Subjects physics

Compressive Stress 3Fdcb5

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1. **State the problem:** We have a square concrete column with base length 24 cm supporting a mass of 31,000 kg. We want to check if the column is safe given the maximum compressive stress concrete can withstand is 30 MPa. 2. **Relevant formula:** Compressive stress $\sigma$ is given by $$\sigma = \frac{F}{A}$$ where $F$ is the force applied and $A$ is the cross-sectional area. 3. **Calculate the force $F$:** Force due to the mass is weight, $F = mg$, where $m=31,000$ kg and $g=9.8$ m/s$^2$. $$F = 31,000 \times 9.8 = 303,800 \text{ N}$$ 4. **Calculate the cross-sectional area $A$:** Base length is 24 cm = 0.24 m. Since the base is square, $$A = (0.24)^2 = 0.0576 \text{ m}^2$$ 5. **Calculate the compressive stress $\sigma$:** $$\sigma = \frac{303,800}{0.0576} = 5,273,611.11 \text{ Pa} = 5.27 \text{ MPa}$$ 6. **Compare with maximum allowable stress:** Maximum compressive stress = 30 MPa. Calculated stress = 5.27 MPa. Since $5.27 < 30$, the column is safe under the given load. **Final answer:** The column will be safe because the compressive stress is less than the maximum allowable stress.