Structural Deflection Calculator
How far will your aluminum (or steel / polycarb) arm tube, rail, or plate bend under load — and will it yield? Pick a support, load case, material and FRC-stock section; deflection, bending stress and safety factor recompute live.
Material moduli are physical constants from primary datasheets (do not change by season). A first-order, ideal-beam estimate — verify your own geometry & wall thickness against your vendor stock.
E = 68.9 GPa (10,000 ksi) · The most common FRC structural aluminum (tube & plate).
276 MPa (40 ksi) — MatWeb / ASM 6061-T6. Verified; editable.
Free length from the fixed end to the tip.
Single force applied at the free tip.
1×1 in square tube, 0.0625 in (1/16) wall — WCP MaxTube / TheThriftyBot / 80-20 stock.
Horizontal outer dimension.
Vertical outer dimension — the bending direction. Bigger h = much stiffer (h³).
Tube wall. FRC stock is often 1/16 in (0.0625).
SF = yield ÷ max bending stress. 2× is a common FRC design target for static loads — your team may require more. Impact, vibration, fatigue and hole stress-concentration are not included, so a drilled/notched member yields below this.
Notes & sources
- First-order estimate using idealized Euler-Bernoulli beam theory. It assumes a straight, uniform, single-piece beam with an ideal fixed or pinned support.
- Real FRC structures usually deflect more than this predicts, because bolted/riveted joints, gussets, bearing mounts, and gearbox plates flex — joint/mount compliance often dominates real-world sag and is not modeled here.
- Ignores transverse shear deflection (minor for long slender beams, larger for short stubby ones) and stress concentrations at lightening holes, bends, and welds — drilled tube yields below the plain-section safety factor shown.
- Polycarbonate modulus varies by grade/temperature and the material creeps (keeps deflecting) under sustained load, so treat polycarbonate results as approximate and design conservatively.
- The yield-based safety factor is for static loads only; impact, vibration, and fatigue from a competition robot are not captured. Not a substitute for physical load testing.
- Verify member dimensions and wall thickness against your actual vendor stock; nominal tube sizes vary slightly by supplier.
- Cantilever, point at tip: δ = P·L³/(3EI); M = P·L
- Cantilever, distributed (total W): δ = W·L³/(8EI); M = W·L/2
- Simply supported, center point: δ = P·L³/(48EI); M = P·L/4
- Simply supported, distributed (total W): δ = 5·W·L³/(384EI); M = W·L/8
- Rectangular tube: I = (b·h³ − bᵢ·hᵢ³)/12 · Round tube: I = π(D⁴ − d⁴)/64 · Solid: I = b·h³/12
- Bending stress σ = M·c/I (c = h/2) · Safety factor = σ_yield / σ_max
- Source: Euler-Bernoulli beam theory — Hibbeler, Mechanics of Materials; Roark's Formulas for Stress and Strain, Table 8.1.
- 6061-T6: E = 68.9 GPa (10,000 ksi), yield 276 MPa (40 ksi) — MatWeb / ASM 6061-T6 datasheet. asm.matweb.com
- 7075-T6: E = 71.7 GPa (10,400 ksi) — MatWeb / ASM 7075-T6 datasheet (yield not in our verified set; enter your own).
- Steel (mild 1018 / 4130): E = 200 GPa (≈29,000 ksi) — ASM material data (1018 ~200, 4130 ~205 GPa).
- Polycarbonate: E = 2.3 GPa (≈0.33 Msi), grade-dependent 2.0–2.4 — MatWeb Polycarbonate overview + Lexan datasheets.
- Section stock: 1×1 & 2×1 in, 1/16 in (0.0625) wall; 1/8 & 3/16 in polycarb plate — WestCoast Products / TheThriftyBot / 80-20 stock. I is computed live from these dimensions, never stored. westcoastproducts.com
- Unit constants: 1 in = 25.4 mm (0.0254 m), 1 lbf = 4.4482216 N, 1 ksi = 6.894757293 MPa — defined/exact.
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