Lab · Structural Mechanics

Axial Members Lab

A member built from prismatic segments, loaded along its own axis. The engine cuts it at every material boundary and every load, so the internal force, stress and strain are exact on each interval rather than averaged over the member.

Member

Scroll the schematic sideways to see the whole member; every solved quantity is also listed in the interval table below.

Dashed verticals mark computational stations — material boundaries and load positions alike. Arrow direction shows the sign of Fx along +x. Hover a segment for its full properties; a load whose text cannot fit shows its tag, with the full magnitude and position in its hover title and in the interval table.

Total deformation ΔL

0.25 mm

the member lengthens

Largest tensile stress

50 MPa

interval 1

Largest compressive stress

none

no interval is in compression

Internal axial force N(x)

Normal stress σ(x)

Normal strain ε(x)

Interval results

#	x range [m]	A [m²]	N	σ	ε	δ	Sense
1	0 – 1	5.000e-4	25000 N	50 MPa	250 µε	0.25 mm	tension

Summary

Member length L	1 m
Computational intervals	1
Total deformation ΔL	0.25 mm
Reaction implied at the restrained end	-25000 N
Largest tensile force	25000 N
Largest compressive force	none

The Lab does not solve for supports. It reports the reaction the restrained end must supply to hold this load set in equilibrium — equal and opposite to the sum of the applied axial loads.

Assumptions

· Linear-elastic material and small strains.
· Uniform stress over each cross-section (Saint-Venant away from load introduction).
· The left end (x = xStart) is the restrained reference; its reaction is implied, not solved.

What this Lab models

A straight member carrying load along its own axis only. It is built from prismatic segments, each with its own area and modulus, and concentrated axial loads may sit anywhere along it. The engine cuts the member at every material boundary and every load, so N, σ and ε are constant and exact within each resulting interval rather than averaged over a segment.

Model scope

· Internal force from the right free body: N(x) is the sum of every axial load beyond the cut. N > 0 is tension.
· One restrained reference end at x = 0; the Lab reports the reaction that end must supply and never invents a second support.
· Linear-elastic, prismatic segments. No self-weight, no thermal strain, no buckling check — a compressive result says nothing about stability.
· Stresses are section averages, valid away from load introduction points and geometric discontinuities.