Structural Analysis Calculators: Beams, Deflection & Trusses

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Engineering reference

Structural Analysis: theory, method, and sources

This civil & structural engineering workspace publishes 8 governing equations, 2 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Ten unit-aware modules connect equilibrium, internal force, stiffness, and stress.

Every plot labels physical axes and units.

Calculators and topics covered

structures
beams
trusses
stress
deflection
buckling
support reactions
shear force
bending moment
Euler buckling
section modulus
combined stress

Core equations

\text{point load reactions:}\quad R_{A} = \frac{P \left(L - a\right)}{L},\; R_{B} = \frac{\mathrm{Pa}}{L}

\text{uniform load reactions:}\quad R_{A} = R_{B} = \frac{wL}{2}

\text{cantilever tip deflection:}\quad \delta = \frac{PL^{3}}{3 EI}

\text{simply supported centre deflection:}\quad \delta = \frac{PL^{3}}{48 EI}

\text{axial stress and strain:}\quad \sigma = \frac{P}{A},\; \varepsilon = \frac{\delta }{L},\; E = \frac{\sigma }{\varepsilon }

\text{rectangular section:}\quad I = \frac{bh^{3}}{12},\; S = \frac{I}{c},\; c = \frac{h}{2}

\text{Euler buckling:}\quad P_{cr} = \frac{\pi ^{2} EI}{\left(kL\right)^{2}}

\text{combined axial and bending stress:}\quad \sigma = \frac{P}{A} \frac{\pm Mc}{I}

Method and assumptions

Assumptions

Linear elastic material behavior unless otherwise stated.
Ideal supports and small deformations.

Limitations and design boundaries

Educational preliminary analysis only; not a substitute for governing building codes, load standards, detailed finite-element analysis, or review by a licensed structural engineer.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Hibbeler, Structural AnalysisClassical determinate structures, influence of support conditions, and elastic deflection.
Beer, Johnston et al., Mechanics of MaterialsStress, strain, beam flexure, and column stability relationships.

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