I-beam on two supports with a load at midspan
The I-section is the standard answer for beams in buildings and machine frames. Almost all of its material sits far from the neutral axis, in the flanges, where it does the most useful work in bending, while the thin web mainly carries the shear.
This page models an IPE 120 profile in ASTM A36 structural carbon steel, spanning 3 m between a pin and a roller and carrying 2 kN at midspan. That is a realistic small lintel, shelf support or machine frame member.
The calculator takes the flange width, the depth, the flange thickness and the web thickness, so you can replace the profile with any rolled or welded I-section.
Calculator
This calculator is already set up for the problem above. Change the length, the load, the profile or the material and it recalculates immediately; the address bar keeps a shareable link to your exact configuration.
Input data:
Beam:
Material: Construction steel (Generic)
Profile:
| Ax: 78.54mm2 | Jxx: 981.75mm4 |
| Asy: 78.54mm2 | Iyy 490.87mm4 |
| Asz: 78.54mm2 | Izz: 490.87mm4 |
Simulation results:
Displacements (mm):
| # | x | y | zz |
|---|
Reactions (newtons):
| # | x | y | zz |
|---|
Direct link to this setup: https://beamcalc.net/en/solve/i-beam-mid-load#v1-AUsAgDtFAACAQgAA8EJmZqZAzcyMQJcBAQIAAAAAAAD6RAAAAAA
How the beam is modelled
- The left support is a pin, the right one a roller.
- A vertical point load of 2000 N acts at midspan, pointing down.
- The section is an I-profile: 120 mm deep, 64 mm wide flange, 5.2 mm flange thickness and 4.4 mm web thickness.
- The span is 3000 mm and the material is ASTM A36 structural carbon steel.
How to read the results
The beam bends about its strong axis, the one the depth contributes to. The moment of inertia grows with the cube of the depth, so the 120 mm dimension is what makes this profile useful — laying an I-section on its side removes most of its advantage.
Compare the reported deflection with the limits that apply to your structure. For a floor or a shelf a common serviceability target is span divided by 200 to 360, while machine parts usually need much less.
The web does not carry much bending, so the two flanges do the work: check the bending stress in the calculator against the yield strength of your steel grade before trusting the deflection figure.
If the flange becomes thicker than half the depth, or the web becomes as wide as the flange, the section is rejected as geometrically invalid.
Formulas
| Formula | What it gives |
|---|---|
I_z = (b * d^3 - (b - t_w) * (d - 2 * t_f)^3) / 12 | Moment of inertia about the strong axis. b is the flange width, d the depth, t_f the flange thickness and t_w the web thickness. |
delta_max = F * L^3 / (48 * E * I_z) | Deflection at midspan. |
M_max = F * L / 4 | Bending moment under the load. |
sigma = M_max * (d / 2) / I_z | Bending stress in the outer flange fibre, in MPa when M is in N·mm and I in mm⁴. |
FAQ
What is the difference between IPE and other I-sections?
IPE is a European standard beam series with parallel flanges and standardized dimensions. The calculator does not use a catalogue: you enter the dimensions, so it works equally well for HEA, HEB, W-shapes or a welded plate girder.
Why is an I-section so much better than a solid bar?
Because bending stress is highest at the outer fibres. Moving material into the flanges, away from the neutral axis, raises the moment of inertia enormously while removing the nearly unused material around the neutral axis.
Can I load the beam sideways?
You can, but the weak axis is far more flexible. An I-section loaded perpendicular to its web is meant to be avoided in real designs unless it is laterally restrained.
Does the calculator check buckling?
No. This is a linear static analysis: it reports deflections, reactions and internal forces. Lateral torsional buckling and member stability have to be checked separately with the code you follow.
More beam examples
- Simply supported beam with a load in the middle The classic pin-and-roller beam loaded at midspan: deflection, moment and reactions, solved online.
- Simply supported beam with an eccentric load A rectangular steel bar supported at both ends and loaded at the third point: where the load sits decides which support works harder.
- Simply supported beam with two point loads A steel tube on two supports carrying two equal loads: the middle section bends without shear, exactly like a four-point test.
- Simply supported beam with an inclined load A force pushing at an angle onto a supported beam: split it into bending and axial parts, and only the first one visibly bends the beam.