Multiply Redundant Structures - Page 1 of 5
Multiply Redundant Structures
Objectives:
1.
Set up the coordinate systems for virtual work in a beam
2.
Calculate the moment equations for sections of a beam
3.
Integrate using the Virtual work formulas to get displacements
4.
Calculate the reactions for a multiple-degree indeterminate beam structure
For each redundant, there is a compatibility equation and an un-known force.
The end result is a set of simultaneous equations.
Multiply Redundant Structure Example
Given the structure in the figure, find the reactions.
Step 1) is to form the determinate base structure.
The structure chosen is:
We can label the applied loads as case 0.
The unit loads applied to the removed redundants for
Step 3) are labeled case 1 and 2.
Load case 1 and 2 are also the virtual load cases.

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