OFFSHORE TECHNOLOGY CONFERENCE6200 North Central ExpresswayDallas, Texas 75206

Plastic Consideration on Punching ShearStrength of Tubular Joints

ByM. S. Lee, A. P. Cheng~ Amoco International Oil Co., C. T. Sun, Purdue U., and R. Y. Lai.

U-. of--Wi searls in

THIS PAPER IS SUBJECT TO CORRECTION

©Copyright 1976Offshore Technology Conference on behalf of the American Institute of Mining, Metallurgical, and PetroleumEngineers, Inc. (Society of Mining Engineers, The Metallurgical Society and Society of Petroleum Engineers),American Association of Petroleum Geologists, American Institute of Chemical Engineers, American Societyof Civil Engineers, American Society of Mechanical Engineers, Institute of Electrical and Electronics En~

gineers, Marine Technology Society, Society of Exploration Geophysicists, and Society of Naval Architectsand Marine Engineers. .This paper was prepared for presentation at the Eighth Annual Offshore Technology Conference, Houston,Tex., May 3-6, 1976. Permission to copy is restricted to an abstract of not more than 300 words. Illustrationsmay not be copied. Such use of an abstract should contain conspicuous acknowledgment of where and bywhom the paper is presented.

ABSTRACT

An alternative procedure is presentedfor calculating the punching shearstrength of a tubular joint. Thedevelopment is based on the fullyplastic consideration of the, chordmember. Both in-plane and out-of­plane bending moments are consideredin the formulation. The resultsindicate that, for certain combina-_tions of loads, the proposed approachyields a more rati()nal and economicaljoint design compared to the currentAPI approach.

INTRODUCTION

An important criterion for offshorestructure- tubular joint design is t4epunching shear requirements r§com­mended by the API (1). The currentcalculated punching shear equation isbasically a combination of the axial ­stress and the maximum bendingstresses, with no distinction betweenin-plane and out-of-plane bendingstresses. As a result, the calcu­lated punching shear stress is under­estimated under some loading condi­tions. On the other hand, the currentallowable punching shear equation isReferences and illustrations at endof paper.

derived from the correlation of theaxial load test data. This generallyresults in a conservative design whenthe bending stress is predominant.This paper presents an improvementfactor· for bending to the currentallowable punching shear equation._The development is based on the fullyplastic consideration of the chord.Also presented is a punching shearequation which combines the axialstress with both the in-plane andout-of-plane bending moments. Designcurves and a sample problem arepresented for the users who desire toapply the proposed procedure to checktheir joint designs.

EQUATIONS DERIVATION

Calculated Punching Shear Stress

A typical "Y" connection joint isshown in Fig. 1. All the jointgeometrical notations defined byAPI RP2A are followed. The right­hand rectangular Cartesian coordinatesystem is used with the x-axis alongthe chord member center line and the_y-plane coinciding with the chord­brace plane. The brace member is

260PLASTIC CONSIDERATION ON PUNCHING SHEAR

STRENGTH OF TUBULAR JOINTS OTe 2641

• •• (2)

X tan 2 e F(cos8)+(2-sec 2 8) E(COS8)]-tan 2 8 F(cos8)+(1+sec 2 8) E(cos8)

carrying an axial_ f()_y-c~_ P, an Jll- _plane bending moment Ml and an out­of-plane bending moment MO. Thepunching shear ~qrthe joint can beapproximated by superimposing the ~

axial stress to bending stresses;namely,

tan- 1[

.1m sine

••• (1 )

with

brace axial stress

brace maximu~in-plane

bending stress

brace maxj.rr1llm__out-Clf __planebending stress

angle at the point of ellipsewhere maximum punching shearoccurs

and

where

m

Observe that ¢ is a function of forceratio m and geometry 8. For a givenjoint geometry and brace memberforces (stresses), Equations (1) and(2) constitute the formulae for cal­culating the maximum punching shear.

