Axial Loading Simulator

Modified: Jun. 9, 2026

Published: Jun. 5, 2026

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In a compound bar the load does not split equally by area: the stiffer material quietly takes the larger share, and the softer one carries far less than its cross-section might suggest. Textbook exercises hide this because the numbers work out neatly on paper. In practice, one member can be operating close to its yield stress while the other is barely loaded, and the difference is invisible until you run the numbers member by member. This simulator puts both members on screen, ramps the total load, and shows the force, stress, and elongation in each one as they evolve together. #AxialLoading #CompoundBars #SolidMechanics

What You Can Analyze

Key Features

1. Animated bar with exaggerated elongation The canvas shows both members stretching under load. The elongation is exaggerated for visibility and the stress colour heats up from cool to warm as the load rises.

2. Play ramps the load from zero Press Load and the total force rises from zero to the set value, letting you watch how each member’s stress climbs at its own rate toward its yield line.

3. Live force and stress readouts Force in each member, stress in each member, the load share ratio, the common deflection, total stiffness, and the governing safety factor all update continuously as you move any slider.

4. Four analysis charts in two groups The load-sharing group shows member force and member stress against total load. The material group shows each member on its stress-strain line with the current operating point, and common deflection against total load.

5. Four material presets and single-member mode Switch between steel-aluminium, single steel bar, steel-titanium, and aluminium-brass, or build a custom assembly from steel, aluminium, titanium, brass, or copper with diameter and length sliders.

6. A/B assembly comparison Save the current curves as Assembly A, change the materials or diameters, and every chart overlays Assembly B on top of A so the two configurations can be compared directly.

7. Downloadable resources A lab report with watermark-free diagram and all four charts, the full force-stress-deflection dataset as CSV, and design data with a load-ramp animation video.

Preset Configurations

Equations

Cross-sectional area of each circular member:

A1 = pi * d1^2 / 4
A2 = pi * d2^2 / 4

Axial stiffness of each member (E in GPa converted to MPa, L in mm):

k1 = A1 * E1 / L
k2 = A2 * E2 / L
ktot = k1 + k2

Common deflection (equal deformation condition for a parallel assembly):

delta = P / ktot

Force in each member from equal deformation:

F1 = k1 * delta = P * (E1 * A1) / (E1*A1 + E2*A2)
F2 = k2 * delta = P * (E2 * A2) / (E1*A1 + E2*A2)

Normal stress in each member:

sigma1 = F1 / A1
sigma2 = F2 / A2

Axial strain (same in both members for a parallel assembly):

epsilon = delta / L

Safety factor for each member against yielding:

SF1 = sigma_yield_1 / sigma1
SF2 = sigma_yield_2 / sigma2
governing SF = min(SF1, SF2)

Guided Experiments

Work through the Axial Loading Experiments lesson for structured exercises with Python-verified results:

1. Normal stress and elongation in a single bar
2. Load sharing in a steel-aluminium compound bar
3. Effect of diameter ratio on stress in parallel members
4. Operating points on the stress-strain curve
5. Safety factor and the governing member
6. Stiffness mismatch: steel-titanium versus aluminium-brass

Related Resources

• Axial Loading Experiments: the hands-on lesson that pairs with this simulator.
• Fundamental Stress Concepts: the lesson that defines normal stress and direct loading.
• Strain and Mechanical Properties: the lesson covering Young’s modulus, stress-strain curves, and yield.
• Compound Bars and Composite Systems: the lesson that derives the equal-deformation load-sharing rule used here.
• Solid Mechanics Analyzer: the full suite of stress-analysis simulators.
• Shaft Torsion Simulator and Pressure Vessel Simulator: the adjacent simulators in the suite.