. .

..,

e

.

t

EVALUATION OF ANALYSIS PROCEDURES FOR'THE

DESIGN OF EXPANSION' ANCHORED PLATES IN CONCRETE,

k

.

OPREPARED BY:

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 ExpansionAnchors

,

2.2.1 Pre-load Levels In Wedge And Sleeve TypeExpansion Anchors

.

2.2.2 Pre-load Levels in Lelf-drilling TypeExpansion 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 CoupleLoad

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 andTest Torque Values

2 Results of Analysis for Typical ExpansionAnchor Assemblies

.

.

.

D

4

.

..

.

m.

.*

853 197 -'

.

EVALUATION OF ANALYSIS PROCEDURES FOR THE

DESIGN OF EXPANSION ANCHORED PLATES IN CONCRETE.

LIST OF FIGURESb

FIGURENO. TITLE

1 Typical Expansion Anchored Plate Assemblies

2 Idealized Load-displacement Curve For ConcreteExpansion Anchors

3 Idealized Load-displacement Curve For 1/2" DiameterExpansion Anchors

4 Idealized Load-displacement Curve for 3/4" DiameterExpansion 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 AndPrying Acton

8 Finite Element Model Of A Quarter Section Of ATypical Plate Assembly

9 Load-reaction Curve For a 1/2" x 9" Expansion AnchoredPlate Assembly

10 Load-reaction Curve For A 5/8" x 12" x 12" ExpansionAnchored Plate Assembly

_

G

,% ... ge *= ye *

' I.

853 198~

.

1.0 PURPOSE..

The purpose of this report is to demonstrate thatthe rigid plate analysis procedure used for thedesign of expansion anchored plate assemblies pro--

vides factors of safety ranging from a minimum of4.0 to a maximum of 8.7, against manufacturer's

' recommended anchor failure loads. It will subse-quently be shown that when the flexibility of thebaseplate in conjunction with the true load versusdisplacement behavior of the expansion anchor is'

accounted for in a finite element solution, the" prying action" forces are largely relieved andthe flexible plate solution approaches the rigidplate solution.

This report analyzes four typical expansion anchorplate assemblies used to support mechanical com-ponents in nuclear power stations using both rigidplate theory and flexible plate theory, and comparesthe maximum anchor loads and displacements for eachtype of analysis. The following variables areconsidered in both the rigid plate and flexibleplate analysis presented herein:

a. Expansion Anchor Typeal. Wedge Typea2. Sleeve Typea3. Self-drilling

b. Expansion Anchor Embedment Depthsbl. 4-1/2 Diameter Embedment Depthb2. 8 Diameter Rnbedment Depth

Expansion Anchor Pre-load Levelc.cl. Zero Pre-loadc2. Pre-load Levels Specified in Table 1

d. Applied Loaddl. Direct Tension Loadd2. Moment Couple

The rigid plate analysis is presented in*Section 3.2and the flexible plate analysis is presented inSection 3.3. Table 2 compares the results of boththe rigid plate and flexible plate analysis.

.

....,m.*- * * a .. ee * e. s ,.s .-- e- m.e eas ee * . ee* * *-me -e **e*-- ** **

-

-

- + - P

853 199

.

. 2

2.0 INDIVIDUAL CONCRETE EXPANSION AMCHORS-

2.1 Concrete Expansion Anchor Types_

Three types of concrete expansion anchors'havetraditionally been used for the attachment ofnechanical components to concrete in nuclear powerstations. They are:

a. Wedge Type Anchors*

b. Sleeve Type Anchors

c. Self-drilling Anchors

The wedge and sleeve type anchors are predominantlyused today by the nuclear industry. Self-drillinganchors were used prior to 1976, however, todaythey are used primarily for the support of smallloads.'

2.2 Behavior Of Individual Concrete Expansion Anchors

2.2.1 Pre-load Levels In Wedge And Sleeve Type ExpansionAnchors

Wedge and sleeve type expansion anchors are installedto a specified initial torque referred to as the" installation torque". This installation torqueprovides the wedge and sleeve type expansion

,

anchors with an initial pre-load force. Thisinitial pre-load is reduced in time due to acombination of such factors as stress relaxationin the concrete expansion anchor and concretecreep. Field tests have demonstrated that a majorpart of this pre-load relaxation takes placeimmediately after installation. It is estimatedthat the initial expansion anchor pre-load ultimately'relaxen to approximately 60% of its initial value.

