Beam Analysis Simulator

Modified: Jun. 9, 2026

Published: Jun. 5, 2026

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Every textbook beam problem gives you one answer for one fixed loading. Change the span, shift a load, or swap the cross-section and you restart the algebra by hand, redraw the shear-force and bending-moment diagrams from scratch, and still cannot see where the critical section actually falls until the very end. This simulator makes the analysis move: drag any parameter and the shear-force diagram, bending-moment diagram, deflected shape, and bending stress all update live, with the critical section marked automatically. #BeamAnalysis #SolidMechanics #StructuralDesign

What You Can Analyze

Key Features

1. Animated probe sweep Press the Probe button to sweep a section marker along the span and read the local shear and moment at every point. The deflected shape is exaggerated for clarity throughout.

2. Live result readouts Every result updates as you drag any slider: reaction forces RA and RB, maximum shear Vmax, maximum moment Mmax and its position, maximum deflection and its position, second moment of area I, section modulus S, maximum bending stress, and the safety factor.

3. Four analysis charts in two tab groups The Diagrams group holds the shear-force chart (V vs. x) and the bending-moment chart (M vs. x). The Response group holds the deflection chart (y vs. x) and the bending-stress chart (sigma vs. x) with the yield line overlaid. Per-chart PNG export is available on every panel.

4. Four beam presets Switch between realistic starting configurations with a single click: two point loads on a simply-supported beam, uniformly distributed load on a simply-supported beam, cantilever with a tip point load, and cantilever with a full-span distributed load.

5. A/B beam comparison Save the current beam as Beam A, then change the span, cross-section, or loads to configure Beam B. Both datasets overlay on every chart as dashed and solid curves so you can see exactly how each change moves the diagrams.

6. Downloadable resources A lab report with watermark-free beam diagram and all four charts (as Markdown, PNG images, and a DOCX converter), a full span-by-span CSV dataset, and a design-data sheet with reactions, peak moment, safety factor, and a probe-sweep animation video.

Preset Beam Configurations

Equations

Second moment of area and section modulus for a rectangular cross-section (b wide, h deep):

I = b * h^3 / 12           (mm^4)
c = h / 2                  (mm, distance to outermost fibre)
S = I / c                  (mm^3, section modulus)

Support reactions, equilibrium about the left support (x = 0):

Simply supported:
  sum of loads:  W = P1 + P2 + w * (wb2 - wb1)
  moment arm:    M_about_0 = P1*a1 + P2*a2 + w*(wb2-wb1)*((wb1+wb2)/2)
  RB = M_about_0 / L
  RA = W - RB

Cantilever (fixed at x = 0):
  RA = W
  M0 = -M_about_0        (reaction moment at the wall)

Shear force at position x (up-positive, evaluated just to the right of x):

V(x) = RA
       - P1           if x > a1
       - P2           if x > a2
       - w * max(0, min(x, wb2) - wb1)   if x > wb1

Bending moment at position x (sagging-positive):

M(x) = M0 + RA*x
       - P1*(x - a1)            if x > a1
       - P2*(x - a2)            if x > a2
       - w*len*(x - (wb1+xx)/2) if x > wb1
         where xx = min(x, wb2), len = max(0, xx - wb1)

Maximum bending stress at the critical section (peak moment location):

sigma_max = |M_max| * c / I        (MPa)
safety_factor = sigma_allowable / sigma_max

Deflection by numerical double integration of the elastic curve equation:

EI * d^2y/dx^2 = M(x)
EI = E * I       (E in MPa = N/mm^2, I in mm^4, EI in N*mm^2)

Boundary conditions:
  Simply supported:  y(0) = 0, y(L) = 0
  Cantilever:        y(0) = 0, dy/dx(0) = 0

Guided Experiments

Work through the structured experiments in the Beam Analysis Experiments lesson for Python-verified exercises that pair directly with this simulator:

1. Reactions and equilibrium check for a two-load beam
2. Shear-force and bending-moment diagrams from first principles
3. Critical section location and maximum bending stress
4. Deflection and the span-to-deflection stiffness ratio
5. Cantilever versus simply-supported: A/B comparison
6. Section sizing: meet a deflection or stress limit by adjusting b and h

Related Resources

• Beam Analysis Experiments: the hands-on lab lesson that pairs with this simulator.
• Shear Force and Bending Moment in Beams: the lesson that owns the underlying shear and moment theory.
• Bending Stresses in Simple Beams: derivation of the flexure formula and the critical-section concept.
• Beam Deflections and Stiffness Analysis: the elastic curve, double integration, and stiffness ratios explained.
• Solid Mechanics Analyzer: the full suite of stress-analysis simulators.
• Mohr’s Circle Simulator: take the bending stress at the critical section and analyse the full stress state with Mohr’s circle.
• Shaft Torsion Simulator: the companion simulator for members under torsion rather than bending.