Parameters
Beam Type
Material 1 (Bottom Layer)
Width b₁ [mm]
80 mm
Height h₁ [mm]
60 mm
E₁ [GPa] (Steel)
200 GPa
Material 2 (Top Layer)
Width b₂ [mm]
80 mm
Height h₂ [mm]
40 mm
E₂ [GPa] (Aluminum)
70 GPa
Bending Moment M [kN·m]
10.0 kN·m
—
Neutral Axis ȳ [mm]
—
I_tr [mm⁴·10⁶]
—
Modular Ratio n
—
σ₁_max [MPa]
—
σ₂_max [MPa]
Theory (Transformed Section Method)
Modular ratio: $n = E_2 / E_1$
Transformed width of material 2: $b_{tr} = n \cdot b_2$
Neutral axis position (from bottom): $$\bar{y} = \frac{A_1 \bar{y}_1 + n A_2 \bar{y}_2}{A_1 + n A_2}$$
Stress in material 1: $\sigma_1 = \dfrac{M(y - \bar{y})}{I_{tr}}$
Stress in material 2: $\sigma_2 = n \cdot \dfrac{M(y - \bar{y})}{I_{tr}}$
CAE Integration: RC beam design, bimetal actuator analysis, preliminary design of CFRP-metal hybrid beams. Results can be used as reference values for multi-layer shell and solid element analyses in ABAQUS and LS-DYNA.