materials used, and other relevant information, RLCA identified the interaction equation which represents the strength of a solid circular section subjected to combined shear, tension, and bending loads. The interaction equation was then adjusted to the shear, tensile, and bending allowables consistent with both codes. -

The modified interaction equation was recommended by RLCA to be used as the design interaction equation for threaded rods / bolts at CPSES.

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6.0 REFERENCES

1. " Manual of Steel Construction," AISC, 7th Edition.
2. 1983 ASME Boiler and Pressure Vessel Code,Section III, Division I.
3. "High-strength Bolts Subjectd to Tension and Shear,"

E. Chesson, Jr., N. L. Faustino, and W. H. Munse, Journal of the Structural Division, ASCE, Vol. 91, October 1965.

. 4. " Guide to Design Criteria for Bolted and Riveted Joints," John W. Fisher and John H. A. Struik, John Wiley & Sons, 1973. .

5. " Steel Structures," Second Edition, Charles G.

Salmon and John E. Johnson, Harper & Row, Publishers, 1980.

. 6. ASCE, Manuals and Reports on Engineering Practice, No. 41, " Plastic Design in Steel, A Guide and Commentary," Second Edition, 1971.

7. RLCA, Calculation No. P142-1-515-5

~

8. " Plastic Behavior of wide-Flange Beams," W. Luxion

. and B. G. Johnson, The Welding Journal, Vol. 27, No. 11, Nov. 1948.

9. " Interaction Relation for a Structural Member of Circular Cross Section," CPSES Technical Report 15454.05-N(c)-001.

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t

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% t

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( ASME DESIGN )

\

I v 1 I

t "

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( AISC DESIGN )

I f" = 1.0 7'

I' O.0 5 f 0.0 1.0 - pY-- Shear v

Figure 2.1 Design Interaction Equations for Combined Shear and Tension

( Bearing Type Connections )

6

~~ - - - -. ___

1.2 i i i  :

A325 and A 354 BD Bolts

.. 1. 0 t r ~ a .

N, N

NA NA 0%

^ \

h 0.8 - b -

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2 +,

$ nU 0.6

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o ep _

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03 'a E 2

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(0.6)2 + y \

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\'\

O.2 I -

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\

l 0.0

' ' d' '

O.0 0.2 0.4 0.6 0.8 1.0 Shear Stress Tensile Strength ( x )

Figure 2.2 Interaction Equation Derived from Tests for Combined Shear and Tension 0

T I

  • T Y

d Exact

1. 0 - 7.

+y + "-t I

- P ,

l

. N N

N

. N N

l 0.5 N

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l y

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0.0 0.5 1.0 Figure 3.1 Interaction curves for Bolts under Combined Tension and Bending G

4

l Theoretical Curves G Experimental Maximum Strength 1.0 ( A Experimental First Yield

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, I I f , 'A f 1 'l 0.0 0.0 0.5 1.0 N/M p Figure 3.2 Test Results and Theoretical Curves for Combined Axial Compression and Bending 4

's a

p 1.0 -

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v = V/V p

~

~_

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l l l l l l I l I l 0.0 0.0 0.5 1.0 P/P y Figure 3.3 Comparison of Interaction Equations for Circular Cross Section k

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