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Statics 1 & 2
Interactive, step-by-step calculators for determinate and indeterminate structural systems. Every formula is annotated with its source textbook and section number.
Simple Beam — N, V, M Diagram
Point load, distributed load, point moment. Ra, Rb. V(x) and M(x) plots via canvas.
Cantilever Beam — V, M Diagram
Fixed support. Ra, Ma reactions. Distributed + point load. M diagram.
Gerber (Hinged) Beam
Internal hinge condition M(c)=0. Splitting the system into two sub-beams. Ra, Rc, Rb solution.
Truss — Method of Joints
2D truss. ΣFx=ΣFy=0 at each joint. Tension/compression. Matrix stiffness solution.
Influence Lines
Simple beam. Müller-Breslau. IL for R, V, M. Maximum effect of a moving load.
Three-Hinge Arch / Frame
Horizontal thrust H. Three-hinge arch. Shear and moment diagrams.
Cross — Moment Distribution
DF distribution factor. CO=0.5 carry-over. 2–4 span beams. Iteration table.
Euler Buckling — Critical Load
Pcr = π²EI/(KL)². K factor. Slenderness KL/r. 5 end-condition diagrams.
Unit Load Method — Deflection
δ = ∫mM/EI dx. M and m diagrams. Simpson's rule integration. Analytical comparison.
Slope-Deflection Method
θA, θB, Δ. Fixed-end moments (FEM). Equilibrium equations.
Clapeyron (Three-Moment) Equation
Continuous beam. Force method. MA, MB, MC unknowns.
Matrix Stiffness Method
General beam element. Global K. Boundary conditions. {u}=K⁻¹{f}.
Simple Beam — Two Point Loads
L=10m, P1=20kN@3m, P2=30kN@7m. Ra=23, Rb=27 kN. V, M diagram.
Cantilever — Distributed + Point Load
L=4m, q=8kN/m, P=10kN at tip. Ra=42kN, Ma=88kNm. Diagram.
Gerber Beam — Classic Example
L=12m, hinge@6m, P=24kN@9m. Two-part solution. Ra, Rc, Rb and M.
Cross — 2 Spans, Both Ends Fixed
L=6m, q=12kN/m. DF, FEM, 5 iterations. MA=MC=36, MB=−18 kNm.