Problem 916 | Combined Axial and Bending

 

 

$\Sigma M_A = 0$

$3B_H = 6(20)$

$B_H = 40 ~ \text{kN}$
 

 

$\Sigma M_E = 0$

$6B_V + 3(40) = 3(60)$

$B_V = 10 ~ \text{kN}$
 

Axial force at D

$P_a = B_H \cos \theta - B_V \sin \theta + 60 \sin \theta$

$P_a = 40\left( \dfrac{2}{\sqrt{5}} \right) - 10\left( \dfrac{1}{\sqrt{5}} \right) + 60\left( \dfrac{1}{\sqrt{5}} \right)$

$P_a = 26\sqrt{5} ~ \text{kN compression}$

 

 

Maximum Moment Will Occur at D

$M_D = 1.5B_H + 3B_V$

$M_D = 1.5(40) + 3(10)$

$M_D = 90 ~ \text{kN}\cdot\text{m}$

Just in case you need to see the whole picture
 

$P_1 = B_H \cos \theta = 40 \left( \dfrac{2}{\sqrt{5}} \right) = 16\sqrt{5} ~ \text{kN}$

$P_2 = B_V \sin \theta = 10 \left( \dfrac{1}{\sqrt{5}} \right) = 2\sqrt{5} ~ \text{kN}$

$P_3 = 60 \sin \theta = 60 \left( \dfrac{1}{\sqrt{5}} \right) = 12\sqrt{5} ~ \text{kN}$

$P_4 = E_H \cos \theta = 40 \left( \dfrac{2}{\sqrt{5}} \right) = 16\sqrt{5} ~ \text{kN}$

$P_5 = E_V \sin \theta = 50 \left( \dfrac{1}{\sqrt{5}} \right) = 10\sqrt{5} ~ \text{kN}$

$P_1 - P_2 = 14\sqrt{5} ~ \text{kN}$

$P_4 + P_5 = 26\sqrt{5} ~ \text{kN}$
 

$V_1 = B_H \sin \theta = 40 \left( \dfrac{1}{\sqrt{5}} \right) = 8\sqrt{5} ~ \text{kN}$

$V_2 = B_V \cos \theta = 10 \left( \dfrac{2}{\sqrt{5}} \right) = 4\sqrt{5} ~ \text{kN}$

$V_3 = 60 \cos \theta = 60 \left( \dfrac{2}{\sqrt{5}} \right) = 24\sqrt{5} ~ \text{kN}$

$V_4 = E_H \sin \theta = 40 \left( \dfrac{1}{\sqrt{5}} \right) = 8\sqrt{5} ~ \text{kN}$

$V_5 = E_V \cos \theta = 50 \left( \dfrac{2}{\sqrt{5}} \right) = 20\sqrt{5} ~ \text{kN}$

$V_1 + V_2 = 12\sqrt{5} ~ \text{kN}$

$V_5 - V_4 = 12\sqrt{5} ~ \text{kN}$