Approximate Analysis of Statically Indeterminate Structures - Examples

The Portal Method Examples

Example 1: Single-Story, Two-Bay Frame (Portal Method)

A single-story frame has two bays. The left bay is 6 m6 \text{ m} wide, and the right bay is 8 m8 \text{ m} wide. The height is 4 m4 \text{ m}. A lateral wind load of 30 kN30 \text{ kN} is applied at the roof level (top left joint). Analyze the frame using the Portal Method to find the base shears and column moments.

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Example 2: Two-Story, Single-Bay Frame (Portal Method)

A two-story frame has one 6 m6 \text{ m} wide bay. The first story is 5 m5 \text{ m} high, the second is 4 m4 \text{ m} high. A lateral load of 20 kN20 \text{ kN} acts at the roof, and 40 kN40 \text{ kN} acts at the 2nd floor. Find the column shears in both stories.

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Example 3: Three-Story, Three-Bay Frame (Portal Method)

A three-story frame has three bays (all 5 m5 \text{ m} wide). All stories are 4 m4 \text{ m} high. Lateral loads are 10 kN10 \text{ kN} (roof), 20 kN20 \text{ kN} (3rd floor), and 20 kN20 \text{ kN} (2nd floor). Find the shears in the 1st-story columns.

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The Cantilever Method Examples

Example 1: Single-Story, Two-Bay Frame (Cantilever Method)

Let's use the exact same frame from Portal Method Example 1 (Left bay 6 m6 \text{ m}, right bay 8 m8 \text{ m}, height 4 m4 \text{ m}, 30 kN30 \text{ kN} roof load). Assuming all columns have the same cross-sectional area AA. Analyze it using the Cantilever Method.

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Example 2: Varying Column Areas

Use the same single-story, two-bay frame (6 m6 \text{ m}, 8 m8 \text{ m} bays, 4 m4 \text{ m} high, 30 kN30 \text{ kN} load), but now the interior column is a W12x50 (Area = 2A2A), and the two exterior columns are W10x33 (Area = AA). Find the column axial forces.

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