Most beam sizing starts with the same few questions. How far does it span, what does it carry, and how much can it bend before it becomes a problem? A hand calculation won’t replace a proper design, but it will tell you whether your idea is sensible before you spend money on it. This post walks through the steps and finishes with a worked example.
Start with the span and the load
Span is the distance between the supports, not the overall length of the steel. Be clear about how the ends are held. A beam resting on supports (simply supported) behaves very differently from one fixed at both ends or sticking out as a cantilever. The formulas below assume simply supported, which is the conservative starting point for bending.
Then work out the load. Split it into:
- Dead load: the weight of the things that stay there, including the beam itself.
- Live load: people, stored goods, equipment, and anything that moves or changes.
- Point loads vs distributed loads: a machine on two feet is a point load, while decking or a conveyor is closer to a uniformly distributed load (UDL).
Most sizing errors come from leaving out a load, not from the maths. Impact, vibration and dynamic loads from moving equipment need extra thought, and a simple static check won’t capture them.
Reactions and bending moment
The reactions are the forces the supports push back with. For a simply supported beam with a UDL of w over span L:
- Each reaction is wL / 2.
- The maximum bending moment, at mid-span, is wL² / 8.
For a single point load at mid-span the maximum moment is instead PL / 4. The bending moment is the number that drives most beam selections, and the reactions matter for the supports and connections. If your loading is more complicated, the free beam calculator handles a range of common support and load cases and gives you reactions, moment and deflection together.
Section modulus, factor of safety and deflection
Section modulus
The section modulus (Z) is a property of the cross-section that links bending moment to stress. Stress = M / Z, so the required Z is the moment divided by the stress you are prepared to allow. A deeper section has a much larger Z for the same amount of steel, which is why beams are I-shaped.
Factor of safety
The allowable stress is the material’s yield stress divided by a factor of safety. The factor covers uncertainty in loads, material and construction. A higher factor suits uncertain loads, people, or serious consequences of failure. Formal design to Australian standards uses limit state methods with specific load factors and capacity reductions rather than a single factor of safety, so treat the approach here as a preliminary check only.
Deflection
A beam can be strong enough and still be too floppy. Deflection depends on the second moment of area (I), not Z. For a simply supported beam with a UDL, the maximum deflection is 5wL⁴ / (384EI), where E is the modulus of elasticity, about 200,000 MPa for steel. A common limit is span/250 for general work, but span/360 or tighter may be needed where brittle finishes, machinery alignment or ponding are concerns. [CHECK: confirm span/250 is a fair general rule-of-thumb to quote, and that the span/360 example is appropriate]
Worked example
Say we have a beam spanning 4.0 m, simply supported, carrying 10 kN/m in total, with an allowance for its own weight already included. Assume steel with a yield stress of 300 MPa and a factor of safety of 2. [CHECK: confirm 300 MPa is a reasonable assumed yield for a typical Australian-grade universal beam, and that FoS of 2 is a sensible illustration]
- Reactions: 10 × 4 / 2 = 20 kN at each support.
- Maximum moment: 10 × 4² / 8 = 20 kN·m (20 × 10⁶ N·mm).
- Allowable stress: 300 / 2 = 150 MPa.
- Required section modulus: 20 × 10⁶ / 150 = about 133,000 mm³, or 133 cm³.
- Deflection limit: span/250 = 4000 / 250 = 16 mm.
- Required second moment of area: with w = 10 N/mm, I = 5wL⁴ / (384 × E × 16 mm) = about 10.4 × 10⁶ mm⁴, or 1,040 cm⁴.
You now need a section with Z of at least 133 cm³ and I of at least 1,040 cm⁴ about the strong axis. Look at a supplier’s or manufacturer’s section table, or use the section properties calculator to check candidate shapes. A universal beam somewhere around 180 mm deep is a likely starting point. [CHECK: confirm a ~180 mm deep UB is a reasonable candidate for Z ≥ 133 cm³ and I ≥ 1,040 cm⁴] Confirm the figures from the actual table, then recalculate the deflection with the real I of the section you chose.
What a hand check doesn’t cover
The example only deals with bending and deflection. A real beam also needs checking for:
- Shear near the supports, especially on short, heavily loaded spans.
- Lateral buckling, where an unrestrained compression flange twists and moves sideways. How the beam is braced matters a great deal.
- Web bearing and local effects where loads or supports concentrate force.
- Connections, including bolts, welds and what the beam sits on.
- Fatigue, corrosion and fire, depending on the environment.
Where a beam supports people, a building, a lifting arrangement or anything with serious consequences if it fails, a qualified structural engineer should design it and a certifier may need to sign it off. A hand calculation is not a substitute for that.
Where to start
Write down the span, the supports and every load you can think of, then run the numbers above or use the beam calculator to check them. Pick a candidate section, confirm its properties from a reliable table, and leave yourself a margin. If the result is borderline, don’t squeeze it. Go up a size or get a second opinion.
If you are sizing a frame for a machine, a platform, a conveyor support or a materials handling structure, Drafting Central can help with the mechanical engineering and the fabrication drawings, and with safety in design where people will be working around the equipment. For anything needing structural certification, we’ll tell you plainly when a certifier needs to be involved. If you have a project in mind, you can request a quote and send us what you have, even if it’s only a sketch.
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