WORLD FOR CIVIL

Topic 8.7a - Special Topics - Problem Assignment 1

1. A loaded beam (shown in Diagram 1) is pinned to the wall at point A, and is supported by a rod DB, attached to the wall at point D and to the beam at point B.

The beam has a load of 8,000 lb. acting downward at point C and a second load of 10,000 lb. acting downward at point B. The supporting rod makes an angle of 25^o with respect to the beam. The beam cross section is a W8 x 24 I-Beam, with the characteristics shown in Diagram 1.

Determine the maximum axial stress acting in the beam cross section and state where it occurs. [25,400 psi @ x = 6' at bottom of beam, compression]

2. A loaded beam (shown in Diagram 2) is pinned to the wall at point A, and is supported a vertical support at point C.

A force of 20,000 lb. is applied at the centroid of the beam, at an angle of 30^o with respect to the horizontal as shown in the Diagram. The beam cross section is a WT12 x 34 T-Beam, with the characteristics shown in Diagram 2.

Determine the maximum axial stress acting in the beam cross section and state where it occurs. [20,192 psi @ x = 6' at bottom of beam, tension]

3. As shown in Diagram 3, a solid 1 foot long shaft with a radius of 1" is attached to a wall at point A, and has a disk with a radius of 2" attached at end B.

A force of 2000 lb. is applied to the outer edge of the disk, as shown.

Determine the maximum shear stress in the shaft, and state where it acts.
[849 psi + 2,546 psi = 3,395 psi at top of beam]

4. In Diagram 4, we have shown a rectangular, 2" by 1.5", section in tension with a normal force of 6000 lb. acting on each end.

Determine the axial and shear stress on a 35^o incline plane cut through the section.[axial 1,342 psi., shear 940 psi.]

5. A cantilever beam is shown in Diagram 5. At end B at 2000 lb. downward load is applied at the centroid of the beam, and a 5000 lb. horizontal force is applied in the vertical center, but at the far outside edge as shown in Diagram 5.

The beam cross section is a 2" by 2" square.

Determine the maximum axial stress in the beam, and state where is acts.[ = 36,000 psi. + 3750 psi. + 1250 psi. = 41,000 psi @ wall and at top of beam on far edge]