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Advanced Package Training Scaffolding 2011.1 - Scia-Software GbR

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Manual calculation of KG<br />

50<br />

<strong>Advanced</strong> <strong>Training</strong><br />

The principle of a stability calculation and the meaning of the matrix KG will be explained with a simple<br />

example:<br />

Suppose the next situation:<br />

This beam with length L has a pinned support at the left and a flexible spring support at the right with<br />

rigidity: KE.<br />

Two point loads are inputed on the beam: a vertical R and a compression force N.<br />

Standard analysis says that R and N are independent (in the un-deformed configuration) and the<br />

stiffness relationship is:<br />

∙ = <br />

With r the vertical translation of the right point of the beam.<br />

But, if the structure is allowed to deform, we can calculate equilibrium in the deformed configuration as<br />

shown below:<br />

Summing moments about the pinned end we get:

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