structural details to increase ductility of connections

8/8/2019 Structural Details to Increase Ductility of Connections

1/12

STRUCTURAL STEEL EDUCATIONALCOUNCIL

TECHNICALINFORMATION & PRODUCTSERVICE

APRIL 1995

Structural Details to IncreaseDuctility of Connections

By: Omer W. Blodgett, P.E.Senior Design Consultant

The Lincoln Electric Company

INTRODUCTION

Materials used in steel structures are increas-

ingly becoming thicker and heavier. A greater

chance of cracking during welding of beams

to columns, for example, has resulted due to

increased thickness of material. With weld

shrinkage restrained in the thickness, width,and length, triaxial stresses develop that may

inhibit the ability of steel to exhibit ductility.

This paper will attempt to explain why these

cracks may occur, and what can be done to

prevent them, by expanding on information

presented in the AISC Supplement No. 1

(LRFD) or Chapter J 9th Ed. AISC Manual.

Ostress

psi

I I I I I I

strain in/in

Figure 1

FIELD RESULTSI learned about the stress-strain curve (Figure

1) while taking "Strength of Materials" along

with laboratory work at the University of Min-

nesota. It took me a long time before I real-

ized that this applied only to simple tensile

specimens in the laboratory.

During World War II while I was working in a

shipyard, a docked, all-welded tanker, the

Schenectady, suddenly broke in two. At the

time, we had no answer as to what could have

caused such a catastrophic failure. We passed

it off as perhaps a poor grade of steel or poor

workmanship, and kept on welding our ships.

A short time later, we received a bulletin from

The Lincoln Electric Company in which it was

stated that ductility values come from simple

tensile specimens which are free to neck down.

The bulletin pointed out that if the same plate

had many transverse stiffeners welded to it,

the ability to neck down would be greatly re-

stricted, and the plate would fail with less ap-parent ductility.

DEFINING DUCTILITY

In Figure 2, Mohr's Circle of Stress has been

drawn, showing a tensile stress of 10 ksi up to

the ultimate of 70 ksi (numbered from 1 to 7).


2/12

The corresponding maximum shear stress is at

the top of each ci rc le . For convenience, each

point of shear (illustrated as a solid dot) is moved

horizontally until it l ies directly above the corre-

sponding tens i le s tress (depicted as an open

dot). Notice that the se points form a straight line,represent ing a simple tensi le specimen. From

this l ine, i t is possible to read off the maximum

shear stress for a given tensi le stress. This is

the basic f igure used by Professor Gensamer,

as shown in Figure 3.

Gensam er introduced the concept of graphically

illustrating the maximum shear-stress theory of

fai lure. In Figure (4), the horizontal axis repre-

sents the tensile stress (o), and the vertical axis

represents the sh ear stress (-[). The critical ten-

sile stress would be the ultimate tensile strength,

but exceeding this value causes immediate fail-

cr it icat shear ? Zc/stress r o

7 tensil estress(ksi)

30 '

20 '

10

Figure 2 ,'

I 0

/ ia

: : t I I I II 2 3 /4 5 6 7

tensile stress (ksi)

Figure 3

40 II

--30 ., ,,,th .. I ., I

v, crlticat shear stress t ":1

, n i ..," - ; ' 1." / ,,


3/12

In Figure 5a, the membe r is subjected to a ten-

sile stress (o) under the yield strength (ay). This

results in elastic strain and is recoverable when

the stress is removed. Notice also in Figure 5a

that a shear occurs which has a maximum value

of :--1/20 on a plane at 45, with the axis of theapplied tensile stress. If the applied stress (o) is

increased to a value of (0), the resulting shear

stress exceeds its critical value-tcR=l/2ov , then apermanent s lip occurs on p lanes a t 45, as

shown in Figure 5b and 5c.

