Deformations

Todo

Documentation of computation of deformations

Introduction

In the following the computation of deformations from curvatures are described in general. Further detailed description is given for deformation computation of composite structures acting as a solid section and under consideration of the load-slip-behaviour of the shear connectors.

General

The deformation of an infinite small beam-element is computed as given by formula (1) taking into account the moment acting at the element \(M(x)\) as well as the corresponding .

(1)\[w(x) = - \int\int \frac{M(x)}{E \cdot I_\mathrm{y}}dx\]

Using the principle of virtual forces formula (1) changes to formula (2).

(2)\[w(x) = \int \frac{M(x) \cdot \overline{M}(x)}{E \cdot I_\mathrm{y}}dx\]

Where term in formula (3) applies to the curvature \(\kappa\) at the given position.

(3)\[\frac{M(x)}{E \cdot I} = \kappa(x)\]