How much will my FRC arm or elevator deflect?

Deflection depends on the load, the unsupported length, how the beam is supported, and the material and cross-section's stiffness (its area moment of inertia). Long cantilevered arms made from small tubes deflect the most. Enter your geometry, material, and load above to get the tip or center sag in inches, plus the bending stress and a safety factor.

Is aluminum or steel better for FRC structure?

It depends on your priority. Steel is about three times stiffer than aluminum for the same shape, so it deflects less, but it is also roughly three times denser. Aluminum (usually 6061-T6) gives far better stiffness-per-weight, which is why most FRC structure is aluminum — you add stiffness with a larger cross-section rather than by switching to steel.

What is a good safety factor for FRC parts?

A safety factor of at least 2 against yield is a common rule of thumb for FRC structural parts, and more for anything subject to impact or near a person's hands. A factor below 1 means the part is predicted to yield under the given load. This calculator reports the factor so you can add material wherever it is marginal.

STRUCTURES

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.

Beam, load & section

Material

E = 68.9 GPa (10,000 ksi) · The most common FRC structural aluminum (tube & plate).

Yield strength (MPa)verified

276 MPa (40 ksi) — MatWeb / ASM 6061-T6. Verified; editable.

Support condition

Load type

Beam length / span

Free length from the fixed end to the tip.

Point load (lb)key

Single force applied at the free tip.

Cross-section

1×1 in square tube, 0.0625 in (1/16) wall — WCP MaxTube / TheThriftyBot / 80-20 stock.

Outer width b

Horizontal outer dimension.

Outer height hkey

Vertical outer dimension — the bending direction. Bigger h = much stiffer (h³).

Wall thickness

Tube wall. FRC stock is often 1/16 in (0.0625).

Computed section: I = 0.0345 in⁴ (1.435 cm⁴), c = 0.500 in — from the exact section formula, not a stored value.

Max tip deflection

0.116

= 2.95 mm

Deflection vs span

L/172

Noticeable flex

Max bending stress

30.0

MPa

4.35 ksi

Safety factor vs yield

9.20×

Comfortable margin

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.

Load case (schematic — deflection exaggerated)

Create a free accountto save named member presets, compare sections & export this report.

For reference only — verify your own geometry. Real FRC parts deflect MORE than this ideal beam predicts because bolted joints, gussets, and mounts flex. Not a substitute for physical load testing.

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.

Formulas

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.

Number sources

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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Structural Deflection Calculator

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.