Fast strain estimates for real cantilever beams online. Supports point loads, UDL, and moments together. Enter dimensions, pick units, then review results instantly below.
For small deflections in linear elastic bending, the curvature is: κ(x) = M(x) / (E·I). The longitudinal strain at a distance y from the neutral axis is: ε(x) = κ(x)·y.
| Scenario | Inputs (summary) | Approx. output |
|---|---|---|
| Steel cantilever, end load, rectangular section |
L = 2 m, x = 0 m, P = 500 N, E = 200 GPa b = 50 mm, h = 100 mm, y = c = 50 mm |
I ≈ 4.17×10−6 m⁴ M(0) ≈ −1000 N·m ε(0) ≈ −60 µε, σ(0) ≈ −12 MPa |
| Aluminum cantilever, UDL, solid circular section |
L = 1.5 m, x = 0.25 m, w = 200 N/m, E = 69 GPa d = 40 mm, y = c = 20 mm |
M(x) varies with (L−x)² ε(x) depends on E, I, and y |
| Combined loading with end moment |
Enable P, w, and M₀ together Use any section mode for I and y |
M(x) = MP(x) + Mw(x) + M0 ε(x) follows from κ(x)·y |
Strain (ε) is a unitless measure of deformation. In bending, the top fibers compress and the bottom fibers stretch as the cantilever deflects. A common estimate uses ε = σ / E, linking strain to bending stress and Young’s modulus.
The key drivers are load, span, cross‑section size, and modulus. Longer spans increase bending moment; larger sections reduce strain through a bigger second moment of area (I). For rectangles, I = b·h³/12, so height has a strong cubic effect.
Typical models include an end point load, a uniformly distributed load (UDL), and an applied end moment. At the fixed end, the peak moment is M = P·L for a point load, M = w·L²/2 for a UDL, and M = M₀ for an end moment. These moments drive strain.
Peak bending strain occurs at the fixed support and at the outermost fiber, a distance c from the neutral axis (c = h/2 for a rectangle). The relationship is ε = (M·c)/(E·I). Holes, weld toes, and sharp corners can amplify local strain beyond ideal beam theory.
Approximate room‑temperature moduli: steel ≈ 200 GPa, aluminum ≈ 69 GPa, and many hardwoods along the grain ≈ 10–16 GPa. Some plastics are much lower (about 0.5–3 GPa) and can creep under steady load. Yield strain is roughly σy/E; for mild steel (σy ≈ 250 MPa) that’s about 0.00125, or 1250 με.
Stay consistent. Convert GPa to Pa (1 GPa = 10⁹ Pa) and mm to m (1 mm = 0.001 m). Loads may be N or kN, and moments N·m or kN·m. One unit slip can change strain by 10×, 100×, or 1000×.
Microstrain (με) is convenient: 1 με = 10⁻⁶ strain. Many elastic service cases fall around 50–800 με for metals. If you see values above ~1500–2500 με in steel, you may be near or beyond yield, depending on grade and temperature.
To validate results, place a strain gauge near the fixed end on the tensile face and align it with the beam axis. Record temperature, because modulus and gauge factor drift slightly. If deflection is large, small‑deflection assumptions can break, and a finite‑element model may be more reliable. For design, consider safety factors, dynamic loads, and support flexibility.
As a rough guide, many designs keep service strain well below yield. Mild steel yield is about 1250 microstrain, so staying under ~600–800 microstrain provides margin, but codes, fatigue, and buckling checks still govern.
Bending strain relates to bending stress by ε = σ/E. A stiffer material (higher E) produces less strain for the same stress and geometry, which is why E is required for strain output.
Place it near the fixed support where moment is highest, on the tensile face for positive bending. Align the gauge with the beam’s length and avoid placing it directly on a weld toe or sharp corner.
Multiply strain by 1,000,000. For example, 0.000350 strain equals 350 microstrain (350 με). Microstrain is commonly used because values are easier to compare and record.
No. It focuses on bending strain from common cantilever loads. If shear strain is important (short, deep beams) or torsion exists, use a more detailed model or finite‑element analysis.
Real beams have support compliance, residual stresses, and local stress concentrations. Load application may not match the ideal case, and temperature affects both modulus and gauge factor. Small unit or geometry input errors also create big differences.
Use the correct second moment of area I and outer‑fiber distance c for your shape (c = distance from neutral axis to surface). If unsure, compute I from CAD or published tables, then enter the equivalent values.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.