Solution to Problem 433 | Relationship Between Load, Shear, and Moment | Strength of Materials Review at MATHalino

Problem 433
Overhang beam loaded by a force and a couple as shown in Fig. P-433.

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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 433

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$\Sigma M_C = 0$

$5R_1 + 2(750) = 3000$

$R_1 = 300 \, \text{lb}$

$\Sigma M_A = 0$

$5R_2 + 3000 = 7(750)$

$R_2 = 450 \, \text{lb}$

To draw the Shear Diagram

V_A = R₁ = 300 lb
V_B = V_A + Area in load diagram
V_B = 300 + 0 = 300 lb
V_C = V_B + Area in load diagram
V_C = 300 + 0 = 300 lb
V_C2 = V_C + R₂ = 300 + 450 = 750 lb
V_D = V_C2 + Area in load diagram
V_D = 750 + 0 = 750
V_D2 = V_D - 750 = 750 - 750 = 0

To draw the Moment Diagram

M_A = 0
M_B = V_A + Area in shear diagram
M_B = 0 + 300(2) = 600 lb·ft
M_B2 = V_B - 3000
M_B2 = 600 - 3000 = -2400 lb·ft
M_C = M_B2 + Area in shear diagram
M_C = -2400 + 300(3) = -1500 lb·ft
M_D = M_C + Area in shear diagram
M_D = -1500 + 750(2) = 0

Solution to Problem 433 | Relationship Between Load, Shear, and Moment

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