journal of the structural division
JOURNAL OF THE
Behavior of Continuous Beams, by Shien T. Wang
and Sheng S. Yeh (June, 1974. Prior Discussions:
Mar., May, 1975).
closure . . . . . . . . . . . . . . . ..
for Concrete Beams, by Lennart
Elfgren, Inge Karlsson,
and Anders Losberg
(Aug., 1974. Prior
Mar., July, Aug., 1975).
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 289
Illustrations of Reliability-Based Design, by Mayasandra
Neils C. Lind, and Wilfred Siu (Sept., 1974. Prior Discussion: Aug.,
closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
Concrete Encased Steel Columns-Design
Tables, by Richard W.
Furlong (Sept., 1974. Prior Discussion: Aug., 1975).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Buckling of Composite Beams in Negative Bending," by Sumio Hamada
and Jack Longworth (Nov., 1974. Prior Discussion: Sept., 1975).
by Mik/os Ivanyi . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Linear Structural Analysis of Multistory Buildings," by R. Shankaran
Nair (Mar., 1975).
by William H. Mooseker . . . . . . . . . . . . . . . . . . . . . . . . . .
by Edward L. Wilson and J. P. Hallings
. . . . . . . . . . . . . . . ..
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,
a Discussion period closed for this paper. Any other discussion received during this
discussion period will be published in subsequent Journals.
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
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,
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.
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 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
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,
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
give a lower value of the torsionai strength than what is predicted
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
of beams with high percentages
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
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,
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,
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 nI rOI' R 'lllll ular Bcams," Magazine of Concrete Research,
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,
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 ,
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
Page 1712, Eq. 41: Should read
Page 1713, line 2: Should read cot o.T instead of cot o.t
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) we re 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.
sSr. Engrg. Analyst, Sargent & Lundy, Chicago, IlI.
6Prof., Dept. of Civ. Engrg., Univ. of Waterloo, Waterloo, Ontario, Canada.
7Taskmaster Computer Systems, Edmonton, Alberta, Canada.