This is plastic strain and, if continued, will cause

the specimen to neck down (Figure 5d). As the

c ross- sec ti ona l a rea con t inues to become

smaller , the tensi le stress f inal ly exceeds the

critical normal stress (tensile strength) and themember fails.

All of this can be seen in the stress-strain curve

of Figure 6. Region (a) below the yield strength

covers the elastic strain portion. Region (c) cov-

ers the plastic strain portion with the member

necking down. Point (d) is tensile failure. In the

stress-strain curve of Figure 6, region (a) is all

elastic strain. The resulting shear stress () is

under the critical value -OcR=l/2 ay, so no plasticstrain takes place.

In region (c) the resulting shear stress exceeds

the critical value and plastic strain takes place

with mo re and more necking down. The ductility

of the simple tensi le stress specimen occurs

because there is a shear stress component from

the particular load condition and, more impor-

tantly, it exceeds the critical value by a consid-

erable amount . Let us see if we can find out whythis test spec imen is ductile; then we can check

the ductility o f other loaded members or details.

The ducti li ty of a simple tensi le specimen oc-

curs because there are two shea r stresse (%-3)

and ('2-3) result ing from the applied tensile stress

(o3), as shown in Figure 7a and 7b. Notice thatwhen the stress (%) reaches its critical value

for failure (70 ksi in this example), the two shear

stresses have already exceeded their critical

value of 20 ksi. There are two shear stressesbecause there are two circles: circle (1-3) and

circle (2-3). The third circle, (1-2), has no ra-

dius, and hence no shear stress, s ince it is a

point.

=zer

tension

g

w 'r i'3 el

r--TT7--- , _ .%!0 ' 2 0'3

Figure 7A

-- 6aT

e 3Of4t.=20

lo! - - I ' I - -

.oi .02 .03' i I I '

.G4 .OS .Q6 .107 ,.(}6Total $tra;n E Tn/in

: ; ,I '.09 .10 .11 .t2

,G$rGt.e 1-3

Ptqstic , movement' / ' I

m4ke; Sl)g;men I I

r w e O . t = zen=

i3(l-i)

aircte 2-3

Z-3)

I . Th i sm q ve r ne n t c .i . 3) i oi r lt h edirion Of (3

PtasticmYJvement

makes sp4K:imenthinner

This movement 'a(z.alis ;n the Idirection af 0'3 I

tatar ptost; strain ]n d;rectlon of

JZ 3 ( I-3) ' [' '3 C2-3} Ifram framt-3 'rz-3

wiU tend to reduce the residual stres. ((T3)

Figure 6 Figure 7B

Steel April 1995 3


4/12

Any value o f shear for 1;1.3 and 1;2-3 above thecrit ical 20 ksi wil l cause plastic strain. Notice in

Figure 7a that both circle (1-3) and circle (2-3)

cause plastic strain $3(1-3) and 3(2-3)' Therefore

(o3) wil l be: 3 = E3(1-3)+ s3(2-3).

Since E3( 1.3) ' - 3(2-3)' we then have: s3 = 2s3.3),w h ic h w il l t en d t o r ed uc e r es id ua l s tr es se s

caused by welding.

If the s pecime n is pulled to failure, o3 will reach

its critical value, o r tensile strength; s ee Figure

8. By this time, the two sh ear stresses are above

the critical value and plastic strain or movem ent

will have taken place. Notice th at the total plas-

tic strain consists of two values: C3(1.3) and 3(2-3)'The movement 3 acts in the di rection o f the

40 ;

t..-

crlticot shear \ I

!

lr'cr_, s toad tine It.''} r e p r e s e n t s I

{ O ' I II

; : .* I I I I10 20 30 40 50 60 70

normqt stress 0'3

Figure 8

I 2 3 4

normal elastic total plasticstress strain s tr ai n strain

0 3 e T Ep

10 .00033 .0003315 .00050 .00050

20 .00067 .00067

25 .00083 .00083

30 .00100 .0010035 .00117 .00117

40 .00133 .00133

45 .0015 .00236 .00086

50 .0017 .00485 .00315

55 .0018 .01200 .0102060 .0020 .03185 .02985

65 .0022 .08234 .08014

70 .0023 .20229 .20000

Table 1

stress o3 and would tend to reduce any residual

stress. This me mber should behave in a ducti le

manner. Plastic behavior takes place from 03 = *

40 ksi up to 70 ksi, and is caused by two differ-

ent plastic strains E3(1.3) and 3(2-3)'

