# Problem 914 | Combined Axial and Bending

**Problem 914**

The structure shown in Figure P-914 is hinged to fixed is hinged to fixed supports at *A* and *C*. Assume that the pin connections at *A*, *B*, and *C* are frictionless. The bars are each 4 in. by 4 in. in section. Compute the maximum compressive stress developed in bar *AD*.

**Solution 914**

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$C_V = B_V = 400 ~ \text{lb}$

$\Sigma M_A = 0$

$8B_H = 6B_V + 8(500)$

$8B_H = 6(400) + 8(500)$

$B_H = 800 ~ \text{lb}$

Moment at *B*

$M_B = 500(2) = 1000 ~ \text{lb}\cdot\text{ft}$

Axial Force at *B*

$P_a = 400 + B_V \cos \alpha + B_H \cos \theta$

$P_a = 400 + 400(4/5) + 800(3/5)$

$P_a = 1200 ~ \text{lb compression}$

Maximum Compressive Stress Will Occur at Point *B*

$\sigma_c = \dfrac{P_a}{bd} + \dfrac{6M_B}{bd^2}$

$\sigma_c = \dfrac{1200}{4(4)} + \dfrac{6(1000)(12)}{4(4^2)}$

$\sigma_c = 1200 ~ \text{psi}$ *answer*

**Axial, Shear, and Moment Diagrams**

Not actually necessary but just in case you need it.

$P_2 = 900 \sin \theta = 900(4/5) = 720 ~ \text{lb}$

$P_3 = 800 \cos \theta = 800(3/5) = 480 ~ \text{lb}$

$P_4 = 400 \sin \theta = 400(4/5) = 320 ~ \text{lb}$

$P_5 = 500 \sin \theta = 500(4/5) = 400 ~ \text{lb}$

$V_1 = 800 \sin \theta = 800(4/5) = 640 ~ \text{lb}$

$V_2 = 900 \cos \theta = 900(3/5) = 540 ~ \text{lb}$

$V_3 = 800 \sin \theta = 800(4/5) = 640 ~ \text{lb}$

$V_4 = 400 \cos \theta = 400(3/5) = 240 ~ \text{lb}$

$V_5 = 500 \cos \theta = 500(3/5) = 300 ~ \text{lb}$

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