When the section is subjected to an axial load and a moment, the ratio of the moment to the load is called:
Eccentricity
Understanding Axial Load and Moment
When a structural section is subjected to forces, these forces can cause various types of stresses. An axial load is a force acting along the longitudinal axis of the member. A moment is a rotational effect caused by a force acting at a distance.
Combined Loading: Axial Load and Moment
Often, a section is subjected to both an axial load and a moment simultaneously. This happens when the applied load is not acting perfectly through the centroid of the section. When the load acts away from the centroid, it is called an eccentric load.
Eccentricity and its Relationship to Moment and Axial Load
Eccentricity is defined as the distance between the point of application of the axial load and the centroid of the section. An eccentric load 'P' acting at a distance 'e' from the centroid creates a moment 'M'. This moment is calculated as the product of the load and the eccentricity.
The formula for the moment is:
\( M = P \times e \)
Where:
- \( M \) is the moment
- \( P \) is the axial load
- \( e \) is the eccentricity
We are asked about the ratio of the moment to the load, which is \( \frac{M}{P} \). From the formula \( M = P \times e \), we can rearrange it to find this ratio:
\( \frac{M}{P} = e \)
Therefore, the ratio of the moment to the axial load is equal to the eccentricity.
Why Other Options Are Not the Answer
- Direct Stress: This is the stress caused by the axial load acting through the centroid (\( \sigma_{\text{direct}} = \frac{P}{A} \), where A is the area). It is a stress value, not a ratio of moment to load.
- Combined Stress: This refers to the total stress at a point in a section subjected to multiple types of loading (like axial load and bending). It is the sum or combination of different stress components, not a ratio of moment to load.
- Bending Stress: This is the stress caused by a bending moment (\( \sigma_{\text{bending}} = \frac{My}{I} \), where I is the moment of inertia and y is the distance from the neutral axis). It is a stress value, not a ratio of moment to load.
Based on the relationship \( \frac{M}{P} = e \), the ratio of the moment to the axial load is known as eccentricity.
Important Questions from Bending Moment
For a simply supported beam carrying distributed load w per unit length, consider the following relations between shear force F and bending moment M.
A. \(\rm w=-\frac{dF}{dx}\)
B. \(\rm w=-\frac{d^2M}{dx^2}\)
C. \(\rm F=\frac{dM}{dx}\)
Which of the above statements is/are correct ?
A simply supported beam of 4 m span carries a uniformly distributed load all over the span of 20 kN. The maximum bending moment is
When a beam is subjected to a bending moment, the strain in a layer is _____ the distance from the neutral axis.
- A cantilever and a simply supported beam have the same length and are subject to the same uniformly distributed load. The ratio of their maximum bending moments is
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