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For a beam with the cross-section shown (w = 15.0 in. and h = 21.5 in.), find the distance from the bottom surface of the beam to the centroid.

Consider a point on the free surface of a structure made of AISI-C 1040 normalized steel [E = 200 GPa, ν = 0.29] that is tangent to the (x,y) plane. Determine the smallest principal strain ε3 for the following stresses.σxx = 170 MPaσyy = –80 MPaσxy = –180 MPa

The nonzero strain components at a critical point in a machine component made of 2024-T4 aluminum [E = 74.5 GPa, ν = 0.33] are measured on a free surface as follows. Determine the corresponding stress σyy.εxx = 0.0020εyy = 0.0008εxy = 0.0011

An aluminum rod with a 24.0-in. gage length and a 0.605-in. diameter is loaded in tension. At the proportional limit, a load of 14,000 lb elongates the gage length by 0.115 in. and reduces the diameter by 0.00073 in. Determine the modulus of elasticity.

A thin-wall brass [G = 28.6 GPa] tube with an equilateral triangular cross section is subjected to a torque of 26 N·m. The mean length of one side of the triangle is 25 mm, and the wall thickness is 2.1 mm. Determine the maximum shear stress.

A tensile test specimen of stainless steel alloy having a diameter of 0.495 in. and a gage length of 2.00 in. was tested to fracture. Stress and strain data obtained during the test are shown. Note that the “Lower scale” is a zoomed-in portion of the Upper scale. Determine the ultimate strength.

The nonzero strain components at a critical point in a machine component made of 6061-T6 aluminum [E = 69 GPa, ν = 0.33] are measured on a free surface as follows. Determine the corresponding shear stress τxy.εxx = 0.0035εyy = 0.0005εxy = 0.0008

A machine part made of AISI-C 1018 cold drawn [E = 200 GPa, ν = 0.29] is subjected to a state of plane strain (εzz = εzx = εzy = 0). Determine σzz for the following stresses.σxx = 60 MPaσyy = –95 MPaσxy = 30 MPa

A 0.6-m-long steel [G = 80 GPa] channel is subjected to a torque of 690 N·m. Determine the unit angle of twist of the channel. Assume bf = 90 mm, tf = 11 mm, d = 180 mm, and tw = 8 mm.

The design loads of a member made of a brittle material produce the following nonzero stress components at a critical section in the member. The ultimate strength of the material is 420 MPa. Determine the factor of safety used in the design based on the maximum principal strain criterion. Assume ν = 0.22.σxx = –90 MPaσyy = 70 MPaσxy = 80 MPa