Problem 451 - Components of Hinge Forces of a Frame | Engineering Mechanics Review at MATHalino

Problem 451
The frame shown in Figure P-451 is hinged at E and roller supported at A. Determine the horizontal and vertical components of the hinge forces at B, C, and D. Neglect the weights of the members.

Solution 451

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From the FBD of the whole frame

$\Sigma M_E = 0$

$6R_A + 3(30) = 5(24)$

$R_A = 5 ~ \text{kN}$

$\Sigma M_A = 0$

$6E_V + 5(24) = 9(30)$

$E_V = 25 ~ \text{kN}$

$\Sigma F_H = 0$

$E_H = 24 ~ \text{kN}$

From the FBD of member CE

$\Sigma M_D = 0$

$2C_H = 2(24)$

$C_H = 24 ~ \text{kN}$

$\Sigma M_C = 0$

$2D_H = 4(24)$

$D_H = 48 ~ \text{kN}$

From the FBD of member BF

$\Sigma M_B = 0$

$3C_V = 3(24) + 4(24)$

$C_V = 56 ~ \text{kN}$

$\Sigma F_H = 0$

$B_H = 24 + 24$

$B_H = 48 ~ \text{kN}$

$\Sigma F_V = 0$

$B_V = C_V$

$B_V = 56 ~ \text{kN}$

From the FBD of member AG

$\Sigma F_V = 0$

$D_V + 5 = 56 + 30$

$D_V = 81 ~ \text{kN}$

Check at member CE

$\Sigma F_H = 0$

$C_H + E_H = D_H$

$24 + 24 = 48$ (okay!)

$\Sigma F_V = 0$

$C_V + E_V = D_V$

$56 + 25 = 81$ (okay!)

Answer Summary

B_H = 48 kN
B_V = 56 kN

C_H = 24 kN
C_V = 56 kN

D_H = 48 kN
D_V = 81 kN

Problem 451 - Components of Hinge Forces of a Frame

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