tools / frc-deflection-calculator
Deflection, bending stress and safety factor for an arm tube, an elevator rail or a plate. Pick a support, a load case, a material and a stock section, and every number recomputes as you type.
Moduli are physical constants from primary datasheets, so they do not change by season. This is an ideal single-piece beam: real parts with bolted joints deflect more.
height in the bending direction is cubed
off the shelf
1x1 in square tube with a 0.0625 in (1/16) wall. WCP MaxTube, TheThriftyBot, 80-20 stock.
verdict / cantilever, point load
0.116 in of sag and 9.20 times margin against yield, on an ideal beam with no joints in it.
0.116inches of sag, 2.95 mm
L/172span over deflection, noticeable flex
9.20xmargin against yield
the member / what it is and what pushes
lengths in
force in
E = 68.9 GPa (10,000 ksi). The most common FRC structural aluminum, in tube and plate.
276 MPa (40 ksi), MatWeb and ASM. This one is verified, and still editable.
An arm bolted to a gearbox plate at one end and free at the other.
A single force at the free tip.
Free length from the fixed end to the tip.
Self weight is not added for you. Include it here if it matters.
the section / drawn and measured
dimensions / 1x1 tube
The horizontal outer dimension.
The bending direction. This one is cubed, so it is the number that matters.
FRC stock is usually 1/16 in, which is 0.0625.
Computed live from the dimensions above, never read out of a stored table.
load case / deflection drawn far larger than it is
Fixed at the left, free at the right. The tip carries the whole moment back to the mount, which is why an arm fails where it bolts on.
the working / nothing hidden
| what | formula | with your numbers |
|---|---|---|
| Area moment of inertia | I = (b h^3 - bi hi^3) / 12 | I = 0.0345 in⁴ = 1.435e-8 m⁴ |
| Outer fibre distance | c = h / 2 | c = 0.500 in = 12.70 mm |
| Span and load, in SI | L in metres, P or W in newtons | L = 0.5080 m, load = 66.72 N |
| Max deflection | d = P L^3 / (3 E I) | d = 0.1161 in = 2.948 mm |
| Deflection against span | L / d | L/172, noticeable flex |
| Max bending moment | M = P L | M = 33.895 N·m |
| Max bending stress | sigma = M c / I | sigma = 29.99 MPa = 4.350 ksi |
| Safety factor | SF = yield / sigma | SF = 276 / 29.99 = 9.20 |
what a safety factor of two does not coverTwo against yield is the usual FRC target for a static load. It says nothing about impact, vibration or fatigue, and a lightening hole or a notch concentrates stress well above the plain-section figure, so a drilled tube yields before this number says it should.
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