How to use this calculator
Enter the layers from the bottom up: width, thickness and modulus. Layer 1 is the reference material. Enter the bending moment (positive puts the top in compression) and the shear force; add a fastener capacity for the spacing.
Formulas
Modular ration = Ei/E1, bt = nb
Neutral axisȳ = ΣAtȳi/ΣAt
Stressσ = −nMy/It
Shear flowq = VQ/It
Fastener spacings = nfF/q
Worked example
Hibbeler Example 6.22-type: wood 150 × 150 mm (E = 12 GPa) on a steel strap 150 × 20 mm (E = 200 GPa), M = 2 kN·m
- Transform the wood into steel: n = 12/200 = 0.06, bt = 9 mm.
- Neutral axis 36.4 mm above the bottom; It = 9.36 × 10⁶ mm⁴.
- Top of the wood: σ = 0.06 × 2000 × 0.1336/9.36 × 10⁻⁶ = 1.71 MPa compression.
- Bottom of the steel: σ = 2000 × 0.0364/9.36 × 10⁻⁶ = 7.78 MPa tension.
Frequently asked questions
Why do the stresses jump at the interface?
Strain is continuous through the depth, but stress is E times strain, so it jumps by the modulus ratio where the material changes.
Which Q do I use for shear flow?
The first moment, about the neutral axis, of the transformed area on one side of the interface (the part the fasteners hold on).
Can I use this for reinforced concrete?
Not directly: cracked concrete carries no tension, so only the concrete above the neutral axis counts. Use a cracked-section analysis for that.