Beam Bending Moment Types Explained
A bending moment represents the internal effect of external forces causing a beam to bend. The type of bending moment determines the direction and shape of this curvature.
Understanding Beam Curvature
Beams bend under load. The shape of this bending is crucial in structural analysis. Two primary types of bending moments describe this curvature:
- Sagging Bending Moment: This moment causes the beam to curve downwards, forming a shape like a smile (concave upwards). Tension occurs at the bottom fiber and compression at the top fiber.
- Hogging Bending Moment: This moment causes the beam to curve upwards, forming a shape like a frown (convex upwards). Tension occurs at the top fiber and compression at the bottom fiber.
Identifying the Correct Bending Moment
The question asks for the specific type of bending moment that produces "convexity above the centre line". This visual description directly corresponds to the upward curvature characteristic of a hogging bending moment.
Therefore, the bending moment resulting in convexity above the centre line is the hogging bending moment.
Important Questions from Shear Force and Bending Moment
For a simply supported beam of length L with a triangular load that varies gradually (linearly) from zero at both ends to w per unit length at the centre, the maximum bending moment is
For simply supported beams, the bending moment at supports (or ends) is always
A cantilever of length L carries a gradually (linearly) varying load from zero at its free end to w per unit length at the fixed end. The product of deflection and flexural rigidity at the free end is
If the shear force at a section of a simply supported beam is zero, the bending moment at the section is
Shear force at any point of the beam is the algebraic sum of
