on the behavior of fasteners and plates with holes proc. asce

8/10/2019 On the Behavior of Fasteners and Plates With Holes Proc. ASCE

1/48

Lehigh University

Lehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1-1-1965

On the behavior of fasteners and plates with holes,Proc. ASCE, Vol. 91, ST6, 1965, Publication No.

280J. W. Fisher

Follow this and additional works at: hp://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports

is Technical Report is brought to you for free and open access by the Civil and Environmental Engineering at Lehigh Preserve. It has been accepted

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Recommended CitationFisher, J. W., "On the behavior of fasteners and plates with holes, Proc. ASCE, Vol. 91, ST6, 1965, Publication No. 280" (1965). FritzLaboratory Reports. Paper 160.hp://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/160
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2/48

~ ~ ~ ~ ~ -

LEHIGH UNIVERSITY LIBRARIES

1

I

1111

11

1

11111

1111111111111

3 9 8976 8 2

OF

f

ST

f

l

lE

by

John W

ish

ecember

96


3/48

ON

THE

BEH VIOR OF F STENERS

N PL TES WITH HOLES

by

John

W

Fisher

This work was carried out as part of

the

Large Bolted Connections Project sponsored

f inancial ly by the Pennsylvania Depar tmen t o f

Highways

the Department

of Commerce Bureau

of Public Roads

and

the American ns t i tu te of

Steel Construction

Technical

guidance is

pro-

vided by

the Research

Council on

Riveted

and

Bolted Structural Joints

ri tz Engineer ing Laboratory

Department

of Civi l Engineering

Lehigh

University

Bethlehem Pennsylvania

December

1964

ri tz

Engineering

Laboratory

Report

No 288 18


4/48

1 BSTR CT

T

L E

F

CON TEN

T S

2 INTRODUCTION

3 TENSILE STRESS STR IN REL TIONSHIP FOR

PL TES WITH

HOLES

1 Plates

in

Tension

2 Description

of Tests

3

Development

of

Stress Strain

Relationship

4 A

General

Stress Strain

Relationship

5 Evaluation

of

the

Parameters

which Influence

the Stress Strain Relationship

6

Comparison

of Theory and

Experimental

Data

4

SHE R DEFORM TION REL TIONSHIP FOR MECH NIC L F STENERS

1 The Behavior

of

Mechanical

Fasteners

2

Assumptions

3 Evaluation of

Parameters

4 Comparison of Computed and Experimental Resu lts fo r

Single Fastene rs

5 SU RY

6

CKNOWLEDGEMENTS

T BLES ND FIGURES

8

REFERENCES


5/48

S T R A e T

In

this

repor t

the behavior of the

individual

components

of

bolted or r iveted joints is discussed. General s t ress s t r in relationships

are developed for

a

plate with h oles in the el st ic range and beyond.

he

relat ionships

are

applicable to

low

al loy

low carbon s teels

such as

A7

A36 A242 A44 and A44l.

hey are able

to

accommodate various

specimen

geometries. he analyt ical models are

compared

with

experimental

results

and

show good

agreement.

In

addit ion a

load-deformation

relationship is developed

for

mechanical fasteners

in

shear.

he

shape

of the

curve

was

observed

to be

governed

by the

ultimate

shear

strength and

two

empirical parameters.

he

analyt ical model for

the shear-deformat ion relationship

of mechanical

fasteners was

in excellent agreement

with the

tes t data.


6/48

2. I N

TROD

U C T ION

Several

theoret ical

studies

of

the

load

par t i t ion

in riv ete d

and

(

1 2 3

4)

bolted joints in and beyond the elas t ic

range

were reported recently ,

Solutions

were achieved

by

es tabl ishing

the

relat ionship between deforma-

t ion

and load for the jo in t components throughout the

e las t ic

and

in-

elas t ic regions.

Both Francis

1)

and Rumpf(2)

used actual load-deformation curves

derived

from

t es t s

of

specimens which

simulated

components

of the

specimen

proper. However, this

approach has seriqus drawbacks. The semi-graphical

construction used

by Francis

and

Rumpf is convenient only for the analysis

of

short jo in ts

Analysis of longer

joints

is extremely tedious

and time-

consuming, i f

not

impossible. In

addition,

i t is necessary to establ ish

load-deformation

curves

for each

geometrical

specimen considered

by

t e s t

in g plate specimens.

A more ef f ic ien t means

of solution

was sought.

I t

was con-

sidered desirable to develop analyt ical expressions to d esc rib e th e load-

deformation

relationships

of

the component

par t s These

were

intended to

be adaptable to

di f fe ren t

mater ia l p rope rt ie s and

geometric configurations.

Such

expressions would

provide a means of extrapolat ing and interpolat ing

to

various

geometric forms without requir ing

the

extensive tes t ing neces-

sary w ith the previous method.

This report describes

t es t s of th e

component par ts of joints and

the development of sui table mathematical models which can predict the load-

deformation charac te r i s t ics of the component par ts The study is

confined

to

low al loy,

low carbon

s teels

such

as

A7,

A36 A242 A44 or

A441.

-2-


7/48

Although the mechanical fasteners

considered

are primarily A 5

high-

strength bolts Al41 s t l r v ts

an d A 9

high strength bolts are also

studied.


8/48

3.

TEN

S I L E

S T RES S S R A I N

R L A T ION S H IP S

FOR

PL T S W I T H

H L

E

S

1.

PL T S

IN T NSION

ny plate with

one

or more fastener

holes

in

an i nt eg ra l p a rt

of

a

mechanically-fastened

jo in t .

s

was

noted in

the

introduction

the load

par t i t ion

and

strength of

any

such jo in t

can be

determined only

i f the

load-deformation relat ionships of the

fasteners

and plates are known

These

relat ionships must

be

determined

experimentally.

The

standard

p la te c a li br at ion

coupon

which yields the load-

deformation

relat ionship

for the

connected plate i s shown in Fig. 1. The

p la te c a li br at ion ~ o u p o n should be

cut

from

the

same

mater ia l

as the

t e s t

connections.

I ts

geometrical properties

should be

s imilar :

the

thickness

gage pi tch

and

hole

diameter

must

be

the same as those of

the

t e s t or

prototype connections.

I f a

duct i le

p o l y r y s t l l ~ n e metal bar is loaded continuously

and the

result ing

stresses are

plotted as

a function of the s t ra in the

character is t ic s t ress - s t ra in as a

function

of

the

s t ra in

th e

character-

i s t ic

s t ress - s t ra in relat ionship

shown in Fig. 2 is observed.

This curve

is

character is t ic

of

most s t ruc tura l

s tee ls . The

material f i r s t s t retches

e la s ti ca ll y u n ti l the load reaches a value a t

which

permanent deformations

s tar t

to

develop.

After

a

short

t ransi t ion

curve from

the

e las t ic

to the

plast ic

range

of s t ra ins a re la t ively f la t plateau is reached during

which the

bar con tinue s to stre tch

without

any

appreciable

change in load.

When the s t ra in is about

ten

times the

yield

s tra in

the

material begins

to

The data is plotted to two different l ongi tudina l s ca le s to more clear ly

des cr ib e th e behavior in the plast ic regipn.

-4-


9/48

-5-

strain-harden

and

addi t ional s t ra in results in an increase in

load.

This

increase

continues unt i l

the

ult imate tensile

st rength

i s reached. There

af ter the material begins to neck

and

f inally ruptures.

When the

standard

p la te c a li br at io n

coupon i s loaded

con

t inuously

and

the average s tre sse s a t the net sect ion are

plotted

as a

function of the

average

s t ra in between

the

two

holes the s t ress-s t ra in

relationship

shown in Fig.

i s observed.

