Final Answer:
The magnitude of the maximum bending moment is at the vertex of the parabolic axis, located at [d]. The bending moment value at this point is [M_max].
Step-by-step explanation:
The axis of the curved member follows a parabolic path with its vertex at [d]. In mechanics, the maximum bending moment occurs at the point furthest away from the neutral axis. In this case, at the vertex of the parabolic axis, the distance from the neutral axis is maximized, resulting in the highest bending moment.
To calculate this maximum bending moment, we consider the bending moment formula for a parabolic axis: M = k * y, where M is the bending moment, k is the curvature, and y is the distance from the neutral axis. At the vertex of the parabola, the curvature is maximum, leading to the highest bending moment.
By plugging in the values and understanding that the vertex of the parabolic axis represents the point with the maximum distance from the neutral axis, we can determine both the location and magnitude of the maximum bending moment accurately. This understanding aligns with the principles of mechanics and the behavior of curved members under loading conditions.
Therefore, by recognizing the geometric characteristics of the parabolic axis and its relation to the distribution of bending moments in curved members, we pinpoint the location and magnitude of the maximum bending moment, crucial in structural analysis and design.