Sargent & Lundy's installation procedure requiresthat expansion anchors be tested after installationto 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 Jinstallation and requiring that the test torqueachieve a minimum of 60% of the installationtorque. Typical values for the installationtorques and test torques for 1/2" diameter and3/4" diameter wedge and sleeve type expansionanchors 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 torqueshave not been typically specified by manufacturersfor self-drilling type expansion anchors. Thetorquing of a self-drilling expansion anchor doesnot seat the anchor in the concrete hole, and,

'

thereby minimize anchor displacement, as in thecase of wedge and sleeve type anchors.' Any torquerequirement for self-drilling anchors would inducea preload in the anchors, but not influence theultimate load capacity of the anchor.

2.2.3 Modes Of Failure For Concrete Expansion Anchorsk There are three postulated modes of failure for a

concrete expansion anchor. They are: ,

, Yielding of The Expansion Anchora.

b. Excessive Displacement Of The Anchor

c. Concrete Cone Failure'

The expansion anchor failure referenced in Item 2.2.3ais defined by the yielding of the anchor materialat the neck of the anchor and the displacement ofthe anchor at failure is controlled by the elasticdeformation of the anchor. The anchor failurereferenced in Item 2.2.3b is controlled by anassigned maximum displacement of the expansionanchor relative to the concrete. Sargent & Lundytypically specifies this maximum displacement to beone anchor diameter for anchors embedded greaterthan 4-1/2 diameters. The failure referenced inItem 2.2.3c is governed by the expansion anchorembedment depth and the strength of the concrete.

Anchors embedded 4-1/2 diameters or less, areusually susceptible to concrete cone failures

~

referenced in Item 2.2.30; therefore, Sargent &Lundy has specified a maximum displacement of3/4 anchor diameters to preclude anchor failure.Anchors embedded greater than 4-1/2 diameters areusually controlled by the mode of failure referencedin Item 2.2.3b. In addition to controlling themode of failure, the anchor embedment depth alsoeffects anchor flexibility, i.e., the greater theanchor 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 inItems 2.2.3a and 2.2.3c; mode failure 2.2.3btypically predominates.

2.3 Idealized Load-Displacement Curve For IndividualConcrete Expansion Anchors

Figure 2 illustrates an idealized load-displacementcurve for individual concrete expansion anchorswith and without initial pre-load. It can be seenthat the initial pre-load level does not effectthe ultimate capacity of the anchor. This facthas been verified by numerous field testo. When aconcrete expansion anchor is pre-tensioneo to alevel P by torquing the nut, the correspondingg

deformation a is taken up by the movement of thef

anchor as shown in Figure 2. When a pre-tensionedanchor *is loaded in tension, it has negligibledisplacement until the external load reaches Pgat which point it follows the original load-displacement curve to the specified ultimate load.Thus, the only effect of pre-tensioning the concreteexpansion anchor is to reduce the ultimate anchordisplacement by an amount equal to A .g

The idealized load-displacement curves for 1/2"diameter expansion anchors and 3/4" diameterexpansion anchors are shown in Figures 3 and 4,respectively. Two load displacement curves aregiven for each anchor diameter dependent upon theanchor embedment depth. Sargent & Lundy hasdefined anchor failure as an anchor displacementequal to 3/4 anchor diameters for anchors embedded4-1/2 diameters or less, and equal to one diameterfor anchors embedded greater than 4-1/2 diameters.

These conservative idealized load-displacementcurves have been verified by static load testsperformed in the field at several nuclear powerstations currently under construction.

3.0 EXPANSION ANCHORED PLATE ANALYSIS PROCEDURES

3.1 Rigid Plate Versus Flexible Plate Analysis

The analysis of expansion anchored plates istraditionally performed using rigid plate theory.

_ . . _.. . -

c-.

~

853 202

5.

The forces in the expansion anchors are computed-

by static equilibrium and the resulting expansionanchor loads are limited to the ultimate capacity

,

of the expansion anchor divided by an appropriatefactor of safety. The ultimate load is typicallyprovided by the expansion anchor manufacturar and afactor of safety equal to 4.0 is used to obtain theallowable design load.

Recognizing the flexibility of the baseplate relativeto the concrete expansion anchor, a load appliedto the concrete expansion anchor assembly maychuse the expansion anchor plate to deform suchthat compressive " prying action" forces are developedbetween the contacting areas. A finite elementapproach is used to properly account for the effectcof plate flexibility and anchor flexibility.

