Consider the beam's cross-sectional area shown in (Figure 1). Suppose that a = 3 in., b = 4 in. , and c = 1 in. Pt A. Determine the distance y¯to the centroid of the beam's cross-sectional area. Pt B. Determine the moment of inertia about the centroidal x′ axis.

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…

Suppose that aaa = 5.29 in. and b = 2.3 in. Determine the moment of inertia for the shaded area about the x axis.

3. Consider the following shape with a = 1 ft and b = 3 ft. a. Determine the centroid. b. Determine the moment of inertia about the horizontal centroidal axis Determine the moment of inertia about the vertical centroidal axis. c. a b

PROBLEM 4: The region is symmetric about the x-axis. Calculate the moment of inertial about the centroidal x and y axes. ANS: I = 10.35 x 106 mm², I = 1.74 × 106 mm² 17 mm y 68 mm 17 mm 18'mm 27 mm --x

The moment of inertia of an area about an axis is equal to the area moment of inertia about a parallel axis passing through the centroid. True or false?

16 in. 20 in. r = 38 in. x In the fig. shown, compute the following: (a) Components of the centroid ; y = (b) The total moment of inertia with respect to the centroidal y axis lý = in4

PROBLEM 4: The region is symmetric about the x-axis. Calculate the moment of inertial about the centroidal x and y axes. ANS: 1x = 10.35 × 106 mm², I₁ = 1.74 × 106 mm² 17 mm y 68 mm 17'mm 18 mm 27 mm x

1. A circular disk has a density p(r) which varies as a function of distance from the center of the disk. The disk has a radius R and a thickness t. Assuming p(r) = Po(1-r/R): Calculate the total mass of the disk. a. b. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point G. C. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point O. G R

Dont forget to draw the FREE BODY DIAGRAMS ALSO PLEASE! (: