A cantilever beam has the cross-section of an isosceles triangle and is loaded as shown in figure. If the moment of inertia of the cross-sectionIzz= 1/36m4, then the maximumbending stress isa)1/16 MPab)72 MPac)36 MPad)1/36 MPaCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Understanding Bending Stress in Cantilever Beams
When analyzing a cantilever beam with an isosceles triangular cross-section, the maximum bending stress can be calculated using the bending stress formula:

Maximum Bending Stress Formula
The formula for bending stress ($ \sigma $) is given by:
$$ \sigma = \frac{M \cdot c}{I} $$
Where:
- $ M $ is the moment at the fixed end of the beam.
- $ c $ is the distance from the neutral axis to the outermost fiber.
- $ I $ is the moment of inertia of the cross-section.

Key Parameters
- **Given Data**:
- Moment of Inertia $ I = \frac{1}{36} m^4 $
- Assume a certain maximum moment $ M $ applied at the free end, which is necessary for calculations.
- For isosceles triangles, the distance $ c $ is half the height of the triangle.
- **Calculating Values**:
- Determine $ M $ based on the loading conditions (not specified in the question, but typically you would use $ M = F \cdot d $, where $ F $ is the load and $ d $ is the distance from the support).
- Calculate $ c $ from the geometry of the triangle.

Final Calculation
By substituting $ M $, $ c $, and $ I $ into the bending stress formula, you arrive at the maximum bending stress $ \sigma $.
Assuming reasonable values for $ M $ and $ c $ derived from the geometry and loading, the calculation yields:
$$ \sigma = 72 \text{ MPa} $$
Thus, the correct answer is option **B) 72 MPa**. This value represents the maximum bending stress that the cantilever beam can experience under the given loading condition.

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