Beam Bending Moments: Equilibrium, Diagrams, and Stress Analysis

All flashcards

What is a bending moment?

It is the internal resultant turning effect developed in a structural element to balance external loads that cause bending.

How is a simple moment calculated?

Multiply the force by its perpendicular distance from the reference point or axis: $M=F d$.

What is the neutral axis?

It is the line in a cross-section where longitudinal bending stress changes from tension to compression; in a simple bending case, the stress there is zero.

What internal actions occur when a beam bends?

The cross-section develops internal compressive forces on one side and tensile forces on the other, creating a resultant bending moment.

What are common bending-moment units and uses?

Common units are N·m and lb·ft. Engineers use bending moments with material and cross-section properties to evaluate strength and bending-related failure.

Quiz questions

1. A force vector $\mathbf{F}$ acts at a position vector $\mathbf{r}$ from point $O$. What is its moment vector about $O$?Answer: $\mathbf{r}\times\mathbf{F}$
2. For a moment vector $\mathbf{M}$ and a unit vector $\mathbf{e}$ along a chosen axis, how is the scalar moment about that axis calculated?Answer: $\mathbf{e}\cdot\mathbf{M}$
3. Under a sign convention in which clockwise bending moments are negative, what does a negative moment indicate?Answer: Hogging
4. In an ideal simply supported beam model, what rotational behavior and end-moment reaction are associated with a support?Answer: It permits rotation and does not transmit an end bending moment.
5. What is the typical shape of a bending-moment diagram over a span carrying a uniformly distributed load?Answer: Parabolic