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Flexural Rigidity Formula:
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Flexural rigidity (EI) is a measure of a beam's resistance to bending. It is the product of the modulus of elasticity (E) and the moment of inertia (I) of the beam's cross-section. Higher EI values indicate stiffer beams that resist deformation under load.
The calculator uses the flexural rigidity formula:
Where:
Explanation: The modulus of elasticity represents the material's stiffness, while the moment of inertia depends on the cross-sectional shape and size of the beam.
Details: Flexural rigidity is crucial in structural engineering for designing beams, determining deflection under load, and ensuring structural integrity. It helps predict how much a beam will bend when subjected to forces.
Tips: Enter the modulus of elasticity in Pascals (Pa) and the moment of inertia in meters to the fourth power (m⁴). Both values must be positive numbers.
Q1: What is the difference between flexural rigidity and stiffness?
A: Flexural rigidity (EI) specifically refers to a beam's resistance to bending, while stiffness is a more general term for resistance to deformation.
Q2: How does cross-sectional shape affect flexural rigidity?
A: Different cross-sectional shapes have different moments of inertia. For example, I-beams have high I-values for their weight, making them efficient for bending resistance.
Q3: What are typical values for modulus of elasticity?
A: Steel has E ≈ 200 GPa, aluminum ≈ 70 GPa, wood varies from 8-15 GPa depending on species and grain direction.
Q4: Can this calculator be used for composite materials?
A: For composite beams, you would need to calculate the equivalent flexural rigidity considering all materials and their arrangement.
Q5: How is flexural rigidity related to beam deflection?
A: Deflection is inversely proportional to flexural rigidity. Doubling the EI value halves the deflection under the same load.