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.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. 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.