Application of the Portal Method

Given: The rigid frame shown in Fig. E11.1a.

Determine: The axial force, shear force, and bending moment in the beams and columns using the Portal method.

Question

Application of the Portal Method

Given: The rigid frame shown in Fig. E11.1a.

Determine: The axial force, shear force, and bending moment in the beams and columns using the Portal method.

Accepted Answer

The portal method assumes the exterior column shear, [latex]V_{E}[/latex], is equal to one-half the interior column shear force [latex]V_{I}[/latex], which is taken to be equal for all the interior columns.

[latex]V_{E}=\frac{1}{2}V_{I}[/latex]

Summing the column shear forces for this structure leads to an expression for the total story shear.

[latex]V_{T}=2V_{E}+V_{I}[/latex]

[latex]=2V_{I}[/latex]

Then,

[latex]V_{I}=\frac{1}{2}V_{T}[/latex]

[latex]V_{E}=\frac{1}{2}V_{I}=\frac{1}{4}V_{T}[/latex]

We range over the stories and generate the column shear for each story. The calculations are summarized below.

Story	[latex]V_{ T }[/latex] (KN)	[latex]V_{ I }[/latex] (KN)	[latex]V_{ E }[/latex] (KN)
Top	16	8	4
Bottom	48	24	12

Given the column shear forces, one can determine the column end moments using the assumption that there are inflection points at certain locations in the columns. For this structure, since the base is pinned, the inflection points for the first story are at the base. The inflection points for the second story are taken at mid-height. The free body diagrams for the various segments are shown below along with the final results. Once the column end moments are known, we can determine the end moments and shear forces in the beams and lastly, the axial forces in the columns using equilibrium equations (Figs. E11.1b, E11.1c, E11.1d, E11.1e, E11.1f, E11.1g, E11.1h).

Question : Application of the Portal Method Given: The rigid frame show...

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