ML19207B432

Evaluation of Analysis Procedures for Design of Expansion Anchored Plates in Concrete.

ML19207B432
Person / Time
Site:	Marble Hill
Issue date:	05/31/1979
From:	Kostal K SARGENT & LUNDY, INC.
To:
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ML19207B430	List: ML19207B429 ML19207B432
References
NUDOCS 7908290328
Download: ML19207B432 (25)

Text

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EVALUATION OF ANALYSIS PROCEDURES FOR'THE DESIGN OF EXPANSION' ANCHORED PLATES IN CONCRETE k

PREPARED BY: O REVIEWED BY:  %/

APiROVED BY: L, 0;*/

May 31, 1979

. Sargent & Lundy Engineers Chicago, Illinois

~. .

g 853 195"

EVALUATION OF ANALYSIS PROCEDURES FOR THE ,

DESIGN OF EXPANSION ANCHORED PLATES IN CONCRETE TABLE OF CONTENTS 1.0 PURPOSE 2.0 INDIVIDUAL CONCRETE EXPANSION ANCHORS 2.1 Concrete Expansion Anchor Types 2.2 Behavior of Individual Concrete Expansion Anchors ,

2.2.1 Pre-load Levels In Wedge And Sleeve Type Expansion Anchors .

2.2.2 Pre-load Levels in Lelf-drilling Type Expansion Anchors 2.2.3 Modes of Failure For Concrete Expansion Anchors 2.3 Idealized Load-Displacement Curve For Individual Concrete Expansion Anchors 3.0 EXPANSION ANCHORED PLATE ANALYSIS PROCEDURES 3.1 Rigid Versus Flexible Plate Analysis 3.2 Rigid Plate Analysis 3.2.1 Rigid Plate Analysis Theory 3.2.2 Rigid Plate Analysis For Direct Tension Loads 3.2.3 Rigid Plate Analysis For Pure Moment Couple Load 3.224 Rigid Plate Analysis For Applied Shea Loads 3.3 Flexible Plate Analysis 3'. 3.1 Description of the Flexible Plate Model 3.3.2 Behavior of the Flexible Plate Assembly

4.0 CONCLUSION

. 853 196 I

. EVALUATION OF ANALYSIS PROCEDURES FOR THE DESIGN QP EXPANSION ANCHORED PLATES IN CONCRETE LIST Of TABLES .

TABLE NO. TITLE 1 Typical Expansion Anchor Installation and Test Torque Values 2 Results of Analysis for Typical Expansion Anchor Assemblies D

4 m.

853 197 -

EVALUATION OF ANALYSIS PROCEDURES FOR THE DESIGN OF EXPANSION ANCHORED PLATES IN CONCRETE LIST OF FIGURES b

FIGURE NO. TITLE 1 Typical Expansion Anchored Plate Assemblies 2 Idealized Load-displacement Curve For Concrete Expansion Anchors 3 Idealized Load-displacement Curve For 1/2" Diameter Expansion Anchors 4 Idealized Load-displacement Curve for 3/4" Diameter Expansion Anchors 5 Rigid Plate Behavior Under Direct Tension Load 6 Rigid Plate Behavior Under Pure Moment Couple Load 7 Plate Deflection Due To Applied Tension Load And Prying Acton 8 Finite Element Model Of A Quarter Section Of A Typical Plate Assembly 9 Load-reaction Curve For a 1/2" x 9" Expansion Anchored Plate Assembly 10 Load-reaction Curve For A 5/8" x 12" x 12" Expansion Anchored Plate Assembly G

= ye * ,% ...

ge

• I

~

853 198

.. 1.0 PURPOSE The purpose of this report is to demonstrate that the rigid plate analysis procedure used for the

- design of expansion anchored plate assemblies pro-vides factors of safety ranging from a minimum of 4.0 to a maximum of 8.7, against manufacturer's

' recommended anchor failure loads. It will subse-quently be shown that when the flexibility of the baseplate in conjunction with the true load versus displacement behavior of the expansion anchor is accounted for in a finite element solution, the

" prying action" forces are largely relieved and the flexible plate solution approaches the rigid plate solution.

