Analysis of Statically Indeterminate Structures - Examples & Applications

Analyze a propped cantilever beam (fixed at support A, roller at support B) of total length $L$ subjected to a uniform downward load $w$.

Case Study: Why Use Indeterminate Structures for Seismic Design?

Case Study: The Impact of Support Settlement on Determinate vs. Indeterminate Structures.

Analyze a two-span continuous beam ABC using the Three-Moment Equation. Span AB ($L_1 = 4\text{ m}$) carries a uniform load $w_1 = 12\text{ kN/m}$. Span BC ($L_2 = 6\text{ m}$) carries a uniform load $w_2 = 8\text{ kN/m}$. The beam is supported by pins/rollers at A, B, and C. The flexural rigidity $EI$ is constant throughout.

Analyze the effect of a support settlement on a two-span continuous beam ABC ($L_1 = 4\text{ m}$, $L_2 = 5\text{ m}$) using the Three-Moment Equation. The beam carries no external loads. However, the middle support B settles downwards by an amount $\Delta_B = 10\text{ mm}$ ($0.01\text{ m}$). Assume constant $EI = 40,000\text{ kN}\cdot\text{m}^2$. Supports A and C do not settle ($h_A=0, h_C=0$).