Blog

A steel I-beam [E = 200 GPa] has a depth of 132 mm, width of 73 mm, moment of inertia of Ix = 4.08 × 106 mm4, and length of 5 m. It rests on a hard rubber foundation. The value of the spring constant for the hard rubber is k0 = 0.250 N/mm3. If the beam is subjected to a concentrated load, P = 80 kN, at the center of the beam, determine the maximum flexural stress at the center of the beam. The bending moment at the center of the beam is 13.01 kN·m.

Determine the distance e to the shear center O for the beam cross section. Assume the following dimensions and moment of inertia.a = 55 mmb = 45 mmc = 90 mmt = 6 mmI = 4,254,000 mm4

The design of a white oak [E = 12.3 GPa, σPL = 26 MPa] column of square cross section has the following requirements. It must be 8.0 m long, it must have pinned ends, and it must support an axial load of 80 kN with a factor of safety of 2.0 against buckling. Determine the required width of the cross section.

If w = 9.25 in., find the moment of inertia Iz about the z axis. The centroid of the section is located 2.8885 in. above the bottom surface of the beam.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000220/°C, E = 70 GPa, ν = 0.32], has an inside diameter of 210 mm, and has an outside diameter of 830 mm. Determine the circumferential stress at r = 385 mm for a steady-state temperature change with the temperature at the inner radius 85°C greater than the temperature at the outer radius.

Four yellow pine [E = 12.3 GPa] boards are glued together to form a column with outer dimensions of 160 mm by 160 mm and a length of 6.9 m. The thickness of each board is 20 mm. One end of the column is clamped and the other end is pinned. Determine the critical buckling load.

A thick-wall closed-end cylinder is made of an aluminum alloy [E = 71 GPa, ν = 0.32], has an inside diameter of 180 mm, and has an outside diameter of 820 mm. The cylinder is subjected to an external pressure of 150 MPa and an axial load of P = 1,500 kN. Determine the axial stress.

A cast iron disk has an inner radius of a = 160 mm and an outer radius of b = 295 mm, with material properties ρ = 7,100 kg/m3, E = 73 GPa, ν = 0.27. Determine the maximum circumferential stress in the disk for a speed of revolution of 5,400 rpm.

A thick-wall closed-end cylinder is made of an aluminum alloy [α = 0.0000235/°C, E = 70 GPa, ν = 0.34], has an inside diameter of 210 mm, and has an outside diameter of 760 mm. Determine the circumferential stress at the inner radius for a steady-state temperature change with the temperature at the inner radius 115°C greater than the temperature at the outer radius.

For a beam with the cross-section shown (w = 81 mm and h = 162 mm), find the distance from the bottom surface of the beam to the centroid.