Table 1 lists the data from a typical stress-straincurve f or structural steel. Total elastic plus plas-

tic strain is listed in Colum n 3. Th e elastic strain,

calculated from s = /E, is listed in Column 2. By

subt racting the e last ic s train f rom the corre-

sponding total rain, w e obtain the plastic strain,

shown in Column 4.

RESIDUAL STRESSES ISOLATED

Figure 9 i l lustrates that two important residual

stresses exist in the weld's termination zone. Thebutt joint in the flange has a residual stress lon-

gitudinal to the length of the flange (o3), as well

as a stress transverse to the f lange (%). Longi-

tudinal stress is tensile along the center l ine of

the f lange where the weld access hole termi-

nates. It can be compared to t ightening a steel '

weld (accesshole

roG,ew e l d

o4 _3

Figure 9

4 Steel Tips April 1995


5/12

30 ''I u : critit shear sts,. . . . . . . . . -

ut t' 2 _ :

10 2O 30 &O SO 60 70 80

Figure 10

cable lengthwise in the center in tension, with

compression spread out on both s ides. The

transverse stress (Ol) is tensile in the weld zone,including a portion of the adjacent plate, going

through zero, and then compression, beyond the

adjacent plate. This transverse stress (o) is also

similar to tightening a steel cable.

RESIDUAL STRESSES APPLIED

These res idual s tresses may be applied to a

weld detail having a narrow weld access hole,

as shown in Figure 10. This hole terminates at

a point where (0) and (03) are in tension. Sincethe web a t the edge o f the weld access hole

offers some restraint against movement in thethrough thickness direction of the flange plate,

stress in the (02) direction may have an appre-

ciable value. All of the circles will be small. Nei-

the r (T2.3) nor (T.3) will probably ever reach thecritical shear stress value, and plastic strain or

ductility will not occur, as th e right hand of Fig-

ure 10 illustrates.

If the weld access hole can be made wider, asrecommended by AISC Specification, Ninth Edi-

t ion, so that i t terminates in a zone where the

transverse residual stress (0) is compressive

(see Figure 11), then a more favorable stress

condition will result in greater ductility in the (03)

direction. In this case, s hear stress (-c.3) will be

high as shown on Mohr's Circle of Stress, and

the critical shear value will be reached at a much

lower tensile stress or load value. This will pro-

duce more ductility in the (o3) direction, greatly

reducing the chance of a transverse crack in theflange at the termination o f the weld access hole.

EXAMPLE #1

Consider the unrestrained section, similar to a

simple tensile specimen, shown in Figure 12.

W hen the re is no app li ed s tr ess ( o) in the

through thickness direction or (o2) across the

width, these values are zero. This will produce

the largest of Mohr's circles, and the greatest

value of shear (;2.3) and ('-3)' In both cases,these shear stresses are equal to one half of

the applied tensile stress (o3). These two shear-

tensile l ines are drawn in the lower portion of

the figure. Although the re are two lines, which

would indicate good ductility, there is a differ-

ence between the two. One line represents neck-lng down through the thickness, and the other

represents necking down across the width. Al-

though the unit strains are the same in this case,

the strain acting across the width would result

in greater overall movement or elongation overthe length of the specimen.

'o, . .

