Calculator Input
Example Data Table
| Span | Tube Size | Wall | Uniform Load | Support | Modulus | Limit |
|---|---|---|---|---|---|---|
| 120 in | 2 in × 4 in | 0.25 in | 50 lb/ft | Simply supported | 29000 ksi | L/360 |
| 3 m | 50 mm × 100 mm | 5 mm | 2 kN/m | Fixed at both ends | 200 GPa | L/300 |
| 72 in | 3 in × 3 in | 0.1875 in | 35 lb/ft | Cantilever | 29000 ksi | L/180 |
Formula Used
Rectangular tube inertia: I = (B × H³ − b × h³) / 12
Area: A = B × H − b × h
Section modulus: S = I / c
Bending stress: σ = M × c / I
Simply supported uniform load: δ = 5wL⁴ / 384EI, M = wL² / 8
Fixed end uniform load: δ = wL⁴ / 384EI, M = wL² / 12
Cantilever uniform load: δ = wL⁴ / 8EI, M = wL² / 2
B is outer width. H is outer depth. b and h are inner tube dimensions. w is uniform load. L is span. E is elastic modulus.
How To Use This Calculator
Enter the clear span between supports. Enter the outside width, outside depth, and wall thickness. Use the depth value in the bending direction. Select the correct unit system. Add the uniform load and support condition. Choose a deflection limit, such as L/360. Press calculate. Review deflection, stress, inertia, section modulus, and support reaction. Use the export buttons to save the result.
Understanding Rectangular Tube Deflection
Steel rectangular tubing is common in frames, gates, rails, platforms, trailers, and light structural supports. It is strong for its weight, but every member still bends under load. A uniform load spreads weight along the full span. Examples include decking weight, evenly stored material, cladding, or a long distributed service load.
This calculator estimates midspan deflection, bending moment, bending stress, reactions, and section properties. It uses the outside width, outside depth, wall thickness, span, modulus of elasticity, and uniform load. The tool also lets you compare deflection with a selected limit. That makes early sizing easier before a detailed engineering review.
Why Section Shape Matters
A rectangular tube resists bending mainly through its moment of inertia. Depth is very important. A deeper tube usually deflects less than a shallow tube with similar steel area. Wall thickness also matters, because it changes the hollow core and the available steel near the outer fibers.
The calculator assumes a straight, prismatic tube. The load is applied in the strong axis direction. It also assumes elastic behavior and small deflection. These assumptions match many preliminary checks. They do not replace project drawings, connection checks, buckling checks, weld checks, or code design.
Reading The Results
Deflection is the predicted movement at the critical point. Bending stress is the calculated stress at the outer fiber. A ratio near one means the chosen limit is being approached. A lower ratio is better for serviceability. For visual finishes, doors, glazing, or equipment alignment, service deflection may control before strength does.
Practical Input Tips
Measure the tube after confirming the actual orientation. Enter the vertical dimension as depth when the load bends the tube downward. Use the clear span between supports, not the overall stock length. Include self weight if it matters. Convert line loads carefully, and keep all project records with the exported report for review.
Use Results Safely
Always confirm the real support condition. A simply supported tube bends differently from a fixed tube or cantilever. Check concentrated loads, vibration, impact, corrosion, holes, local crushing, and lateral stability. Steel grades also vary. Use conservative inputs when the field condition is uncertain. For permitted structures, final sizing should be reviewed by a qualified professional.
FAQs
What is uniform load?
A uniform load is spread evenly along the tube span. It is usually entered as force per length, such as lb/ft, kN/m, or N/m.
Which tube dimension is depth?
Depth is the vertical dimension resisting bending. If the tube is rotated, use the dimension aligned with the load direction as the depth.
Does wall thickness affect deflection?
Yes. Wall thickness changes inner dimensions, steel area, moment of inertia, and section modulus. Thicker walls usually reduce deflection and stress.
What does L/360 mean?
L/360 means the allowed deflection equals span divided by 360. A 360 inch span would allow 1 inch of deflection.
Can this calculator replace engineering design?
No. It is useful for preliminary checks. Final design should include code rules, connections, buckling, local bearing, and professional review.
Why include self weight?
Self weight adds load to the tube. It may be small for short members, but it can matter for long spans or heavy sections.
What support condition should I choose?
Choose the condition closest to reality. Use simply supported for pinned ends, fixed for restrained ends, and cantilever for one free end.
Why is steel modulus important?
Elastic modulus controls stiffness. Common structural steel is near 200 GPa or 29,000 ksi, but project specifications should confirm the value.