Composite Beam Stiffness Calculator

This tool uses an E-weighted transformed-section approach for a stacked composite.

• A_i = b_i t_i, I_{cg,i} = b_i t_i^3 / 12
• \bar{y} = (\sum E_i A_i y_{cg,i}) / (\sum E_i A_i)
• EI_{eq} = \sum E_i \big(I_{cg,i} + A_i (y_{cg,i}-\bar{y})^2\big)
• Curvature for a bending moment: κ = M / EI_{eq}
• Layer stress at a distance y from NA: σ_i(y) = E_i κ y

1. Select the number of layers and enter each layer’s E, width, and thickness.
2. Pick a support condition and a load type, then enter span and load values.
3. Click Calculate to view results above the form.
4. Download CSV or PDF to document your design iteration.

Composite beams combine materials, so bending response depends on geometry and modulus. Equivalent flexural rigidity EI_eq controls curvature, deflection, and overall stiffness.

Typical moduli: polymers 2–5 GPa, aluminum ~70 GPa, steels ~200 GPa. The layer stack turns these differences into a single EI_eq value.

1) Why EI is the key stiffness metric

For slender beams, curvature follows κ = M / EI, so higher EI means less bending. Thickness is powerful because a rectangular layer’s inertia scales with thickness cubed.

2) Neutral axis in heterogeneous stacks

In a single material, the neutral axis sits at the geometric centroid. In layered beams, it shifts toward stiffer regions because each layer contributes in proportion to E A. The tool uses an E-weighted centroid to capture this shift. Stiffer faces pull the neutral axis toward them, while a thick low‑E core mainly adds separation for higher stiffness.

3) Equivalent rigidity from the parallel-axis concept

Each layer adds centroidal inertia E I_{cg} plus an offset term E A d^2 (d is distance to the neutral axis). Offset terms often dominate when stiff layers are placed far from the neutral axis.

4) Deflection scaling with span and loading

Deflection is span-sensitive. For a simply supported beam, midspan deflection under a center point load scales as δ ∝ L^3/EI, while uniform load scales as δ ∝ L^4/EI. This makes span one of the strongest levers in stiffness design.

5) Layer stresses and material utilization

With perfect bonding and linear strain, stress varies linearly with distance from the neutral axis, but the magnitude depends on modulus: σ_i = E_i κ y. Two layers at the same y can carry different stress if their moduli differ. Use the stress table to check whether the highest-modulus layer is approaching its allowable stress first. The sign of σ indicates tension or compression depending on which side of the neutral axis you are evaluating.

6) Thickness and width effects in practice

Wider layers increase area and inertia proportionally, improving EI and lowering bending stress. Thickness changes are more dramatic because inertia scales with thickness cubed for rectangular slices.

7) Engineering checks and common limitations

This calculator focuses on elastic bending stiffness and classic beam deflection formulas. For final design, also consider shear deformation, interface slip, time-dependent effects, local buckling, and suitable safety factors for your application. For anisotropic laminates, use the bending-direction effective modulus and confirm results with laminate theory or FEA.

1) What does EI_eq represent?

EI_eq is the beam’s effective resistance to bending. Higher EI means less curvature, smaller deflection, and lower strain for the same bending moment, assuming elastic behavior and good layer bonding.

2) Why does the neutral axis move in composites?

Different materials carry different proportions of bending strain energy. The neutral axis shifts toward layers with larger E·A contribution, so stiffer layers pull the neutral axis closer to themselves.

3) Can I model a sandwich panel with a soft core?

Yes. Enter the core as a low-modulus, thicker layer and the faces as thin, high-modulus layers. The faces placed far from the neutral axis typically dominate EI and bending stresses.

4) Are shear effects included?

No. Deflection formulas here are bending-dominated. For short spans or deep beams, shear deformation can be significant, especially with soft cores. Consider a Timoshenko approach when L/h is small.

5) What stress does the tool report for each layer?

It reports bending stress at the top and bottom of each layer for the maximum moment of the selected load case, using linear strain and perfect bonding: σ = Eκ y.

6) How accurate are the fixed–fixed and cantilever cases?

They use standard closed-form beam solutions for ideal boundary conditions. In real assemblies, fixtures may be semi-rigid, reducing stiffness. Use the results as a baseline and calibrate with tests if needed.

7) What units should I use?

Enter E in GPa, widths and thicknesses in mm, span in meters, and loads in N or N/m. The calculator returns EI in N·m² and stresses in MPa for clear engineering interpretation.