WORLD FOR CIVIL

Statics & Strength of Materials

Topic 4.4b1 Problem Assignment - Shear Forces & Bending Moments 1

For the loaded, simply supported beams shown in the diagrams below:
A. Draw a Free Body Diagram of the beam, and determine the external support reactions.
B. Find expressions for the Shear Forces and Bending Moments in each section of the beams.
C. Draw the Shear Force and Bending Moment Diagrams for each beam. Use a sheet of graph paper, use topic half for shear diagram and the bottom half for the bending moment diagram.
Beams in these problems are considered weightless.

1. A 10 foot cantilever carries a point load of 800 pounds at its free end.
[V= 800 lb., M = 800x -8000 ft-lb.]

2. A 12 foot cantilever carries a load of 1200 pounds 4 feet from the wall and a load of 600 pounds at its end, 12 feet from the wall. [V1 = 1800 lb., M1 = 1800x - 12,000 ft-lb., V2 = 600 lb., M2 = 600x - 7200 ft-lb.]

3. A 10 foot cantilever has a uniformly distributed load of 400 pounds per foot over its entire length. [V = 4000 - 400x lb., M = -2000x² +4000x - 20,000 ft-lb.]

4. A 16 foot cantilever has a uniformly distributed load of 400 pounds per foot from the wall to the 10 foot mark and a load of 200 pounds per foot from that point to the end of the beam. [V1 = 5200 - 400x lb., M1 = -200x² +5200x - 35,600 ft-lb., V2 = 3200-200x lb., M2 = -100x²+3200x - 25,600 ft-lb.]

5. A 6 foot cantilever has a point load of 600 pounds at its mid point and a uniformly distributed load of 100 pounds per foot from the midpoint to the free end. [V1 = 900 lb., M1 = 900x - 3150 ft-lb., V2=600-100x lb., M2 = -50 x² + 600x - 1800 ft-lb.]

6. An 8 foot cantilever was designed to carry a point load of 800 pounds at its free end. The beam joint of the beam with the wall was found to be failing and a prop was placed 4 feet from the wall that exerted a 400 pound upward point force on the beam. [V1 = 400 lb., M1 = 400x -4800 ft-lb., V2=800 lb., M2 = 800x - 6400 ft-lb.]