Advanced Cantilever Beam Inputs
Use positive magnitudes. The fixed support is at the left side. The free end is at the right side.
Example Data Table
| Case | Length | Load | Material | Section | Useful Check |
|---|---|---|---|---|---|
| Free-end point load | 2.5 m | 1.2 kN | Steel, 200 GPa | 75 mm × 150 mm rectangle | Compare deflection with L / 360 |
| Full uniform load | 3.0 m | 0.85 kN/m | Aluminum, 69 GPa | 90 mm solid round | Review stress and fixed moment |
| Point load inside span | 4.0 m | 2.0 kN at 2.5 m | Custom | Custom I and c | Check free-end movement |
Formula Used
The calculator uses Euler-Bernoulli beam theory for a prismatic cantilever.
The fixed support is assumed perfectly rigid.
The elastic modulus is E, beam length is L,
and second moment of area is I.
- Free-end point load:
δ = PL³ / 3EI,θ = PL² / 2EI,M = PL. - Full uniform load:
δ = wL⁴ / 8EI,θ = wL³ / 6EI,M = wL² / 2. - Point load at distance a from fixed end:
δ = Pa²(3L - a) / 6EI,θ = Pa² / 2EI,M = Pa. - Free-end moment:
δ = ML² / 2EI,θ = ML / EI,M = M. - Bending stress:
σ = Mc / I. - Rectangular section:
I = bh³ / 12. - Solid round section:
I = πd⁴ / 64. - Hollow round section:
I = π(D⁴ - d⁴) / 64.
These formulas are for small deflection, linear elastic behavior. Verify final designs with applicable engineering codes.
How to Use This Calculator
- Select the cantilever load case that matches your beam.
- Enter the beam length and choose the proper length unit.
- Add the load, uniform load, point position, or moment.
- Select a material preset or enter your own elastic modulus.
- Choose a section shape and enter the required dimensions.
- Turn on self weight when member mass should affect deflection.
- Pick output units and a serviceability limit.
- Press the submit button to view results above the form.
- Download the CSV or PDF file for project records.
Article: Cantilever Beam Deflection in Practice
What a Cantilever Beam Does
A cantilever beam is fixed at one end and free at the other. It is common in balconies, brackets, signs, shelves, machine arms, and crane booms. The fixed end supplies vertical reaction and bending resistance. The free end moves when load is applied. That movement is called deflection. Deflection matters because a beam can feel unsafe before it breaks. It can also damage finishes, cladding, bearings, and attached equipment.
Why Stiffness Controls Movement
Beam deflection depends on load, length, material stiffness, and section stiffness. Length is very important. A longer cantilever bends much more than a short one. A strong material helps, but shape often helps more. A deeper rectangular section is usually much stiffer than a shallow one. This happens because height is cubed in the rectangular moment of inertia formula.
Loads and Support Effects
Different load cases create different bending patterns. A point load at the free end is severe. A uniform load spreads force across the member. A point load placed closer to the support creates less free-end movement. An applied end moment creates rotation and curvature without direct vertical reaction. Self weight can also be important. Heavy steel, concrete, or timber members may deflect under their own mass.
Using Results Wisely
The calculated deflection should be compared with a practical limit. Common limits include L over 180, L over 240, L over 360, and L over 480. A stricter limit means less visible movement. Stress should also be reviewed. Low deflection does not always mean low stress. This tool helps with fast estimates and early sizing. It is not a replacement for code checks, connection design, lateral stability review, or professional judgment. Use conservative inputs when data is uncertain.
FAQs
What is cantilever beam deflection?
It is the displacement of a beam that is fixed at one end and free at the other. The largest deflection usually occurs at the free end.
Which load case should I choose?
Choose the case that best matches the actual loading. Use point load for a concentrated force, uniform load for spread weight, and moment for applied rotation force.
Why does beam length affect deflection so much?
Length appears with high powers in common cantilever formulas. Small increases in span can cause large increases in deflection.
What is the second moment of area?
It measures section resistance to bending. A larger value means the beam shape is stiffer against bending about the selected axis.
Can I include self weight?
Yes. Select the self weight option and enter material density. The calculator adds it as an equivalent full-span uniform load.
What does L over 360 mean?
It means the allowable deflection equals beam length divided by 360. Higher ratio limits are stricter and allow less movement.
Does this calculator check beam strength codes?
No. It estimates elastic deflection, slope, reaction, fixed moment, and bending stress. Formal design should follow the relevant code.
Why are my results very large?
Large results often come from long spans, low modulus, small moment of inertia, wrong units, or loads entered much larger than intended.