1. **Problem Statement:** Calculate the Flexural Euler Stress $F_e$ for a compression member with given slenderness ratio $\frac{KL}{r} = 200$ and modulus of elasticity $E = 200,000$ MPa. 2. **Formula:** The Euler buckling stress for a compression member is given by: $$F_e = \frac{\pi^2 E}{\left(\frac{KL}{r}\right)^2}$$ 3. **Explanation:** - $E$ is the modulus of elasticity. - $\frac{KL}{r}$ is the slenderness ratio, where $K$ is the effective length factor, $L$ is the length, and $r$ is the radius of gyration. - The formula calculates the critical stress at which buckling occurs. 4. **Calculation:** Substitute the given values: $$F_e = \frac{\pi^2 \times 200,000}{200^2}$$ Calculate the denominator: $$200^2 = 40,000$$ Calculate numerator: $$\pi^2 \times 200,000 \approx 9.8696 \times 200,000 = 1,973,920$$ Now divide: $$F_e = \frac{1,973,920}{40,000} = 49.348$$ 5. **Result:** The Flexural Euler Stress $F_e$ is approximately $49.35$ MPa. This matches the option 49 MPa given in the choices.