Answer :
Final answer:
The vertical displacement of joint C in the truss can be determined using the method of virtual work by considering the equilibrium of forces at the joint and applying the principle of virtual work.
Explanation:
To determine the vertical displacement of joint C in the truss using the method of virtual work, we need to consider the equilibrium of forces at the joint and apply the principle of virtual work.
- First, let's analyze the forces acting on joint C. There are three members connected to joint C: AB, BC, and CD.
- Assuming the vertical displacement of joint C is δC, we can consider a virtual displacement δv in the vertical direction.
- By applying the principle of virtual work, we can equate the work done by the internal forces to the work done by the external loads.
- For joint C, the only external load acting in the vertical direction is the vertical component of the force in member BC, which can be calculated using the equation FBC = EAδC / LBC, where FBC is the vertical component of the force in member BC, E is the modulus of elasticity (29000 ksi), A is the cross-sectional area of the members (18 in²), and LBC is the length of member BC.
- Since the virtual displacement δv is in the same direction as the force in member BC, the work done by the external load is given by Wext = FBC * δv.
- The work done by the internal forces can be calculated by summing the forces in members AB, BC, and CD and multiplying them by their respective displacements.
- By equating the work done by the internal forces to the work done by the external load, we can solve for the vertical displacement of joint C, δC.
Learn more about vertical displacement here:
https://brainly.com/question/31876158
#SPJ14