The

average s t ra in

between the

two holes has been

computed

as the

average

change in length divided by the

pi tch p.

Also shown

are the

points at which the

average s ta t ic

yield

stress

is

reached

on

the net

and

gross

sect ions.

The

material

f i r s t stretches e la s ti ca ll y u n ti l

the

load reaches

a

certain value

at which permanent deformation

s tar t s

to develop around

the holes. However there is no y ie ld p la te au

at

which the material

stretches without

an

appreciable change in load as there is for the plain

bar.

Strain-hardening

begins a lmost immedia te ly

and

addit ional s t ra in

is

accompanied by an

increase

in

load.

This

continues

un t i l

the ultimate ten

s i le strength of

the

mate r ia l

is reached

a t

the net

sect ion. The

specimen

has necked considerably a t the net sect ion

and

ruptures almost invariably

a t

t he u lt imat e load.

I t can

be seen

that the

yield

plateau

observed

dur

ing

the

t e s t of

the standard bar

coupon

over an 8 in . gage

length

did not

occur in the

plate

cal ibra t ion

coupon

when yielding

star ted at

the

net sec

t ion

around

the holes

and

the plateau did not appear when the yield level

was reached

in

the gross

sect i6n.

That

the

presence o f h oles in a s tee l plate i nf luence s the

s t ress-s t ra in relationship can

be

seen

in

the

comparison

in Fig. of the

resul ts

of the standard

pla te

cal ibrat ion coupon t es t with

the s tress-


10/48

s t r a i n re la t ionship of the

standard

f l a t

bar coupon

o

E l a s t i c

s tudies have

shown t h a t the e f f e c t of the s t r e s s concentrat ion a t the

holes

is not uni-

formly

d i s t r i b u t e d

around the hole but occurs

a t

~ i s r t points on the

boundary of the hole 5 a s shown

schematical ly

i n . F i g . Sa. The contour

l ines of r a d i a l

s t r e s s computed according to e l a s t i c th eory are shown. In

Fig. 5b

the

s t r e s s e s perpendicular to l ine A A are compared

with

th e

s t r e s s e s

in

the

bar some distance from the hole

o

F i r s t yield begins a t

the points of maximum s t r e s s concentrat ion around the hole . As

the

t e n s i l e

s t r e s s

i s

increased, yie lding spreads and very soon tends to progress along

two

comparatively

narrow

s t r i p s

symmetrically

s i t u a t e d

with

respect

to

the

axis of load and

a t

angles of approximately 45

degrees

with t h e

d i r e c t i o n

of the load 5,6

as

shown schematical ly

in Fig. 6. This

type

of behavior

has been

observed in

both

A and

A44 s t e e l specimens

a

Fo r many

pi tches

and gages,

the yie ld

s t r i p s which form symmetri-

c ~ l l y

about

adjacent holes w i l l overlap

as

indicated i n Fig.

6b

and

i n t e r

ference of the

s l i p

bands

takes place.

The

photographs

of

t yp ic al y ie ld

pat te rns

shown

i n

Fig. 7

c l e a r l y indica te

t h a t i n t e r f e r e n c ~ has occurred

G

Because

compatibil i ty a t gra in boundaries i s necessary, s l i p occurs in

several

s l i p

systems. This causes severe deformation of

the

c r y s t a l

l a t t i c e

of each grain

which

r e s u l t s in

the

s tr es s r is in g

continuously.with

6

n c r e s ~ n g

s t r a 1 n

A number

of

i n v e s t i g a t o r s

have

developed a n a l y t i c a l

models for

the plain p l a t e .

Hollomon 7

developed an

expression

for

the

re la t ionship

between t r u e s t r e s s and natural

stlrain. Nadai 8

proposed an analyt ical

e x p r ~ s s i o n for the c onvention al s t r ~ s s s t r i n curve

for

use i n s t u d i e s of

p l a s t i c

buckling.

Later

Ramberg and Osgood 9 suggested a s l i g h t l y

d i f f e r e n t a n a l y t i c a l

expression.

Unfortunately, none of these

are

s u i t


11/48

able

for th e s ta ndar d

plate

cal ibrat ion coupon

because they are

unable

to

account for the

varia t ions

in mater ia l p rope rt ie s or plate

geometry

no r

did

they f i t the t e s t data.

The semi-graphical solution of Francis l and Rumpf 2) uses the

actual

s t ress - s t ra in relat ionship for the standard

p la te c a li br at io n

coupon. Because

the

semi-graphical analysis of long jo in ts is

extremely

tedious

and

time-consuming, i f not impossible, there i s a need

to develop

an

analyt ical model

which

wil l describe

the

s t ress - s t ra in behavior

of

the

coupon throughout

the

e las t ic and ine las t ic ranges. Ideal ly this model

should account

for

varia t ions in both

material

proper t ies

and

plate

geo-

metry.

2 DESCRIPTION OF TESTS

The specia l p la te c a li br at io n

coupon

tes ts were conduct ed by

h 10,11

t s t ~ n

a p a t e 0 t e same materla use 1n arge JO lnts

pla tes

tested

had

a

width equal

to

the gage distance

g,

a

thickness

t ,

and two

holes

dr i l led

a

distance p on

center

as shown in

Fig.

1.

The

ten-

sian-elongation data was recorded for the material with t he d is ta nc e be t -

ween tIle

hole

centers

as

gage length, which was equal to the

pitch

length

in

large

joints .

The tes t specimens, described

in

Table 1, were flame

cut

and

then

milled

to the desired width.

The dimensions of each ca l ibra t ion

specimen

are l i s ted along with

th e

measured

ult imate

t ens i le strength of

the

plate

and the

t ens i le strength determined

in the tes ts of s ta ndar d bar

coupons.

The

s tee l

plates for

specimens

A7-1

to

A7 6 were in .

wide

universal mil l s t r ips of

thickness

varying

from

9/16

in .

to 7/8

in .

All

s t r ips

were rol led from the same

heat .

The s ta t ic yield poi nt s v ar ie d

-7-


12/48

-8-

from 32.0

to

34.0 ksi

and the

ult imate tensi le s t rengths

from

63.5

to

65.3

ksi .

A7

s tee l t e s t specimens 7 31 to 709le were cut from 24 x 1

in .

uni

versa l

mill p la te s rol led from

the

same heat . Their mean s ta t ic yield

point

was 28.2 ksi

and

the mean u lt ima te s tr eng th 60.0 ks i . A44 s tee l

t e s t specimens PE4la to

PEl6l were cut

from 26 x

1 in . universa l mill

plates rol led from

the same

heat .

The mean

s ta t ic yie ld

point was 43

k s i

and the mean ult imate

s t rength

76

ks i .

Additional

deta i l s

.o f th e sta nda rd

bar coupon tes ts

are given in

Refs. 1 and 11.

The specimens were

tes ted in

800 000 lb . screw-type

tes t ing

machine.

In

the e las t ic

range

t he c ro ss -h ead separation was

0.055 in .

per m in. while

in

the

ine las t ic range

a speed of 0.40 in . per min. was

used. In the e las t ic

range

equal

load

increments

were

applied and the

elongation

center- to-center of

the

holes was meaRured with a s l ide bar

extensometer. Strain increments were used in the ine las t ic

range_

Elonga

t ions were

measured

on

one edge

of

the specimen with the

tes t ing machine in

motion.

When

the

desired s t ra in

increment

was

reached

the

cross

head

mov emen t w as

stopped

and the

load

was

allowed

to

s tab i l ize

to a constant

value.

Elongation measurements and changes

in

hole

diameter were

then

measured. This procedure was repeated unt i l

fai lure

occurred.

3.

