Most people are familiar with the concepts of stiffness and compliance from childhood: jumping on a trampoline barefoot is fun, jumping on pavement is not. While the average person may not consciously think about these concepts, it is crucial for engineers to pay attention to stiffness and compliance when designing and building structures. Learn about stiffness and compliance and then test your knowledge by building a structure of your own!
Stiffness is defined as the ability to resist deformation when loads are applied and can be categorized as either axial stiffness or torsional stiffness. High stiffness means that more force can be applied with minimal displacement. Compliance is the inverse of stiffness. A material or structure that is highly compliant displaces significantly when a load is applied.
Axial stiffness: k = AE⁄L, where A is the cross sectional area of the material, E is the Young’s modulus of the material, and L is the length of the member.
Torsional stiffness: k = GJ⁄L, where G is the rigidity constant of the material, J is the torsional constant of the cross section, and L is the length of the material.
Stiffness of a structure at a certain point: k = F⁄Δ, where F is the applied force and Δ is the displacement at that point.
Most structures, such as buildings, are stiff. For example, you don't want your house bending or deforming. However, compliant parts are important under special circustances.
Buildings in earthquake-prone areas must be able to shift slightly with respect to earthquake loads in order to minimize damage. Since skyscrapers are subject to high wind loads, they must be flexible enough to sway slightly or else they will be more likely to fail or take on damage.
Suspension bridges are also designed to sway slightly due to different loading conditions.
The stiffness or compliance of an object can completely transform the use of the object. For example, let's consider a flat surface with four legs. Choose stiff or compliant for each member and see how different combinations can create completely different objects!
Created by Tessa Carty, Harshitha Gogineni, and Karolina Ohstrom