A fundamental property in any structure is its ability to resist deflection or deformation from loads. We call this rigidity (or stiffness) of a structure.
WeTheStudy lets you connect ideas
Learn more

A fundamental property in any structure is its ability to resist deflection or deformation. We call this rigidity (or stiffness) \(k\).

Rigidity Types

Difference among rigidity types

Below are the types of rigidity present in any structure which would depend on the type of internal force:

Flexural

This type measures a structure's resistance to flexural (or bending) loads. It is the product of Young's Modulus \(E\) and the moment of inertia \(I\) of a cross-section.

\(k_f=EI\)

Axial

This type measures a structure's resistance to axial loads. It is the product of Young's Modulus \(E\) and the area \(A\) of a cross-section.

\(k_a=EA\)

Torsional

This type measures a structure's resistance to torsion. It is the product of Shear Modulus \(G\) and the polar moment of inertia \(J\) of a cross-section.

\(k_t=JG\)

Implications

From these different types, we can observe that rigidity is a product of two variables: (1) the inertial properties of the cross-section and (2) the mechanical property of a material.

It implies several things when it comes to the structure's deflection or deformation:

  • Rigidity will depend on the cross-section. For example, if we have a tapered beam, the rigidity on its bigger end is more significant than its other end. It means that the smaller end is more prominent to deform or deflect.
  • If we want our structure to deform/deflect less, for example, there are two things we can do. First, we may increase its mechanical properties \(E\) or \(G\). It implies that we must find a better material to carry the loads. Second, we may have a larger cross-section. What this does is increase its inertial properties. A bigger \(I\) or \(J\) means the structure will deform less.

Summary

Let's summarize:

A fundamental property in any structure is its ability to resist deflection or deformation. We call this rigidity (or stiffness) \(k\).
There are several types of rigidity: flexural, axial, and torsional. Each rigidity respectively measures resistance with bending, axial, and torsion loads.
Rigidity is a product of two variables: (1) the inertial properties of the cross-section and (2) the mechanical property of a material.
Want to access the remaining content?
You're a Member!
Click to expand on exclusive content
Want to access the remaining content?

Become a Member

When you sign-up and subscribe to WeTheStudy, you’ll get the following benefits:

No ads! (yey!)
Complete access to all articles
Ability to track your progress in the tree

SIGN-UP

Complete Your Checkout

When you complete your account, here are the following benefits:

No ads! (yey!)
Complete access to all articles
Ability to track your progress in the tree

PROCEED CHECKOUT

N/A

Tree Navigation

See how this article relates to other ideas
Children
No children (yet)
Siblings
No siblings (yet)
Connections
No connections (yet)
Created On
June 5, 2023
Updated On
February 23, 2024
Contributors
Edgar Christian Dirige
Founder
References

WeTheStudy original content

Revision
1.00
Got some questions? Something wrong? Contact us