Question

An A572 steel beam has a modulus of elasticity of 28,150 ksi and a Poisson's ratio of 0.26. It is known that the beam is embedded in one of its supports and free in its second support. Furthermore, a horizontal axial compressive stress of -235 MPa is known. a) Determine the magnitude(s) necessary in Y so that the unitary deformation of the beam does not exceed a value of 2 x 10⁻⁴ in this direction.

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Answer to a math question An A572 steel beam has a modulus of elasticity of 28,150 ksi and a Poisson's ratio of 0.26. It is known that the beam is embedded in one of its supports and free in its second support. Furthermore, a horizontal axial compressive stress of -235 MPa is known. a) Determine the magnitude(s) necessary in Y so that the unitary deformation of the beam does not exceed a value of 2 x 10⁻⁴ in this direction.

Expert avatar
Sigrid
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116 Answers
1. **Given Data:**

- E = 28,150 \text{ ksi}

- \nu = 0.26

- \sigma_x = -235 \text{ MPa}

- \epsilon_y = 2 \times 10^{-4}

2. **Convert Units:**

- E \approx 194,030.75 \text{ MPa}

3. **Calculate Poisson's Effect:**

- \epsilon_y = -0.26 \times \frac{-235}{194,030.75} \approx 0.000315

4. **Calculate Additional Strain:**

- 2 \times 10^{-4} = 0.000315 + \epsilon_y (applied)

- \epsilon_y (applied) = -0.000115

5. **Calculate Additional Stress:**

- \sigma_y (applied) = 194,030.75 \times (-0.000115)

- \sigma_y (applied) \approx -22.31 \text{ MPa}

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