# Slender Structures Flashcards

Extension

Kinematic Relation

Extension

Constitutive Relation

- σ = Eε
- N = int( σ dA )

= int ( E ε dA )

= int ( EAε )

Extension

Equilibrium

Extension

ODE

Extension

Free Body Diagram

Extension

FBD components & BC

Shear

Kinematic Relation

Shear

Constitutive Relation

τ = V / A

- τ = Tau
- V = GAγ
- γ = Gamma (shear strain)
- GA = k (Stiffness)

- A = Area

Shear

Equilibrium

Shear

ODE

Shear

Free Body Diagram

Shear

FBD components & BC

Shear + Bending

What relation is affected?

How to account for bending in calculations?

The **Kinematic Relations** if affected:

- Add additional term (Φ) to account for rotation due to Bending

Moment is the integration of Shear

Euler-Bernoulli

Assumptions?

Also known as?

- Bernoulli-Navier hypothesis:
- plane cross-sections remain planar and normal to the beam axis in a beam subjected to bending.

- Shear strains = 0
- small displacements
- straight longitudinal axis
- symmetric about y-axis

Euler-Bernoulli

Kinematic Relation

Assumptions?

Plane C-S remain planer and normal to the beam axis.

Euler-Bernoulli

Constitutive Relation

Euler-Bernoulli

Equilibrium

Euler-Bernoulli

ODE

Euler-Bernoulli

Free Body Diagram