D-04 — shear + moment

Shear + Moment

shear + moment plotter

build a beam. watch it respond.

Add point loads and distributed loads, then watch the shear and moment diagrams draw in real time.

beam setup
24 ft
point loads
pos (ft)
mag (kips)
distributed loads
start (ft)
end (ft)
w (k/ft)
beam diagram
shear force diagram — V (kips)
bending moment diagram — M (kip·ft)
live equation
V = Internal vertical force at a cut through the beam
M = Internal moment at a cut through the beam
w = Load spread along the beam length
R = Support force found from equilibrium
explained
The shear diagram plots the internal vertical force at every point along the beam. The moment diagram plots the internal bending moment. Both are derived from equilibrium of the loads and reactions — they tell you what the beam is experiencing inside.
key concepts
overview How shear and moment arise from loads and reactions

A beam carries loads and hands them off to supports. The supports push back — those pushback forces are called reactions. Slice the beam anywhere: add up all the forces on one side and you get the shear at that cut. Integrate the shear across the span and you get the moment. The moment diagram tells you where the beam is working hardest — that's the number you design to.

two diagrams, one story Shear and moment reveal a beam's internal state

The shear diagram and moment diagram together tell you everything about a beam's internal state. Shear (V) shows the transverse force at every cross-section — it's highest near supports and jumps at point loads. Moment (M) shows the bending at every cross-section — it's highest where shear crosses zero. Together they reveal where the beam is working hardest and where it has capacity to spare.

the key relationships Load, shear, and moment are linked by calculus

Three relationships connect load, shear, and moment: (1) The slope of the shear diagram equals the distributed load intensity: dV/dx = −w. (2) The slope of the moment diagram equals the shear: dM/dx = V. (3) The area under the shear diagram between two points equals the change in moment. These aren't just math — they're how engineers sketch diagrams by hand and instantly check software output.