Strength of materials — beam flexure terminology: What is the name given to the product of Young's modulus (E) and the second moment of area (I) of a beam cross-section?

Introduction / Context:
In strength of materials, the bending stiffness of a prismatic beam is governed by both the material's elastic property and the cross-sectional geometry. The compound quantity that measures this bending stiffness is the product E * I, widely used in deflection and slope calculations.

Given Data / Assumptions:

• E = Young's modulus (material stiffness in tension/compression).
• I = second moment of area about the neutral axis (geometric stiffness in bending).
• Small deflection theory (Euler–Bernoulli) is assumed.

Concept / Approach:
Beam curvature under bending follows M / I = E / R, which rearranges to M = (E * I) / R. The larger the product E * I, the smaller the curvature R for a given bending moment M. Hence E * I quantifies resistance to bending and is termed flexural rigidity.

Step-by-Step Solution:

Verification / Alternative check:
Deflection formulas for standard cases (e.g., simply supported beam with central load) contain E * I in the denominator, confirming that deflection decreases as E * I increases.

Why Other Options Are Wrong:

• Bulk modulus: volumetric elasticity, unrelated to flexure directly.
• Torsional rigidity: G * J for twisting, not bending.
• Modulus of rigidity: the shear modulus G alone, not multiplied by I.
• Section modulus: geometric term Z = I / y, not multiplied by E.

Common Pitfalls:
Confusing section modulus Z with second moment I; only E * I represents flexural rigidity.

Final Answer:
Flexural rigidity