How this calculation works
A stepped bar can contain different lengths, areas and materials while transmitting one common axial force. Its total extension is the sum of segment extensions. This is a series-compliance calculation, different from members sharing force in parallel.
δtotal = Σ FLi/(AiEi); equivalent axial stiffness = 1/Σ[Li/(AiEi)]A worked example
A 1000 mm steel segment with 100 mm² area and 200 GPa modulus extends 0.5 mm under 10000 N. A 500 mm aluminium segment with 200 mm² area and 70 GPa modulus extends 0.357143 mm. Total extension is 0.857143 mm.
Good to know
Linear elastic uniform axial stress within each segment only. Transitions can create local concentrations that this average-stress model omits. Compression results do not check buckling, and the page does not include thermal strains or plastic deformation.
Reference: MIT — mechanics of materials (opens in a new tab) ↗
What this model answers
A stepped bar can contain different lengths, areas and materials while transmitting one common axial force.
Its total extension is the sum of segment extensions. This is a series-compliance calculation, different from members sharing force in parallel.
The Fully restrained bar thermal stress and force calculator imposes zero total length change and develops thermal stress. These series segments instead carry an entered common force and may extend.
Keep the input conventions consistent
Every row describes one segment along the load path. Enter Young modulus in GPa, area in mm² and length in mm.
Positive force represents tension and negative force compression. There are no intermediate applied forces in this model.
Read the result carefully
The smallest area does not necessarily dominate extension by itself: length and modulus also matter.
Segment compliance L/(AE) reveals each contribution. Equivalent stiffness combines those compliances before taking a reciprocal; averaging individual stiffness values would be wrong.
Segments connected in series share the stated axial-force path, but each contributes its own extension from length, modulus and area. A short soft or thin segment can contribute disproportionately to total movement. Preserve signed force conventions when adding extensions rather than summing their absolute magnitudes without a physical reason.
Work through the numbers
A 1000 mm steel segment with 100 mm² area and 200 GPa modulus extends 0.5 mm under 10000 N.
A 500 mm aluminium segment with 200 mm² area and 70 GPa modulus extends 0.357143 mm. Total extension is 0.857143 mm.
Where the calculation stops
Linear elastic uniform axial stress within each segment only.
Transitions can create local concentrations that this average-stress model omits. Compression results do not check buckling, and the page does not include thermal strains or plastic deformation.
A few questions, answered
Can the segments have different forces?
Not in this series model without intermediate loads. A different internal-force diagram would require separate force values by segment.
What should I change in the comparison?
Reverse the common load and observe signed shortening instead of extension.