For a beam with the cross-section shown, find the distance from the bottom surface of the beam to the centroid. Let w = 1.95 in. and h = 2.25 in.

For a beam with the cross-section shown (w = 98 mm and h = 130 mm), find the distance from the bottom surface of the beam to the centroid.

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 400 MPa. Determine the factor of safety used in the design based on the maximum principal stress criterion.σxx = –110 MPaσyy = 80 MPaσxy = 70 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.

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 largest principal strain ε1 for the following stresses.σxx = 300 MPaσyy = –140 MPaσxy = –210 MPa

At a point subjected to plane stress on the surface of a structural-steel member, the stresses are σx = 34 MPa, σy = 57 MPa, and τxy = 20 MPa. Determine the center σcenter of the corresponding in-plane Mohr’s circle.

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 = 1.31 lb, w = 0.59 lb/in., a = 3.94 in., b = 2.76 in., and c = 5.31 in. The reaction forces for this beam are By = 2.980 lb and Dy = 1.463 lb (both upward).

A 1.144-in.-diameter shaft failed when the shear stress reached 80 ksi on the outer surface. Assuming the shaft did not yield prior to failure, determine the torque that caused this failure.

Structure ABC is subjected to load P = 12 kN. Determine the vertical reaction force at B. Assume L1 = 2.6 m, L2 = 2.1 m, and EI = 7.3 x 107 N·m2. Only consider the strain energy related to bending moments.

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 = 85 mmt = 3 mmI = 1,936,000 mm4