'F 0 / . I cr;tiCOt .sh_ Str_

- --(ki) 2 f - ; ? - - - : - -- -.,--"2d'k,; -

Figure 11

Apri11995 5


6/12

In the case of the restrained section shown in

Figure 13, (here L=W/4), the angle of maximum

shear stress lies along an angle of o - 76and

the resulting shear value is : -- .23 03. The two

shear values (%-3) and ('2-3) produce two shear-

tensile lines. The lower line acting across thewidth does not produce enough shear to exceed

the critical value, hence no plastic yielding. The

upper line indicating good plastic yielding, how-

ever, acts only through the thickness and the

overall movement would be less than the ex-

ample on the right. To get a better picture of this

behavior, the stress-strain curve shown in Fig-

ure 14 has been created for the two details.

' , - : : r I t - I . .

I I I I

TO

,, sa

? o

41t

$ 0

.01 . 02 . 03 . 04 .05 .OG . 07 14 . 09 JO .!1 .12 J ) . 14 .lis Jll J? J!) .2Q

unit strO)n in/in

Figure 14

EXAMPLE#2

There has been some discussion about the weld

connecting the beam flange to the column flange

as being brittle. Referring to Figure 15, the ma-

terial at point (A), whether it be weld metal or

base metal it cannot exhibit the ductility of a

J_

necking dcTw thru thickness ]

necking ocross wk neckbJ downthru tlcknesS

2

necking down across widthlrZ.3

I

al

40'

30.

10'

I

. ',.,ec' ' ;b

10 20 30 40 SO 60 70

tensite stress (ksi)

40

v

2o

10

i.

I

Hti shear stress _ ',. . . . . . . - -- - . . . . . . . . . .l

qr'cr:2O ks, ( Y . . . . . . . . . .i '

/ !

10 20 30 40 5 GO 70tensite stress (ksD

Figure 12 Figure 13

6 Steel April 1995


7/12

simple tension test. Ductility can only take place

if the material can slip in shear along numerous

slip planes. Four condi tions are required for duc-

tility:

1. There must be a shear stress () componentresulting from the given load condition.

2. This shear s tress must exceed its cri tical

value by a reasonable amount. The more it

exceeds this value, the greater wil l be the

resulting ductility.

3. The plastic shear strain result ing from this

shear stress must act in the direction which

wil l rel ieve the particular stress which can

cause cracking.

4. There m ust be sufficient unrestrained lengthof the me mber to permit "necking down."

If conditions (1) and (2) are not met, there will

be no ductility and no yield point. The stress will

simply build up t o the ultimate tensile strength

with little or no plastic energy absorbed. We call

this condition a brittle failure.

Figure 15 shows two regions in question:

Figure 15

I

Point (A) at the weld joining th e bea m flange to

the f ace of the column flange. Here there is re-

straint against strain (movement) across the

width of the beam flange () as well as through

the thickness o f the beam flange (s2)-

Point (B) is along the length of the beam flange

away from the connecting weld. There is no re-

straint across the width of the flange or through

its thickness.

Figure 16 shows the three equations for strain

given in most strength of material texts, shown

O2

(1 O3

1

3 = "E (O3-.[%-[[,[(1)

12= (-%+%-o)

1

s,= - (-%-%+o)

or it can be shown that

E [E3+2+(1-),]

o= (l+tz) (1-21z)

E [3+(1-!Z)2+[Lt]02= (1+) (1-2)

E [(1-tZ)3+2+p.]

03= (1+[) (1-21Z)

Figure 16

steel Tips April 1995 7


8/12

- - - r I1' IIr I... , , : , . - . ; - - , v, +

02=0

ai

,

!

!

!

L.

-

ol=O

o3=30ksi

3=+.001

.'

E [tz%+ze2+(1-)e l]

%= (1 +lz) (1-2tz)

30000

o, - (1+.3) (1-.6) [.3(+.001 ) +.3(-.O003)+.7(-.O003)]=Zero

in the flange. By using Poisson's ratio of iz=0.3

for steel the fol lowing strains are found for a

s im p le t en si le s pe ci me n w he n s tr es se d t o

o3=30ksi.

