Problem Title: Optimum Design of a Roof Truss Related topic: Constraint optimization Shown in Figure 1 is a steel roof truss of an industrial building. In addition to its own weight, the roof truss is subjected to a live load of 0.5 kN/m to allow for maintenance as well as a uniform uplift of 0.8 kN/m due to wind load. It is required to find the required cross sections of the truss members that produce the minimum total weight of the truss satisfying the following conditions: 1- The stress in each member is less than the allowable stress of 55 MPa, 2- The stress in each member is less than the buckling stress, 3- Each member group, i.e., top chord (orange), webs (red), and bottom chord (black) has the same cross-sectional properties, and 4. All other reasonable geometrical constraints. Assume elastic design and circular cross sections for all the members. Note: The supports are hinges( have horizontal and vertical components). In addition, treat the given loads as acting in the vertical direction