Question

2. The rigid bar AB, attached to two vertical rods as shown in Fig. below, is horizontal before the load P is applied. Determine the vertical movement of P if its magnitude is 50 kN. Figure P-213 Aluminum L= 3 m A = 500 mm² E = 70 GPa k 3.5 m Steel L= 4m A = 300 mm² E = 200 GPa 2.5 m​

Answer 1

To determine the vertical movement of the load P, we can use Hooke's Law and consider the elongation of the aluminum and steel rods. By calculating the elongation, we can find the final vertical movement of P when its magnitude is 50 kN.

In order to determine the vertical movement of the load P, we need to consider the deformations of the rods and the rigid bar AB.

First, we determine the elongation of the aluminum rod AC using Hooke's Law: ΔL = (F * L) / (A * E), where F is the load on P, L is the length of the aluminum rod, A is the cross-sectional area of the aluminum rod, and E is the Young's modulus of aluminum.

After calculating ΔL, we can determine the vertical movement of P by subtracting the elongation of the steel rod BC from ΔL.

By plugging in the given values for the aluminum and steel rods, and solving for the elongation, we can find the vertical movement of P when its magnitude is 50 kN.