The maximum bending stress typically occurs at the top or bottom of the beam, furthest from the neutral axis.
To determine the maximum bending stress in a beam made from three boards nailed together, subjected to a bending moment
of 600 N·m, we would typically follow these steps:
1. Identify the cross-sectional area of the beam: This includes the width, height, and arrangement of the boards.
2. Calculate the Moment of Inertia (I): For a rectangular cross-section, the moment of inertia can be calculated as
where
is the base width of the rectangle, and
is the height. If the beam is made of three boards, you would either consider them as a single unit (if they are arranged to form a single, wider rectangle) or calculate the moment of inertia for each board and then add them together (if they are stacked on top of each other).
3. Calculate the Neutral Axis: For symmetrical cross-sections, the neutral axis is at the centroid of the section. For non-symmetrical sections or sections with varying material properties, the neutral axis location would have to be calculated taking into account the distribution of material.
4. Determine the Maximum Bending Stress using the formula:
![\[ \sigma = (M y)/(I) \]](https://img.qammunity.org/2024/formulas/physics/high-school/9sd5mg4544fhddts1q64miah7jeuiksu63.png)
where
is the stress,
is the bending moment, is the distance from the neutral axis to the outermost fiber (where the stress is maximum), and
is the moment of inertia.
5. Identify the location of the maximum stress: The maximum bending stress typically occurs at the top or bottom of the beam, furthest from the neutral axis.
6. Sketch the stress distribution: The stress distribution for a beam under bending is linear, going from compression (negative) on one side to tension (positive) on the other, with zero stress at the neutral axis.