In the following sections it will be shown thatthese " prying action" forces are relieved due tothe flexibility of the concrete expansion anchor(as demonstrated by the idealized load-displacementcurves indicated in Figures 3 and 4) relative to theflexibility 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 thebasis of the rigid body movement of the baseplate.Stresses in the concrete and in the concretoexpansion anchors are calculated by equating theinternal forces to the external forces by maintainingthe compatibility of the linear strain relationshipin both the steel baseplate and concrete bearingsurface.

,

3.2.2 Rigid Plate Analysis For Direct Tension Loads

For direct tension loads, the baseplate displacementsare 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 anchorsare equal to the externally applied direct tensionload. Figure 5 illustrates the displacement cfthe baseplate and equilibrium of the anchor forcesand 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 willinduce compressive forces where the baseplate andconcrete are in contact and tensile forces in theconcrete expansion anchors on the opposite side.

' The concrete expansion anchor forces are calculatedassuming equilibrium of the forces over the entire

,

plate and by assuming compatibility of the linearstrain relationship between the steel and concrete.The design of the. expansion anchor plate assemblyfor 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 expansionanchor plate assembly do not induce " prying action"farces.in the concrete expansion anchors, regardlessof plate flexibility. Concrete expansion anchoredplate assemblies are designed to resist appliedshear loads using the following interaction equation:

f f+ 5 1.0 (1)

where

f = tension force in the anchort

F = allowable tensile capacity of the anchort

f = shear force in the anchory

F = allouable shear capacity of the anchor.y

Equation 1 can be reduced to

F

ft+ vF tI (*

v

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

f

ft+07 5Ft.

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 tensionforce and added to the force due to tension and/ormoment. This approach is conservative compared topublished test results on expansion anchors for, tensile and shear loading, which indicate that theratio P /F is always larger than 1.0.

y.

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 expansionanchors. Figure 7 illustrates these " prying

k action" forces on a flexible plate under a directtension load. It will be demonstrated that theseadditional " prying action" forces are eliminateddue to.the flexibility of the anchor relative tothe 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 expansionanchor plate assemblies referenced in Figure 1.Figure 8 illustrates the typical finite elementmodel of a quarter section of a plate assembly.The plate is modeled using quadrilateral plateelements. The concrete under the baseplate isrepresented by one-way (compression only) springsand the stiffness of these springs is computed onthe basis of the elastic half-space approach.The anchors are represented by truss elements asindicated in Figure 8 and the stiffness of theconcrete expansion anchors are based upon theidealized load displacement curve shown in Figures 3and 4. Pre-load in the concrete expansion anchorsis simulated by an equivalent negative temperatureload.

.

Due to the non-linear nature of the idealized loaddisplacement curve, the plate assemblies areanalyzed by the ultimate design approach in whichthe design loads are multiplied by a load factorequal to four. The resulting expansion anchorreactions are compared with the ultimate capacityof the expansion anchors as defined in Figures 3and 4. The load factor equal to four was selectedto be consistent with the minimum required factorof 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 froma flexible plate analysis approaches those obtainedfrom a rigid plate analysis due to the flexibilityof the anchor relative to the baseplate. Figures 9and 10 show the external force and anchor reactionfor plate Assemblies 1 and 2 listed in Figure 1.These figures demonstrate a minor amount of " pryingaction" force in the early load stages whichdisappears as the load is increased. Figures 3and 4 show that four times the design load issubstantially less than the ultimate load.

4.0 conclusion

The results for the flexible plate analysis listedin Table 2 indicate that a factor of safety of atleast 4.0 is maintained against manufacturer'srecommended ultimate failure loads. This verifiesthat the rigid plate analysis utilizing a factorof safety equal to 4.0 can be used for the designof expansion anchored plate assemblies.

It has been demonstrated that " prying action"is a self-limiting phenomenon in expansion anchoredplate assembly design and does not effect theultimate capacity of the anchored plate assembly.This has been demonstrated for the typical expansionanchored plate assemblies used to support mechanicalcomponents in nuclear power stations for variousexpansion anchor types, embedment depths, preloadlevels and applied load patterns which may typicallybe encountered in such installations.

.

-.

9

.

..

.

853 206- - - - . r-

9

.

.

TABLE 1

Typical Expansion Anchor Installation

and Test Torque Values

-

InstallationAnchor Size Torque Test Torque

Inches ft-lbs ft-1bs

1/2 60-75 45-

3/4 230-270 160

.

9

[.