3 = +.001

s2 =-.0003

s =-.00 03

Using th ese strains in the three formulas for re-

sisting stresses w e find:

o = Zero

02 = Zero

o3 = 30 ksi

o2=% =Zero

E [(1-p,)3+$S:+!,te,]

3= (1 +It) (1-21Z)

30000

3:- (1.3) (1-.6)[.7(.001)+.3(-.0003)+.3(-.0003)]=30.0 ksi

ac1.3=35

:

Figure 17

0.=70

in upper box. For our use, these have been con-

verted into corresponding equations for stress,

shown in lower box.

Figure 17 is an element of the beam flange from

F ig ur e 15 p oi nt (B). There is no re stra in t

(%+o2=0) against the 30 ksi longitudinal stress

This is p lo tted as Mohr's ci rc le of s tress in a

dotted circle. The larger solid line circle is for a

stress of 70ksi or ultimate tensile stress. The

resulting maximum shear stresses (%-3) and

(-c2.3) are the radii of the se two circles or 35 ksi.The ratio of shear to tensile stress is 0.5. Figure

18 plots this as line (B). No tice at a yield point of

55 ksi, the cri tical shear value is 1/2 of this or

27.5 ks i. W hen thi s c ri tical shea r s tr ess is

reached, plastic straining or movement takesplace and ductile behavior will result up to the

ultimate tensile strength, here 70 ksi. Figure 19

shows a predicated stress-strain curve indicat-

ing ample ductility.

Figure 20 shows an element from Point (A) (Fig-

ure 15) at t he junction o f the beam and column

flange. Wh ether w e consider weld metal or the

material in the column or beam makes little dif-

ference because this region is highly restrained.

Suppose we assume:e3 = +.001 (as before)

2 = Zero '. (but now highly restrained

E1 = Zero J with little strain)

From the given equations, we find the followingstresses:



9/12

30 27.5

. . . h e

m 20fJ

tll

ID

I 0

critical shear stress 'c=1/2 o b o y.Y't.J,

";''', iv , i ,10 20 30 40 50 55 60 70

Figure 18

% = 17.31 ksi ) Increase to ( = 30.0 ksi

(72 : 17.31 ksi ult imate tensile I, = 30.0 ksi

(73 = 40.38 ksi strength = 70.0 ksi

The lower portion o f the sheet is a plot of Mohr's

circle of stress. T he maximum stresses are:

-c. 3 = 1:2.3 = 20 ksi

The ratio of shear to tensile stress is 0.286. In

Figure 18, this condition is plotted as line (A).

Notice it never exceeds the value of the critical

shear stress (27.5 ksi); therefore, there will beno plastic strain or movement, and it will behave

as a brittle material. Figure 19 shows a predi-

cated stress-strain curve going upward as a

straight l ine (elastic) until the ultimate tensile

stress is reached in a brit tle manner with no

energy absorbed plastically.

Would it help if the strength and ductility of the

weld metal or base metal were changed? See

Figure 21. The top figure is for lower strength,

more ductile steel, tensile strength of 60 ksi and

a yield strength of 40 ksi. The lower figure is for

a higher strength, lower ductile steel, tensile

strength of 70 ksi and a yield strength of 55 ksi.

Notice in the case of no restraint (B) that the

lower strength material will result in more ductil-

i ty. However, in the real wor ld where there is

80

70

60

50(/3

40(/3

30

20

10

.05 .1 ,15strain in/in

Figure 19

.2 .25 .3 .35

Steel Tips April 1995 9


10/12

t

v

restraint (A), the lower strength material does

not provide any help against cracking. Neither

material will provide any ductility. It might be ar-gued that the higher strength material (lower fig-

ure) would be stronger. It still will perform in abrittle manner if over stressed.

