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When value of EI is more, than deflection of beam is
More
Equal to
Less
Both B and C
Less
The deflection of a structural beam is inversely proportional to its flexural rigidity, denoted as EI. Since deflection (delta) is a measure of how much a beam bends under load, a higher value of EI indicates a stiffer member that resists deformation, resulting in less deflection.
The deflection of a structural beam is inversely proportional to its flexural rigidity, denoted as EI. Since deflection (delta) is a measure of how much a beam bends under load, a higher value of EI indicates a stiffer member that resists deformation, resulting in less deflection.
╬┤тИЭEI1тАЛ тАФ Inverse proportionality between deflection and flexural rigidity
EI=EтЛЕI тАФ Definition of flexural rigidity
Flexural rigidity (EI) represents the product of the Young's Modulus of the material (E) and the Area Moment of Inertia of the cross-section (I). In the Euler-Bernoulli beam theory, the governing differential equation EIdx2d2yтАЛ=M shows that for a given bending moment (M), the curvature is inversely proportional to EI. Consequently, integration of this curvature leads to deflection terms where EI appears in the denominator, confirming that as stiffness increases, displacement decreases.
E represents the material's inherent stiffness (Young's Modulus).
I represents the geometric efficiency (Moment of Inertia) of the beam's cross-section.
Increasing either E or I effectively increases the resistance of the beam to bending loads.
This principle is fundamental in designing structural members to limit serviceability limit state violations.
Higher EI improves structural serviceability.
Reduces vibration and sagging in floor systems.
Higher EI often requires more material or higher grade materials, increasing structural weight and cost.
Design of steel beams to meet L/360 deflection limits.
Selecting I-sections for long-span bridge girders.
Standard limit for deflection is typically L/250 to L/360 depending on the code of practice (e.g., IS 800:2007).
Option A is incorrect as it describes the inverse of the actual physical behavior.
Option B is incorrect as deflection is a variable function of length, load, and boundary conditions, not just a constant relationship.
C is correct тАФ Deflection is inversely proportional to flexural rigidity (EI), so increasing EI leads to less deflection.
In competitive exams, always remember that I (moment of inertia) contributes more significantly to rigidity than E for standard sections; choosing a deeper section often increases I cubically, drastically reducing deflection.