Ultimate Punching Shear CapacityFully Plastic Analysis

In a normal elastic analysis, themaximum allowable loads for a jointshown on Figure 1 must satisfy thecondition

2. .~E (cos8)'TfSln8

+ (2-sec 2 e) E(cosB)]

vp

+

P e sin8

2tdE(cos8)

i _. 23Me Sln e casp

td2[tan2eF(COSe)+(2-se~2e)E(~OSe)J

3M~ sin8 SincP

kc

-,.-_4,-'--;:- -[-tan 2 eF(Cos8)-­3'Tfsin8 -

with

• •• (3)

where F and E are complete ellipticalintegrals of the first kind andsecond kind, respectively. Note thatk a , kb and k c arethe~owest r~lative

length and section factors for- a-­noncircular intersection curve.Thus, Equation (1) giYE!s a conserva­tive result in design~ An inspectionof k a and kb values indicates thatthey agree_with those_~hownoJ:l APIRP2A, Fig. 2.22-1. Taking thediff-erenEiationof Equation (1) withrespect to ¢ yields the equation fordetermining the angle ¢ where p is ~

maximum; i. e. ,

d = 2rb

where Pe, M~ and Mg are maximum loadsfor axial force, in-plane bendingmoment and out-of-plane bendingmoment, respectively, in elasticanalysis. And vp is the maximumultimate punching shear stress. Byintroducing the parameter

• •• (4)

GTC 2641 M. S. LEE, A. P. CHENG, C. T. SUN, AND R. Y. LAI 261

and

Equation (3) can be rewritten as

Vptd f 1f + A I 2 .. 21-cos 8sin w dW

sin8 B

Vptd-- h(8,A,B) ••. (9)sin8

tan 2 S F (cos8) +(2-sec 2 8) E (cos8)

Vptd ![ 1si n

2 e 2B(cos8)

. 2 2 J3A~COS</J (1+m tan p)+

Pe

••• (5)

The above quantity is the maximumaxial load th~t the brace can carryfor a given ;\~ .. and m. The correspond­ing maximum bending moments are

with

f(8,A,B)

••• (6)

Following the conventional approachfor plastic design as outlined byAISC(2), the stress diagram for anintersection at the chord-brace con­nection is idealized as shown in Fig.2. The axial load P p is assumed tobe supported entirely by a centrallylocated portion of the total cross­section area and the bending momentis resisted by the rest of the area.Furthermore, the entire section isstressed to the level correspondingto the ultimate punchi~g shear stress.The bending moments and the axialload in the brace shown by Fig. 2 canbe easily evaluated. We obtain

+ c~se [sin-1

(cos8sinB)

- sin- 1 (cosSsinA) ]

g(8,A,B)

cos8

h(B,A,B) E(1f+A,cos8) - E(B,cos8)

·2V t fB X dsP A

... Or-

Note the values of A and Barerelated to A and m by

f(8,A,B)/4sin8h(8,A,B)

••• (1 0)

and

f(8,A,B)/sinSg(S,A,B) ••• (11)m

The increase in the load-carryingcapacity due to plastification can berepresented by the "improvementfactor" n, i.e.,

••• (8)g(8,A,B)4sin8

2

Vptd-- f B sinw/1-cos 2 8sin 2 w dw2sin8 A

V td 2P

P p Mi MOn ---E.. = ---E. ... (12 )

P e Mi MOe e

a -L-lwzllx LI.LI’I UJI .Iu.DuhfiK LJULLWLD U-L-G .40%

Substituting Eqs. (5) and (9) into is a tedious job to calculate theseEq. (12) results in numbers. However, the following

discussions may help those who areinterested in preparing numerical

~ = sine h(e,A,B) l-(e,A,B) ...(13) ‘data for design. Taking advantageof the fact that the joint punchingshear capacity is not affected by

with the bending moment’s sign, we assumeMfi and M: both to be positive. Thisassumpt~onr together with the engi-

l(e,A,B) =1

neering properties of material, lead2E(cose) ‘ to the following restriction on A and

3~iC0S$(l+m2tan2@)B:

+

tan26F(cos0) +(2-sec28) E(cose)sinB-sinA>O; COSA-COSB20 . . . (16)

or

and

~=L f(e,A,B) l(O,A,B) . ..(14).1 < A ~ ~; B-As?r4ai2- 2.

. . . (17)

It follows that q actually depends on

A, m and @ only. Once the A and B values are obtained,

the improvement factor rI can be cal-culated from Eq. (13) and tables or

APPLICATION curves of rIvalues for different A;,.. .. ..m and 0 can be prepared.

If more exact punching shear stresscalculations are needed, Equation (1) Since n becomes the minimum forshould be used in lieu of the constant Ai and m when 0 approachesequation..shown on_APIRP2A_, page 17. 900, it will be conservative to useHowever; the angle @ in Equ”ation- (1) values at e = 900 for all inter-has to be determined from Equation section angles. It is also observe~(2) before the calculation can that the orientation of the moment isproceed. Values of @ vs. moment immaterial to q for this particularratios m for several intersection intersection <angle. Thus, by settingangles 0 are plotted in Fig. 3. Also MO = 0 and ML z iv and noting B = -A,the curve for kc vs. 0 is added to Equations (10) and (13) are reducedthe current API RP2A Fig. 2.22-1 and tois shown ‘in Fig. 4. Note that thekc value is considerably lower thanthe kb value for a chosen e. As for -sinA

A=—, -:5 A ~ O (18)

the allowable punching shear in the

. . .?I’+2A

chord wall, the authors propose to

incorporate the improvement factor ~ and

to the current API RP2A Eq. (23),i.e. ,

Fy n = (I+4A)(1+2Ay) (19)

‘P — (plus 1/3 increase...

