Р, 3D 10 lb P, = 25 lb 1 = 50 in Figure 1.24 Beam-column. Formulate the problem of minimizing the cost of the pipeline. 1.19 A beam-column of rectangular cross section is required to carry an axial load of 25 lb and a transverse load of 10lb, as shown in Fig. 1.24. It is to be designed to avoid the possibility of yielding and buckling and for minimum weight. Formulate the optimization problem by assuming that the beam-column can bend only in the vertical (xy) plane. Assume the material to be steel with a specific weight of 0.3 lb/in, Young's modulus of 30 x 10° psi, and a yield stress of 30,000 psi. The width of the beam is required to be at least 0.5 in. and not greater than twice the depth. Also, find the solution of the problem graphically. Hint: The compressive stress in the beam-column due to P, is Py/bd and that due to P is Pld 6Pl 212 bd? The axial buckling load is given by n'Ebd³ (P,)cri 412 48/2
Р, 3D 10 lb P, = 25 lb 1 = 50 in Figure 1.24 Beam-column. Formulate the problem of minimizing the cost of the pipeline. 1.19 A beam-column of rectangular cross section is required to carry an axial load of 25 lb and a transverse load of 10lb, as shown in Fig. 1.24. It is to be designed to avoid the possibility of yielding and buckling and for minimum weight. Formulate the optimization problem by assuming that the beam-column can bend only in the vertical (xy) plane. Assume the material to be steel with a specific weight of 0.3 lb/in, Young's modulus of 30 x 10° psi, and a yield stress of 30,000 psi. The width of the beam is required to be at least 0.5 in. and not greater than twice the depth. Also, find the solution of the problem graphically. Hint: The compressive stress in the beam-column due to P, is Py/bd and that due to P is Pld 6Pl 212 bd? The axial buckling load is given by n'Ebd³ (P,)cri 412 48/2
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:P = 10 lb
P, = 25 lb
1 = 50 in
%3D
Figure 1.24 Beam-column.
Formulate the problem of minimizing the cost of the pipeline.
1.19 A beam-column of rectangular cross section is required to carry an axial load of 25 lb
and a transverse load of 10lb, as shown in Fig. 1.24. It is to be designed to avoid the
possibility of yielding and buckling and for minimum weight. Formulate the optimization
problem by assuming that the beam-column can bend only in the vertical (xy) plane.
Assume the material to be steel with a specific weight of 0.3 lb/in', Young's modulus of
30 x 10° psi, and a yield stress of 30,000 psi. The width of the beam is required to be at
least 0.5 in. and not greater than twice the depth. Also, find the solution of the problem
graphically. Hint: The compressive stress in the beam-column due to Py is Py/bd and
that due to P, is
P,ld
6Pl
212
bd?
The axial buckling load is given by
1El nEbd
(Py)eri =
412
4812
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