Introduction to Mechanics of Materials: Part II by Branislav Hučko; Roland Jančo

Author:Branislav Hučko; Roland Jančo
Language: eng
Format: epub
Publisher: Bookboon.com Ltd.
Published: 2015-03-13T00:00:00+00:00

Fig. 5.15

Substituting for from (5.23) and (5.25) into the equation (5.24), and making we obtain the slope at point B for a given load

(5.26)

The positive sign indicates the counterclockwise direction since we assumed the fictitious counterclockwise load.

(5.27)

5.6 Statically Indeterminate Beams

Statically indeterminate problems can be solved in the usual way by removing the redundant supports and replacing them by unknown reactions. Then we can apply the step-by-step approach for determining internal force distribution functions. But these functions involve unknown reactions. To determine those reactions we can apply deformation conditions that correspond to the removed supports.

Let us consider the cantilever beam BC with a length L subjected to the distributed load w, see Fig. 5.15. The presented beam is statically indeterminate to the first degree. We replace the redundant support at B by the unknown reaction . To get the same deformation response we need to impose the deformation condition

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