Simply supported beam with an inclined load
Real forces are rarely perfectly vertical. A stay rod, a guy wire, a bracing diagonal or a belt tension pulls at an angle, and the resulting deformation is a combination of bending and axial compression or tension.
The simplest way to handle it is to split the force into components: the component across the beam causes bending, the component along the beam causes axial load. For slender beams the axial part produces displacements that are orders of magnitude smaller, so bending usually dominates the result.
This page models a 30 mm steel rod over a 1500 mm span, loaded at midspan with 300 N applied at 30 degrees from the vertical.
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/simply-supported-inclined-load#v1-AQsAgLtEAADwQZQBAQIAAAAAAACWQwAA8EE
How the beam is modelled
- The left support is a pin, the right one a roller.
- A point load of 300 N acts at midspan, tilted 30 degrees away from the vertical.
- The angle is measured from the vertical direction: 0 degrees is a load pointing straight down, 90 degrees is a horizontal pull along the beam.
- The beam is a solid steel rod, 30 mm in diameter and 1500 mm long.
How to read the results
Only the perpendicular component bends the beam. Here that is 300 N times the cosine of 30 degrees, so the bending part is smaller than the full 300 N and the deflection is correspondingly smaller than for a vertical load of the same magnitude.
The parallel component pulls the beam axially. Because one support is a roller, that axial force is not resisted along the span — it produces a small elongation instead of a large stress build-up, which is precisely the reason one of the two supports is modelled as a roller.
The reactions combine both effects: the supports react against the vertical component directly, and the pin takes the horizontal component.
Formulas
| Formula | What it gives |
|---|---|
F_perp = F * cos(alpha) | Component perpendicular to the beam axis; it causes bending and deflection. |
F_axial = F * sin(alpha) | Component along the beam axis; it causes tension or compression rather than bending. |
delta_max = F_perp * L^3 / (48 * E * I) | Midspan deflection, using only the perpendicular component. |
M_max = F_perp * L / 4 | Bending moment under the load. |
FAQ
Does the axial part of the load contribute to the deflection?
Only through second-order effects, which this small-deflection analysis does not model. For a slender beam the contribution is negligible compared with bending.
How do I enter a horizontal force?
Set the load angle to 90 degrees. The load then acts entirely along the beam axis, and with a roller at one end the model reports almost no bending at all.
Why is the angle measured from the vertical?
Because that keeps the common case simple: a straight downward load stays at 0 degrees, and the angle grows as the force tips over towards the beam axis.
What changes if both supports were fixed instead?
The beam would resist the axial component as well, building up real axial force, and the bending deflection would drop because both ends would also restrict the rotation.
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.
- Steel pipe loaded in the middle A steel pipe on two supports with a load at midspan: how much it bends, and which pipe dimensions actually matter.