To determine the normal compressive stress induced in a simply supported beam subjected to a moment, we use the flexural formula:

$\sigma = \frac{M \cdot y}{I}$

Where:

• $\sigma$ is the normal stress at a given point (in Pa or N/m²).
• $M$ is the bending moment (in N·m or kN·m).
• $y$ is the distance from the neutral axis to the point where the stress is being calculated (in meters).
• $I$ is the second moment of area (in m$^4$).

Given:

• $M = 100 \, \text{kN·m} = 100 \times 10^3 \, \text{N·m}$
• $y = 50 \, \text{mm} = 50 \times 10^{-3} \, \text{m}$

To find the normal compressive stress, we also need the second moment of area $I$, which depends on the cross-sectional shape of the beam. However, since the shape is not provided, we cannot calculate the exact value of $\sigma$ without this information.

General Approach:

If the cross-sectional shape is, for example, a rectangle, the second moment of area $I$ for a rectangle is calculated as:

$I = \frac{b \cdot h^3}{12}$

Where $b$ is the width and $h$ is the height of the rectangular cross-section.

Substituting in the Values:

For a given $I$, you would substitute into the equation:

$\sigma = \frac{100 \times 10^3 \times 50 \times 10^{-3}}{I}$

This formula provides the stress in N/m². Once $I$ is known, you can compute $\sigma$.

If you know the beam's cross-sectional dimensions, I can help calculate $I$ and find the exact compressive stress.

Would you like to provide the cross-sectional dimensions or need further details on any of the steps?

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Relative Questions:

1. What is the significance of the neutral axis in beam theory?
2. How does the shape of the beam's cross-section affect the second moment of area?
3. What would be the normal stress if the distance $y$ was doubled?
4. How does the bending moment distribution vary along the length of a simply supported beam?
5. What assumptions are typically made in deriving the flexural formula?

Tip: In problems involving bending stress, always verify the cross-sectional shape of the beam to calculate the second moment of area accurately.