This report analyzes four typical expansion anchor plate assemblies used to support mechanical com-ponents in nuclear power stations using both rigid plate theory and flexible plate theory, and compares the maximum anchor loads and displacements for each type of analysis. The following variables are considered in both the rigid plate and flexible plate analysis presented herein:

a. Expansion Anchor Type al. Wedge Type a2. Sleeve Type a3. Self-drilling

b. Expansion Anchor Embedment Depths bl. 4-1/2 Diameter Embedment Depth b2. 8 Diameter Rnbedment Depth

c. Expansion Anchor Pre-load Level cl. Zero Pre-load c2. Pre-load Levels Specified in Table 1

d. Applied Load dl. Direct Tension Load d2. Moment Couple The rigid plate analysis is presented in*Section 3.2 and the flexible plate analysis is presented in Section 3.3. Table 2 compares the results of both the rigid plate and flexible plate analysis.

• *-me -e **e*--

• * .. ee

• e. s ,.s .-- e- m.e eas ee * . ee*

....,m.*- a -

- + - P 853 199

. 2 2.0 INDIVIDUAL CONCRETE EXPANSION AMCHORS 2.1 Concrete Expansion Anchor Types Three types of concrete expansion anchors'have traditionally been used for the attachment of nechanical components to concrete in nuclear power stations. They are:

a. Wedge Type Anchors

b. Sleeve Type Anchors

c. Self-drilling Anchors The wedge and sleeve type anchors are predominantly used today by the nuclear industry. Self-drilling anchors were used prior to 1976, however, today they are used primarily for the support of small loads.'

2.2 Behavior Of Individual Concrete Expansion Anchors 2.2.1 Pre-load Levels In Wedge And Sleeve Type Expansion Anchors Wedge and sleeve type expansion anchors are installed to a specified initial torque referred to as the

" installation torque". This installation torque provides the wedge and sleeve type expansion anchors with an initial pre-load force. This initial pre-load is reduced in time due to a combination of such factors as stress relaxation in the concrete expansion anchor and concrete creep. Field tests have demonstrated that a major part of this pre-load relaxation takes place immediately after installation. It is estimated that the initial expansion anchor pre-load ultimately' relaxen to approximately 60% of its initial value.

Sargent & Lundy's installation procedure requires that expansion anchors be tested after installation to assure a minimum pre-load value after relaxation.,

This minimum pre-load value is verified by applying ,

a test torque tc the expansion anchors after J installation and requiring that the test torque achieve a minimum of 60% of the installation torque. Typical values for the installation torques and test torques for 1/2" diameter and 3/4" diameter wedge and sleeve type expansion anchors are given in Table 1.

gi

, 853 200

- 3 2.2.2 Pre-load Levels In Self-drilling Type Expansion Anchors The initial installation torques and test torques have not been typically specified by manufacturers for self-drilling type expansion anchors. The torquing of a self-drilling expansion anchor does not seat the anchor in the concrete hole, and, '

thereby minimize anchor displacement, as in the case of wedge and sleeve type anchors.' Any torque requirement for self-drilling anchors would induce a preload in the anchors, but not influence the ultimate load capacity of the anchor.

2.2.3 Modes Of Failure For Concrete Expansion Anchors k There are three postulated modes of failure for a concrete expansion anchor. They are: ,

a. , Yielding of The Expansion Anchor

b. Excessive Displacement Of The Anchor

c. Concrete Cone Failure The expansion anchor failure referenced in Item 2.2.3a is defined by the yielding of the anchor material at the neck of the anchor and the displacement of the anchor at failure is controlled by the elastic deformation of the anchor. The anchor failure referenced in Item 2.2.3b is controlled by an assigned maximum displacement of the expansion anchor relative to the concrete. Sargent & Lundy typically specifies this maximum displacement to be one anchor diameter for anchors embedded greater than 4-1/2 diameters. The failure referenced in Item 2.2.3c is governed by the expansion anchor embedment depth and the strength of the concrete.

Anchors embedded 4-1/2 diameters or less, are ~

usually susceptible to concrete cone failures referenced in Item 2.2.30; therefore, Sargent &

Lundy has specified a maximum displacement of 3/4 anchor diameters to preclude anchor failure.

