Consider the steel truss shown in $($Eipure $1)$ to answer Parts A$,$ B$,$ and C below, where $P_1=38kN$ and $P_2=48kN.$ The cross$-$sectional area of each member is $A=400m{m}^2,$ and $E=400$GPa.

Learning Goal:

The principle of virtual work, also referred to as the unit$-$load method, provides a method for determining the slope or displacement at a specific point in a structure For a truss, the method of virtual work can be used to determine the displacement caused by an extemal load or a temperature change.

The displacement of a truss joint caused by exdernal loading can be determined using the equation

$1*={\displaystyle \underset{?}{\overset{?}{}}}\frac{nNL}{AE},$ where $1$ is the external virtual unit load acting on the truss joint in the direction of $,n$ is the internal virtual normal force in a truss member caused by the exdemal virtual unit load, $$ is the external joint displacement in the desired direction caused by the real loads on the truss, $N$ is the internal normal force in a member caused by the real loads, $L$ is the member's length, $A$ is the member's crosssectional area, and $E$ is the member's modulus of elasticity. To use this method, start by removing the real loads and placing a unit load on the truss at the desired joint in the direction the displacement is to be determined. Calculate the internal force, $n,$ in each truss member assuming tensile forces are positive and compressive forces are negative. Next, determine the real normal force, $N,$ in each member caused by the real loading. Finally, apply the virtual work equation to determine the displacement at the desired joint. Due to the relatively large number of members in a truss, it is often helpful to arrange the data in a table. If a negative value results, the displacement is in the opposite direction of the applied unit load.

The displacement of a truss joint caused by a change in temperature can be determined using the equation $1.={\displaystyle \underset{?}{\overset{?}{}}}nTL,$ where $$ is a coefficient of thermal expansion and $T$ is a member's change in temperature

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