11819 JANUARY 1976 ST1

JOURNAL OF THESTRUCTURAL DIVISION

DISCUSSION

Proc. Paper 11819

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

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

Torsion-Bending-Shear Interaction for Concrete Beams, by LennartElfgren, Inge Karlsson, and Anders Losberg (Aug., 1974. PriorDiscussions: 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 Hamadaand Jack Longworth (Nov., 1974. Prior Discussion: Sept., 1975).

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

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

by William H. Mooseker . . . . . . . . . . . . . . . . . . . . . . . . . . 296by 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 thisdiscussion 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 StainlessSteel Mernber," Report No. 327, Department of Structural Engineering, CornellUniversity, Ithaca, N.Y., 1967.

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

25. Wang, S. T., "Nonlinear Analysis of Locally Buckled Thin-Walled Structures,"Proeeedings of the International Conferenee on Computational Methods in NonlinearMechanics, Austin, Tex., Sept., 1974, pp. 809-818.

26. Wang, S. T., "Post-Local- Buckling Behavior of Continuous Box Girders ," Proeeedingsof 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-WalledContinuous 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 SteelMembers ," 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 StressGradient," Proeeedings of the Third International Speciaity Conference on Cold-FormedSteel Struetures, St. Louis, Mo., Nov., 1975.

TORSION-BENDING-SHEAR INTERACTION FOR CONCRETE BEAMS3

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

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

Solanki first deals with the question of the contribution of the concretecompression zone. This is an interesting problem and the writers have recentlydiscussed it in another paper (39). Solanki then discusses the ratio of torsionto shear resistance of the be am section and arrives at a couple of interactionequations. However, as the derivation of the equations as weil as the underlyingassumptions are unknown, it is not possible to comment on them.

a August, 1974, by Lennart Elfgren, Inge Karlsson, and Anders Losberg (Proc. Paper10479).

7Assoc. 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 range0.5 < cot o.T < 2. The writers agree with Pandit that this limit is rather crudeand that further investigation is needed to establish morc rcfined limits forthe different modes of failure and for different load cornbination . Sorne progressin 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 maygive 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 madein 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 armsare functions of the amount of reinforcement and of the concrete compressionstrength, as is the case of beams loaded in pure bending. This can be takeninto account in a more refined theory (4,41). In this way a more correct valuefor the torsionai strength of beams with high percentages of longitudinalreinforcement can be obtained.

HelmyaIso discusses the values of the inclination of the concrete compressionstruts. 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 graduallyas more torsionai moment is applied. The expressions given in the paper forcot o. T and cot o. v do only apply to the cases pure torsion' and pure shearrespectively. This fact should have .been more emphasized in the paper. InEq. 18, which Helmy discusses, the variation of cot aT gives rise to differentvalues of the seeond term for different load ratios. Only for pure torsion willcot 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 publishedin 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 RcctangularReinforced 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 Failureof Prestressed Beams in Torsion und 1\ milli ." UNICIV Report No. R-136, Schoolof 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 theUltimate Torslonal Morn nI rOI' 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' leBearns lind r ornbln d Londin ," tructurai Engineering Report No. 48, Departmentof 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 II 111M, "th 'sis pI' S nI d to th nivcrsity of Toronto, at Toronto, Ontario, Cannd l, 11 11)75,in plutinI 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.vPage 1670, last line, denominator of first term under radical sign: Should readh' 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 (August1975):

Awcr;vb' h'Page 1712, Eq. 41: Should read T= 2 cot aT instead of T

s

sPage 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. Theobjective of the paper is to illustrate reliability-based design. The choice ofexamples and parameter values does not cover the entire range of designs asrightIy pointed out by the discusser. Development of a complete set of structuraldesign criteria based on the proposed probabilistic format and using latest strengthprediction theories and data is under way (31,32).

At the time of writing this paper, the references (26,27,28,29,30) were notavailable to the writers. As such, the latest contributions of the discusser werenot 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.7TaskmasterComputer Systems, Edmonton, Alberta, Canada.