Lab · Structural Mechanics
Beam Analysis Lab
One determinate beam, solved once. Reactions, shear, bending moment, extreme-fibre stress and the deflected shape all come from the same exact piecewise solution, so every diagram agrees with the others at every station.
Beam
Scroll the schematic sideways to see the whole beam; every result is also listed in the tables below.
Beam and loads
The beam runs from x = 0 to x = L.
Supports
Point loads
Point moments
Uniform distributed loads
Downward loads are negative (q < 0, Fy < 0); an applied couple is positive counter-clockwise. Internally, M > 0 is sagging, v > 0 is upward and θ > 0 is counter-clockwise.
Section and material (optional)
Leave a field empty to leave it unspecified: reactions, shear and bending moment are reported without any section data. A value that is zero or negative is not unspecified — it is reported as an invalid entry. Bending stress additionally needs I and an extreme-fibre distance c; slope and deflection need both E and I.
What this Lab models
A planar beam with rigid supports, solved by planar equilibrium and Euler–Bernoulli bending.
Model scope
- · Statically determinate support arrangement: cantilever, simply supported or overhanging.
- · Small displacements on the undeformed geometry, linear-elastic material, constant EI along the span.
- · Shear deformation is neglected, so deflections are those of a slender beam.
- · Loads act in the plane; downward is negative and an applied couple is positive counter-clockwise.
- · Indeterminate beams, continuous beams over three or more supports, frames and support settlement are outside this Lab.
- · Bending stress is elementary flexure; stress concentrations and local effects at supports and point loads are not modelled.