Discussion
Which one of the following options is the CORRECT absolute value of the bending moment at R in the frame as shown in the figure?
Figure is not to scale
Answer: B
The bending moment at R is Fl.
The roller at Q gives only a horizontal reaction H, along the member QR. Cut the frame just at R and take moments of the forces on the part Q-R about R:
- H acts along the line of QR, so it has no moment about R.
- The load F acts at the midpoint of QR, a distance l from R, giving a moment Fl.
So \(|M_{R}| = Fl\). (For completeness, moments about P give H = F/3, but its value does not affect the moment at R.)
Zero would need F to act at R, and 2Fl or 3Fl take lever arms of 2l or 3l, the length of QR or the frame's height, instead of the distance from F to R.
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