How this calculation works
Support conditions matter as much as span and stiffness. This page compares two precisely defined cases: a simply supported beam carrying one central load, and a cantilever carrying one load at its free end. The deflection table follows the whole length.
Centre point load: δmax = FL³/(48EI); cantilever end load: δmax = FL³/(3EI)A worked example
For a 1000 N load, 2000 mm span, 200 GPa modulus and I of one million mm⁴, the central deflection is 0.833333 mm. The maximum moment is 500 N m, and each simple support carries 500 N.
Good to know
The model assumes a slender prismatic beam, linear elasticity and small deflection. It omits self weight, shear deformation, settlements and lateral instability. It does not establish a building-code deflection limit or a structural capacity.
Reference: MIT — mechanics of materials (opens in a new tab) ↗
What this model answers
Support conditions matter as much as span and stiffness.
This page compares two precisely defined cases: a simply supported beam carrying one central load, and a cantilever carrying one load at its free end. The deflection table follows the whole length.
The Euler column buckling and effective length calculator considers instability under axial compression. Its effective length is a different boundary-condition assumption from a transverse beam support.
Keep the input conventions consistent
Enter bending second moment of area about the loaded axis, not polar moment or cross-sectional area.
Length and inertia use millimetres and mm⁴. The cantilever length is measured from its fixed face; the other case uses the distance between supports.
Read the result carefully
The same load, span and EI produce sixteen times as much maximum deflection in the cantilever case.
This comparison is about these two load arrangements; moving the load elsewhere requires another equation. The reported reactions and moment help check the free-body diagram.
Before comparing two beam cases, identify whether the load coordinate is measured from the same support. A load moved across the span changes the reactions and the deflected shape. It cannot be treated as the original centered-load example with a different maximum bending value substituted.
Work through the numbers
For a 1000 N load, 2000 mm span, 200 GPa modulus and I of one million mm⁴, the central deflection is 0.833333 mm.
The maximum moment is 500 N m, and each simple support carries 500 N.
Where the calculation stops
The model assumes a slender prismatic beam, linear elasticity and small deflection.
It omits self weight, shear deformation, settlements and lateral instability. It does not establish a building-code deflection limit or a structural capacity.
A few questions, answered
Can I enter the area instead of I?
No. Bending resistance depends on the distribution of area about the loaded axis, represented by I.
What should I change in the comparison?
Use the same section as a free-end-loaded cantilever and compare its deflection curve.