Torsion-Bending-Shear Interaction for Concrete Beams: Closure of discussion

11819 JANUARY 1976 ST1

JOURNAL OF THE STRUCTURAL DIVISION

DISCUSSION Proc. Paper 11819

Post-Local-Buckling Behavior of Continuous Beams, by Shien T. Wang and Sheng S. Yeh (June, 1974. Prior Discussions: Mar., May, 1975).

closure . . . . . . . . . . . . . . . .. 287

Torsion-Bending-Shear Interaction for Concrete Beams, by Lennart Elfgren, Inge Karlsson, and Anders Losberg (Aug., 1974. Prior Discussions: Mar., July, Aug., 1975).

closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Illustrations of Reliability-Based Design, by Mayasandra K. Ravindra, Neils C. Lind, and Wilfred Siu (Sept., 1974. Prior Discussion: Aug., 1975).

closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

Concrete Encased Steel Columns-Design Tables, by Richard W.

Furlong (Sept., 1974. Prior Discussion: Aug., 1975).

closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

Buckling of Composite Beams in Negative Bending," by Sumio Hamada and Jack Longworth (Nov., 1974. Prior Discussion: Sept., 1975).

by Mik/os Ivanyi . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 293

Linear Structural Analysis of Multistory Buildings," by R. Shankaran Nair (Mar., 1975).

by William H. Mooseker . . . . . . . . . . . . . . . . . . . . . . . . . . 296 by Edward L. Wilson and J. P. Hallings . . . . . . . . . . . . . . . .. 298 Note.- This paper is part of the copyrighted Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, Vol. 102, No. ST!, January,

1976.

a

Discussion period closed for this paper. Any other discussion received during this discussion period will be published in subsequent Journals.

285

ST1

Appendix.-References

DISCUSSION

289

22. Bleustein, J. L., and Gjelsvik, A., closure to "Rational Design of Light Gage Beams,"

Journal of the Struetural Division, ASCE, Vol. 97, No. STI2, Proc. Paper 8557, Dec., 1971,pp. 2884-2885.

23. Johnson, A. L., and Winter, G., "The Structural Performance of Austenitic Stainless Steel Mernber," Report No. 327, Department of Structural Engineering, Cornell University, Ithaca, N.Y., 1967.

24. Tien, Y. L., "Local Buckling of Plates and Sections of Flexural Members Under Stress Gradients," thesis presented to the University of Kentucky, at Lexington, Ky., in 1975, in parti al fulfilJment of the requirements for the degree of Doctor of Philosophy.

25. Wang, S. T., "Nonlinear Analysis of Locally Buckled Thin-Walled Structures,"

Proeeedings of the International Conferenee on Computational Methods in Nonlinear Mechanics, Austin, Tex., Sept., 1974, pp. 809-818.

26. Wang, S. T., "Post-Local- Buckling Behavior of Continuous Box Girders ," Proeeedings of the ASCE Specialty Conierence on Metal Bridges, St. Louis, Mo., Nov., 1974, pp. 173-200.

27. Wang, S. T., and Jsa, S. T., "Post-Local-Buckling Behavior of Multistory Frarnes ,"

Proceedings of the Symposium on Tall Buildings: Planning, Design, and Construction, Nashville, Tenn., Nov., 1974, pp. 459-476.

28. Wang, S. T., and Jsa, S. T., "Stiffness Analysis of Locally Buckled Thin-Walled Continuous Bearns," International Journal of Camputers and Struetures, Vol. 5, No.

1, Apr., 1975, pp. 81-93.

29. Wang, S. T., Errera, S. J., and Winter, G., "Behavior of Cold-Rolled Stainless Steel Members ," Journal of the Struetural Division, ASCE, Vol. 101, No. ST11, Proc.

Paper 11724, Nov., 1975, pp. 2337-2357.

30. Wang, S. T., and Tien, Y. L., "Buckling of Plates and Beam Sections Under Stress Gradient," Proeeedings of the Third International Speciaity Conference on Cold-Formed Steel Struetures, St. Louis, Mo., Nov., 1975.

TORSION-BENDING-SHEAR INTERACTION FOR CONCRETE BEAMS

3

Closure by Lennart Eltgren,? Inge Karlsson," and Anders Losberg"

•

The writers would like to thank Solanki, Pandit, and Helmy for their interest in the paper and for their vaIuable comments.

Solanki first deals with the question of the contribution of the concrete compression zone. This is an interesting problem and the writers have recently discussed it in another paper (39). Solanki then discusses the ratio of torsion to shear resistance of the be am section and arrives at a couple of interaction equations. However, as the derivation of the equations as weil as the underlying assumptions are unknown, it is not possible to comment on them.

a

August, 1974, by Lennart Elfgren, Inge Karlsson, and Anders Losberg (Proc. Paper 10479).

7

Assoc. Prof. of Struct. Engrg., Univ. of Luleå, Luleå, Sweden.

8Project Engr., Cementa AB, Malmö, Sweden.

9Prof. and Head, Div. of Concrete Structures, Chalmers Univ. of Tech., Göteborg,

Sweden.

290

_{JANUARY 1976 ST1}

Panditgives several valuable comments and lists pertinent addirional references.

The main question he rises concerns the justificati n for the proposed range 0.5 < cot o.

T

< 2. The writers agree with Pandit that this limit is rather crude and that further investigation is needed to establish morc rcfined limits for the different modes of failure and for different load cornbination . Sorne progress in this area has recently been reported by BeJow, et al. (37,38), Misic (40), and Rabbat (41).

