Abstract
The subject matter of this paper, which is a continuation of the author's former works is the research of the optimum form of a prestressed concrete beam. Sec. 2 brings a solution of the design problem of a rectangular beam by equalizing normal stresses at the ends. The considerations of Sec. 3 concern a rectangular beam designed for minimum potential of elastic forces produced by the useful load. Sec. 4 discusses the design of a double-tee beam with the same condition. In. Sec. 5 devoted also to the design of a double-tee beam is considered a factor originating form the shear forces and hitherto disregarded. In the last section is described an approximate method for determining the influence of shear forces on the form of a double-tee beam. Each particular solution is illustrated by numerical examples and diagrams of the functions obtained expressing the form of the beams.References
[1] A. BRANDT, Pewne twierdzenie Z zakresu kształtowania wytrzymałościowego belek sprężonych, Rozpr, Inzyn., 4, 11 (1963).
[2] Z. WASIUTYŃSKI, A. BRANDT, Aktualny stan wiedzy o kształtowaniu wytrzymałościowym konstrukcji, Rozpr. Inzyn., 2, 10 (1962).
[3] Z. WASIUTYŃSKI, A. BRANDT, The present state of knowledge in the field of optimum design of structures, Appl. Mech. Rev., 5, 16 (1963).
[4] A. BRANDT, Kształtowanie belek sprężonych przez wyrównywanie skrajnych naprężeni, Rozpr. Inzyn., 2, 8 (1960).
[5] H. G. HOPKINS, Limits of economy of material in plates, J. Appl. Mech., nr 55-APM-2.
[6] E. T. ONAT, W. SCHUMANN, R. T. SHIELD, Design of circular plates for minimum weight, J. Appl. Math. Phys., 6, 7 (1957).
[7] W. PRAGER, R. T. SHIELD, Minimum weight design of circular plates under arbitrary loading, J. Appl. Math. Phys., 4, 10 (1959).
[8] R. T. SHIELD, Plate design for minimum weight, Quart. Appl. Math., 2, 18 (1960).
[2] Z. WASIUTYŃSKI, A. BRANDT, Aktualny stan wiedzy o kształtowaniu wytrzymałościowym konstrukcji, Rozpr. Inzyn., 2, 10 (1962).
[3] Z. WASIUTYŃSKI, A. BRANDT, The present state of knowledge in the field of optimum design of structures, Appl. Mech. Rev., 5, 16 (1963).
[4] A. BRANDT, Kształtowanie belek sprężonych przez wyrównywanie skrajnych naprężeni, Rozpr. Inzyn., 2, 8 (1960).
[5] H. G. HOPKINS, Limits of economy of material in plates, J. Appl. Mech., nr 55-APM-2.
[6] E. T. ONAT, W. SCHUMANN, R. T. SHIELD, Design of circular plates for minimum weight, J. Appl. Math. Phys., 6, 7 (1957).
[7] W. PRAGER, R. T. SHIELD, Minimum weight design of circular plates under arbitrary loading, J. Appl. Math. Phys., 4, 10 (1959).
[8] R. T. SHIELD, Plate design for minimum weight, Quart. Appl. Math., 2, 18 (1960).