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.
Compressive Stress 3Fdcb5
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.