Problem Statement: The Matrix Stiffness Equation (Basic) You modeled a simply supported beam of length $L = 8$ meters subjected to a uniform distributed load (UDL) $w = 15$ kN/m. In the Post-Processing module, STAAD reports a maximum shear force of 60 kN at the supports. Verify this manually using static equilibrium formulas to ensure the model's load application is correct.

Problem Statement: The Matrix Stiffness Equation (Intermediate) For the same $8 \text{ m}$ beam with $w = 15 \text{ kN/m}$, verify the maximum bending moment reported by STAAD at midspan.

Problem Statement: The Matrix Stiffness Equation (Advanced) A cantilever beam is subjected to a point load $P = 100 \text{ kN}$ at its free end. The length is $L = 5 \text{ m}$, Modulus of Elasticity is $E = 200\times10^6 \text{ kN/m}^2$, and Moment of Inertia is $I = 0.0005 \text{ m}^4$. Calculate the tip deflection $\Delta$ to verify STAAD's node displacement table.

Problem Statement: P-Delta Modified Stiffness (Basic) A cantilever column of height $H = 4$ meters is subjected to an axial load $P = 500$ kN and a lateral wind load $V = 20$ kN at the top. First-order linear analysis shows a tip displacement $\Delta = 30$ mm. Calculate the secondary moment caused by the P-Delta effect at the base.

Problem Statement: P-Delta Modified Stiffness (Intermediate) For the same column, STAAD's P-Delta analysis converges after 3 iterations. Assume the new tip displacement is $\Delta_f = 35.6 \text{ mm}$. What is the final exact overturning moment at the base?

Problem Statement: P-Delta Modified Stiffness (Advanced) A highly flexible, heavily loaded column experiences a primary lateral displacement of $\Delta_0 = 40 \text{ mm}$ under a primary moment of $M_0 = 100 \text{ kN-m}$. The axial load is $P = 800 \text{ kN}$. The critical buckling load of the column is $P_{cr} = 2000 \text{ kN}$. Estimate the final converged overturning moment using the direct magnification factor approach instead of an iterative approach.

Case Study: Identifying Instability from the Output File (Conceptual) After running a static analysis on a steel truss, STAAD produces an error: **WARNING** INSTABILITY AT JOINT 5 DIRECTION X. The structure has a roller support at joint 5. How do you interpret this error and resolve it?

Case Study: Reviewing the Output File (.ANL) (Conceptual) You just completed a massive structural analysis for a high-rise tower. The GUI shows no errors, but the client requires proof that the total applied load equals the total foundation reactions (equilibrium check). Where is this found?