Shear Force & Bending Moment Builder
What's on screen
Three stacked panels. Top panel is the beam with supports and applied loads. Middle panel draws the Shear Force Diagram (SFD) in blue. Bottom panel draws the Bending Moment Diagram (BMD) in red. All three update instantly every time you add or change a load.
5 toolbar buttons:
Load tools (tap beam to place):
Point load (red) — adds a 10 kN downward force. Creates a step jump in SFD. Changes BMD slope.
UDL (orange) — adds an 8 kN/m distributed load spanning 30% of the beam around your tap. Creates a linear slope in SFD. Makes BMD parabolic.
Moment/Couple (purple) — adds a 5 kNm couple. No effect on SFD. Creates a step jump in BMD. This is the key difference students must understand.
Support selectors:
Pin+Roller (green) — simply supported beam. RAy at left, RBy at right. Statically determinate.
Cantilever (purple) — fixed at left, free at right. RAy and MA at the wall.
3 pre-built examples:
Example 1: Simply supported, single 10 kN point load at midspan. Classic textbook case. SFD is a step function. BMD is a triangle with Mmax = PL/4 at center.
Example 2: Simply supported with two unequal point loads (8 kN at 1/3, 12 kN at 2/3) plus a 5 kNm couple at midspan. Shows multiple SFD jumps, BMD slope changes, and the couple causes a visible BMD step without any SFD change.
Example 3: Cantilever with full-span 6 kN/m UDL plus 10 kN tip load. SFD is a sloping line (from UDL) with a step at the tip (from point load). BMD is a parabolic curve. MA is large at the wall.
Key slider experiments::
SFD zero crossings marked with a dot and "V=0" label. This is where BMD has its maximum (dM/dx = V, so when V=0, M is at a peak).
BMD inflection points marked where M changes sign (M=0). This is where the beam switches from sagging to hogging.
Vmax and Mmax labeled with dots on each diagram.
Positive/negative labels: +V (upward shear) and -V (downward) on SFD. +M (sagging) and -M (hogging) on BMD.
Relationship reminder at the bottom of BMD: "dM/dx = V (slope of BMD = shear)".
Filled regions with light tint showing positive vs negative areas.
Green dashed reaction arrows at supports with calculated values.
Purple moment arc for the fixed support reaction MA.