Anchors embedded greater than 4-1/2 diameters are usually controlled by the mode of failure referenced in Item 2.2.3b. In addition to controlling the mode of failure, the anchor embedment depth also effects anchor flexibility, i.e., the greater the anchor length, the greater the anchor flexibility.

"e

_. . _ . . . . . . _ _ . _ . . . . _ _ . . . . . . . . . . . _ . . _._._._ _ ._ . 8 5 3 - 2 0 1 46 -

4

- Concrete expansion anchors are not usually controlled by the modes of failure referenced in Items 2.2.3a and 2.2.3c; mode failure 2.2.3b typically predominates.

2.3 Idealized Load-Displacement Curve For Individual Concrete Expansion Anchors Figure 2 illustrates an idealized load-displacement curve for individual concrete expansion anchors with and without initial pre-load. It can be seen that the initial pre-load level does not effect the ultimate capacity of the anchor. This fact has been verified by numerous field testo. When a concrete expansion anchor is pre-tensioneo to a level P g by torquing the nut, the corresponding deformation a f is taken up by the movement of the anchor as shown in Figure 2. When a pre-tensioned anchor *is loaded in tension, it has negligible displacement until the external load reaches Pg at which point it follows the original load-displacement curve to the specified ultimate load.

Thus, the only effect of pre-tensioning the concrete expansion anchor is to reduce the ultimate anchor displacement by an amount equal to A g.

The idealized load-displacement curves for 1/2" diameter expansion anchors and 3/4" diameter expansion anchors are shown in Figures 3 and 4, respectively. Two load displacement curves are given for each anchor diameter dependent upon the anchor embedment depth. Sargent & Lundy has defined anchor failure as an anchor displacement equal to 3/4 anchor diameters for anchors embedded 4-1/2 diameters or less, and equal to one diameter for anchors embedded greater than 4-1/2 diameters.

These conservative idealized load-displacement curves have been verified by static load tests performed in the field at several nuclear power stations currently under construction.

3.0 EXPANSION ANCHORED PLATE ANALYSIS PROCEDURES 3.1 Rigid Plate Versus Flexible Plate Analysis The analysis of expansion anchored plates is traditionally performed using rigid plate theory.

~

. c 853 202

5

- The forces in the expansion anchors are computed by static equilibrium and the resulting expansion anchor loads are limited to the ultimate capacity of the expansion anchor divided by an appropriate factor of safety. The ultimate load is typically provided by the expansion anchor manufacturar and a factor of safety equal to 4.0 is used to obtain the allowable design load.

Recognizing the flexibility of the baseplate relative to the concrete expansion anchor, a load applied to the concrete expansion anchor assembly may chuse the expansion anchor plate to deform such that compressive " prying action" forces are developed between the contacting areas. A finite element approach is used to properly account for the effectc of plate flexibility and anchor flexibility.

In the following sections it will be shown that these " prying action" forces are relieved due to the flexibility of the concrete expansion anchor (as demonstrated by the idealized load-displacement curves indicated in Figures 3 and 4) relative to the flexibility of the baseplate.

3.2 Rigid Plate Analysis 3.2.1 Rigid Plate Analysis Theory In a rigid plate analysis, the forces in the concrete expansion anchors are calculated on the basis of the rigid body movement of the baseplate.

Stresses in the concrete and in the concreto expansion anchors are calculated by equating the internal forces to the external forces by maintaining the compatibility of the linear strain relationship in both the steel baseplate and concrete bearing surface.

3.2.2 Rigid Plate Analysis For Direct Tension Loads For direct tension loads, the baseplate displacements are constant over the entire surface of the base-plate; therefore, the tensile forces in all concrete expansion anchors are equal and the sum of the i tensile forces in the concrete expansion anchors are equal to the externally applied direct tension load. Figure 5 illustrates the displacement cf the baseplate and equilibrium of the anchor forces and the externally applied direct tension load.

r05 9

6

. 3.2.3 Rigid Plate, Analysis For Pure Moment Couple Load Under a pure moment coup'.e, the rigid plate will rotate about a neutral e.>-is. The rotation will induce compressive forces where the baseplate and concrete are in contact and tensile forces in the concrete expansion anchors on the opposite side.