Helmy points out that high percentages of longitudinal reinforcement may give a lower value of the torsionai strength than what is predicted by Eq.

19b. As is pointed out in the paper, several simplifications have been made in order to arrive at a simple and compact theory.

One of them is that the length of the moment lever arms have been approximated to the distances, h' and b'. It is obvious that the lengths of the lever arms are functions of the amount of reinforcement and of the concrete compression strength, as is the case of beams loaded in pure bending. This can be taken into account in a more refined theory (4,41). In this way a more correct value for the torsionai strength of beams with high percentages of longitudinal reinforcement can be obtained.

HelmyaIso discusses the values of the inclination of the concrete compression struts. These inclinations var y with the applied loading ratio. For example, the angle o.

T

is 'zero for pure bending and the angle then increases gradually as more torsionai moment is applied. The expressions given in the paper for cot o.

T

and cot o. v do only apply to the cases pure torsion' and pure shear respectively. This fact should have

.been

more emphasized in the paper. In Eq. 18, which Helmy discusses, the variation of cot

aT

gives rise to different values of the seeond term for different load ratios. Only for pure torsion will cot o.

T

have a eonstant value which gives the value unity to this term.

Finally, Helmy comments on the case with not yielding stirrups. This is an important problem. Models to analyse this case have rcccntly been published in Refs. 37,38,40, and 41.

Appendix.-References

37. Below, K. D., Rangan, B. V., and Holl, A. S" "O

11'1'111

'fh'ol'Y for Rcctangular Reinforced and Prestressed Beams in Törslon

IIlld

B

lIuin ," UNIC!V

Report No.

R-13I, School of Civil Engineerlng, nlv rslty of N 'w

SOUl.h

Wales, Kensington, New South Wales, Au tralla, Apr. 1974, p, 2 ,

38. Below, K. D., Rangan, B, V" und lInii, A, S"

"Rllliol

ul Theory for Balanced Failure of Prestressed

Beams in Torsion und 1\ milli ." UNICIV

Report No. R-136, School of Civil Engineering, niv orslty or ^{N w South Wales,} Kensington,New South Wales, Australia, Nov.rl 74, p, 15,

39. Elfgren, L., Karlsson, 1.. nnd I.osh

I' •

A" "Nodal Forces in the Analysis of the Ultimate Torslonal

Morn nIrOI' R 'lllll ular Bcams,"

Magazine of Concrete Research, London,

nglnnd, Vol. 2(j, NI, H6. MUl'"

1974,

pp. 21-28,

Discussion in Vol. 27,

No, 90, Mar" 1975, pp, 42-45, .

40, Misic, V" and

Wurwnruk,

V" " ulid

And Hollow

Rectangular

Prestressed Con

I'

le Bearns lind r

ornbln

d

Londin ,"

tructurai Engineering Report No. 48, Department of lvII Bngln

l'ill[l,

Unlv 'I'slty of Alberta, Edmonton, A1berta, Canada, S pt., 1974,

p,274,

^I

41. Rabbut, I~, ,," A Vurlnb) ' Angle Space Truss Modelfor Structural Coner ( Il

II111M, "

th 'sis

^pI'

S nI d to th nivcrsity of Toronto, at Toronto, Ontario, Cannd

^l, 11

11)75,

inplutinI Vulflllm ni or the

requirernents for the degree of Doctor of

Philo

uph ,

ST1 DISCUSSION 291

Errata.- The following corrections should be made to the original paper:

Page 1657, name of first writer: Should read "Elf'gren" instead of "Elfren "

Page 1661, line 3: Should read "at failure" instead of "failure"

Page 1666, Eq. 12, last line: Should read cot

aT - av

instead of cot

aT

+ cot o. v

Page 1670, last line, denominator of first term under radical sign: Should read h' instead of b' + h'

Page 1671, caption, Fig. 14: Should read "Ref , 6" instead of "Ref. 5"

Page 1673, Ref. 4: Should read "Elfgren" instead of "Elfreri"

Page 1674, line 2: Should read "in 1971" instead of "in 1972"

Page 1674, Ref. 5: Should read "Elfgren" instead of "EIfren"

Page 1674, Ref. 6: Should read "Elfgren" instead of "EIfren"

The following corrections should be made to the discussion by Helmy (August 1975):

Awcr;vb' h'

Page 1712, Eq. 41: Should read T= 2 cot

aT

instead of T

s

s

Page 1713, line 2: Should read cot o.

^T

instead of cot o.

^t

ILLUSTRATIONS OF RELIABILITY- BASED DESIGN a

Closure by Mayasandra K. Ravindra," M. ASCE, Niels C. Lind,' A. M..

ASCE, and Wilfred Siu

7

The writers wish to thank Bjorhovde for his discussion of the paper. The objective of the paper is to illustrate reliability-based design. The choice of examples and parameter values does not cover the entire range of designs as rightIy pointed out by the discusser. Development of a complete set of structural design criteria based on the proposed probabilistic format and using latest strength prediction theories and data is under way (31,32).

At the time of writing this paper, the references (26,27,28,29,30) were not available to the writers. As such, the latest contributions of the discusser were

not utilized in the paper. ' .'

'September, 1974, by Mayasandra K. Ravindra, Niels C. Lind, and Wilfred Siu (Proc.

Paper 10779).

sSr. Engrg. Analyst, Sargent

&

Lundy, Chicago, IlI.

6Prof., Dept. of Civ. Engrg., Univ. of Waterloo, Waterloo, Ontario, Canada.

7Taskmaster Computer Systems, Edmonton, Alberta, Canada.