At any point, vertical distance between the axis of original beam and the axis of deflected beam is known as _

Question

At any point, vertical distance between the axis of original beam and the axis of deflected beam is known as ___________ at that point.

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Option A: Deflection

Explanation & Concepts:
Deflection is defined as the vertical displacement of a point on the neutral axis of a beam from its original position under the action of applied loads. It represents the transverse shift of the centroidal axis perpendicular to the beam's longitudinal span.

Working Principle: When a beam is subjected to external loads (such as point loads or uniformly distributed loads), it experiences bending moments. These moments induce internal stresses causing the beam to deform. The vertical distance between the undeformed centroidal axis and the deformed centroidal axis at any cross-section is quantified as the deflection (usually denoted by $y$ or $\delta$).

Key Formulas: $EI \frac{d^2y}{dx^2} = M(x)$ — The governing differential equation for beam deflection where $E$ is Young's modulus, $I$ is moment of inertia, and $M(x)$ is the bending moment.; $y = \int 	heta dx$ — Deflection is the integral of the slope $	heta$ along the length of the beam.

Key Points: Deflection is the vertical displacement ($y$ or $\delta$).; Slope is the angle of rotation ($	heta = \frac{dy}{dx}$) of the cross-section relative to the original axis.; The Elastic Curve is the shape adopted by the neutral axis after loading.; For small deflections, the slope is approximately $	an(	heta) \approx 	heta$ in radians.

Advantages: Critical for checking serviceability limit states.; Prevents structural damage and ensures occupant comfort.

Disadvantages: Excessive deflection can lead to cracking in partitions or finishes.; Can cause ponding of water in roofs.

Applications: Structural design of beams and girders.; Bridge engineering to ensure structural stiffness.; Aerospace components where deformation must be within tight tolerances.

Additional Info: Option B (Slope) is the rate of change of deflection with respect to the beam axis ($dy/dx$).. Both Deflection and Slope are geometric properties of the deformed beam, but they represent different physical measurements.

Answer: A is correct — The vertical distance between the original beam axis and the deflected beam axis at any given cross-section is formally defined as the deflection.

Exam Tip: Remember: Deflection has units of length (mm/m), whereas slope is dimensionless (radians), representing the derivative of the deflection function.

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Option B: Slope

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Option C: Both Deflection and Slope

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Option D: None of these

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