DEVELOPMENT OF

STRESS STRAIN RELATIONSHIP

In order to

es tabl ish

the

behavior

of the plate

element in

a

bolted

jo in t

the s t ress s t ra in re la t ionship of the mater ia l was deter

mined fr om a s tandard p l at e c a li br a ti o n coupon as shown in Fig. 1. The

data

from

such

a t e s t

is

plotted

in

Fig.

3.

The

re sp on se o f

the

plate

cal ibrat ion

coupon can be

idealized as

shown

in

8.

Under

i n i t i a l

loading

the material remains e las t ic and the

s t ra in

increases

l inear ly


13/48

-9-

with the

applied

s t ress .

The primary cr i te r ion in the

choice of

a

s u it ab l e a n a ly ti ca l

model

to

d efine the s t ress s t ra in

relat ionship

of

the p la te c a li b ra ti on

coupon is

the

degree

of

correlat ion between th e observed t e s t data and the

corresponding

values calcula ted

from

the

analy t i ca l

expression. I f

possi-

ble

is

desirable to obtain

a

single general relat ionship

which

wi l l

take into account a l l

the

physical

and

geometrical fac tors

which inf luence

the

s t ress s t ra in relat ionship.

The

major variables

inf luencing th e s t ress

s t ra in relat ionship of the

plate

cal ibrat ion coupon

are:

1 the

width or

gage

of

the

plate

g,

2)

the

ho le d iame te r

d,

3)

the spacing or pi tch

of

adjacent

holes

p,

4)

the yield point of the coupon

0

Y

5 )

the ultimate tens i le

strength

of the coupon

au

6)

the

type

of s tee l

and

7)

the

speed

of

t es t ing

of the

p la te c a li b ra ti o n

coupon.

The ra t io of the net plate area to the gross plate

area,

governed by the f i r s t two

variables

g and d, i nf lu en ce s th e shape of the

s t ress s t ra in curve see

Fig.

3). In

a

plate having

a large

width

g, the

hole , i f

small,

wi l l have

l i t t l e inf luence on the

average s t ress s t ra in

relat ionship.

However, with increasing plate w idth-g, the resis tance to

necking

is

greater .

When the

hole

spacing

p,

the

third var iable,

is

close , in te r

ference occurs between the

s l ip

bands.

was

pointed out

ear l ier this

wi l l

a lso influence the

s t ress s t ra in

curve. When the

holes are

placed

far ther

apar t ,

the i r ef fec t

on the

deformation occurring

between the two


14/48

-10-

holes

is

probably

lessened.

Hence, the

plate

calibra t ion coupon

wil l

approach the behavior of the standard coupon

without

holes.

In

a

bolted or

riveted

jo in t

the

f i r s t

three var iables,

g,

d,

and p, wil l be

l imited

to practical ranges. inimum gage and pitch

distances

are usually

speci f ied.

I f

not,

a re la t ive minimum can be es t i -

mated

from

the dimensions of pi tch and gage, which

can

be estimated from

practical considerations i f they are not speci f ied.

he fourth variable , the yield point of

the

p la te c al ib ra ti on

coupon, is influenced by residual s t resses and s tress concentrations in

the vicinity of the holes which cause

non-l ineari ty

in the p la te c al ib ra

tion coupon before i t re ache s th e yield

point

of th e standard bar coupon.

he t es t data indicates that the

point

of

deviation

from l inear i ty for the

p la te c a li br at ion coupon is approximately equal to the s ta t ic yield

point

of the standard coupon t e s t Hence, the influence of residual stress, con

centrat ions can be accounted

for

by using this lower

yield

value.

he ultimate strength of

the

perforated

p lates at the net sec

t ion, the f i f th variable,

is usually

higher

than

the

coupon ultimate

strength

of the main pla te . I t

is well

known from early

experimental

work

that

the

ultimate strength of

a

cyl indrical bar, having

a

short circum

ferentia l groove is considerably higher

than

th e u lt imat e

strength

of

a

round

bar

because normal necking

i s prevented in the

const ri ct ed port ion 6 .

I t

is

to

be

expected

that

a

f l a t

plate

having

a

hole

wil l

behave

in

a

simi

lar manner. he free l a tera l

contraction

which must accompany an axial

extension canno t develop and a higher

ultimate

strength results This

behavior was reported in Ref. in work on r iveted

jo in ts

I t was found,

part icularly

at th e smaller gage or r ive t spacings, tha t the strength was


15/48

greater than. one would

normally

expect on the basis of the jo int geometry.

The increase

attr ibuted

to the

reinforcement

or b i ~ x i l stress effect

-11-

created

the

closely-spaced holes.

s the

gage

is

increased,

th is e ffe ct

is less

noticeable.

Addit ional informat ion on th is behavior is given in

Ref. 13 where th e efficiency

coeff ic ient is discussed.

The

type

of s teel the s ix th var ia bl e, is obviously import an t

and is

re la ted to

the

fourth

and f i f th variables. Two

different

grades

of

s teel

and

A44 were

considered

in th is study. The u lt ima te s tr eng th

of

the

p la te c a li br at ion coupon is compared in Fig.

9 with the mean

ul t i

mate

strength

of

the

same

material

given

by

standard laboratory bar

coupon

tes ts . The rat io

of

these

strengths

is

greater

with

the

A44 s teel . In

general,

th e behav io r of these tes t

specimens

was similar to t he behav io r

reported

by

other investigators

6,12)

The seventh and l as t variable , the speed of test ing, may

also

influence the s t ress s t ra in re la t ionship. The

dynamic

s t ress s t ra in

relationship

was

used

because

the

analyt ical

model

was

needed

to aid

in

predict ing

the

ultimate strength

of

the bolted joints .

Genera lly , th e

bolted

jo ints f a i l when load is being applied and thus

the speed of

t es t

ing p robably

affects the

tes t resu l t s .

The following assumptions were made in the development of a

s ui ta bl e ana ly ti ca l r el at ion sh ip based in part

upon

the above-mentioned

factors:

1) stress is proport ional to strain when the s tra in is

less than

the yield

strain

2)

the average computed e la st ic s tr ai n

is based

on th e

gross s ec ti on a re a,

3) th e

deviat ion from

l in ea ri ty i n

the

plate

calibra t ion

coupon can be approximated by considering the

s ta t ic

yield point of

the standard bar

coupon,


16/48

-12-

(4)

(5

(6 )

the s t ress s t ra in re la t ionship beyond the e las t ic l imi t i s

based

on the dynamic s tr es s- st ra in measu remen ts o f t he

plate cal ibrat ion

coupon,

a t


17/48

a r e a .

y ie ld in g commences i n

th e

net

s e c t i o n o f

th e p l a t e the

l in e a r r el at io n sh ip between s t r e s s

an d

s t r a i n i s

no

longer v a l i d . A

r e -

la tio n s h ip

must be

developed

t h a t follows a p a t h

from

B to C

as

i n Fig. 8 .

