Question

Write down the equation (or expression) for the following terms from Euler-Bernoulli beam theory: 5 points

a) Moment of inertia
b) Flexural rigidity
c) Shear force
d) Bending stress

Answer 1

The equations for the terms in Euler-Bernoulli beam theory are: moment of inertia - I = ∫ r² dm, flexural rigidity - EI, shear force - V = -dM/dx, and bending stress - σ = My/I.

Step-by-step explanation:

1. The equation for moment of inertia is I = ∫ r² dm, where I is the moment of inertia, r is the perpendicular distance from the axis of rotation to the element of mass, and dm is the mass of the element.
2. The equation for flexural rigidity is EI, where E is the modulus of elasticity and I is the moment of inertia.
3. The equation for shear force is V = -dM/dx, where V is the shear force, M is the bending moment, and x is the distance along the beam.
4. The equation for bending stress is σ = My/I, where σ is the bending stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia.