Lessons · Engineering · shear and moment along a beam
Two diagrams that say where a beam is working hardest
Shear is the force trying to slice the beam across; bending moment is the effect trying to bend it. Both vary along the span, and the design is governed by their peaks. For a simply supported beam under a uniform load, shear is largest at the supports and moment is largest at midspan.
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Not yet checked by a licensed engineer. This lesson was written for Hone. Practice material, not professional advice. What that means.
What it is for
A beam is not uniformly stressed, and checking it at the wrong place passes a member that fails somewhere else. Knowing where each peak sits is most of what these diagrams are for.
How to think about it
Find the reactions first -- for a symmetric uniform load, each is half the total. Then remember the two standard results for that case: peak shear equals the reaction, and peak moment is wL squared over eight. Anything more complicated is built from the same two steps.
Worked example
Uniform load w over span L, simply supported.The standard case.
Total load wL, so each reaction is wL/2.Symmetry.
Peak shear = wL/2, at the supports.Where the reaction is delivered.
Peak moment = wL squared / 8, at midspan.The number worth remembering.
Your turn
A simply supported beam spans 6 m under 12 kN/m. Write the peak bending moment in kN·m.
w L squared / 8 = 12 x 36 / 8 = kN·m
Solve one, graded on the server
The trap
Using the midspan moment formula on a beam that is not simply supported under a uniform load. Change the supports or the loading and the peak moves and changes size.