20.7 : 由多种材料制成的构件的弯曲

Consider a member of two different materials that have the same cross-sectional area. The equation of stress for such a member is expressed in terms of elastic moduli for each segment separately.

The normal strain in the two different segments of the member varies linearly with the distance from the neutral axis.

By writing the expression for the force exerted on the area element for each segment of the member and defining the ratio of elasticity of moduli as a constant, the resistance to the bending can be estimated.

Here, the force exerted on one segment of the member can be expressed in terms of the force exerted on the other member by multiplying it with the ratio of the elastic moduli of the two materials.

If the ratio of elastic moduli is greater than 1, then a widening occurs. If the ratio is less than 1, then a narrowing of the cross-sectional area occurs. This effect occurs parallel to the neutral axis, and the new cross-section is known as the transformed section.