WORLD FOR CIVIL

Statics & Strength of Materials

Topic 4.4b2 Problem Assignment - Shear Forces & Bending Moments 2

For the loaded, cantelever 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 = 20,00 lb. Mext= 168,000 ft-lb.,V1 = 20,000 lb.,M1 = 20,000x -168,000 ft.-lb.
V2 = 28,000 - 2,000x lb., M2 = 28,000x - 1,000x² - 184,000 ft.-lb.
V3 = 36,000-3000x lb.,M3 = 36,000 x -1500x²-216,000 ft.-lb.

2

A_y = 18,000 lb. M_ext = 168,000 ft.-lb.
V1 = 18,000 lb., M1 = 18,000x - 168,000 ft.-lb.
V2 = 26,000 - 2,000x lb.,M2 = 26,000x - 1,000 x² - 184,000 ft.-lb.
V3 = 10,000 lb.,M3 = 10,000x -120,000 ft.-lb.
V4 = 0, M4 = 0

3.

A_y = 9,000 lb., M_ext = 60,500 ft/lb.
V1 = - 1,000x + 9,000 lb.,M1 = -500x² + 9,000x - 60,500 ft/lb.
V2 = 4,000 lb.,M2 = 4,000x - 48,000 ft/lb.
V3 = 2,000 lb.,M3 = 2,000x - 32,000 ft/lb.

4.

A_y = 17,000 lb. M_ext = 156,500 ft.-lb.
V1 = 1,000x + 17,000 lb.,M1 = - 500x² + 17,000x - 156,000 ft.-lb. ft.-lb.
V2 = 12,000 lb.,M2 = 12,000x - 143,500 ft.-lb.
V3 = -1,500 + 24,000 lb.,M3 = -750x² + 24,000 - 192,000 ft.-lb.

5.

A_y = 5,600 lb. M_ext = 42,000 ft.-lb.
V1 = 5,600,M1 = [5,600x - 42,000] ft.-lb.
V2 = 3,600 lb., M2 = [3,600x - 36,000] ft.-lb.
V3 = [3,600 - 100(x-6)²] or V3 = [-100x² + 1,200x]lb., M3 = [-33.3x³ + 600x² - 28,800] ft.-lb.