المادة: مقاومة المواد sub.: strength of materials

1. جامعة الكوفة – كلية الهندسة –قسم المنشات و الموارد المائيةالمرحلة الثانيةuniversity of Kufa – College of engineering –structures and water resources department2nd class. • المادة: مقاومة المواد sub.: strength of materials الهدف من المحاضرة : التعرف على موضوع مقاومة المواد-الجزء2 Aim of the lecture: To understand the strength of materials concept- part2

2. 1.2 STRENGTH OF MATERIALSsubject which concerned with the behaviour and calculations of the response of the bodies subjected to external loads. • 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

3. 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

4. 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

5. 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.

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

7. Tension and Compression

8. Structures lab

9. Testing for strength

10. Applying Loads

11. 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:

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

13. Measuring: Stress = Load/area

14. 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:

15. Shear stress Area resisting shear Shear Force Shear force

16. 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 : 

17. 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

18. 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

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

20. 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

21. Measuring: Strain = extension/length

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

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

24. Steel Test in Laboratory

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

26. 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

27. 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

28. Measuring modulus of elasticity

29. Initial Tangent and Secant Modulus

30. 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

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

32. 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

33. Fatigue Failure Stress Strain

34. 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

35. 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.

36. 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

37. Conclusion: When the loads (forces) applied at any body their were resistance to theses force called strength of the body material (stress) and their were a deformation happened due to these loads called (strain) , the both subject are explained in our lecture with their types, examples, and calculations. 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

38. Now we are waiting your questions , notes , misunderstanding , and opinions about the subject or it’s applications in different fields especially most engineering analysis and design depend on our current subject, also in next lecture we take more mathematical examples to explain the concepts and applications.

39. المصادر : references 1- R.C. Hibbeler “ Mechanics of materials “ 8th edition , 2011 2- F. L. Singer “ strength of materials “ 10th edition , 2008 3- Pete Claisse “ lectures in strength of materials concepts “ 2010 4- محاضرات مقومة المواد لجامعة بابل للأستاذ عبد الرضا محمد 1992