Mini-Project Stress stiffening & buckling in beams

Course Coordinator:Dr. Vasant MatsagarMini-ProjectCEL 431: SeminarStress stiffening & buckling in beams Presented By:Aditya Kumar2010CE10318

Department of Civil EngineeringIndian Institute of Technology (IIT) DelhiStress stiffening & BucklingBuckling occurs when a membrane or a structure converts membrane strain energy into strain energy of bending with no change in externally applied load.As membrane stiffness is much greater than bending stiffness, when buckling happens bending stiffness is reduced to zero.If the membrane forces are reversed, however, bending stiffness is increased. This is called stress stiffening.The effect of membrane forces are accounted for by a matrix

Strain- Displacement RelationshipThe total axial strain of an arbitrarily located fibre is:

When small lateral displacement v=v(x)takes place, each differential length dx is changed to ds.

Strain energyStrain energy in the element is:

Noting that

where P is the axial force, positive in tensionStrain energy becomes

The first integral yields for a bar element and the third integral yields for a beam element. The second integral yields

Stress stiffness matrixWith nodal d.o.f and shape function [N],

The second integral becomes

whereUsing standard N for beam element,

Thank You!