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A composite section made of two materials has moduli of elasticity in the ratio 1 : 2 and lengths in the ratio 2 : 1. The ratio of the corresponding deflection under a direct load is
  • a)
    2 : 1
  • b)
    1 : 2
  • c)
    4 : 1
  • d)
    1 : 4
Correct answer is option 'C'. Can you explain this answer?
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A composite section made of two materials has moduli of elasticity in ...
Given data:
Modulus of elasticity ratio = 1:2
Length ratio = 2:1

To find: Ratio of corresponding deflection under a direct load

Solution:
Let us consider a composite section made of two materials A and B.

Let the cross-sectional area of material A be A_A and that of material B be A_B.

Let the length of material A be L_A and that of material B be L_B.

Let the modulus of elasticity of material A be E_A and that of material B be E_B.

Let the direct load applied be P.

The total deflection of the composite section can be obtained by considering the deflection of material A and that of material B separately.

The deflection of material A can be obtained using the formula:

δ_A = (PL_A^3)/(3E_AA_A)

Similarly, the deflection of material B can be obtained using the formula:

δ_B = (PL_B^3)/(3E_BB_B)

The total deflection of the composite section can be obtained as the sum of the deflections of material A and material B:

δ = δ_A + δ_B

Substituting the given data in the above equations, we get:

δ_A/δ_B = (E_A/E_B) * (A_B/A_A) * (L_B/L_A)^3

Substituting the given values, we get:

δ_A/δ_B = (1/2) * (1/1) * (1/2)^3 = 1/8

Therefore, the ratio of corresponding deflection under a direct load is:

δ_A : δ_B = 1 : 8

Multiplying both sides by 8, we get:

8δ_A : 8δ_B = 8 : 1

Simplifying, we get:

δ_A : δ_B = 4 : 1

Therefore, the correct option is (C) 4 : 1.
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A composite section made of two materials has moduli of elasticity in the ratio 1 : 2 and lengths in the ratio 2 : 1. The ratio of the corresponding deflection under a direct load isa)2 : 1b)1 : 2c)4 : 1d)1 : 4Correct answer is option 'C'. Can you explain this answer?
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