Question 5.87: The symmetrical shelf is subjected to a uniform load of 4 kP...
The symmetrical shelf is subjected to a uniform load of 4 kPa. Support is provided by a bolt (or pin) located at each end A and A’ and by the symmetrical brace arms, which bear against the smooth wall on both sides at B and B’ Determine the force resisted by each bolt at the wall and the normal force at B for equilibrium.
Equations of Equilibrium: Each shelf’s post at its end supports half of the applied load, ie, 4000 (0.2) (0.75) = 600 N. The normal reaction N_B can be obtained directly by summing moments about point A.
\hookrightarrow + \Sigma M_A=0 ; \quad N_B(0.15)-600(0.1)=0 \quad N_B=400 \mathrm{~N}
+→ \Sigma F_x=0 ; \quad 400-A_x=0 \quad A_x=400 \mathrm{~N}
+↑ \Sigma F_y=0 ; \quad A_y-600=0 \quad A_y=600 \mathrm{~N}
The force resisted by the bolt at A is
F_A=\sqrt{A_x^2+A_y^2}=\sqrt{400^2+600^2}=721 \mathrm{~N}