1. **Problem statement:** Calculate the reaction force at pin A in a static system. 2. **Understanding the problem:** The reaction force at a pin is the force exerted by the support to keep the system in equilibrium. We use the conditions of static equilibrium: $$\sum F_x = 0, \quad \sum F_y = 0, \quad \sum M = 0$$ where $F_x$ and $F_y$ are forces in horizontal and vertical directions, and $M$ is the moment. 3. **Step-by-step solution:** - Identify all external forces and moments acting on the system. - Write the equilibrium equations based on the geometry and loading. - Solve the system of equations to find the reaction force components at pin A. 4. **Example:** Suppose the system has a beam with a load $P$ at a distance $d$ from pin A. - Sum of moments about A: $$\sum M_A = 0 = P \times d - R_B \times L$$ where $R_B$ is the reaction at the other support and $L$ is the length of the beam. - Sum of vertical forces: $$\sum F_y = 0 = R_A + R_B - P$$ - Solve for $R_B$ from moment equation: $$R_B = \frac{P \times d}{L}$$ - Substitute $R_B$ into vertical force equation to find $R_A$: $$R_A = P - R_B = P - \frac{P \times d}{L} = P \left(1 - \frac{d}{L}\right)$$ 5. **Interpretation:** The reaction force at pin A depends on the load $P$, its position $d$, and the beam length $L$. It balances the load to maintain equilibrium. **Final answer:** $$\boxed{R_A = P \left(1 - \frac{d}{L}\right)}$$