BEHAVIOUR OF MATERIALS

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BEHAVIOUR OF MATERIALS

• stress

• strain

• elasticity - plasticity - brittleness

• safety factors

• selecting appropriate materials

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STRESS

• internal forces developed within a structure
• due to action of external forces

• stress is force intensity -

force per unit area

• similar to (internal) pressure

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STRAIN

• response to stress

• have stress --gt get strain

• strain to do with change in size or shape

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STRAIN (cont.1)

• for member subject to simple tensile force

• dimensionless - millimetres / millimetre

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STRAIN (cont2.)

• except for rubber bands, strains very small
• usually not visible

• more a material strains under load -
• more the structure deflects

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STESS STRAIN SUMMARY
force
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BEHAVIOUR OF MATERIALS

• how materials respond to stress
• (i.e. how they strain)
• determined by whether they are

• properties of materials only explicable in
• terms of internal forces in the material at
• the molecular or atomic level

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ELASTICITY

• until you damage the molecular structure
• the material remains elastic

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MODULUS OF ELASTICITY

• within elastic range
• stress is proportional to strain

• linear relationship (Hookes Law)

• the modulus of elasticity, E,
• is a property of a material

• E is stress divided by strain
• slope of line (tan a)

• same units as stress (MPa)

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MODULUS OF ELASTICITY (cont.)

• the modulus of elasticity, E, is a property of a
  material

steel bar 1m long under stress of 150 MPa
extends 0.75mm
too small to see by eye - measured by micrometer
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MODULUS OF ELASTICITY (cont.)

• the modulus of elasticity, E,
• is a property of a material

• measures the resistance to deformation
• higher E more resistant to deformation

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DUCTILITY - PLASTICITY

• as long as atomic bonds unbroken material
  remains
• elastic recovers original size and shape

• when break atomic bonds material fails in
• one of two ways - plastic (ductile) or brittle

• in ductile material, material deforms
  permanently

• material can be greatly bent and reshaped
  (plasticene)

• no loss in strength

• eventually fracture occurs but after lot of
  energy

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DUCTILITY - PLASTICITY (cont1.)

• ultimate deformation of plastic material much
  greater
• than elastic deformation - visible to naked
  eye

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DUCTILITY - PLASTICITY (cont2.)

• ductility - able to deform permanently prior to
  fracture

• most materials ductile at low stresses

• most metals ductile (not cast iron)

• need also strength

wrought iron highly ductile but not very strong
high-carbon steel very strong but less ductile
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ELASTO - PLASTIC MATERIALS

• ductile materials can be used safely
• below the yield stress

• overstress --gt deform dramatically

• good warning

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BRITTLENESS
SNAP !

• sudden breaking of atomic bonds

• material fails suddenly - like glass

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BRITTLENESS (cont.)

• brittle failure occurs with
• little energy absorption

• stone, brick, concrete, glass

• high compressive strength -
• poor tensile strength

• most traditional structures designed to
• eliminate tensile stresses - domes , vaults
• timber not durable - 19thC iron then steel

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CURE FOR BRITTLENESS

• reinforced concrete invented in 2nd half of 19thC

• steel bars placed in parts of
• concrete that are in tension

• concrete cracks but
• steel resists the tension

• cracks very fine - important that
• water does not reach steel

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CURE FOR BRITTLENESS (cont.)
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SELECTING THE RIGHT MATERIAL

• timber - not fireproof

strength per volume just less than R.C - much
less than steel
strength per weight not much less than steel -
long span glulam

• stone rarely used today as structural material

• brick and block - loadbearing walls

for multistorey buildings of medium height

• steel - needs fireproofing, rustproofing

• reinforced concrete (R.C.) - slow construction

• prestressed concrete (P.C.) - expensive

• aluminium - lightweight, expensive

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SAFETY FACTORS

• must ensure that structures do not collapse

• factor of safety allows for

• imperfections in materials

• loads not considered

• slightly undersized members

• simplifications in assumptions made in analysis

• two philosophies

ultimate strength method
elastic method
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SAFETY FACTORS Ultimate Strength Method

• load that structure carries x a factor of safety

• factored load called the Ultimate Load

• factor of safety must be greater than 1.0

• 1.0 would mean that structure collapses
• as soon as service load put on

• factors of safety for buildings vary from 1.5 to
  2.5

• depends on structure and material

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SAFETY FACTORS Elastic Method

• ensure that actual maximum stress in structure
• less than Maximum Permissible Stress

• Maximum Permissible Stress nearly always falls
• within elastic range of material

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SERVICEABILITY

• factor of safety ensures that structure does not
  
• collapse under most situations

• but also need to avoid excessive deflection

• leads to cracking - elements and finishes

• excessive deflection - instantaneous / creep

• creep - slowly over time - timber, concrete

• creep deflection may be 2-3 times as much as
• instantaneous deflection

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