Question

Solve for the deflection of the following beam using Conjugate Beam Method: Assume: Assume the beam is rectangular with b=423 mm and h=522 mm. P=31 kN, w=8 kN/m, L=7 m, E=20 GPa.

Answer 1

To solve for the deflection of the rectangular beam using the Conjugate Beam Method, calculate the moment of inertia and use the formula for deflection. The deflection of the beam is 0.083 mm.

Step-by-step explanation:

To solve for the deflection of the rectangular beam using the Conjugate Beam Method, we need to calculate the moment of inertia of the beam, which is given by the formula I = (1/12) * b * h^3, where b is the width and h is the height of the beam. In this case, b = 423 mm and h = 522 mm. Plugging in the values, we get I = (1/12) * 423 * (522^3) = 1.03 * 10^10 mm^4.

The deflection of the beam can be calculated using the formula δ = (5 * w * L^4) / (384 * E * I), where w is the distributed load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia. In this case, w = 8 kN/m, L = 7 m, and E = 20 GPa. Plugging in the values, we get δ = (5 * 8000 * 7^4) / (384 * 20 * 10^9 * 1.03 * 10^10) = 0.083 mm.