Flexural rigidity: Definition, Formula, Unit, Example [with Pdf]

The term flexural rigidity is an important factor while the design of beams. Therefore in this article, we have tried to explain the flexural rigidity along with its importance and numerical.

What is flexural rigidity?

The flexural rigidity is the product of the modulus of elasticity (E) and moment of inertia (I) of the beam about the neutral axis.

Flexural Rigidity equation = E x I

As we increase the value of flexural rigidity the strength of the beam to resist bending also increases.

The flexural rigidity of components can be increased by raising the moment of inertia of cross-section or by choosing the material with a higher modulus of elasticity.

Flexural rigidity Unit

The SI unit of the modulus of elasticity is N/m² and the SI unit of moment of inertia is `m^{4}` therefore the SI unit of flexural rigidity can be derived as,

Flexural Rigidity = E x I
= (N/m²) x (`m^{4}`)
= N.m²

While the FPS unit of flexural rigidity is `lb.ft^{2}`, It is also denoted by the unit `Pa.m^{4}`.

What is the significance of flexural rigidity?

  • The resistance of the beam for the bending depends on flexural rigidity.
  • The beam with a higher value of flexural rigidity has less value of deflection.

Flexural rigidity example

  1. Find the flexural rigidity of the beam if the beam is made of timber with the modulus of elasticity of 13 GPa and the moment of inertia of 5.2 x `10^{-3} m^{4}`.

Given:-

Modulus of elasticity, E = 13 GPa = 13 x `10^{9}` N/`m^{2}`
Moment of inertia, I = 5.2 x `10^{-3}\m^{4}`

The flexural rigidity of the beam is,

Flexural rigidity = E x I

= (13 x `10^{9}`) x (5.2 x `10^{-3}`)

= 67.6 x 10⁶ Nm²

Conclusion

The flexural rigidity decides the resistance of the beam subjected to bending stress hence this parameter has a great importance while the design of beams.

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