# Problem Breakdown **Given:** - A frame structure with: - A uniformly distributed load of 25 kN/m over a 15 m horizontal beam. - A 40 kN point load applied at an angle on the inclined member. - Supports at node 1 (roller) and node 3 (fixed). **Asked:** - Find the **nodal displacements** and **reaction forces**. --- ## Step 1: **Support Reactions** ### Support Types: - **Node 1:** Roller (vertical reaction only) - **Node 3:** Fixed (vertical, horizontal, and moment reactions) --- ## Step 2: **Equivalent Loads** ### Distributed Load: - Total load = \( 25 \text{ kN/m} \times 15 \text{ m} = 375 \text{ kN} \) - Acts at the center of the 15 m span (7.5 m from node 1). ### Point Load: - 40 kN applied on the inclined member at node 2. --- ## Step 3: **Static Equilibrium Equations** Let: - \( A_y \) = Reaction at node 1 (vertical) - \( C_x, C_y, M_C \) = Reactions at node 3 (horizontal, vertical, moment) #### \(\Sigma F_x = \): - Only the horizontal component of the 40 kN load and \( C_x \) act. #### \(\Sigma F_y = \): - Sum all vertical loads and reactions. #### \(\Sigma M_C = \): - Take moments about node 3. --- ## Step 4: **Nodal Displacements** This requires structural analysis (e.g., stiffness matrix method or deflection formulas). You need: - Beam and column properties (E, I) - Geometry (provided) --- ## **Summary Table** | Step | What to Do | |---------------------|-----------------------------------------------------------------| | 1. Supports | Identify support reactions | | 2. Loads | Calculate total and equivalent loads | | 3. Equilibrium | Write equations for force/moment balance | | 4. Displacements | Use structural analysis (matrix or moment methods as needed) | --- ## **Note** **To fully solve for nodal displacements**, you need: - Modulus of Elasticity (E) - Moment of Inertia (I) **If you provide these values, I can help with the displacement calculations.** --- ### **Would you like to see the step-by-step static reaction calculation or the general method for nodal displacements?**