WORLD FOR CIVIL

Statics & Strength of Materials

Topic 4.4a2 Problem Assignment - Shear Forces & Bending Moments 2

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.

1.

A_y = 8,000 lb, D_y = 8,000 lb.
V1 = 8,000 lb., M1 = 8,000 x
V2 = 0 lb., M2 = 24,000 ft-lb
V3 = -8,000 lb.; M3 = - 8,000x + 96,000 ft.-lb.

2.

A_y = 4,400 lb. C_y = 15,600 lb.
V1 = -2,000x + 4,400 lb.; M1 = -1,000 x² + 4,400x + 0
V2 = -5,600 lb., M2 = - 5,600x + 25,000 ft.-lb.
V3 = 10,000 lb., M3 = 10,000x - 99,800 ft.-lb.

3.

A_y = 2,000 lb. C_y = 6,000 lb.
V1 = 2,000 lb., M1 = 2,000x ft.-lb.
V2 = -4,000x + 10,000 lb., M2 = -2,000x² + 10,000x - 8,000 ft.lb.

4.

B_y = 24,000 lb. D_y = 8,000 lb.
V1 = -2,000x lb.,M1 = -1,000 x² ft.-lb.
V2 = -2,000x + 24,000 lb.; M2 = -1,000 x² + 24,000x - 96,000 ft.-lb.
V3 = 8,000 lb.,M3 = -8,000x + 160,000 ft.-lb.5.

B_y = 24,000 lb. E_y = 8,000 lb.
V1 = -3,000x lb.,M1 = -1,500 x² ft.-lb.
V2 = -3,000x + 24,000 lb., M2 = -1,500 x² + 24,000x - 72,000 ft.-lb.
V3 = 0, M3 = 24,000 ft.-lb.
V4 = - 8,000lb.,M4 = - 8,000x + 120,000 ft.-lb.