Furthermore, i t should

f i t th e

boundary

c o n d i t i o n so

th a t a t

- 1 3 -

where

The following

e x p r e s s i o n wa s

s e l e c t e d :

{ J

= e E + K l - e -Q l3

y -

cr

a ve ra ge s t r e s s

on the net a r e a ,

3)

Q

e m p i r i c a l

pa r a m e t e r s ,

e = base

of n a t u r a l logarithm,

an d

e -e

y

=

i n e l a s t i c

s t r a i n =

t - e y p

Equation

3

was s e le c te d a f t e r i n v s t i ~ t i o n

o f

s e v e r a l

o t h e r

a n a l y t i c a l

models, i nc lu d in g t ho se r e p o r t e d

i n

Refs. 7, 8, an d 9. \ This equation

e x h i b i t s

th e

following c h a r a c t e r i s t i c s :

1) as

th e

i ne la st ic s tr a in approaches z e r o, th e s t r e s s

approaches

th e

y i e l d s t r e s s cr ,

which

i s the l i m i t o f Eq. 1.

y

2) with a p p r o p r i a t e values o f Q

an d th e

term e -

a

a pproa c he s zero as

th e

s t r a i n approaches t h e ~ l t i m a t e

s t r ai r i

u t

3)

th e e qu at io n s a t i s f i e s t he e xp er im e nt al ly observed

behavior i n t h a t th e s t r e s s cr

i n c r e a s e s

a t a

d e c r e a s

in g

r a t e as

th e

u ltim a te s t r e s s

1

i s approached.

u

t

Taken to g e th e r , Eqs. 1

an d

3

d e s c r i b e the.

complete r e l a t i o n s h i p

between

s t r e s s an d s t r a i n from P o i n t A to P oi nt C

i n

F i g . 8.


18/48


19/48

A fter obta in ing the values of a S, and K

from

the t e s t data for

A7 and s t e e l specimens with l arge d i ff er ences in p la te width, the

f i n a l analysis was made by evaluating

these

c o e f f i c i e n t s i n terms of

the

known boundary

conditions.

The

c o e f f i c i e n t

K was evaluated from the

boundary

condit ion

a t

e

=

u l t

=

a u l t .

Therefore, from Eq.

3

-15-

cr

7

which

yie lds

J

u

J +K

Y

8

Therefore K cr

-cr

where cr

=

ultimate

t e n s i l e

strength a t the

u y u

net

sect ion of a perforated p l a t e and a

yie ld

point a t

the net

sect ion.

y

The parameter a

which

varied

from p l a t e

to

p l a t e

was f i n a l l y

evaluated

as a function

of

the geometry and

mater ia l

propert ies . I t was

evaluated

from the regression

c o e f f i c i e n t

as

where

O = (cr a --L

u

y

g-d

g

the

width of

the specimen

th e d iame te r

of

the

hole .

9

The r a t i o gj g-d i s i n e f f e ct a r a t i o of

the gross

area t o

the net

area,

and

a

could

be wri t ten

as

(cr cr A /A

u Y

g

n

The

parameter

was found

to

be a constant common to

a l l

materials

and

conditions.

I t

was

evaluated

from

the

r eg r es sion analysi s

as

3/2 10

The f inal general relationship for s t r e s s s t r a i n applicable

to

both

A7

and A s t e e l and various specimen

geometries was found to

have

the form:


20/48

-16-

3/2

a = a a

[l_e- au-ay g/ g-d e/

P

J

y u y -

where

p

pitch or distance

center

to

ce nter o f the holes

11

This

equation

is

app lic ab le f or

values

e

to ta l deformation in the

pitch

af ter yielding

on net

section

elp

e p la st ic s tr a in

For stresses

lower

than

the

y ie ld p oin t, Eq.

1

i s

applicable.

Equation 11

takes

into

account

variations

in

mater ia l propert ies

cr

and

geometri

u

y

cal

configuration

of

the plate

calibra t ion

coupon

g, p, d

6. COMPARISON OF THEORY AND

EXPERIMENTAL

DATA

The tes t

data

for the

plate

cal ibra t ion specimens of different

t hi ckne ss a re plotted

in Fig. 11.

The

load

acting on the

specimen is

plotted as

a

function of

the

measured

elongations,

e,

from center to center

of the holes. Also

shown in Fig. 11 are the computed

load-deformation

curves

based on

Eqs. 1

and 11.

The

agreement between

the computed and

experimental r es ul ts c le ar ly

shows the

applicabil i ty of

the mathematical

models.

Equations l and 11

are further

compared with

the tes t

data for

several l n A

s tee l

p la te in Fig. 12.

The

average st ress

on

the

net

section

i s

plotted as

a function

of the average strain

.for

the

material

between the hole centers .

Each

plot corresponds to a di f fe rent plate

calibra t ion

tes t The

principal

difference

between

the

different

speci-

mens was the

gage

width g.

Also

shown

in each plot is the s ta t ic yield


21/48

point,

determined from

the standard

bar coupon t e s t s This value is

y

reached t

the net

section cr )ne t .

In

addition,

the

average s tress

on the

y

net sect ion t which the

s t t ic

yield value i s

reached

on the

gross section

is indicated as cr gross. The

~ t n r

coupon ult imate strength is ind i -

y

cated as

cr

)coup. For l l cases,

the

strength

of

the perforated plate

was h ighe r t han

the

coupon

ult imate strength .

direc t comparison of

-17 -

these

values

is given

in

Table 1.

The s t t ic y ie ld p oin t, was

deter

y

mined from

coupon

tests as 28.2

ks i

In

the A7 ste el te sts d was maintained

constant

t 0.94 in . and

t he t hi ckne ss t

1 in . Gage g varied from 2.92

to 6.88

in . The theoret i-

cal line

is in excellent agreement with the

tes t data.

A similar comparison is made with A440

s teel t e s t

data in Fig. 13.

The s t t ic yield point

of the

A440 material was 43.0 ks i The gage g

varied

from 3.32

to

6.94 in and the hole

diameter

was aga in const an t

at

0.94

in .

Again the

computed l ine is in excellent agreement with the t e s t

data.

In

the comparisons made in Figs. 12 and 13,

the

pitch p was

constant t 3.5

in.

A special

series

of t es t s performed for an e r l ier

study was used to

evaluate

the effect

of

pitch.

The

pitch

p was varied

from 2.5

to

6 in . while

the hole

diameter and gage width

were

constant .

The computed l ines

are

cumpared in

Fig.

14 with the t e s t data for the

2.5

in .

and

6 in .

pi tch

specimens.

The

agreement

in

l l

cases

is

good.

Figure 14 indicates tha t a yi el d p la teau is approached as

the

pitch between the holes is increased. Figure 5 is a schematic

of

the

el s t ic and in i t i l pl st ic region

for the

plate

cal ibrat ion coupon. The

smooth

t r ns i t ion

curve

between

the

in i t i l yield on the net section,


22/48

-18-

0 net , and the onset o f y ie ld in g on the gross

sect ion, cr gross,

is

to

be expected

as discussed e r l ier For the larger

pi tches ,

the ho les

should

have

a less influence on the

average s t r in and

one would expect a yield

plateau

similar

to

those encountered

with

t he s ta nd ard bar coupon.

s the

distance between

adj acen t hol es is dec re ased, th e sl ip l ine interference

wil l become more pronounced with. a consequent decrease

in

the length of

the

yield

plateau

for the gross section area between

th e h ol es. n

examination

of Fig.

indicates

that

th is

was

the case.


23/48

4

SHE A R

FOR

D E

FOR M A T ION

ME C H A N I C A L

R E L A T ION S H IP

F A S

T E N

E R S

1. THE EH VIOR

MECH NIC L F STENERS

In the

development

o f l oa d -d e fo rm a ti on

r e l a t i o n s h i p s

f or mech

a n i c a l

f a st e n e r s i t is g e n e r a l l y assumed

that

the d ef or ma ti on o f th e f a s

t e n e r

wil l involve

the

ef fec t s

of

s he a r i ng, be nding, an d be a r i ng of the

f a s t e n e r

as

w e l l as the l o c a l i z e d d ef or ma ti on o f th e

main

and

la p pla tes

I f

a

s in gl e f as te n er jo in t is loaded as

shown

in

Fig. 16 ,

the

relat ive movement of

p o i n t s a

an d

b

is influenced by the s h ea r , be nding,

an d be a r i ng

o f

the f a s te n e r . -Fig. 7

shows a

deformed

b o l t

i l lus t ra t ing

this b e h a v i o r . The connected members wil l

a l so deform

an d th e relat ive

movement of

a , an d

b, i f measured a t

th e edges

of

the

pla te wil l

be

g r e a te r

as

a

resu l t of th e compression

of

the

members be hind

th e f a s t e n e r .

