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.
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4.5116 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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2. **Convert Units:**
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3. **Calculate Poisson's Effect:**
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4. **Calculate Additional Strain:**
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5. **Calculate Additional Stress:**
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