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Naddik [55]
3 years ago
6

4. The bar has cross-sectional area A and modulus of elasticity E. If an axial force F directed toward the right is applied at C

: (a) What is the normal stress in the part of the bar to the left of C? [15 pts] (b) What is the resulting displacement of the point C? [15 pts]
Physics
1 answer:
aniked [119]3 years ago
4 0

Answer:

a)  ΔL/L = F / (E A),  b)   L_{f} = L (1 + L F /(EA) )

Explanation:

Let's write the formula for Young's module

     E = P / (ΔL / L)

Let's rewrite the formula, to have the pressure alone

    P = E ΔL / L

The pressure is defined as

    P = F / A

Let's replace

   F / A = E ΔL / L

   F = E A ΔL / L

   ΔL / L = F / (E A)

b) To calculate the elongation we must have the variation of the length, so the length of the bar must be a fact. Let's clear

    ΔL = L [F / EA]

    L_{f} -L = L (F / EA)

    L_{f} = L + L (F / EA)

    L_{f} = L (1 + L (F / EA))

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