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Consider a point on the free surface of a structure made of AISI-C 1030 normalized steel [E = 200 GPa, ν = 0.29] that is tangent to the (x,y) plane. Determine the largest principal strain ε1 for the following stresses.σxx = 180 MPaσyy = –70 MPaσxy = –190 MPa

Determine the total strain energy U in the rectangular beam due to both bending moment and shear force. Assume w = 18 kN/m, L = 0.70 m, b = 40 mm, h = 70 mm, E = 220 GPa, and G = 78 GPa.

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 370 MPa. Determine the factor of safety used in the design based on the maximum principal stress criterion.σxx = –60 MPaσyy = 110 MPaσxy = 120 MPa

Consider a point on the free surface of a structure made of ASTM A36 structural 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 = 300 MPaσyy = –110 MPaσxy = –140 MPa

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 middle principal strain ε2 for the following stresses.σxx = 220 MPaσyy = –140 MPaσxy = –80 MPa

A 0.7-m-long steel [G = 78 GPa] channel is subjected to a torque of 610 N·m. Determine the unit angle of twist of the channel. Assume bf = 90 mm, tf = 12 mm, d = 200 mm, and tw = 6 mm.

A member is subjected to its design loads. The nonzero stress components at the points of maximum stress are as follows. The yield stress of the material is Y = 370 MPa. Determine the factor of safety used in the design, assuming that the material is a von Mises material.σxx = 100 MPaσyy = 80 MPaσxy = 50 MPa

Determine the total strain energy U in the rectangular beam due to both bending moment and shear force. Assume w = 18 kN/m, L = 0.70 m, b = 20 mm, h = 70 mm, E = 180 GPa, and G = 75 GPa.

A thin-wall brass [G = 26.7 GPa] tube with an equilateral triangular cross section is subjected to a torque of 24 N·m. The mean length of one side of the triangle is 23 mm, and the wall thickness is 2.1 mm. Determine the maximum shear stress.

A 14-ft-long simply supported timber beam carries vertical load P = 15.1 kip at midspan. The cross-sectional dimensions of the timber are shown. At section a-a, determine the magnitude of the bending stress in the beam at point H.