For

th e e las t ic

c a s e , Coker

has shown t h a t

th e

lon gitudinal

compressive

s tre ss in

the

plate

d i e s away

a t

a d i s t a n c e

of

ab ou t tw ic e

the

h o l e

d i a

meter from th e edge of th e h o l e 1 6 ) . Hence, t he b ea rin g

de forma tions in

the plate a re l o c a l i z e d . In the

si d e

view of th e jo in t the y are i n d i c a t e d

by

th e

dark e dge s.

In measuring the relat ive

movement o f a

an d b , th e

de

forma tion

of

th e

f a st e n e r

an d plate

a re

combined because

t h e r e is no r e a -

so n

to s e pa r a t e them.

Two type s

of c o n t r o l

t es t s can

b e c on du ct ed with coupons to

de te rmine

th e

load-deformation relat ionship

In

on e type

th e

b o l t s ar e

subjected

t o double shear by p l a t e s

loaded

in

t e n si o n

as

i n d i c a t e d

in

F i g. 18. In th e ot he r c o n tr o l tes t the b o l t s are

subjected

to

double

shear

by a pplying a

compressive

load

to th e

p l a t e s

Fig. 1 8). s long as

th e shear j ig plate is

r e a s o n a b l y

s t i f f an d

nothing

ot he r

than

l o c a l y ie ld -

-19-


24/48

-20-

ing du e

to

b ea ri ng o cc ur s,

an y

p l a t e e l onga t i ons

o t h e r

than those

du e to

bearing a re

n e g l i g i b l e .

The

load-deformation

r el at i ons hi p

fo r

th e

two

c o n tr o l

tes ts

a re

shown

i n

F i g . 8 for a

t y p i c a l

A325 b o l t

lo t Extensive c a l i b r a t i o n te s ts

have

shown t h a t s in g le b o lts te s te d i n p la te s loaded i n

t e n s i o n ha d approxi

mately

5 to 1 le s s shear s tr e n g th than b o l t s loaded in

p la te s

under com-

p r e s s i o n 1 7 ) . The

re la t ive

m e r i t s o f the two types o f c on tr ol tes ts a re

discussed

in

g r e a te r de ta i l in Ref.

17 .

The

r e s u l t s

of the shear te s ts

were

used to develop

t he r eq ui re d

form

of

th e f a s t e n e r

load-deformation

shear-deformation) r el at i ons hi p

shown

schematically

in F i g. 19 . The

r el at i ons hi p is

e s se n ti al ly l in e ar

unt i l

inelas t ic

d ef or m at io ns o cc ur .

T h e r e a f t e r

becomes n o n - l i n e a r .

The u l t i m a t e shear s tr e n g th is assumed to be approached i n an asymptotic

manner,

an d th e reduction

in

s tr e n g th

observed a t

f i n a l f r act ur e i s neg-

le c te d .

No a n a l y t i c a l expressions

a re

known to have

been

developed for

the e las t ic ine las t ic load-deformation r el at i ons hi p

of

a f a s te n e r . For

th e e las t ic region a l in e a r r e la ti on s hi p is u s u a l l y

assumed

such

as

R

=

K 6

12)

The e las t ic

constant

K

has

u s u a l l y been determined from

experimental d a t a .

Reference

8 gives a

s o lu tio n

for th e c o e f f i c i e n t

K

by

assuming

the

f a s te n e r

to

be

a

fixed-end

beam

I t is noted

t h a t

such an

a n a l y s i s

v io la te s s e v e r a l

b a s i c

assumptions

u n d er ly i ng c o n ve n ti o na l

beam t he or y.

The

d e f l e c t i o n caused

by shear, bending, an d bearing was

d e te r

mined s e p a r a te ly .

D e f l e c t i o n was measured

re la t ive

to a

l in e

passing

through

the

c e n t r o i d s

of the en d

c ro ss s ec tio ns o f

f a s te n e r s ,

an d s h e a r i n g ,


25/48

and bending deflect ions

were

found at the

center

of , the

span.

The bol t

bearing deformation was defined

as a percentage

of the bol t diameter.

For

shear i t was found that

-21

1 3

for bending,

f or b ea ri ng ,

K

t + t )

- b r

E t t

14

15

The

localized

bearing e f f e c t

of

the fastener

on

the plate was found

to

be

the

same as Eq 15. Hence, th e c on sta nt K,in Eq 12 was evaluated

as

K

16

K

s

l b2l


26/48

-22-

0.375 1 .3 1 ] 17

dE

E

t

Hence, K

i s

given by bracketed

term

in

Eq . 17.

This

is

assumed

to

hold

for large

diameter r ivets which

are

s t i f f

and do

not

bend appreciably.

For sma ll d iame te r fa ste -n ers the deformation is influenced y large bend-

ing

deformations. t

i s

expressed

as

= R 3.6g+6.Sg

3

Ed

18

where

g

is

an

empir ical

parameter.

In

order to

obtain

a coeff ic ient

giving

the correc t

order

of magnitude of the deformation, an approximate r l t i o n ~

ship i s given as

[ 7 O.8

5]

t

d

19

The parameters rel t ing load and deformation are determined empirically.

However,

the

expr es sion t akes into account the

geometrical

proper t ies of

the

fastener

and

connected

materia l . The re la t ionship

is

valid

only

below

the

l imit

of proport ional i ty .

The slope

of the l ine

representing

the e l s t ic behavior is assumed to be 4

times as

great as the l ine re-

presenting the

inel s t ic behavior.

Equations

and 17 were.

used to make

an

i n i t i l approximation

of the e l s t ic constant K

in

Eq. 12. This in

turn

w s used to help

evaluate the parameters for the

n lyt ic l

model developed.

2.

ASSUMPTIONS

The

cr i ter i

in the choice of the n lyt ic l expression des-

cribing the

load-deformation re la t ionship

of

a

bol t

in

double

shear are


27/48

the boundary conditions

an d

th e

known

experimental

d a t a . A number of

vari-

abIes a re

known

to in flu e n c e th e load-deformation

rel at i onshi p

o f th e

b o l t

c o n t r o l

t es t .

mon

these a r e :

1)

the

diameter o f the

bolt ;

2)

th e

thickness

o f

the

lap pla tes ;

3) th e thickness of the main plate; 4)

the

type or grade

o f

s tee l

plates;

and, 5 )

th e

type

o f

bol t .

Reference 17

d i sc u sse s each of these v a r i a b l e s in de ta i l .

The f ol lo w in g a ss um p ti on s are made for. th e a n a l y t i c a l relat ion

ship developed

h e r e i n .

They

a re

based

i n p a r t on

the

behavior

observed

in

F ig . 18.

1. At

zero

loads

th e

deformation

is

zer o .

2.

Fo r

small v alu es

of

e ~ o r m t i o n

th e

r e l a t i o n s h i p

between

load and deformation is approximately l inear .

3. s

approaches

1

the

bol t force i n c r e a se s a t de

u t

c r e a si n g ra te .

4. The deformation contains

the

c om po ne nt s d ue to sh e a r ,

bending, an d be arin g o f

th e

f a s te ne r as w e l l

as

th e

s h ear in g

deformation

o f

th e

plates .

The

,following

ex p r es s io n

is

s e le c te d

because

i t

sa t is f ies

t he se c on di ti on s

an d because

only

on e

continuous function WaS necessary

-23

where

20)

to ta l deformation

of

b o l t an d b ear in g

deformation

of th e

connected m at eri al ,

~ ~ A

r e gr e s s ion

coeff icients and

e base o f n a t u r a l logarithm.