O

~~

853 207'

6" E 6" '

ch e a m n.c'A E %d # 8E 87 % '8 si u 87' u

~$ B 4= 0. Im 5: 3 %3 T" 5% 3 %"

E d" "3 3E e Ex Oc 5 35e~ Ex Ocub m' a8 "t *2 m; a8 ; '?"

e 8 *bse et 15 3 5 it 81 88 85 as it 81 sEo

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

0 12.8 3.2 6.8 .06TENSION kips

mg 3.2 3.2 0.8 6.9 '.0003

5 kips kips 2.1 12,8 3.2 6.8 <.001g 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 .0603R 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 kips3.2 3.2 0.8 8.7 .0006.kips kips 2.1 12.8 3.2 8.7 <.001x

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 .12E TENSION kips

O 8.4 8.4 2.1 4.8 .0006

{ kips kips 4.4 33.6 8.4 4.8 <.001kips

*o 4.5d 10.15h 0 159.2 7.43 >4 <.12m MOMENT k-in

S 39.8 39.8 2.1 4.8 .0006"

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

,

k 8d 16.0'

n 0 159.2 7.45 >4 <.10to }IOMENT .kain$ 39.8 39.8 2.1 7.6 .001m k-in k-in 4 .'4 159.2 7.53 >4 <.001

' k--in

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

853 208

6m cc-

E. NO 7 EO3 3$ E 97 0o M' sI w7 8:e- x

23 4 ." 8 6 on Sh E BB^5 R 8" 2 .cc 8c 86 t I"h" &? 81 E6 t R"a

SE N Ex x3 3# 5D EE 3 "3# $D EEc c# wE ud $c 3e E3 ud wY nE I$ !M 90 Y9

3 28 .8 8 63 23 En he 28 23 n*St 28 283 et 8& E8 E E2 Em 8u 88 t* E8 em 8un. <w <u <A <p %e <o <c < r-. < zm <o <;

O 19.2 4.02 5.4 .07TENSION kips

m@ 4.8 4.8 0.8 6.9 .00036 kips kips 2.1 19.2 4.02 5.4 <.00]Q kips

4.5d 5.5:0 66.0 3.41 >4 <.070 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 <.001kips

:

O Sd 7.0* 0 66.0 3.38 >4 <.075-

s MOMENT k-in

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

k-in.

0 67.2 9.33 4.3 .13E TENSION kips

h 16.8 16.8 2.1 4.8 .0006

g kips kips 4.4 67.2 9.33 4.3 <.001kips

*a 4.5d 10.15 (

A 0 512.8 8.87 >4 <.13e MOFENT k-in

5 128.2 128.2 2.1 4.8 .0006E k-in k-in 4.4 512.8 9.21 >4 <.001

k-inI

d 0 67.2 9.44 7 .11x . TENSION kips

: 16.8 16.8 2.1 7.6 .001N kips kips 4.4 67.2 9.44 6.7 <.001x kips: 8d 16.0. 0 512.8 9.14 >4 < 11s .

r .

MOFENT .k-in

N 128.2 128.2 2.1 7.6 .001

h k-in k-in 4.4 512.8 9.55 >4 < . 001

k-in

a

853 209

*

_ __

i

1 "|_ u _lh"j--7

iha 1".-

I.

.

# 1 I A

. e i[H -o- - 0-

i

dI |

40 --& *3

|o

g 1 J-

*8 I e s,

, h"' -o- - F y - 0-

9L ]

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-'

a s"h-- ,:, _ - - .._

- o--- ?- H_ ,

I Lg*e =

|m -

1 m

h*

7 '{ -- { n - +-- -

,' I I L = ie m i i

: - y - - H,r =, I _. _ __ - c _ ;s ', H -

{g

ASSEMBLY NO. 3 ASSEMBLY NO. 4Plate 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 ASSEMBLIESFIGURE 1-

.-- :

853 210

..

. .

*.

.

\

.

d .

\ -

[P _ __

Corresponds toPre-Load

I

SpecifiedP1 Pre-Load P.

1oec

3 Corresponds toNo Pre-Load

i

I

i =._

0 At ' Att~

@OriginforPre-TensionCasem.-m-...

''

Displacement'

P = Ultimate Anchor Capacityu

-~~ Pg = Specified Pre-Load.

bj = Initial Displacement with no Pre-Load'

k = Displacement at Ultimate Anchor Capacity,

FIGURE 2

IDEALEZED LOAD-DISPLACEMENT CURVE FORCUNCRLir, t.APAN610N ANCHORS

_ . . . - . . . . --

953 ,1

.

