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