A steel rod with a 1.25-in. gage length and a 0.140-in. diameter is loaded in tension. At the proportional limit, a load of 1,000 lb elongates the gage length by 0.00246 in. and reduces the diameter by 0.000074 in. Determine the modulus of elasticity.

Use the graphical method to construct the shear-force diagram and identify the magnitude of the largest shear force (consider both positive and negative peaks). Use P = 2.68 lb, w = 1.20 lb/in., a = 3.94 in., b = 2.76 in., and c = 5.31 in. The reaction forces for this beam are By = 6.085 lb and Dy = 2.967 lb (both upward).

At a point in a structural-steel member, the principal stresses are σ1 = 142 MPa, σ2 = 44.1 MPa, and σ3 = –26.1 MPa. Determine the absolute maximum shear stress.

Structure ABC is subjected to load P = 19 kN. Determine the vertical reaction force at B. Assume L1 = 2.7 m, L2 = 2.1 m, and EI = 6.7 x 107 N·m2. Only consider the strain energy related to bending moments.

The nonzero strain components at a critical point in a machine component made of ASTM A36 structural steel [E = 200 GPa, ν = 0.29] are measured on a free surface as follows. Determine the corresponding shear stress τxy.εxx = 0.0040εyy = 0.0006εxy = 0.0008

At a point in a structural-steel member, the stresses are σxx = 20 MPa, σyy = 50 MPa, σzz = 80 MPa, σxy = 10 MPa, σxz = 70 MPa, and σyz = 60 MPa. Determine the third stress invariant I3.

The nonzero strain components at a critical point in a machine component made of AISI-C 1040 normalized steel [E = 200 GPa, ν = 0.29] are measured on a free surface as follows. Determine the corresponding shear stress τxy.εxx = 0.0021εyy = 0.0006εxy = 0.0007

Structure ABC is subjected to load P = 15 kN. Determine the vertical reaction force at B. Assume L1 = 2.8 m, L2 = 2 m, and EI = 6.7 x 107 N·m2. Only consider the strain energy related to bending moments.

Structure ABC is subjected to load P = 10 kN. Determine the vertical reaction force at B. Assume L1 = 2.9 m, L2 = 2.3 m, and EI = 7.6 x 107 N·m2. Only consider the strain energy related to bending moments.

Consider a point on the free surface of a structure made of 2024-T4 aluminum [E = 74.5 GPa, ν = 0.33] that is tangent to the (x,y) plane. Determine the smallest principal strain ε3 for the following stresses.σxx = 230 MPaσyy = –120 MPaσxy = –130 MPa