A 250 mm (depth) x 150 mm (width) rectangular steel beam is subjected to maximum
bending moment of 750 kNm. Determine the flexural stress at the extreme tensile layer
corresponding to the applied moment.

The flexural stress in a beam subjected to a bending moment can be determined using the **bending stress formula**:

\[
\sigma = \frac{M \cdot y}{I}
\]

Where:
- \(\sigma\) is the flexural stress (in Pascals or \(N/m^2\)),
- \(M\) is the bending moment (in Newton-meters, Nm),
- \(y\) is the distance from the neutral axis to the extreme fiber (in meters, m),
- \(I\) is the second moment of area (also called the moment of inertia, in \(m^4\)).

### Step 1: Convert dimensions to meters
- Depth \(h = 250 \, \text{mm} = 0.250 \, \text{m}\),
- Width \(b = 150 \, \text{mm} = 0.150 \, \text{m}\).

### Step 2: Calculate the second moment of area \(I\)
For a rectangular beam, the second moment of area \(I\) about the neutral axis is given by the formula:

\[
I = \frac{b h^3}{12}
\]

Substituting values:

\[
I = \frac{0.150 \times (0.250)^3}{12} = \frac{0.150 \times 0.015625}{12} = 0.00019531 \, \text{m}^4
\]

### Step 3: Calculate \(y\) (distance from the neutral axis to the extreme fiber)
For a rectangular cross-section, the distance \(y\) from the neutral axis to the extreme tensile fiber is half of the depth:

\[
y = \frac{h}{2} = \frac{0.250}{2} = 0.125 \, \text{m}
\]

### Step 4: Substitute values into the bending stress formula
Now, using the bending moment \(M = 750 \, \text{kNm} = 750,000 \, \text{Nm}\):

\[
\sigma = \frac{750,000 \times 0.125}{0.00019531} = \frac{93,750}{0.00019531} = 480,000,000 \, \text{Pa}
\]

or:

\[
\sigma = 480 \, \text{MPa}
\]

### Final Answer:
The flexural stress at the extreme tensile layer is **480 MPa**.

---

Would you like further details or have any questions on this?

Here are 5 related questions for further exploration:
1. What is the difference between flexural and shear stress in beams?
2. How would the stress distribution change for a beam with a circular cross-section?
3. What role does the neutral axis play in the analysis of beam bending?
4. How would increasing the beam width impact the flexural stress for the same bending moment?
5. Can flexural stress exceed the yield stress of the material, and what happens if it does?

**Tip:** When designing beams, always ensure that the maximum flexural stress is less than the material's yield strength to avoid permanent deformation.

A 250 mm (depth) x 150 mm (width) rectangular steel beam is subjected to maximum bending moment of 750 kNm. Determine the flexural stress at the extreme tensile layer corresponding to the applied moment.

Explore how to determine the flexural stress for a 250 mm x 150 mm rectangular steel beam under a maximum bending moment of 750 kNm. This problem uses the bending stress formula, moment of inertia calculation, and mechanics of materials concepts to arrive at the flexural stress of 480 MPa. Suitable for engineering students.

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