ST04: Free Body Diagram (Rigid Body Equilibrium)
Problem Definition
Draw the free body diagram of the assembly shown below. Then, write the static equilibrium equations and solve them for the unknown support reactions.
Solution
1. Draw Free Body Diagram
2. Write Equilibrium Equations
\[ \begin{align} & \sum F_x = A_x + 3 = 0 \\ & \sum F_y = A_y + B_y -1 - 2= 0\\ & \sum_{ @ B} M = (3)(2) + (2)(2) + (A_y)(3) = 0 \\ \end{align}
\]
3. Solve the Equations for Unknowns
From the third equations we get: \( A_y = -3.33 \, kN. \) The nagtive sign here means \( A_y \) is acting in the opposite direction to what is shown in the free body diagram. Then, the second equation gives us: \( B_y = 6.33 \, kN. \) Finally. using the first equation, we determine \(A_x\) to be \( -3 \, kN. \)
We can show the results of the analysis graphically, like this:
