BEHAVIOUR OF MATERIALS stress strain elasticity - plasticity - brittleness safety factors selecting appropriate materials 1/23

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 2/23

change in size or shape of element to original size or shape STRAIN response to stress have stress --> get strain strain to do with change in size or shape ratio of change in size or shape of element to original size or shape 3/23

STRAIN (cont.1) DL e = L for member subject to simple tensile force increase in length original length dimensionless - millimetres / millimetre 4/23

STRAIN (cont2.) except for rubber bands, strains very small usually not visible more a material strains under load - more the structure deflects 5/23

STESS & STRAIN SUMMARY force stress strain deformation causes puts material under deformation results in 6/23

BEHAVIOUR OF MATERIALS how materials respond to stress (i.e. how they strain) determined by whether they are: elastic or plastic properties of materials only explicable in terms of internal forces in the material at the molecular or atomic level 7/23

ELASTICITY until you damage the molecular structure the material remains elastic it recovers when the load is removed the spring in a weighing scale deforms in proportion to the load, and returns to zero when you step off 8/23

MODULUS OF ELASTICITY within elastic range stress is proportional to strain strain stress a linear relationship (Hooke’s Law) the modulus of elasticity, E, is a property of a material E = stress strain E is stress divided by strain slope of line (tan a) same units as stress (MPa) 9/23

MODULUS OF ELASTICITY (cont.) the modulus of elasticity, E, is a property of a material steel 200,000 MPa modulus of elasticity, E aluminium 70,000 MPa concrete 25,000 MPa (varies) timber 10,000 MPa (varies a lot) steel bar 1m long under stress of 150 MPa extends 0.75mm too small to see by eye - measured by micrometer 10/23

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 11/24

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 12/24

DUCTILITY - PLASTICITY (cont1.) yield stress yield point elastic range stress strain ultimate failure plastic range ultimate deformation of plastic material much greater than elastic deformation - visible to naked eye 13/24

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 14/24

ELASTO - PLASTIC MATERIALS ductile materials can be used safely below the yield stress overstress --> deform dramatically but don’t immediately break good warning 15/24

SNAP ! BRITTLENESS sudden breaking of atomic bonds material fails suddenly - like glass 16/24

BRITTLENESS (cont.) stress strain brittle failure occurs with yield point stress strain brittle failure occurs with little energy absorption failure 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 17/24

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 18/24

CURE FOR BRITTLENESS (cont.) add elasto-plastic material that can resist tension into brittle material 19/24

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 20/24

SAFETY FACTORS must ensure that structures do not collapse must have a margin of safety 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 21/24

Ultimate Strength Method 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 22/24

SAFETY FACTORS Elastic Method ensure that actual maximum stress in structure less than Maximum Permissible Stress Max Permissible Stress = Ultimate Stress Factor of Safety Maximum Permissible Stress nearly always falls within elastic range of material 23/24

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 24/24