Method of Virtual Work: Trusses

be determined using the equation $1*={\displaystyle \underset{?}{\overset{?}{}}}\frac{n_{2v}}{AE},$ 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 external 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 cross$-$sectional 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 negatlive 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.

Figure

$1$ of $1$

Consider the steel truss shown in $($Figure $1)$ to answer Parts A$,$ B$,$ and C below, where $P_1=34kN$ and $P_2=60kN.$ The cross$-$sectional area of each member is $A=300m{m}^2,$ and $E=100$GPa.

Part A $-$ Horizontal displacement

Use the method of virtual work to determine the horizontal displacement of joint $D$ due to the applied loads. Let a positive answer represent a displacement to the right and a negative answer represent a displacement to the left.

Express your answer in the approprlate units to three significant figures.

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Part B $-$ Vertical displacement

Use the method of virtual work to determine the vertical displacement of joint $E$ due to the applied loads. Let a positive answer represent an upward