For a beam with the cross-section shown, find the distance from the bottom surface of the beam to the centroid. Let w = 1.30 in. and h = 2.15 in.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 71 GPa, ν = 0.34], has an inside diameter of 210 mm, and has an outside diameter of 840 mm. The cylinder is subjected to an external pressure of 170 MPa. Determine the circumferential stress at the outer radius.

Four yellow pine [E = 12.3 GPa] boards are glued together to form a column with outer dimensions of 140 mm by 140 mm and a length of 6.6 m. The thickness of each board is 20 mm. One end of the column is pinned and the other end is guided. Determine the critical buckling load.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000235/°C, E = 71 GPa, ν = 0.33], has an inside diameter of 220 mm, and has an outside diameter of 780 mm. Determine the circumferential stress at the inner radius for a steady-state temperature change with the temperature at the inner radius 80°C greater than the temperature at the outer radius.

A cast iron disk has an inner radius of a = 170 mm and an outer radius of b = 300 mm, with material properties ρ = 7,000 kg/m3, E = 71 GPa, ν = 0.27. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,500 rpm.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 73 GPa, ν = 0.30], has an inside diameter of 200 mm, and has an outside diameter of 790 mm. The cylinder is subjected to an internal pressure of 170 MPa and an external pressure of 120 MPa. Determine the circumferential stress at r = 140 mm.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 74 GPa, ν = 0.33], has an inside diameter of 200 mm, and has an outside diameter of 750 mm. The cylinder is subjected to an internal pressure of 170 MPa. Determine the circumferential stress at r = 300 mm.

An infinite beam on an elastic foundation is subjected to a triangular load w = 29 N/mm over the segment L’ = 5 m. Determine the bending moment at point B. Use E = 200 GPa, Ix = 80 × 106 mm4, and k = 10.0 N/mm2. The value of β is 0.6287 /m.

Consider a 1-m length of an unloaded cylinder at a location in the cylinder some distance from the ends. The long closed cylinder is made of a steel for which E = 205 GPa and ν = 0.28. It has an internal radius a = 95 mm and an external radius b = 275 mm.   Determine the radial displacement at the outer surface after p1 = 95 MPa is applied?

If w = 9.75 in., find the moment of inertia Iy about the y axis.