' The concrete expansion anchor forces are calculated assuming equilibrium of the forces over the entire ,

plate and by assuming compatibility of the linear strain relationship between the steel and concrete.

The design of the. expansion anchor plate assembly for a pure moment couple using rigid plate analysis is shown in Figure 6.

3.2.4 Rigid Plate Analysis For Applied Shear Loads Shear loads applied in the plane of the expansion anchor plate assembly do not induce " prying action" farces.in the concrete expansion anchors, regardless of plate flexibility. Concrete expansion anchored plate assemblies are designed to resist applied shear loads using the following interaction equation:

f f

+ 5 1.0 (1) where f = tension force in the anchor t

F = allowable tensile capacity of the anchor t

f = shear force in the anchor y

F y = allouable shear capacity of the anchor.

Equation 1 can be reduced to F

ft+ vF v

I t * (

Taking F y /F = 0.7, Equation 2 reduces to f

ft+07 5F t .

o 3

- .853' 204'

7

- This is equivalent to the shear friction theory of

. ACI-349, Appendix B, where the shear force in anchors is converted into an equivalent tension force and added to the force due to tension and/or moment. This approach is conservative compared to published test results on expansion anchors for

, tensile and shear loading, which indicate that the ratio Py /F is always larger than 1.0.

3.3 Flexible Plate Analysis

. In a flexible plat'e analynis the deformation of the plate under applied load results in additional

" prying action" forces in the concrete expansion anchors. Figure 7 illustrates these " prying k action" forces on a flexible plate under a direct tension load. It will be demonstrated that these additional " prying action" forces are eliminated due to.the flexibility of the anchor relative to the flexibility of the baseplate and, therefore, do not reduce the required factor of safety.

3.3.1 Description Of The Flexible Plate Model The SLSAP Computer Program was used for the non-linear finite element analysis of the expansion anchor plate assemblies referenced in Figure 1.

Figure 8 illustrates the typical finite element model of a quarter section of a plate assembly.

The plate is modeled using quadrilateral plate elements. The concrete under the baseplate is represented by one-way (compression only) springs and the stiffness of these springs is computed on the basis of the elastic half-space approach.

The anchors are represented by truss elements as indicated in Figure 8 and the stiffness of the concrete expansion anchors are based upon the idealized load displacement curve shown in Figures 3 and 4. Pre-load in the concrete expansion anchors is simulated by an equivalent negative temperature load.

Due to the non-linear nature of the idealized load displacement curve, the plate assemblies are analyzed by the ultimate design approach in which the design loads are multiplied by a load factor equal to four. The resulting expansion anchor reactions are compared with the ultimate capacity of the expansion anchors as defined in Figures 3 and 4. The load factor equal to four was selected to be consistent with the minimum required factor of safety used in the rigid plate analysis.

853 205

~ - - - - -- -

r=

8 3.3.2 Behavior Of The Flexible Plate Assembly Comparing the results of the rigid plate analysis and the flexible plate analysis listed in Table 2, it can be seen that the anchor forces obtained from a flexible plate analysis approaches those obtained from a rigid plate analysis due to the flexibility of the anchor relative to the baseplate. Figures 9 and 10 show the external force and anchor reaction for plate Assemblies 1 and 2 listed in Figure 1.

These figures demonstrate a minor amount of " prying action" force in the early load stages which disappears as the load is increased. Figures 3 and 4 show that four times the design load is substantially less than the ultimate load.

4.0 conclusion The results for the flexible plate analysis listed in Table 2 indicate that a factor of safety of at least 4.0 is maintained against manufacturer's recommended ultimate failure loads. This verifies that the rigid plate analysis utilizing a factor of safety equal to 4.0 can be used for the design of expansion anchored plate assemblies.

It has been demonstrated that " prying action" is a self-limiting phenomenon in expansion anchored plate assembly design and does not effect the ultimate capacity of the anchored plate assembly.

This has been demonstrated for the typical expansion anchored plate assemblies used to support mechanical components in nuclear power stations for various expansion anchor types, embedment depths, preload levels and applied load patterns which may typically be encountered in such installations.

