J-02 — reading shear & moment diagrams

cut the beam. read the forces inside.

shear & moment reader

drag the cut. see what's inside the beam.

Explore how internal shear and moment vary along a simply supported beam under load.

load type
loading
P (kips) 10
position mid
cut position
x (ft) 10.0
—
shear at cut (kips)
—
live equation
—
V(x) = Internal vertical force at position x
M(x) = Internal bending moment at position x
R = Support force at beam ends
explained
The shear at any cut equals the sum of all vertical forces to the left of that cut. The moment equals the sum of all moments of those forces about the cut point. Moving the cut from left to right traces out the complete V and M diagrams — one point at a time.
key concepts
the mental model Every point on the diagram is the internal force at an imaginary cut

If you sliced through the beam at any location and looked at the forces on the left piece, you'd find a vertical force (shear) and a bending moment needed to keep that piece in equilibrium. The shear and moment diagrams simply plot those values at every possible cut location along the span.

reading shapes Jumps mean point loads. Slopes mean distributed loads.

A point load causes the shear diagram to jump vertically by the magnitude of the load. A distributed load causes the shear to slope — linearly for a uniform load w. The moment diagram is always one degree higher: linear under point loads, parabolic under distributed loads. Once you learn to read the shape, you can work backward and figure out the loading.

V and M are linked The moment diagram is the running total of the shear diagram

Mathematically, dM/dx = V. The slope of the moment diagram at any point equals the shear value at that point. Where shear is zero, moment hits a maximum or minimum. The area under the shear diagram between two points equals the change in moment between those points. This relationship is the single most useful fact in structural analysis.