Statics & Strength of Materials
Topic 4.4a1 Problem Assignment - Shear Forces & Bending Moments 1
For the loaded, simply supported beams described 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 beam is simply supported at its ends. A load of 500 pounds is placed 4 feet from the left end.
V1=300 lb, M1= 300x ft-lb; V2=-200 lb, M2 = -200x + 2000 ft-lb
2. An 8 foot beam is simply supported at its ends. It has a uniformly distributed load of 200 pounds per foot along its entire length. V1 = 800 - 200 x lb, M1 = 800x -100 x2 ft-lb.
3. A 24 foot beam is simply supported at the quarter points (6 feet and 18 feet). It has point loads of 800 pounds at each end and a point load of 1000 points at its mid point. V1= - 800 lb, M1= - 800x ft-lb; V2 = 500 lb, M2 = 500 x -7800 ft-lb; V3 = - 500 lb, M3 = - 500x +4200 ft-lb; V4 = 800 lb, M4 = 800x - 19,200 ft-lb
4. A 16 foot beam is simply supported at its ends. It has a uniformly distributed load of 400 pounds per foot over the first 6 feet and a point load of 1200 pounds at the 10 foot mark. V1 = 2400 - 400x lb, M1 = 2400 x - 200x2 ft-lb; V2 = 0 lb, M2 = 7200 ft-lb; V3 = -1200 lb, M3 = 1200 x + 19200 ft-lb
5. A diving board is 16 feet long and pinned at the left end. It has a roller support at the 6 foot mark. A 160 pound person stands at the right end of the board. V1 = -267 lb, M1 = -267 x ft-lb; V2 = 160 lb, M2 = 160 x -2560 ft-lb
V1 = - 500 x lb, M1 = -250x2 ft-lb; V2 = 2000 lb, M2 = 2000 x - 32,000 ft-lb.
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