ME 323: Mechanics of Materials Homework H12 Summer 2021 DUE: July 6, 2021 At a critical location along the length of a beam, the shear force V and bending M on the cross- section of the beam are known. On each of the four beam cross-sections shown below, point O is the centroid, point B is the top-most point and point K is the bottom-most point on the cross- section. The beam is made of a material having a specific weight of ρ ( N / m 3 ). The dimension b is in meters. a) Determine the weight of the beam for each of the four cross-sections shown below. Leave these answers in terms of ρ and b. Rank order these weights from smallest to largest. b) Determine the magnitude of the normal stress at points B, O and K for each cross-section. Leave these answers in terms of M and b. Rank order the maximum of these magnitudes for each point from smallest to largest. c) Determine the magnitude of the shear stress at points B, O and K for each cross-section. Leave these answers in terms of V and b. Rank order the maximum of these magnitudes from smallest to largest. Rank order the maximum of these magnitudes for each point from smallest to largest. d) How do the maximum shear stresses in c) compare with the maximum normal stresses in b) for each cross-section? e) Comment on the cost (weight) vs. maximum stress of these beam cross-sections. This part of the problem will not be graded, but please put some thought into your comments. z y K O B z y K O B z y K O B z y K O B thicknesses of web and flanges = 0.1b b b b b b /2 b /2 beam cross section (1) beam cross section (2) beam cross section (3) beam cross section (4) x y 10b SOLUTION cross section 1 w weight p Aco b p 5 lob Sp B 1 0 C neutral plane XD f 2543 24 3