The model in 3-D
Click a support, load, hinge or the foundation to edit it; click the beam to probe the stresses there or to add a load, support or hinge at that point. Drag to orbit, right-drag or Shift-drag to pan, scroll or pinch to zoom. Colours are the exact stresses at the section outline; displacements and twist are exaggerated, and slender sections are drawn enlarged. Ctrl+Z undoes.
Key results
Free-body diagrams in two planes
Click anything to edit it, or click the beam to add something there; drag supports, loads, hinges and the ends of distributed loads to move them (snaps to supports and 0.5 % steps; hold Alt for free placement). Reactions are teal, drawn in their actual sense and labelled with magnitudes (signed components are in the summary and the solution); the dashed curve is the exaggerated deflection in each plane. Double-headed arrows are moment vectors along the axis (torques), by the right-hand rule.
Internal forces and displacements
Choose what to plot. Hover to read values; click or drag to move the probe section. Blue areas are positive, red negative; jumps are exact one-sided limits at loads and supports. With warping, the torque splits into Saint-Venant and warping parts.
Cross-section at the probe
Seen from the left end, looking along +x (z to the right, y up). Click the beam in Fig. 1 or drag on this section to move the probe point. C is the centroid, S the shear centre, p₁ and p₂ the principal axes; the dash-dot line is the neutral axis of σx. Arrows show the shear flow q = τt along the wall of open sections.
State of stress at the probe point
A beam fibre carries σx and a shear τ along the direction n in the section, so the element is drawn in the x–n plane. Mohr's circle uses Shigley's convention (clockwise shear up); the three circles are the full 3-D state with σ2 = 0.