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Statics Solver

Static Equilibrium — Force & Moment Balance Calculator

Set support conditions, loads, and moments to automatically compute unknown reactions. Real-time free body diagram drawing with numerical equilibrium verification.

Structure Settings
Beam Span L6.0 m
Support Conditions
Left End A
Right End B
Concentrated Loads (max 5)
Magnitude [kN] Angle [°] Position x [m] Label
Concentrated Moment
Magnitude [kN·m]
Position x [m]
Positive: counter-clockwise (CCW)
Ax [kN]
Ay [kN]
By [kN]
Equilibrium Error

Theory (Static Equilibrium Conditions)

Three equilibrium equations for a statically determinate 2D rigid body:

$$\sum F_x = 0 \quad \sum F_y = 0 \quad \sum M_A = 0$$

Determinacy condition: number of unknown reactions = 3 (equals number of equations)

Pin support → $A_x, A_y$ (2 reactions)   Roller → $B_y$ (1 reaction)   Fixed end → $A_x, A_y, M_A$ (3 reactions)

Degree of indeterminacy $= $ (no. of unknowns) $- 3$

CAE Integration: Verify boundary conditions and hand-calculate reactions before FEM analysis / preliminary beam and frame design / check SPC setup errors in NASTRAN, ABAQUS, ANSYS. Early detection of modelling errors by comparing with statically determinate approximations.