Final answer:
The question deals with calculating the maximum force P that can be applied to a rigid support member without exceeding a given deflection, taking into account the elastic properties of the links made from different materials.
Step-by-step explanation:
The student is asking about the maximum force P that can be applied to a rigid member supported by links BD and CE made of different materials with specific Young's moduli and cross-sectional areas without exceeding a certain deflection at point A.
Problem Analysis
To find the maximum force P, we need to establish the relationship between the applied force, the material properties (Young's modulus E, cross-sectional area A), and the allowable deflection at A (deflection limit). We apply the formula for elastic deflection Δ, which is given by P = ΔA * E / L, where P is the force, A is the area, E is the Young's modulus, and L is the length of the link. We have to ensure that the sum of the deflections caused by each link does not exceed the given limit, assuming the links are in series.
Given
E (brass) = 105 GPa, A (brass) = 240 mm²
E (aluminium) = 72 GPa, A (aluminium) = 300 mm²
Deflection limit at A = 0.37 mm
We must set up two separate equations for deflection for each material based on the given properties and the deflection limit, and then solve for P to ensure that the limit is not exceeded when P is applied.