Part A $-$ Calculate the loads in the primary structure

Learning Goal:

To understand how to use the force method of analysis to find the internal forces in a truss that is statically indeterminate to the first degree.

The degree of indeterminacy of a truss can be found using $b+r>2j,$ where $b$ is the number of bar forces, $r$ is the number of support reactions, and $j$ is the number of joints. When a truss is statically indeterminate to the first or second degree, the force method is a suitable method for analyzing the structure.

A redundant force must be chosen for each degree of indeterminacy. For trusses, it is often convenient to "cut" a member so that it cannot sustain a force. Then the redundant force is applied to the cut ends of the member. All the members in a truss are subject to axial loads only, so using the virtual work method, the deflection can be calculated as $={\displaystyle \underset{?}{\overset{?}{}}}\frac{nNL}{AE},$ where the $ns$ are the member forces for the truss subject to a unit virtual load at the cut ends, and the Ns are the member forces in

Figure

$2$ of $3$

The truss is indeterminate to the first degree. To perform an analysis requires one redundant force. For this problem, making the structure statically determinate requires choosing an internal member as the redundant. Make a cut in member $FG$ so that it cannot sustain a force to form the primary structure $($Figure $2).$ To use the virtual work method to find ${}_{FG},$ the displacement of the cut ends of member $FG$ due to the loading, the member forces in the primary structure subject to the real loads must be calculated. Find all the member forces and enter them on the diagram below. Use positive values for tension and negative values for compression.

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