Problem 1. Calculate the area moment of inertia of the beam cross-section shown about the x' and y' axes, which pass through the centroid of the area.

A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensions of b₁ = 12 in., d₁ = 1.9 in., b2 = 1.9 in., d₂ = 11 in., b3 = 6 in., and d3 = 1.9 in. (a) Determine the distance from the bottom edge of the section to the centroid. (b) Determine the moment of inertia of the section about the z axis. (c) Determine the maximum shear stress in the cross section if the internal shear force is V = 400 lb. Assume that the shear force V acts in the y direction. (d) Consider nail B that connects the bottom flange to the beam web. If the nails used at B can provide 95 lb of horizontal resistance (in the x direction), determine the maximum nail spacing s (in the x direction) that can be used for nail B. Assume V = 400 lb. Ox (e) If a bending moment applied about the z axis produces a tension normal stress of ox = 650 psi at the bottom of the cross section, determine the compression normal stress produced at the top of the cross section. Z Z- & b₂- b₁ | y Nail A FE…

Determine the principal moments of inertia for the beam’s cross-sectionalthe area is shown in Figure with respect to an axis passing through the centroid C.

Determine the moment of inertia of the cross-sectional area of the beam about: A. the x-axis B. the y-axis 3 in. 1 in. y -1 in. 10 in. -1 in. 8 in.