$2\mathrm{.}13$ Design the steel framework shown in Fig. E$2-13$ at a minimum cost. The cost of a

horizontal member in one direction is $$20w$ and in the other direction it is $$30d.$

The cost of a vertical column is $$50h.$ The frame must enclose a total volume of at

least $600m^3.$ Formulate the design optimization problem.

Design of a two$-$bar truss. Design a symmetric two$-$bar truss $($both members have the same

cross section$)$ shown in Fig. $1$ to support a load W$.$ The truss consists of two steel tubes

pinned together at one end and supported on the ground at the other. The span of the truss

is fixed at s$.$ Formulate the minimum mass truss design problem using height and the cross$-$

sectional dimensions as design variables.