(Solved): Problem 3 A single-span steel beam with simple supports is uniformly loaded as shown in Figure 1. ...

Problem 3 A single-span steel beam with simple supports is uniformly loaded as shown in Figure 1. Three options are provided in Table 1 for the beam section profile. A) Select the lightest profile among the three that satisfies the bending strength and deflection requirements. Given: - Distributed dead load, \( \mathrm{qDL}_{\mathrm{D}}=400 \mathrm{lbf} / \mathrm{ft} \) Figure 6- Beam Diagram - Distributed live load, \( \mathrm{qu}_{\mathrm{u}}=500 \mathrm{lbf} / \mathrm{ft} \) - \( \quad \) Yield stress, \( \mathrm{F}_{\mathrm{y}}=50 \mathrm{ksi} \) - Allowable bending stress, \( F_{b}=30 \mathrm{ksi} \) - Modulus of Elasticity (Young's modulus), E= 29,000 ksi - Deflection limits: - Assume the section profile is compact and the beam is adequately braced. Parameters: - \( \quad \mathrm{L}=50 \mathrm{ft} \) (span) Table 1- Section Profile Options