9 853 206

- - - - . r-

9 TABLE 1 Typical Expansion Anchor Installation and Test Torque Values Installation Anchor Size Torque Test Torque Inches ft-lbs ft-1bs 1/2 60-75 -

45 3/4 230-270 160 9

[

O

~~

853 207'

.c ch e a 6" E m n 6"

'A E %d # '

8E u 87  %

'8 si u 87

~$ B 4= 0. Im 5: 3 %3 T" 5% 3  %

d" 3E e Ex Oc 35e~ Ex Oc e

E u 8 *b "3 b m' a8 "t *2 5

m; a8 " ; '?

o se et 15 3 5 it 81 88 85 as it 81 sE

1. $2 CE Et tt 18 t* ta 50 Ex t# t" to M so so 28 ke Re e% 4% et k< ee et e%

0 12.8 3.2 6.8 .06 TENSION kips m

g 3.2 3.2 0.8 6.9 '.0003 5 kips kips 2.1 12,8 3.2 6.8 <.001 g kips

- 4.5d 5.5 q 0 43.6 2.85 >4 <.06

- un*NT k-in g 10.5 10.9 0.8 6.9 .0603 R k-in k-in 2.1 43.6 2.94 >4 <.001 M k-in d:

2m , 0 12.8 3.2 8.7 .06 M TENSION kips

. 3.2 3.2 0.8 8.7 .0006 x kips kips 2.1 12.8 3.2 8.7 <.001

kips R

8d 7.0 0 43.6 2.85 >4 <.06 y 110 MENT k-in 5 10.9 10.9 0.8 8.7 .0006

• k-in k-in 2.1 43.6 2.92 >4 <.001 k-in 0 33.6 8.4 4.8 .12 E TENSION kips O 8.4 8.4 2.1 4.8 .0006

{

kips kips 4.4 33.6 8.4 kips 4.8 <.001 o 4.5d 10.15 h 0 159.2 7.43 >4 <.12 m MOMENT k-in S 39.8 39.8 2.1 4.8 .0006

" k-in 4.4- 159.2 7.35 >4 <.001 k-in m ,' k--in

. ~n O"" 0 33.6 8.4 7.6 .10 TENSION kips

.-m 8.4 8.4 2.1 7.6 .001 kips kips 4.4 33.6 8.4 7.6 <.001 kips kn 8d 16.0 0 159.2 7.45 >4 <.10 to }IOMENT .kain

$ 39.8 39.8 2.1 7.6 .001 m k-in k-in 4 .'4 159.2 7.53 >4 <.001

' k--in

. . . . . . . . r . ,,--

853 208

6m cc E. NO 7 EO x 3 3$ E e 97 0o M' sI w7 8:

^5 R 8" 2 .c 23 4 ." 8 6 on Sh E BB S

a h" &? 81 E6 t R" c 8c 86 t I" E N Ex x3 3# c 5D EE 3 "3# c $D EE wE ud $c 3e E3 ud wY nE I$ !M 90 9 Y 3 28 .8 8 63 23 En he 28 23 n*St 28 28 3 et 8& E8 E E2 Em

<o 8u

<c 88 <t* zm

< r-.

E8 em

<o 8u

n. <w <u <A <p %e O 19.2 4.02 5.4 .07 TENSION kips m

@ 4.8 4.8 0.8 6.9 .0003 6 kips kips 2.1 19.2 4.02 5.4 <.00]

kips Q

4.5d 5.5 0 0 66.0 3.41 >4 <.07

• sg\ k-in MOFENT .

d 16.8 16.8 0.8 6.9 .0003

• k-in k-in 2.1 66.0 3.39 >4 <.001 "8 k-in c

Z" . 0 19.2 3.99 7.0 .075

• TENSION kips

. 4.8 4.8 0.8 8.7 .0006 x kips kips 2.1 19.2 3.99 7.0 <.001 kips O*

Sd 7.0 0 66.0 3.38 >4 <.075 s MOMENT k-in

$ 16.8 16.8 0.8 8.7 .0006 k-in k-in 2.1 66.0 3.35 >4 <.001

. k-in 0 67.2 9.33 4.3 .13 E TENSION kips 16.8 16.8 2.1 4.8 .0006 h kips kips 4.4 67.2 9.33 4.3 <.001 g kips a 4.5d 10.15 (

A 0 512.8 8.87 >4 <.13 e MOFENT k-in 5 128.2 128.2 2.1 4.8 .0006 E k-in k-in 4.4 512.8 9.21 >4 <.001 I k-in d 0 67.2 9.44 7 .11 x .

