Partially Prestressed Concrete Beam Optimization
Publication: Journal of Structural Engineering
Volume 110, Issue 3
Abstract
A comprehensive method for minimum cost design of simply supported, uniformly loaded, partially prestressed concrete beams is presented. Nine design variables are used—six geometrical dimensions, area of prestressing steel and area of tensile and compressive mild reinforcement. The optimum design is in accordance with ACI 318/77. The imposed constraints are on the four flexural stresses, initial camber, dead and live load deflections, ultimate shear and ultimate moment capacity with respect to both the cracking moment and the applied load. The nonlinear optimization is performed using the Penalty‐Functions method coupled with Quasi‐Newton unconstrained optimization techniques. The method, successfully applied to several design problems, both cracked uncracked, clearly indicates that numerical optimization can be used to solve design problems of interest to practicing engineers.
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References
1.
Abeles, P. W., “Design of Partially Prestressed Concrete Beams,” Journal of the American Concrete Institute, Vol. 64, No. 10, Oct., 1967, pp. 669–677.
2.
ACI Committee 318, Building Code Requirements for Reinforced Concrete, (ACI 318–77), American Concrete Institute, Detroit, Mich., 1977.
3.
Avriel, M., Non Linear Programming, Analysis and Methods, Prentice‐Hall Inc., Englewood Cliffs, N.J., 1981.
4.
Bond, D., “An Examination of the Automated Design of Prestressed Concrete Bridges Decks by Computer,” Proceedings Institution Civil Engineers, Vol. 59, Dec., 1975, pp. 669–697.
5.
Building Construction Cost Data 1982, R. S. Means Company.
6.
Chou, T., “Optimum Reinforced Concrete T‐Beam Sections,” Journal of the Structural Division, ASCE, Vol. 103, No. ST8, Proc. Paper 13120, Aug., 1977, pp. 1605–1617.
7.
Gallagher, R. H., and Zienkiewicz, O. C. (ed.), Optimum Structural Design, Theory and Applications, John Wiley and Sons Inc., New York, N.Y., 1973.
8.
Goble, G. G., and Lapay, W. S., “Optimum Design of Prestressed Beams,” Journal of the American Concrete Institute, Vol. 68, No. 9, Sept., 1971, pp. 712–718.
9.
IMSL Reference Manual, 8th edition, International Mathematical and Statistical Library, Houston, Texas, 1980.
10.
Kirsch, U., “Optimized Prestressing by Linear Programming,” International Journal for Numerical Methods in Engineering, Vol. 7, No. 12, 1973, pp. 229–246.
11.
Kirsch, U., Optimum Structural Design, McGraw Hill Book Co. Inc., New York, N.Y., 1981.
12.
Lev, O. (ed.), Structural Optimization, Recent Developments and Application, ASCE, special publications, 1981.
13.
Liebman, J. S., Khachaturian, N., and Chanaratna, V., “Discrete Structural Optimization,” Journal of the Structural Division, ASCE, Vol. 107, No. ST11, Proc. Paper 16643, Nov., 1981, pp. 2177–2197.
14.
Morris, D., “Prestressed Concrete Design by Linear Programming,” Journal of the Structural Division, ASCE, Vol. 104, No. ST3, Proc. Paper 13612, Mar., 1978, pp. 439–442.
15.
Naaman, A. E., “Ultimate Analysis of Prestressed and Partially Prestressed Section by Strain Compatibility,” Journal of Prestressed Concrete Institute, Vol. 22, No. 1, Jan., 1977, pp. 32–51.
16.
Naaman, A. E., “A Proposal to Extend Some Code Provisions on Reinforcement to Partial Prestressing,” Journal of Prestressed Concrete Institute, Vol. 26, No. 2, Mar.–Apr., 1981, pp. 75–91.
17.
Naaman, A. E., “Optimum Design of Prestressed Concrete Tension Members,” Journal of the Structural Division, ASCE, Vol. 108, No. ST8, Proc. Paper 13120, Aug., 1982, pp. 1722–1738.
18.
Nilson, A. H., “Flexural Stresses After Cracking in Partially Prestressed Beams,” Journal of Prestressed Concrete Institute, Vol. 21, No. 4, July–Aug., 1976, pp. 72–81.
19.
Nilson, A. H., Design of Prestressed Concrete, John Wiley and Sons Inc., New York, N.Y., 1978.
20.
Rajagopalan, K., “Optimization of Prestressed Concrete Solid and Voided Slabs,” Computer Methods in Applied Mechanics and Engineering, Vol. 20, No. 1, Oct., 1979, pp. 71–89.
21.
Ramamurthy, S., “Optimum Design of Prestressed Concrete Slabs Using Primal Geometric Programming,” International Journal for Numerical Methods in Engineering, Vol. 13, No. 2, 1978, pp. 229–246.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 110 • Issue 3 • March 1984
Pages: 589 - 604
Copyright
Copyright © 1984 ASCE.
History
Published online: Mar 1, 1984
Published in print: Mar 1984
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