Questions -

Q1. An 8 x 8 x 1 -in. angle is used for a beam that supports a positive bending moment of 7500 ft-lb. The moment is applied in the XY-plane as shown in Figure 1. The moments of inertia from a structural steel handbook are I_y = I_z = 89 in⁴ and I_min = 36 in⁴. Determine:

a. The maximum flexural stress and its location on the cross section.

b. The orientation of the neutral axis; show on a sketch of the cross section.

Q2. A crank hook having a capacity of 15 tons has a trapezoidal cross section as shown in Figure 2. Find the maximum tensile and compressive stresses that exist when the hook is carrying its rated load.

Q3. Determine the maximum torque that can be applied to the aluminum (G = 4000 ksi) section shown in Figure 3 if the maximum allowable shearing stress is 24,000 psi.

Q4. A 12-in. steel (G = 12,000 dsi) I-beam is subjected to a torque of 35,000 in-lb.

a. Determine the maximum shear stress and the angle of twist in a 12-in. length.

In order to reduce the maximum shear stress, ½-in. steel plates were welded onto the section ash shown by the dotted lines. For the modified section,

b. Determine the maximum shear stress and the angle of twist in a 12-in. length.

Need proof of final answers using equations.