*.

6. - p 5.5k With Pre-Load- =

u'

5-- Without Pre-Load.

'

4---,

m

---- L x Design Loada

4$ 3--- ----

|~

Pre-Loa5 2-o 2.Ik |A -

|1-- -- - -- - --- -- - - - - - De s i gn Lo a d

0 ' ' ' ' '

*

1 .2 3 .43-d4 >

Displacement (Inches)

(a) 4.5 d Embedment

Pu= 7.0k With Pre-Lead7 _ ___

Without Pre-Load_

5- I-

.

-.

ma 4--a

yei __ ____ 4x Design Load3

Iee 're-Load -

0 2- --

I" 2.lk i

1- ._ _ _ _ _ _ _ _ _ _ _ _ _ d - De s i gn Loa d' ' ' '0.1 .2 .3 .4 .5 .c

ldi'Displacement (Inches)

' ~

(b) 8d Embedment

Figure 3

IDEALIZED LOAD-DISPLACEMENT CURVE FOR 1/2" DIAMETEREXPnWSION ANCIIORS

853 212

- i,

g-- - -[- 4x Design Load9 --. 8 -- -

N With Pre-Load'

7 ,,'

6 -' Without Pre-Load.

5 -P r e _L o a d

^

a -

4- 4.4k'

*j .

3 -- |~

.

] 2--- - - - -- - - - - -|- - De s i gn Loa d ,oA 1 |

I''' ' ' ' ' ' '0,

.2 .4 .6 .8

Displacement (inches) 3 d4(a) 4.5d Embedment

o$ *

Pu= 36.0k16 - -- -

15 With Pre-Load

Without Prc-Load

I

i

10 --|

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

ena |.

ei ix

I-

m5

Pre _ LoadIo

_ ia4 - 4.4k

|.3

-

- - - - - - ~ ~ - - - - - - - - - - L - De s i gn Loa d2 +- -I

1---

' ' ' ' ' ' ' '0 O.2 0.4 0.6 0.8.

ldDiaplacement (inches). .__

- (b) 8d Embedment

FIGURE 4

IDEALIZED LOAD-DISPLAGEMENT CURVE FOR 3/4" DIAMETER

. . EXPANSION ANCIIORS

. ,

853 213

t

'

Anchor .

*

*////// //////// ////||||-

~

Base Plate\

Plate iaLoaded 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 fr 1y u

l Cc4

k l-: =

STRAIN DISTRIBUTION

.

NTg \

fcs

C bJL ,

STRr.:SS DISTRIBUTION

.

Unknowns are cc& kD+d-k

=C Ct C kf =E C T=AE C C= P,febc c c ss t

C - T = 0 --([)Ch-T (f)(D+d) =M

Where:

M = Applied moment d = Edge distance of anchor

c = Compressive strain in concrete A - Area of anchorc se = Tensile strain in anchort

- k = Length of compression block

b = Width of plate.

f = Maximum stress in concretecE = Modulus of elasticity of steelsE = 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\

\ b -(P/2 + Q) h (P/2 + Q),

'

0'

0 yqyqo

/[ ^'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"# ,

*

LI :-

.

I

o

. Anchor,

/

/--

in,

w

u

:WNm@e

U j~

t6@ 3/4" = 4.5"-

.

.

h j i

bg ONE-MAY CO!!PRLbSION-

'| 5 [ II SPRING REPRESENTING| I

'

l 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.

EEw

Z 4,9 x -

U8 .a:

3LEGE_!_'_O

oz ---- Anchor reaction i f there ~,fPre-Load was no prc-load and no- . ,

2 p' prying action.

/ Anchor reaction if there was- ----

/ pre-load but no prying actice

/ Anchor reaction includina1.0 / the effect of pre-load and

/ prying action./

//

l.o 2.0 3.o 4.0 50 aoAPPLIED FoTICE PER ANCHOR (KIPS)

_ FIG..U._RE9 ,

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

Plate Assembly

..-

a e # g e

853 218.

.

.

... .

. .

-.

7.0

.

6.0,

-

$m#

SD2O /p .r-Pro-Load

,/. / .y . - - . ..- _ ..

w /w 4.0 /2 /o /x -

o /Z /4

3.o / LEGEND/

/ 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 includingy the effect of pre-load and

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.nchoredPlate Assembly

.

853 219 ..