The centroid is the point through which the entire cross-sectional area of a beam can be assumed to act. The neutral axis is the line through the cross-section where there is no bending stress. These two are not the same because the neutral axis depends on the bending moment and the shape of the cross-section, whereas the centroid is a fixed point based on the geometry of the cross-section.
The neutral axis is not always located at the centroid because the bending moment is not always evenly distributed across the cross-section. In asymmetric beams or beams with varying cross-sectional shapes, the bending moment is not evenly distributed, resulting in the neutral axis being shifted from the centroid.
The position of the neutral axis plays a crucial role in determining the bending moment. The farther the neutral axis is from the centroid, the greater the bending moment will be. This is because the larger the distance between the neutral axis and the centroid, the larger the lever arm, which results in a larger moment arm and higher bending moment.
No, the neutral axis must always lie within the cross-sectional area of the beam. This is because any point outside of the cross-section will not experience any bending stress and therefore cannot be considered the neutral axis.
The neutral axis in a beam with a non-uniform cross-section can be determined using the principle of superposition. This involves splitting the cross-section into smaller, simpler shapes for which the location of the neutral axis is known, and then finding the overall neutral axis by combining the individual neutral axes. Alternatively, numerical methods such as the moment-area method can also be used to determine the neutral axis in non-uniform beams.