TENSION kips

16.8 16.8 2.1 7.6 .001 N kips kips 4.4 67.2 9.44 6.7 <.001 x kips

. 8d 16.0 s 0 512.8 9.14 >4 < 11 r .

MOFENT .k-in N 128.2 128.2 2.1 7.6 .001 k-in k-in 4.4 512.8 9.55 >4 < . 001 h k-in a

853 209

i iha u _lh"j-- 1" 1 "l 7

. I

1. 1 I A H -o- - 0-d e i[ i I l 4 0 --&

• 3 o l -

8

• g 1 J

, I e s

, h -o- -

F y -

0-9 L

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ASSEMBLY NO. 1 ' ASSEMBLY NO. 2 Plate 1/2" x 9" x 0'-9" Plate 5/8" x 12" x l'-0" Anchors 4-1/2" Dia. Anchors 4-3/4" Dia.

9" =

l'-9"

=

1 " 6" 1 " lh" 9" 9" lb"

~ - E' = = = ='m

1 h- -

o---  ?-

a s" H

h-- _

I L g

e =

m l 1

m 7

'{ -- { n -

+-- h -

,' I I L = i e m i i

- y - - H,r =, I _. _ __ - c _  ;

{

s ', H g

ASSEMBLY NO. 3 ASSEMBLY NO. 4 Plate 1/2" x 9" x l'-3" Plate 3/4" x 21" x l'-9" Anchors 6-1/2" Dia. Anchors 8-3/4" Dia.

TYPICAL EXPANSION ANCHORED PLATE ASSEMBLIES FIGURE 1 853 210

\

d

\ -

P _ _ _ [

Corresponds to Pre-Load I

Specified P

1 Pre-Load P.1 o

ec 3 Corresponds to No Pre-Load i

I i =._

0 At Att ~

@OriginforPre-TensionCase

- m.-m Displacement P = Ultimate Anchor Capacity u

-~~ Pg = Specified Pre-Load bj = Initial Displacement with no Pre-Load k = Displacement at Ultimate Anchor Capacity FIGURE 2 IDEALEZED LOAD-DISPLACEMENT CURVE FOR CUNCRLir, t.APAN610N ANCHORS 953 ,1

6. -

p = 5.5k u With Pre-Load 5-- Without Pre-Load

- 4-- ,

m a

$ 3-

-- ---- ---- L 4x Design Load

~

Pre-Loa l 5 2-o 2.Ik l A -

1-- -- l

- -- - --- -- - - - - - De s i gn Lo a d 0 ' '

1 .2 3 .4 3

-d 4 >

Displacement (Inches)

(a) 4.5 d Embedment 7

Pu= 7.0k _ ___

With Pre-Lead Without Pre-Load 5- I m

a 4--

a y

ei __ ____ 4x Design Load 3

e I e 're-Load -

0 2- --

I

" 2.lk i 1- ._

_ _ _ _ _ _ _ _ _ _ _ _ d - De s i gn Loa d 0

.1 .2 .3 .4 .5 .c ld i

Displacement (Inches) '

' ~

(b) 8d Embedment Figure 3 IDEALIZED LOAD-DISPLACEMENT CURVE FOR 1/2" DIAMETER EXPnWSION ANCIIORS 853 212

- i 9 --

8 --

g-- - -[- 4x Design Load -

7 ,, N With Pre-Load 6 -' Without Pre-Load

^

5-a P r e _L o a d

• j 4- 4.4k '

~

3 -- l .

] 2--- - - - -- - - -

- -l- - De s i gn Loa d ,

o A 1 l

, 0 ' ' ' '

' I' ' '

.2 .4 .6 .8 Displacement (inches) 3 d 4

(a) 4.5d Embedment

• o$

16 Pu= 36.0k - -- -

15 With Pre-Load Without Prc-Load I

i 10 --

l

- . - _ - - - ------ ----------I-- 4x Design Load en a .

l ei i x

I m

o 5 I a Pre _ Load

_ i 4 - 4.4k l.

