20.7: Bending of Members Made of Several Materials
In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's unique modulus of elasticity. The normal strain changes linearly with distance from the neutral axis, leading to different stress distributions in each material segment and influencing the force exerted on each segment. The composite member's calculation of forces and moments is simplified by relating the force in one material to the other by defining the ratio of their elastic moduli.
The elastic moduli ratio transforms one material's section into an equivalent section of the other, adjusting its contribution to the overall structural behavior. The ratio of elastic moduli significantly influences the geometry of the transformed section. When the ratio is greater than one, the material with the higher modulus appears effectively wider in the transformed section, indicating greater stiffness. Conversely, if the ratio is less than one, the material seems narrower, signifying lower stiffness. This transformation is critical for calculating the neutral axis position and moment of inertia, and it is essential for determining bending stresses and deflections in composite beams, thereby ensuring structural integrity under various loading conditions.
