Let's analyze each structure (b) and (c) step-by-step: --- ## **Step 1: Identify the support types and unknown reactions** ### **Structure (b):** - **Left Support:** Pinned (hinge) support (provides 2 reactions: vertical and horizontal) - **Right Support:** Roller support (provides 1 reaction: vertical) **Total number of unknown reactions = 2 (pin) + 1 (roller) = 3** --- ### **Structure (c):** - **Left Support:** Pinned (hinge) support (provides 2 reactions: vertical and horizontal) - **Middle Support:** Roller support (provides 1 reaction: vertical) - **Right Support:** Roller support (provides 1 reaction: vertical) **Total number of unknown reactions = 2 (pin) + 1 (roller) + 1 (roller) = 4** --- ## **Step 2: Count the available equilibrium equations** In 2D, the available equations of equilibrium for a rigid body: - \(\Sigma F_x = 0\) - \(\Sigma F_y = 0\) - \(\Sigma M = 0\) **Total equations = 3** --- ## **Step 3: Classify the structures** ### **Structure (b):** - **Unknowns:** 3 - **Equations:** 3 \[ \text{Degree of indeterminacy} = \text{Number of unknowns} - \text{Number of equations} = 3 - 3 = 0 \] - **Classification:** **Statically determinate and stable** --- ### **Structure (c):** - **Unknowns:** 4 - **Equations:** 3 \[ \text{Degree of indeterminacy} = 4 - 3 = 1 \] - **Classification:** **Statically indeterminate to 1st degree** - **Stability:** The structure is stable because the supports prevent any rigid body motion. --- ## **Step 4: Explanation** - **Statically determinate:** The structure can be solved using only the equations of equilibrium. - **Statically indeterminate:** The structure has more unknowns than equations. Additional compatibility equations are needed to solve for all unknowns. - **Stable:** The structure does not move as a rigid body when subjected to loads. --- ## **Final Answers:** ### **(b)** - **Statically determinate** - **Stable** ### **(c)** - **Statically indeterminate to 1st degree** - **Stable** --- **Explanation:** - In (b), the number of unknown support reactions equals the available equilibrium equations, so it is statically determinate and stable. - In (c), there is one more unknown than equations, making it statically indeterminate to the 1st degree, but the structure is still stable because it cannot move as a rigid body. If you need the same analysis for another structure, let me know!