Solution to Problem 437 | Relationship Between Load, Shear, and Moment | Strength of Materials Review at MATHalino

Problem 437
Cantilever beam loaded as shown in Fig. P-437.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

Solution 437

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To draw the Shear Diagram

V_A = -1000 lb
V_B = V_A + Area in load diagram
V_B = -1000 + 0 = -1000 lb
V_B2 = V_B + 500 = -1000 + 500
V_B2 = -500 lb
V_C = V_B2 + Area in load diagram
V_C = -500 + 0 = -500 lb
V_D = V_C + Area in load diagram
V_D = -500 - 400(4) = -2100 lb

To draw the Moment Diagram

M_A = 0
M_B = M_A + Area in shear diagram
M_B = 0 - 1000(2) = -2000 lb·ft
M_C = M_B + Area in shear diagram
M_C = -2000 - 500(2) = -3000 lb·ft
M_D = M_C + Area in shear diagram
M_D = -3000 - ½ (500 + 2100)(4)
M_D = -8200 lb·ft

Tags:

concentrated load

Uniformly Distributed Load

cantilever beam

relationship between load shear and moment

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