Beam Bending Equation

\frac{d^2y}{dx^2} = \frac{M(x)}{EI}

Beam curvature equals bending moment divided by flexural rigidity.

By Leonhard Euler, Daniel Bernoulli

Engineering Sciences

1750 · Leonhard Euler

Why it matters: Enabled skyscrapers, bridges, and every beam-based structure.

Discoverers: Leonhard Euler, Daniel Bernoulli (1750)

What does it mean?

Beam curvature equals bending moment divided by flexural rigidity.

Enabled skyscrapers, bridges, and every beam-based structure.

Symbol	Name	Unit	Meaning
$y$	Deflection	m	Vertical displacement
$M$	Bending moment	—	N·m
$E$	Young's modulus	—	Pa
$I$	Moment of inertia	—	m⁴

Simply supported beam: max deflection at center ∝ L⁴.

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\frac{d^2y}{dx^2} = \frac{M(x)}{EI}

Real-world impact

Space systems

Orbital mechanics enables global connectivity and exploration.

Photo: Unsplash — rocket launch

Beam curvature equals bending moment divided by flexural rigidity.

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