= QQ~Qf.9Y.7

The transcendental Equation (18) can.where applicable) ...(15) easily be solved by numerical method.

The curve of improvement factor n vs.pseudo moment/axial load ratio X is

There--is an obstacle to be overcome shown in Fig. (5). When using thebefore ~ ca’n be evaluated, which is curve, A should be taken as the ratioto determine the plastic zone between between the resultant moment M andA and B as shown in Fig. 2. O“bvi- the axial load P, i.e.,ously, A and B can be determinedfrom Eqs. (10) and.(n) numerically.Since the equations are cotipled, it b% and M = ~(Mi)2+(M0)2 ...(20)

OTC 2641 M. S. LEE, A. P. CHENG, C. T. SUN, AND R. Y. LAI 26

EXAMPLE

Given

1. Chord Member Can Section

64.75’’0.D. X 1.125 W.T.Stress in can section: 15.14 ksi

2. Brace Member

28’’o.D. X .5(IW.T.

P=391.21 kip, fa=9.06 ksi.

Mi=3523.36 kip-in, f~=12.08 ksi.

M0=2475.46 kip-in, f~=8.48 ksi.

3. Intersection Angle

0 = 430

4. Material Yield Strength

= 50 ksi

Since m = ~ = 1.42, we obtain from

Equation (2) or from Fig. (3) that

4 = 40.20. Furthermore, from Fig.(4)we have

ka = 1.24, kb = 1.64, kc = 1.37.

Using Eq. (1) we obtain

Vp = * (sin 43°~”.

— .0s 40.20 ;”~”sin 40.2~”-”+ 12.08

1.64 1.37

= 5.83 ksi vs. 5.58 ksi by APIequation.. __

thus from Fig.(5) we obtain rI= 1.36.Therefore, the allowable punchingshear is

Vp = qQ6Qf Fy

.9y”7. . .. (15)

=1.36X50

.9 X 28.28-7

= 1.36 X 5.35

= 7.28 ksi (since Q~=Qf=l)

vs. 5.35 ksi in the API equation.

CONCLUSION

An alternative procedure has beenpresented for calculating the punch-ing shear stress of a tubular joint.The procedure was developed byconsidering the effect of both thein-plane and out-of-plane bendingmoments and the full plastificationof the chord member. The use of. theproposed approach will generallyyield a more economical joint designcompared to the present API method.The sample problem demonstrates thatthe use of the proposed procedure .increased the allowable punchingshear stress by 36%. On the otherhand, the example also shows thatthe present API code somewhat under-estimates the calculated punchingshear stress. This is typical inconventional jacket design where theout–of–plane bending moments areusually less than the in-plane bend-ing moments.

ACKNOWLEDGEMENTS

The authors wish to express theirgratitude to Amoco International OilCompany for permission to presentthis paper. Special recognition isextended to Edmond R. Genois andRudolph A. Hall of Petro-MarineEngineering, Inc., for their contri-bution in conducting this study.Special thanks to Denise Bellon fortyping and editing the manuscript.

BIBLIOGRAPHY

1.

2.

“Recommended Practice for Planning,Designing, and Constructing FixedOffshore Platform,” API RP2A,Sixth Edition, January 1975.

“plastic Design Steel,” AmericanInstitute of Steel Construction,1959.

b

7)*)

)-Y

Location OfY Max. Calculated Vp - “

/ 1tb

Z-=7

.x@=+

( J

Fig. 1l’=+

1111111::1111111111+ Full Plastificetion

II

1111111::111111 Axial Loed

>

++ Plastic Bending

dlsin 0

‘~~ ,

I

Plastic Bending

(11111::1111111+ &daI Loed _

II

11111111::11111111+ Full Plw@ication

Fig. 2

+

4.0 4.!

3.0 3.0

2.0 2.0

1.01.01 I I I I I I ! I ! I I I I I I I I I

ow 60”

0~o o“

o

Fig. 4

1.5

1.4

1.3

T

1.2

1.1

1.02

A

I.5

I.4

1.3

1.2

1.1

1.0

Fig. 5