Equation 20 sa t is f ies th e boundary condition tha t r eq uire s th e

load

to be

zero a t

a zero

deformation.

I f

th e

f un c ti o n d e sc ri be d

by Eq. 20 is

expanded

in a M aclau r in s


28/48

-24-

s e r i e s t her e is obtained

i f

A i s uni t y

f 6

n

21

This

s e r i e s

is

convergent as

long

as

~ ~ l

For

small

values

of

this

con-

dit ion is

sa t is f ied

an d

an approximate s o l u t i o n

is obtained

by considering

only the

f i r s t

term. Hence,

22)

This is

directly a n a ~ o g o u s

to Eq .

2 an d

th e

expressions

used in Refs. 18

an d

19.

t al so

shows

t h a t

Eq . 2

sat i s f ies a ss um p ti on 2 .

The

equation

sa t i s f i es

t h e e xp e ri m en ta ll y

observed

behavior

shown

in Fig.

8

because allows th e b o l t s force

R

to in c r e a s e

a t a

decreasing r a t e as th e ul t i m at e sh e a r st r engt h o f th e b o l t is approached.

3.

EVALUATION

OF PARAMETERS

The

paramete rs

T ,

l 1

an d A were e v a l u a t e d by

r eg re ss io n a n al y si s

an d th e boundary

c o n d itio n s .

Equation

2 was

f i r s t

l i near i zed

as

logR

23)

The coefficients

log

T an d Awere

determined

by th e

s o l u t i o n o f

the simul-

taneous

l e a s t

squares normal e qu atio ns f or

th e

l i n e a r f u n c t i o n

given as

Eq . 23 . t was

necessary

to a s ~ u m e severa l values

o f

l fo r th e

a n a ly s is

made

on

each type o f

c o n t r o l

spe:cimen. Actual values

o f measured

load an d

th e c o rr e sp o nd i ng d e fo r m at io n

as reported in

Refs. an d 7 were used

i n

the a n a l y s i s .

An in i t i a l

e s tim a te of

could be

determined using Eq .

16 ,

17,

an d

22.

A

b e s t

f i t was obtained when

the squared r e s i d u a l s

were

mini-

mized and

th e boundary c o n d itio n

R

R

u 1t

was sat i s f ied Hence,

th e co-

ef f ic ien t

T was found

to be


29/48

= R

u lt

24

The parameter varied

for

the

different fasteners

invest igated.

For

7/8

in . A325 bolts te ste d in one-inch A7 s tee l

plates,

the value is

approximately

18.

For 7/8 in

A325

bolts tested in one-inch A44 steel

plates, the value is approximately

23 .

These values appear to be the

same for

bolts te ste d in

plates

loaded in tension

as

well

plates

loaded

in compression.

The parameter

A

almost

constant

for

the

7/8

in . A325 bolts and

or

A44

connected

materia l ,

is

approximately

unity.

The

f inal

relationship for load-deformation or shear-deformation

is

-25-

25

where

R 1

Ultimate

shear Strength.

u

The

average

values of

R 1 and A

are

tabulated

in

Table 2

for typical

u

t

lots

of bol ts

and r ivets and compared to Eq.

25

in the next sect ion.

The

to ta l

deformation

capacity

1 for a

given

bolt and

u

connected material i s

a

function

of the

shear, bending,

and

bearing

of the

bol t

and

the

bearing

deformation of the plates . As might be expected,

this

wil l vary

with

the type of cal ibra t ion

tes t

the type of connected s tee l

and the thickness of the gripped material .

Values

of are

also tabu

lated

in

Table 2.

4. COMPARISON

OF

COMPUTED

ND

EXPERIMENTAL RESULTS FOR SINGLE BOLTS

The two

types of

control

shear tes ts a re descr ib ed brief ly in

the previous ar t ic les Additional

information

on the t es t

methods

and a

detai led

descript ion of the t e s t specimens and t es t data are given in Ref.


30/48

-26-

17.

The t es t data

for

both types of control tes ts on A325 bolts in

A44

s tee l

are

p lo tte d in

Fig.

for the

same bol t

lo t . Usually

three

dif ferent

specimens

were

tested

each type

of t es t made for

each

bol t

lot .

The load-deformation

data for 7 8

in .

A325

bolts in

A7

stee l is

given in

Fig. 21 .

The type

of ca lib ra t ion t e st had

l i t t l e

effect on the

parameters

and

The predicted l ine is in good agreement with th e tes t

data

in

Figs.

20 and 21 .

The

actual

values of R

u lt

and A for s evera l bo lt

and

r ive t

lots are

given in Table

2.

The exponent

A

is affected

only

s l igh t ly by

th e variations in t he connect ed mate ri al p roper ti es and the specimen

geometry for

7/8

in . A325

bolts .

The type of control tes t

had l i t t l e

in-

fluence

on the parameters

and

Only

the ult imate

strength

R 1 was

u t

affected

as

described ear l ier . Apparently the coeff icient

was

mostly

affected

by

the type of

connected

material .

is

believed

that

the

parameters

and

A

can

be

related

to

the

physical and geometrical

properties

of the

plate

and bol t .

Thus

addi-

t ional

studies are desirable i f a

general ized expression

is

to

be developed.

The to ta l deformation

capacity

of

th e

fasteners is

less

in the

higher

strength

s teels because

th e b ea ring deformation in the plate is

less . However this disadvantage is offset by

the

more favorable redis tr i-

bution

of

th e jo int

load

which occurs

among the A325 bolts in

higher

strength steels 3 .


31/48

S U R Y

Ana lyt ic a l expr es si on s

fo r

the s t r e s s s t r a in r e l a t ionsh ip

0

a

pla te

with h oles

and

for

the shear-deformation relat ionship

of

r ive ts and

high-s t rength

bol ts have

been

developed. Both

expressions

are necessar i ly

applicable to

the e las t ic and

ine las t ic

regions .

The ana ly t ica l expressions for

the

plate with

holes

can be

adapted to

changes

in

the geometrical configuration

as wel l as differences

in the yie ld

point and ul t imate

s trength .

The

analy t i ca l model was com-

pared

with

tes ts of p la te specimens hav ing

two dr i l l ed

holes Among the

var iables che cked wer e p la te width , pi tch

or dis tance

between th,e

cen te r s

of the ho les p la te thickness a n d

grade

of s t ee l . The

analy t i ca l

model

adequately responded to

changes

in geometry and mater ia l proper t ies .

A continuous

function

was used to r ep re se n t t he load-deformation

charac ter i s t i cs of a

s ingle

bol t in

shear . The

shape of the

curve was

governed

by

the

ul t imate

shear

s t rength

and

two

empir ica l

parameter s.

These parameters

were found to

vary for different fas teners and

di f ferent

types o f connected material

-27-


32/48

6.

CKNOWLEDGEMENT S

This

study has

been

carr ied

out

as

a par t

of

the

research

pro

ject on Large Bolted Connections

being conducted a t Fri tz Engineering

Laboratory, Department of Civi l

Engineering,

Lehigh Univ ers ity . P ro fe sso r

W

J. Eney is

head of

the

Department and

Laboratory

and Dr. L

S.

Beedle

is

Director of the Laboratory. The

project

i s sponsored by

the

Pennsylvania

Department of Highways, the

U S.

Department

o f

Commerce

Bureau

of Public

Road s, and the American Insti tu-te of Steel Construct ion.