3 2 +- - - - - - - - ~ ~ - - - - - - - - - - L - De s i gn Loa d I

1--

0 O.2 0.4 0.6 0.8.

ld

. .__ Diaplacement (inches)

(b) 8d Embedment FIGURE 4 IDEALIZED LOAD-DISPLAGEMENT CURVE FOR 3/4" DIAMETER

. . EXPANSION ANCIIORS 853 213

t Anchor .

• ////// //////// ////llll

~

Base Plate

\

Plate ia

~

Loaded Position T At A t g .

I VT BY EQUILIBRIUM t + t = T FIGURE 5 RIGID PLATE BEHAVIOR UNDER DIRECT TENSION LOAD T = Applied Tensile Load t = Corresponding Anchor Reaction 853 214

///// / //////////// 6 d

D d

= _

'C y fr u 1 l

Cc 4

k l

-: =

STRAIN DISTRIBUTION N

Tg \

s fc C b JL ,

STRr.:SS DISTRIBUTION Unknowns are D+d-k cc& k C = C t C k f =E C T=AE ss C C= P,feb c c c t C - T = 0 --([)

Ch-T (D+d) =M (f)

Where:

M = Applied moment d = Edge distance of anchor c c = Compressive strain in concrete A s - Area of anchor e

t

= Tensile strain in anchor k = Length of compression block

. b = Width of plate c = Maximum stress in concrete f

s = Modulus of elasticity of steel E

E = Modulus of elasticity of concrete C = Total compression in concrete

• T = Total tension in steel FIGURE 6 RIGID PLATE BEllAVIOR UNDER PURE MO?iEN" COUPLE LOAD 993 ,;9

'I k h (P/2 + Q) \

\ b -(P/2 + Q) ,

0 yq 0 o yq t /[ ^'

i f P PLATE DEFLECTION DUE TO APPLIED TENSION LOAD AND PRYING ACTION FIGURE 7 P = Applied Tension Load Q = Force Due to Prying Action

~ --- -- - . ~ . - .

853 2 L6 _.

PLATE SIZE = 1/2" x 9" x O'-9" e ANCIIOR BOLT SIZE = 1/2"# ,

L

- I: .

I o

, . Anchor

/

/ -

in w

u W

N m

e U

~

j t

6@ 3/4" = 4.5" h j i

'l 5 II bg ONE-MAY CO!!PRLbSION SPRING REPRESENTING

[

l ,

l >

I CONCRETE SUPPO'RT r;7 r nr n ,- r:v rW ANCIIOR j 77 FIGURE 8 Finite Element Flodel of a Ouarter Section of a Typical Plate Assembly e

. . bb3 Z

\

6 5

E E

w Z 4, 9 x -

U 8

a:

3 LEGE_!_'_O o

z

,fPre-Load

---

Anchor reaction i f there ~

. , was no prc-load and no p'

2 prying action.

/ - ----

Anchor reaction if there was

/ pre-load but no prying actice

/ Anchor reaction includina 1.0 / the effect of pre-load and

/ prying action.

/

/

/

l.o 2.0 3.o 4.0 50 ao APPLIED FoTICE PER ANCHOR (KIPS) 9

_ FIG..U._RE ,

Load-reaction Curve for a 1/2" x 9" Expansion

• Anchored Plate Assembly a e # g e 853 218

7.0 6.0 ,

m SD 2

O /

p .r-Pro-Load y . . - - . ..- _ . ,/ . / .

w /

w 4.0 /

2 /

o /

x -

o /

Z /

4 / LEGEND 3.o

/

/ -~~~ Anchor reaction if there

/ was no pre-load and no

/ prying action.

20 # - - --

j Anchor reaction if there was

/ pre-load bur no prying action

/ Anchor reaction including

/ the effect of pre-load and y

1.0

/ prying action.

/

/

/

/

1.0 2.0 3.0 4.0 50 6.0 7.0 8.0 APPLIED FORCE PER ANCliOR BOLT (KIPS)

FIGURE 10 I. cad-reaction Curve for a 5/8" :e 12_x 12" Expansion 7.nchored Plate Assembly 853 219 .