Part B $-$ Calculate the member forces with the virtual force

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 $n$ s 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

$3$ of $3$

To use the virtual work method, the member forces must be calculated when a virtual unit force is applied to the cut ends of $FG($Figure $3).$ The force is applied so as to counteract the displacement ${}_{FG}$ in Part A$.$ Solve for the forces in all the members when the structure is subjected to this loading.

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