Condition of Linearity
- Stress-strain must be linear and elastic
- Displacements and rotations must be small such that the assumption “plane remain
plane after deformation”
o Zero strain in the direction normal to the axis of the applied tensile stress and
direction of crack growth
Plane strain: If the strain state at a material particle is such that the only non-zero strain
component act in one plane only, the particle is said to be in plane strain
Nonlinear inelastic static analysis – Pushover analysis
The axes are usually chose such that x-y plane is the plane in which the strain are non zero
The straight beam section under consideration is in the state of pure bending (ie transverse
shear force is zero along this section). As
Material Non-Linearity
- Due to inelastic behavior of constituent materials such as concrete steel and when
strained beyond proportional limit resulting to cracking, crushing, sliding, yielding,
fracture
Geometric Nonlinearity
- Due to Change in Shape of the structure
- Includes P-Delta and large displacement/rotation effects
Nonlinear boundary conditions
- Due to contact such as constraints and restraints
- Boundary nonlinearity occurs if the boundary conditions change during the analysis
o Consider the cantilever beam, that deflects under an applied load until it hits a
stop