WORLD FOR CIVIL

Topic 8.8: Special Topics I - Topic Examination

1. A loaded beam (shown in Diagram 1) is pinned to the wall at point A, and is supported a vertical support at point C.

A force of 18,000 lb. is applied at the centroid of the beam, at an angle of 37^o with respect to the horizontal as shown in the Diagram. The beam cross section is a rectangular 2" by 4".

Determine the maximum axial stress acting in the beam cross section and state where it occurs.
[(38880 psi + 1800 psi = 40680 psi. compression, at top of beam 8 ft from left end) This is considering only sum of axial stress acting. If one takes a small section at point indicated and finds principle stresses, the principle axis stress in slightly greater, ~ 41,000 psi @ 4.6^o angle off vertical plane.]

2. A cantilever beam is shown in Diagram 2.

At end B a 8,000 lb. horizontal force is applied in the vertical center, but at the far outside edge as shown in Diagram 5. A second 6,000 lb. horizontal force is applied at the horizontal center of the beam, but at the top edge of the area as shown in Diagram 5. The beam cross section is a 2" by 3" rectangle.
Determine the maximum axial stress in the beam, and state where it acts.

[(2333 psi + 3000 psi + 4000 psi = 9333 psi, tension at top right corner of cross section. Again considering only combined axial stresses. There are two points of zero axial stress in cross section. One would be on horizontal neutral axis .583" to left of center point (2333 psi (t) + 0 + 2333 psi (c) = 0), and the other on the vertical axis 1.167" below the center point of cross section (2333 psi (t) + 2333 psi (c) + 0 = 0)]

3. A structural element with applied axial and shear stresses is shown in Diagram 3.

Determine principal planes, the principal stresses, and the maximum shear stress.
(-22.5^o, +67.5^o, 10,485 psi, -6485 psi, +/- 8485 psi)

Also determine the axial and shear stresses on a plane which makes an angle of 40 degrees counterclockwise from the negative vertical axis in the given element. (6867 psi, 6951 psi)