8. For the cross-section of a beam shown; a) locate the centroidal axis from the bottom of the section; b) determine the centroidal moment of inertia of the section; and, c) determine the moment of inertia about the top of the section.

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. y 30 mm 30 mm 70 mm 140 mm 30 mm x' 170 mm 30 mm

Determine the moment of inertia for the beam's cross-sectional area about the x axis. Suppose that a = 13 in. , b = 10 in. , c = 1 in., and d= 5 in. y b d a

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…

A built-up section fabricated by attaching a C180x15 to a W250x18 shape with 15 mm rivets as shown. Determine the moment of inertia at the centroid of the built-up section. Answer:  Centroidal moment of inertia along x-axis= 48.857x106mm4 Need the complete solution, thanks!

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

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.

a. Moment of inertia about x-axis  b. Moment of inertia about y-axis

Consider the cross section of the beam shown where a = 0.8 in. The beam's centroid is located at point C. 3 in. A) Locate the position of the beams centroid, (.). Show all of your work including how the area was split. Record the location in your written work. 8) Find the inertia of the beam's cross section relative to the x' axis (/) that extends through the centroid. Show all your work. Record your result in your written work and in the space below. Round your answer to 0 decimal places.