To determine the load P, we need to analyze the geometry and the material properties involved in the problem. The important factors here include the displacement at end C, the properties of the guy wire BD, and the modulus of elasticity.
Given:
- Diameter of the guy wire (d) = 0.32 in
- Modulus of Elasticity (E) for A36 steel = 29 x 103 ksi
- Displacement (Δ) = 0.15 in
First, we calculate the cross-sectional area (A) of the wire:
A = π(d/2)2
A = π(0.32/2)2 = π(0.16)2 = π(0.0256) ≈ 0.0804 in2
Next, we can find the axial deformation (δ) in the wire using the formula:
δ = (P * L) / (A * E)
Where P is the load, L is the length of the wire, and δ is the deformation. Since we have Δ as the displacement for end C, we can equate δ to Δ:
Δ = (P * L) / (A * E)
To solve for P:
P = Δ * (A * E) / L
Assuming we know the length L of the wire, we can substitute the known values. Note: L must be provided or estimated to complete the calculation for P.
In conclusion, to find the load P, measure the length L of the wire and use the above formula to substitute the values. Thus, you will arrive at the required load on the pipe from the displacement observed at end C.