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CivilStructural Mechanics-II

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What is the unit of flexural rigidity?

$kN/mm²$

$N \cdot mm²$

$mm²$

$kN$

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilStructural Mechanics-II

Option B

$N \cdot mm²$

Quick Summary:

Flexural rigidity, often denoted as $EI$ , is the product of the Young's modulus of elasticity ( $E$ ) and the second moment of area ( $I$ ). It represents the resistance of a structural member to bending deformations; the higher the value, the stiffer the member.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$EI = E \cdot I$ — Flexural Rigidity definition

$M = EI \frac{d^2y}{dx²}$ — Relationship between moment and deflection

⚙️ Working Principle

In structural mechanics, the bending equation is given by $\frac{M}{I} = \frac{E}{R} = \frac{\sigma}{y}$ . Rearranging to find the moment $M$ leads to $M = EI \cdot \kappa$ , where $\kappa = \frac{1}{R}$ is the curvature. Thus, $EI$ acts as the constant of proportionality between the internal bending moment and the curvature of the beam, measured in units of force multiplied by length squared ( $N \cdot mm²$ or $N \cdot m²$ ).

📌 Key Points

▸
Young's modulus ( $E$ ) is measured in $N/mm²$ (MPa).
▸
Second moment of area ( $I$ ) is measured in $mm⁴$ .
▸
The product $E \cdot I$ results in units of $N \cdot mm²$ or $N \cdot m²$ .
▸
Flexural rigidity determines the resistance to rotation at supports and deflection in spans.

✅ Advantages

▸
Used to calculate beam deflection and rotation accurately.
▸
Essential for analyzing indeterminate structures using stiffness methods.

❌ Disadvantages / Limitations

▸
Assumes linear elastic behavior and small deflection theory.
▸
Does not account for shear deformation (which requires $GA$ ).

🛠️ Applications / Uses

▸
Structural design of beams, columns, and slabs.
▸
Dynamic analysis of vibrating bridge structures.

📄 Additional Information

▸
The SI unit is $N \cdot m²$ , but $N \cdot mm²$ is common in engineering practice for smaller components.
▸
Option A is the unit for Young's Modulus, while Option C is the unit for Area/Second moment of area properties.

📊 Diagram / Illustration

✅

B is correct — The unit of flexural rigidity is the product of force/area and length⁴, resulting in force multiplied by length squared, i.e., $N \cdot mm²$ .

Core Concepts Used

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Elasticity Moment of Inertia Structural Stiffness

💡 EXAM TIP

Always verify units by multiplying the base units of the constituent terms: $[E] \times [I] = (FL^{-2}) \times (L⁴) = FL²$ .

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