# Differential Equation - Why do beams break?

I've never studied physics before and I'm a Maths major. But I do have a physics-related differential equation question which I need help on.

Given the beam deflection equation: $$F(x) = EI \frac{d^4u}{dx^4}$$ where $$E$$ is the Young's Modulus, $$I$$ is the moment of inertia.

I found that $$u(x)$$ implies the displacement, $$u'(x)$$ implies change in displacement, $$u''(x)$$ implies the bending moment and $$u'''(x)$$ is the sheer force of the beam.

And relating this formula to a 'breaking a spaghetti' situation- where a spaghetti eventually breaks when we bend it at both ends. Why does that happen? Does the spaghetti break into two because of the maximum bending moment of the spaghetti is exceeded? or the sheer force is exceeded? Or is there any other reasons?

I apologize if any of the terms here are inaccurate. Thank you!

Given the beam deflection equation: $$F(x) = EI \frac{d^4u}{dx^4}$$ where $$E$$ is the Young's Modulus, $$I$$ is the moment of inertia.
• The load $$F(x)$$ is a continuous function of position.