The author is appreciative

of t he sup erv is io n

and

encouragement

of Dr. L S Beedle durin g th e preparat ion of th i s repor t . Thanks are

also

extended

to

Miss

Valerie Austin

who typed the manuscript; to H

Izquierdo who prepared

the

drawings;

to

H

Digel who reviewed the manu-

scr ip t and

to the guiding committee

of

the

Research Counc il

on Riveted

and Bolted S tr uc tu ra l J o in ts

for

many

helpful

suggestions.


33/48

Table 1.

GEOMETRY N

TEST RESULTS

OF PLATE

CALIBRATION SPECIMENS

Dimension of C al i brat i on Coupon

T en s.

Tens.

St r o f

Str o f

P l.C al. St.B ar

S p e c .

S t e e l Thic kness

Gage

Pi t ch

Hole

Dia.

Coup.

Coup.

t i n g in

p in

dw in.

k si

k s i

A7 1

A

0.580

4.94

3.50

0.94 64.7 63.9

A7 2

0.619

65.5

65.2

A7 3

0.697

67.0

64.7

A7 4

0.760

68.1 65.3

A7 5

0.800

67.1

63.5

A7 6

0.878

67.9 63.7

7031

1.001

2.92

63.0

60.0

7041

1.001

3.58

61.7

7051

1.003

4.24

61.2

7061

1.004

4.90

61.5

7071

1.002

5.56

60.4

7081

1.001

6.22

60.2

7091b

1.002

6.88

60.2

t

709ic

1.002

2.50

62.8

7091d

1.001

4.50

61.5

7091e

1.002

6 . 0 0

61.9

a 1.001

3.32 3.50

81.9

76.0

PE41b

1.002

3.32

81.9

11

PE71

1.001

5.14

79.2

PEIOI

1.004

6.94

80.1

PE131

1 001

4.85

78.4

PE161

1.002

5.74

80.1

-29-


34/48

30

Table

2.

SuMMARY OF TEST RESULTS ND ANALYSIS

OF

MECHANICAL FASTENERS

Type Lot Dia.

Type

Test

Ult.Str. U1t.

Empirical

Bolt or

Conn.

J ig

Rult

Def.

Parameters

Rivet

n MatI. kips

6u

t in.

A

A325

8A 7/8

A440

Tension

98.6

0.187 23

1.00

Bolts

SA

7/8

A440

Compression

102.3 0.200

23

1.00

8B

7/8

A440

Tension

92.5

0.200

25

0.95

8B 7/8 A440

Compression

104.0 0.239

22

1.00

H

7/8

A440

Tension 95.2

22

22

1.00

H

7/8

A

Compression

103.0

0.236

22

1.00

C

7/8

A7

Tension

98.5 0.238

8

1.00

C

7/8

A7 Compression

106.9 0.291 8

1.00

D

7/8 A7

Tension

101.8

0.279 8

1 .00

D

7/8

A7

Compression

102.5

0.300

18

1.00

A354BC

CC

7/8 A440

Tension

103.7

0.178

20

0.40

Bolts

7/8

A514

Tension

101.1

0.137

25

0.40

D

1 A440

Tension

138.2

0.212

20

0.50

DC

1

A514

Tension

131.5

0.156

25

0.50

A354BD ED

7/8

A440 Tension

I

123.9

0.174

25

0.40

Bolts

ED

7/ 8

A514 Tension

123.2

0.113

25

0.40 .

FD

A440

Tension

157.7 0.248

21

0.50

GD

7/8 A440 Tension

122.4

0.173 23

0.50

GD

7/8 A514

Tension

123.4 0.152

25

0.35

A490

KK

7/8 A440

Tension

124.4

0.202

23

0.40

Bolts

1

A514

Tension

151.7

0.155

28

0.35

A141 DR

7/8

A7

Compression

60.0

0.220

19

1.00

Steel

Rivet

AS 2

HR

I

7/8

A440

Tension

77.2

0.195 6

0 45

Grade

2


35/48

31

P

p

l

t

I

I

I

t

I

I

Fig 1

Schematic of Plate

Calibration Coupon

80

Static Yield Stress Level

0 25

0 010

0 2015

STRAIN

IN IN

Yield

Stress Level at 0.2

0 10

05

/

/

/

/

/

/

/

/

0 002/

60

20

STR SS

si

40

Fig

2

Typical Stress Strain

Diagram for

Standard

Bar

Coupon


36/48

-32:

80

60

- - - - - - (O y ) o r o s s

STRESS

Ksi

40

20

o

A440

Steel

Specimon 41

0 005

0,05

STRAIN intl

n

.

0 01

1

Fig

3

Typical Stress Strain

Diagram for

Plate

Calibration

Coupon

STRESS

Ksi

STRESS

Ksi

60

40

o

80

20

o

Plate Calibration

Coupon

41

a

0 01

STRAIN

Plate

Calibration

Coupon 4Ia

0 1

STRAIN

Standard Bar

Coupon

0.02

Standard Bar

Coupon

0 2

Fig

4

Comparison

of

Standard

Bar

and Plate

Calibration

Coupons


37/48

Fig.


38/48

34

Fig

Yield Lines Indicated by hitewashCoating


39/48

C

= 5

8

STRESS

STRAIN

Fig . 8

1.10

Idealized

Stress-Stra in Relationship

fit A7

a

A44

u coup

1.00

I i

1.2 1.3

1.4 1.5

Fig .

9

60

50

40

STRESS

Ksi

20

10

9/

g

_

d

Effect

of Gage

on Ultimate

S tr engt h o f Plate

Calibrat ion

Coupon

A7 Steel

07031 0-2.9210

Il.7041

0-3.38

6.7051 0-4 24

7061

0-

4 90

.7071 0-5 36

7081

0-6.22

o

ig

10

- - O - . J . O - 2 - - - - - 0 L . ~ O - 4 - - - - 0 . : ~ ~ O : - = 6 - - - - - - - - - - - - - : 0 ~ O : : - : 8 : : : . - - - - - - - - - - : 0 - ; : : : 1 - ; ; 0 : : - - - - - - ; : - : 0

STRAIN

Influence

of Geometry

on the Stress-Strain

Relationship


40/48

-36-

A7= Steel

P

=

3.5 in

9

=4.94

in

d =6.94 in.

240

t=

in

t =13/

6

in

200

t =

11

16

in

J)

c.

t

=5/

8

in.

160

..........

t=

9/

6

in


41/48

37

Specimen 7041

g= 3.58 in d=

0.94

in.

p=3 5in

Computed

-(ay)gross

A7

Steel

20

60

80

STRESS

Ksi

40

Specimen

7031

g:;2.92 in.,d=0.94 in

p=3 5in

Computed

-(OY)gross

A7 Steel

20

80

60

40

STRESS

Ksi

o

0.04

0.08 0 12

STRAIN E:;

o

0,04 0.08 0 1 2

STRAIN 1 E:;

Specimen 7061

g=4.90in

1

d=0 94in

p= 3 5in

-(OU)coup

A7 Steel

pecimen 7051

g=

4.24in.,

d=0.94in.

p=3.5In.

OU coup

80

A7

Steel

60

STRESS

Ksi

40

------computed

-(OY)gr055

-(ay>net

STRESS

Ksi

40

-(ay>gross

-(OY>net

Computed

o

0.04 0.08 0.12

STRAIN,E=e/

p

a 0 02

0 06 0 10

STRAIN E=e/

p

0 14

A7 Steel

A7 Steel

Specimen 7081

Specimen

7071

9

=5.56

in d=O 94in

g= 6.22 in d=0 94in

p=3.5in.

p=3 5in

60

0

0

b

OU>coup

coup

STRESS

0

Computed

STRESS

: Computed

Ksi 40

Ksi

40

-(0;>gr055

-(OY)gross

-(OY)net

--


42/48

38

A440 Steel

A440 Ste al

80

80

o

Computed

Specimen 41e

g=3 83 in d=0 94

in.

p=3 5in

60

20

STRESS

Ksi

40

Specimen 410 41 b

{ y } r s s 9 ~ 3 3 ~ i n d = 0 9 4 i n

p-3.5

In.

