Which one of the following statements is correct?
- AThe rate of change of shear force along the length of the beam is equal to bending moment.
- BThe bending moment is zero at the point where shear force changes sign.
- CShear force changes abruptly at the point of application of couple.
- DRate of change of bending moment changes abruptly at the location of point load.Correct
Solution
Concept
dM/dx = V and dV/dx = -w. A point load causes a sudden jump in shear force, so the slope of the BM diagram also jumps.
Formula
dV/dx = -w, dM/dx = V
Step-by-step solution
1. Rate of change of SF is load intensity (dV/dx = -w), not BM. So A is wrong. 2. Where SF changes sign, BM is maximum or minimum, not zero. So B is wrong. 3. At an applied couple, BM jumps suddenly. SF does not change. So C is wrong. 4. dM/dx = V. At a point load, V jumps suddenly, so dM/dx also changes suddenly. So D is correct.
Explanation
The slope of the BM diagram equals the shear force. At a point load the shear force jumps suddenly, so the slope of the BM diagram also changes suddenly. This shows as a kink in the BM diagram.
Why the other options are wrong
A: rate of change of SF equals load intensity, not BM. B: BM is maximum or minimum (not zero) where SF changes sign. C: a couple causes a sudden jump in BM, not in SF.
Shortcut
Point load means a jump in SF and a kink in BM. Couple means a jump in BM and no change in SF.
Common mistake
Mixing up the effects of a point load and a couple on the SF and BM diagrams.
Correct answer: D) Rate of change of bending moment changes abruptly at the location of point load.