Question

(a) For the truss shown below: Using the method of virtual work, determine the vertical deflection dy of joint B. Members BC and DC undergo a +50 °F temperature change. Member AB is fabricated 1 inch too short. For all bars, assume coefficient of thermal expansion a = 6.5 x 10-6 in/in/°F, cross-sectional area A = 4 in², and modulus of elasticity E = 29,000 kip/in². Note: A is roller and C is pinned support. Note: The general form of virtual work equation for trusses can be expressed as: Q \cdot \delta_{P}+W_{Q-R e a c t i o n s}=\sum_{i=1}^{n} F_{Q i} \cdot\left\{\Delta L_{i}\right\}=\sum_{i=1}^{n} F_{Q i} \cdot\left\{\frac{F_{P i} \cdot L_{i}}{A_{i} \cdot E_{i}}+\alpha_{i} \cdot \Delta T_{i} \cdot L_{i}+\Delta L_{i f a b r}\right\} where Q corresponds to the virtual system while P corresponds to the real system.

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