Beam Deflection and Bending Stress Calculator for Steel and Aluminum
Check how much a beam, shaft, rail or frame member will bend and how hard the material is working. Pick a load case, enter the span, material and section, and read deflection, moment and bending stress.
Your numbers
For the uniform case enter the total load, which is w x L.
Total applied load in newtons. 1 kgf is about 9.81 N.
Support-to-support span, or cantilever length.
Young's modulus. Stiffness depends on E, not on strength.
Section property about the bending axis. An IPE 200 steel beam is about 1,943 cm4.
Half the section depth for a symmetric section.
Your results
Elastic, small-deflection formulas for prismatic beams. Does not include shear deflection, self-weight unless added to the load, lateral-torsional buckling or connection flexibility.
Maximum deflection (mm) vs span (mm)
Sweeps Span or length L from 500 to 4000, holding your other inputs fixed.
Controlled engineering changes
Want material substitutions routed through ECN approval in your ERP? Ask for an optional expert review.
Optional. The tool and every export work without this. No spam.
How to use it
Choose the load case that matches the arrangement, enter the total load, span and the second moment of area from your section table, then select the material. For symmetrical sections, c is half the depth. The span chart shows how fast deflection grows with length, since it rises with the cube of the span for point loads and with the cube for the uniform total load as entered. That makes length the first thing to shorten when a member is too flexible.
- Use I about the bending axis, not the weak axis
- Add self-weight to the load for long spans
- Compare L/x against your design standard limit
- Compare stress to allowable stress with a safety factor
The formulas
For a simply supported beam with a uniform total load W, midspan deflection is 5 x W x L^3 divided by 384 x E x I. A cantilever with an end load deflects by W x L^3 divided by 3 x E x I, and a simply supported beam with a center load by W x L^3 divided by 48 x E x I. Peak moment is WL/8, WL and WL/4 respectively, and bending stress is M x c / I. Deflection depends on E and I only, so swapping to a stronger steel does not stiffen the beam.
Worked example
A 2 m steel beam with I of 1,943 cm4 carries 20 kN spread uniformly. Deflection is about 0.54 mm, which is L/3,700, very stiff. The peak moment is 5 kNm and the bending stress about 26 MPa. Replace the steel with aluminum 6061 at E of 69 GPa and the same section, and deflection rises to roughly 1.6 mm because stiffness scales with E. Aluminum needs about three times the I to match steel stiffness, though it weighs about one third as much.
Common mistakes and ERP notes
Frequent errors are mixing cm4 and mm4, forgetting that the uniform load is entered as a total, and checking stress while ignoring deflection on machine bases and gantries. For buyers, a substitution from steel to aluminum or from one profile to another changes stiffness, so route it through engineering change control. In ERP the approved material and profile sit on the item master and BOM, and substitutions should be controlled by an ECN rather than a purchasing note.
- Check units on I before trusting the result
- Include dynamic or impact factors for moving loads
- Treat this as a screening check, not a code design
Frequently Asked Questions
Why does a stronger steel not reduce deflection?
Elastic deflection depends on Young's modulus E and the section's second moment of area I. Almost all steels share about 200 GPa, so higher strength does not stiffen the member. Increase I by using a deeper section or reduce the span.
What deflection limit should I use?
It depends on the application and the governing code. General floor members often use L/360, while machine tool structures and precision gantries can need L/2000 or better. Use the limit your design standard specifies.
How do I get I for my section?
Take it from the manufacturer's section tables, a CAD mass-properties report or a formula such as b x h^3 / 12 for a rectangle. Make sure it is about the correct bending axis and entered in cm4.
Does it include the beam weight?
No. Add the beam's own weight to the total load for long spans. Steel weighs about 7.85 g/cm3, so a heavy section can contribute meaningfully to both deflection and stress.
If material substitutions bypass engineering review today, we can help build a controlled change flow connected to your BOMs.
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