Structural Member Mechanics Workbench

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Member Mechanics: theory, method, and sources

This civil & structural engineering workspace publishes 10 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 modules cover member-level stress checks: bending, transverse shear, torsion, axial deformation, restrained thermal stress, eccentric loading, bolted and welded connections, bearing, and a safety-factor comparison.

The connection modules resolve a load into per-fastener demand and the corresponding shear and bearing stresses, which is the calculation sequence used when sizing a simple shear connection by hand.

Calculators and topics covered

mechanics of materials
bending
torsion
connections
stress
bending stress
shear stress
axial deformation
thermal stress
bolt group
weld group
bearing stress

Core equations

\text{bending stress:}\quad \sigma = \frac{Mc}{I}

\text{rectangular transverse shear:}\quad \tau _{\mathrm{max}} = \frac{3 V}{2 A}

\text{solid shaft torsion:}\quad \tau = \frac{16 T}{\pi d^{3}},\; \theta = \frac{TL}{GJ},\; J = \frac{\pi d^{4}}{32}

\text{axial deformation:}\quad \delta = \frac{PL}{AE}

\text{restrained thermal stress:}\quad \sigma = - E\alpha \Delta T\; \left(\text{compression}\; \text{when}\; \text{heated},\; \text{independent}\; of\; \text{length}\right)

\text{eccentric loading:}\quad \sigma = \frac{P}{A} \frac{\pm Pec}{I}

\text{bolt group shear:}\quad \tau = \frac{P}{\frac{n \cdot \pi d^{2}}{4}}

\text{fillet weld stress:}\quad \tau = \frac{P}{0.707 \cdot a \cdot L_{w}}

\text{bearing stress:}\quad \sigma _{b} = \frac{P}{dt}

\text{safety check:}\quad \text{utilization} = \frac{\text{demand}}{\frac{\text{nominal}\; \text{strength}}{\text{factor}}}

Method and assumptions

Assumptions

Linear elasticity and idealized load paths.
Nominal dimensions without local stress concentrations.

Limitations and design boundaries

Educational mechanics only. It does not implement building-code resistance factors, material specifications, connection detailing, fatigue provisions, fire design, seismic detailing, or professional review.

Sources and references

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

Source policy

Beer, Johnston et al., Mechanics of Materials
Hibbeler, Mechanics of Materials