Stress, Strain and Material Behaviour (wk 2)

Hooke's Law + its general equation

The force (F) applied to an elastic member is directly proportional to the displacement (x)

What assumption do we make about material behaviour

Civil engineering materials are assumed to behave linear elastically

• Elastic = returns to original position when load is removed / no energy stored when load is removed

• Linear elastic = behaves according to Hooke's Law → displacement and force are proportional

HOWEVER

There is a limit to the stress that can be applied and for the material to respond elastically

• Things generally act linear elastically until they reach yield stress value

• Permanently elastic / plastic = permanent deformation -> Not ideal

Factors that affect the elastic coefficient (k) in hookes law

• K depends on cross-sectional area

  • -> greater area = more resistant to extensio

• K depend on the length of the beam

  • -> longer the beam = more it extends

K = EA/L

• E = young’s modulus

• A = cross sectional area

• L = length

Stress

internal, resisting force a material develops to counteract that deformation

• pressure comes from an external load

• stress arises internally to oppose an external load placed on the object

Equation for stress

What is strain

change in original length (also called engineer's strain)

• a ratio

  • compares two lengths

  • dimensionless → i.e. units cancel

Hookes law but in terms of stress and strain

Stress vs strain graph

+gradient meaning

What is young’s modulus

• just the gradient for the linear part of the stress-strain graph

• Measure of stiffness

• Higher E = more stiff/rigid

• Lower E = more ductile/malleable

Define yield stress

Why is it important

stress level where a material transitions from elastic (reversible) to plastic (permanent) deformation

• in structures → keep stress beneath yield stress

• Ensures an elastic response and small deformations

• Plastic straining has uses but not in structures

  • Making curved materials (e.g. doorknobs)

  • To make parts for vehicles (e.g. crumple zone of a car)

Main types of failure

• Material failure

  • Material failure is a possible failure mode for all members

  • Can fail in compression, tension and shear (and bending)

• Instability (buckling)

what is strength

maximum load that a member can handle before failing

why do we need to consider strength of a member in structural design

Strength ≥ applied load

• If a load greater than the strength is applied to the column it will fail

• need to ensure it doesn’t happen

  • will lose money

  • will cost lives

• If the member consists of different parts with different materials, sum the strengths of the individual parts

E.g. if we know a column will be loaded with a compression force of 100kN, we need to ensure that the compression strength of the column is at least 100kN