Assuming w e have good workmanship with no

defects or stress raisers, the real success of this

connection will depend upon getting the adja-

( 7 1 =

0' 2

l!ii

ii ilI

(J1

E [g3+g2+(1-L),](1+) (1-2)

- 03i

,,' E3=+.001

30,000

1- (1+.3)(1-.6)

o2=0=17.31 ksi

O 3 =

30,000

3= (1.3)(1-.6)

[.3(+.001)+Zero+Zero]=17.31 ksi or 30.00 ksi

E [(1-ILL)E3+ -

(1+) (1-2)

- - [(1-.3)(.001)+Zero+Zero]= 40.38 ksi or 70.00 ksi

1 1.3=20

/ , / " - ' " O 3 = 7 0

Figure 20

30

20

(/)(/)

' 10

ID

Steel ITS=60 ksi IYP=40 ksi I.

= i ,10 20 30 40 50 60 70

tensile stress (o) ksi

SteelTS=70 ksi

YP=55 ksi

30 .' 27.5.

20

O'J

ID

U'J

1;=1/2 o=27.5 ksi

' , , , i !

10 20 30 40 50 55 60 70

tensile stress (o) ksi

Figure 21

cent beam to plastically deflect before this criti-

cal section cracks.

C O N C L U S I O N

The way in which a designer selects structural

details under particular load conditions greatlyinf luences whether the condi tion prov ides

enough shear stress component so that the criti-

cal shear value may be exceeded first, produc-

ing sufficient plastic movement before the criti-

cal normal stress value is exceeded. This willresul t in a duc ti le detail and min imize the'

chances of cracking.



11/12

I

REFERENCES

AISC Supplement No. 2, January 1, 1989. Tothe Specification for the Design, Fabrication &Erection of Structural Steel for Buildings.

Bjorhovde, Brozzetti, Alpsten and Tall. "ResidualStresses in Thick Welded Plates," AWS Weld-ing Journal, August 1972.

Blodgett, Omer W. Weight of Weld Metal, TheJames F. Lincoln Arc Welding Foundation, Bul-letin D417, April 1978.

Estuar and Tall. "Experimental Investigation ofWelded Built-Up Columns," AWS Welding Jour-nal, April 1963.

Gayles and Willis. "Factors Affecting ResidualStresses in Welds," AWS Welding Journal, Au-gust 1940.

Gensamer, Maxwell. "Strength of Metals UnderCombined Stresses," American Society of Met-als, 1941.

Parker, Earl R., Brittle Behavior of EngineeringStructures, John Wiley and Sons, Inc., 1957.

Shanley, F.R., "Plastic Strain--Combined Load-ing,'' Strength of Materials, McGraw-Hill BookCo., 1957; Chapter 11.

Steel Tips Apri l 1995 11


12/12

STRUCTURALSTEEL EDUCATIONALCOUNCIL

470 Fernwood DriveMoraga, CA 94556

(510) 631-9570

QSPONSORS

Adams & Smith

Allied Steel Co., Inc.

Bannister Steel, Inc.

Baresel Corp.

Bethlehem Steel Corporation

C.A. Buchen Corporation

Butler Manufacturing Co.

G.M. Iron Works Co.

The Herrick Corporation

Hoertig Iron Works

Hogan Mfg., Inc.

Junior Steel Co.

Lee & Daniel

McLean Steel, Inc.

Martin Iron Works, Inc.

MidWest Steel Erection

Nelson Stud Welding Co.

Oregon Steel Mills

PDM Strocal, Inc.

Reno Iron Works'

H.H. Robertson Co.

Southland Iron Works

Stockton Steel

Verco Manufacturing, Inc.

Vulcraft Sales Corp.

The lcai strUctural Steel industry (aboVe spOnsors)StUdS ready to aSSist YOu in determining the most

economical solution for your products. Our assistance can range from budget prices and estimated tonnageto cost comparisons; fabrication details and delivery ScheduleS.

Funding for this publication provided by the California Iron Workers Administrative Trust.


structural details to increase ductility of connections

Documents