A beam is subjected to equal 12.1 kip-ft bending moments. Assume t = t2 = tw= 2 in., d = 12 in., b1 = 5 in., and b2 =7 in. The cross- sectional dimensions of the beam are illustrated. Determine: (a) the distance y to the centroid (measured from the bottom), the moment of inertia l, about the z axis, and the controlling section modulus Sz about the z axis. (b) the bending stress oy at point H (positive if tension, negative if compression). (c) the bending stress ox at point K (positive if tension, negative if compression). (d) the maximum bending stress omax produced in the cross section (positive if tension, negative if compression). M M d K b2 Cross scction Answers: (a) ỹ = in., Iz = i in.4, Sz = i in.3. i (b) GH i psi. (c) oK = i psi. (c) Ơmax i psi.

A beam is subjected to equal 21.7 kip-ft bending moments. Assume t₁ =t₂ = tw- 3 in., d = 15 in., b₁ = 6 in., and b₂ =8 in. The cross- sectional dimensions of the beam are illustrated. Determine: (a) the distance y to the centroid (measured from the bottom), the moment of inertial₂ about the z axis, and the controlling section modulus S₂ about the z axis. (b) the bending stress at point H (positive if tension, negative if compression). (c) the bending stress ok at point K(positive if tension, negative if compression). (d) the maximum bending stress max produced in the cross section (positive if tension, negative if compression). M Answers: (a) y = (b) 6μ = 6.978 (c) OK (c) omax = = i M in., I₂ = X i psi. psi. psi. 41 1₂ 2886.59 b₁ b₂ Cross section H K in.4, S₂ = i in.³.

1. For the beam shown and given cross-section determine the maximum bending stress and the absolute maximum bending stress.  2. Determine the maximum shear stress in the beam