Computed

60

STRESS

Ksi

o

0.02

0 06 0 10

STRAIN

E= el

p

0.14

o

0.04 0.08 0.12

STRAIN E=e

/p

A440 Steel

---{OU}coup

A440 Steel

o

STRESS

l

60 Specimen 3

9=4 85 in d=Q.94in.

oylgros p=3 5 In.

40

iay>net Computed

20

60

STRESS

Ksi 40

20

Specimen

7

9 ~ 5 4

in d=O 94 in.

p-3.5m.

tOY}gross

Computed

OY}net

o

0.02

0 06

0 10

STRAIN = p

0 14

o

0 02

0.06 0 10

STRAIN

E=

e

p

0 14

60

STRESS

Ks i l OY>gross

40 {Oy}net

20

Specimen

6

g=5.74 in d=O 94in

p=3 5in

Computed

60

STRESS

Ksi TOY>gross

- Dy}net

Specimen

g=

6 94in d=O 94in

p=3 5 in.

Computed

o

0 02 0 06 0 10

STRAIN

=

el

p

0 14

o

0.02

0.06

0 10

STRAIN, e

D

0 14

Fig 13

Comparison Between Computed and Experimental Results -

A

Steel


43/48

80 , . - - - - - - - - - - - - - - - - - - - - - -- - -

A7

Steel

Specimen 7091 c

g=6.88in. d=Q.94in. p= 2.5 in

60

STRESS

Ksi

40

20

39

o

1

0 2 0 3 0.4

ELONGATION e inches

0 5

60

STRESS

Ksi

40

A7 Steel Specimen 7091 e

g= 6.88 in. d=0.94 in. p= 6.0 in

Computed

o

1

0 2

0 3 0.4 5 0 6

Fig

14

ELONGATION e inches

Effect of Pitch

STRESS

Fig 5

~ 1 1 4

gross

y

- - - - _I

ay

net

1

Yield

I

plateau

i

STRAIN

Schematic Stress Stra in Relationship


44/48

40

Fig

Deformation of

a

S ingle Bolt

Fig

Sawed

Section

a

S ingle Bolt


45/48

ailure o d

41

LO D

f Tension

or

t

ompression

DEFORM TION

Fig

Idealized

Load Deformation

Relationship

for

a

Single

Bolt


46/48

42

A7

Steel Plates

7/

8

in. A325 Bolts Lot C

Tension Jig

t=4In

1 2

DEFORMATION tin.

o

3

A44

Steel Plates

lain. A325 Bolts Lot 8B

Tension Jig

t=2In

0.1 0.2

DEFORMATION 6 in.

o

12

100

o

90

75

Cb

Computed

LOAD

o

Kips

LOAD

Computed

Kips

60

50

co

Fig

2

Comparison of Computed and Experimental Results

for A325 Bolts in A44 Steel

A44

Steel Plates

l in. A325 Bolts Lot 8 B

Compression Jig

t=2in

0.1 0 2

DEFORMAT ION1 :::.. in.

0 3

A7 Steel Plates

in. A325 Bolts Lot

D

Tension Jig

t=2 in

0.1

2

DEFORMATION :::.. in.

100

120

o

75

90

Computed

LOAD

o

Kips

Computed

S

50

60

0: 0

Fig 21

Comparison of Computed and Experimental

Results

for

A325

Bolts

in A7

Steel


47/48

8. R

R N e

1. Francis,

A. J .

THE BEHAVIOR

OF ALUMINUM

ALLOY

RIVETED

JOINTS

The Aluminum Development Association,

Research

Report

No. 15 , London 1953

2.

Rumpf J . L.

THE ULTIMATE STRENGTH, OF BOLTED CONNECTIONS, Ph.D

Dissertation,

Lehigh University, 1960

3.

Fisher,

J. W.

THE ANALYSIS OF BOLTED PLATE

SPLICES Ph.D Disserta

t ion, Lehigh University, 1964

4.

Fisher , J . W.

and Rumpf J. L.

THE

ANALY8IS

OF

BOLTED BUTT JOINTS

Fri tz

Engineering

Laboratory

Repor t 28S .17, Lehigh University,

Sept.

1964

5. Baud R. V., Wahl A. M. and Nadai, A.

STRESS

DISTRIBUTION OF PLASTIC

FLOW IN

N ELASTIC

PLATE WITH.A CIRCULAR HOLE, Mechanical Engineering,

p.

187,

March 1930

6. Nadai, A.

THEORY OF FLOW ND

FRACTURE OF

SOLIDS

Vol. 1, 2nd Ed.

McGraw-Hill, 1950, p. 299

7. Hollomon

J . R.

TENSILE

DEFORMATION, Transactions, AIME

Iron

and

S teel D iv is ion ,

Vol. 162,

1945

8.

Holmquist,

J .

L.,

and Nadai, A.

A

THEORETICAL

ND EXPERIMENTAL APPROACH TO THE PROBLEM

OF

COLLAPSE

OF

DEEP-WELL

CASING, American

Petroleum

nsti tut Drill ing and Producing Practice , 1939

meeting, Chicago , pp .

392-420

9.

Ramberg W.

and

Osgood,

W.

R.

DESCRIPTION

ND

STRESS-STRAIN CURVES

BY

THREE PARAMETERS,

N

T.

N.

902,

1943

10 .

Fisher, J. W. Ramse ie r, P.

O.

and Beedle, L. S.

TESTS OF A440

STEEL

,JOINTS FASTENED WITH A325 BOLTS,

Publications,

IABSE Vol.

23 ,

1963

11. Bendigo, R. A

Hansen,

R. M., and Rumpf J. L.

LONG BOLTED JOINTS Jo urn al of

th e Structural Division,

ASCE, Vol. 89, ST6

1963

-43-


48/48

-44-

12. Schutz, F.

W.

T

EFFICIENCY OF RIVETED

STRUCTURAL JOINTS, Ph.D

Dissertation, University of I l l inois 1952

13. Munse,

W.

H., and Chesson, E., Jr .

RIVETED

AND

BOLTED

JOINTS:

NET

SECTION

DESIGN

Journal

of the Structural Division, ASeE Col. 89,

No. STl, 1963

14. Schanker,

L.,

Salmon, C. G., and Johnston, B.

G.

STRUCTURAL STEEL CONNECTIONS AFSWP Report No. 352,

University

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15. Steinhardt, 0 and

Mohler,

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VERSUCHE

ZUR

ANWENDUNG VORGESPANNTER

SCHRAUBEN M

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Cologne,

1959

16 .

Coker,

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G.

THE DISTRIBUTION

OF

STRESS

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RIVET IN

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Trans.

Insti tute

of

Naval

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55, p.

207,

1913

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Wallaert, J.

J and

Fisher, J

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THE

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Fritz

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No. 288.20, Lehigh University,

1964

18. Tate,

M. B.,

and Rosen fe ld , S .

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PRELIMINARY INVESTIGATION OF THE LOADS CARRIED BY

INDIVIDUAL BOLTS IN BOLTED JOINTS,

NACA

T.

N.

1051,

1946

19 . Vogt,

F.

LOAD

DISTRIBUTION

IN

BOLTED

OR

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STRUCTURAL

JOINTS

IN

LIGHT ALLOY

STRUCTURES

U. S. NACA

Tech.

Memo No. 1135, 1947

on the behavior of fasteners and plates with holes proc. asce

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