1.2 STRENGTH OF MATERIALS

1. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

2. Gravity and Mass The mass of an object is defined from its acceleration when a force is applied, i.e. from the equation F = Ma, not from gravity. Gravity is normally the largest force acting on a structure. The gravitational force on a mass M is: The gravitational force on an object is called its weight. Thus an object will have a weight of 9.81N per kg of mass

3. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

4. Types of strength In engineering the term strength is always defined and is probably one of the following ·         Compressive strength ·          Tensile strength ·          Shear strength depending on the type of loading.

5. Forces Compression, tension, bending and shear This cylinder is in compression This cylinder is in Tension Flexural (bending) stress Shear Stress

6. Tension and Compression

7. Structures lab

8. Testing for strength

9. Applying Loads

10. Stress This is a measure of the internal resistance in a material to an externally applied load. For direct compressive or tensile loading the stress is designated  and is defined as:

11. Types of stress Tensile load Compressive load Compressive stress Tensile Stress Compressive load Tensile load

12. Measuring: Stress = Load/area

13. Shear Stress Similarly in shear the shear stress  is a measure of the internal resistance of a material to an externally applied shear load. The shear stress is defined as:

14. Shear stress Area resisting shear Shear Force Shear force

15. Ultimate Strength The strength of a material is a measure of the stress that it can take when in use. The ultimate strength is the measured stress at failure but this is not normally used for design because safety factors are required. The normal way to define a safety factor is : 

16. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

17. Strain We must also define strain. In engineering this is not a measure of force but is a measure of the deformation produced by the influence of stress. For tensile and compressive loads: Strain is dimensionless, i.e. it is not measured in metres, killogrammes etc. For shear loads the strain is defined as the angle  This is measured in radians

18. Shear stress and strain Area resisting shear Shear displacement (x) Shear Force Shear strain is angle  L Shear force

19. Units of stress and strain • The basic unit for Force and Load is the Newton (N) which is equivalent to kg m/s2. One kilogramme (kg) weight is equal to 9.81 N.  • In industry the units of stress are normally Newtons per square millimetre (N/mm2) but this is not a base unit for calculations. • The MKS unit for pressure is the Pascal. 1 Pascal = 1 Newton per square metre • Pressure and Stress have the same units 1 MPa = 1 N/mm2 • Strain has no dimensions. It is expressed as a percentage or in microstrain (s). • A strain of 1 s is an extension of one part per million. A strain of 0.2% is equal to 2000 s

20. Measuring: Strain = extension/length

21. Elastic and Plastic deformation Stress Stress Strain Strain Permanent Deformation Plastic deformation Elastic deformation

22. Stress-Strain curve for steel Yield Plastic 0.2% proof stress Failure Elastic Stress 0.2% Strain

23. Steel Test in Laboratory

24. Energy absorbed Stress (force) Area = average stress  final strain = Energy absorbed = work done Strain (distance) Final strain

25. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

26. Modulus of Elasticity If the strain is "elastic" Hooke's law may be used to define Young's modulus is also called the modulus of elasticity or stiffness and is a measure of how much strain occurs due to a given stress. Because strain is dimensionless Young's modulus has the units of stress or pressure

27. Measuring modulus of elasticity

28. Initial Tangent and Secant Modulus

29. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

30. Flexural Strength Load W d=depth Compression region Tension region b=breadth Span L deflection x

31. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

32. Fatigue Failure Stress Strain

33. 1.2 STRENGTH OF MATERIALS • 1.2.1 Mass and Gravity • 1.2.2 Stress and strength • 1.2.3 Strain • 1.2.4 Modulus of Elasticity • 1.2.5 Flexural loads • 1.2.6 Fatigue Strength • 1.2.7 Poisson's ratio • 1.2.8 Creep

34. Poisson’s Ratio • This is a measure of the amount by which a solid "spreads out sideways" under the action of a load from above. It is defined as: (lateral strain) / (vertical strain) and is dimensionless. • Note that a material like timber which has a "grain direction" will have a number of different Poisson's ratios corresponding to loading and deformation in different directions.

35. Yield Plastic 0.2% proof stress Failure Stress Strain 0.2% How to calculate deflection if the proof stress is applied and then partially removed.If a sample is loaded up to the 0.2% proof stress and then unloaded to a stress s the strain x = 0.2% + s/E where E is the Young’s modulus s 0.002 s/E