Approximate Analysis of Indeterminate Structures - Examples & Applications

Analyze a single-story, two-bay frame with equal bay widths ($L$) and height ($H$) subjected to a lateral load $P$ at the roof level.

Analyze the top story of a building frame using the Cantilever Method. The story has two bays with widths $L_1 = 6\text{ m}$ and $L_2 = 4\text{ m}$. The story height is $H = 4\text{ m}$. A lateral wind load of $P = 100\text{ kN}$ acts at the roof level. Assume all three columns have the same cross-sectional area $A$. Determine the axial forces in the three columns (C1, C2, and C3).

Case Study: Why Use Approximate Methods in the Era of Computer Software?

Use the Portal Method to find the base shear reactions for a two-story, single-bay frame. The first story is $4\text{ m}$ high and the second story is $3\text{ m}$ high. Bay width is $6\text{ m}$. A lateral wind load of $P_1 = 20\text{ kN}$ is applied at the roof level, and $P_2 = 40\text{ kN}$ is applied at the second-floor level.

Case Study: Assumptions of the Factor Method vs. Portal/Cantilever Methods.

Calculate the axial force in the columns of the single-bay, single-story portal frame from the previous example using the Portal Method. Height $h=4\text{ m}$, Width $L=6\text{ m}$, Lateral load $P = 60\text{ kN}$ at the roof. (Combining the $20$ and $40$ to act at roof for a single story analysis).