Intermediate
Beams: Shear Force & Bending Moment
How loads on a beam create internal shear and bending.
STEP 1 · CONCEPT
A beam carries loads perpendicular to its length. Inside it, shear force slides sections past each other; bending moment rotates them.
STEP 2 · SUPPORTS
Simply supported beams rest on a pin and roller. Cantilevers are fixed at one end only.
STEP 3 · KEY RESULT
Maximum bending moment is where shear force crosses zero.
WORKED EXAMPLE
A 4 m simply supported beam with a 10 kN load at the centre: each support carries 5 kN, and M_max = WL/4 = 10 kN·m.
Formulas
Central point load (SS)
M_max = W L / 4
W load, L span
UDL (SS)
M_max = w L² / 8
w load per length
Cantilever end load
M_max = W L
at fixed end
Practice questions
Q1.Max BM for a simply supported beam with UDL w over span L?
Beams: Shear Force & Bending Moment · Medium
Q2.Bending moment is maximum where shear force is…
Beams: Shear Force & Bending Moment · Medium
Q3.Max BM of a cantilever with end load W occurs at…
Beams: Shear Force & Bending Moment · Easy