BME

1. BME For more info. : www.goodwisher.com

2. Syllabus(ME-101-F) • Section-A • Introduction to machine tools • Basic Concepts of thermodynamics • Properties of steam & steam generators • Section-B • Refrigeration & Air conditioning. • Hydraulic turbines & pumps. • Section-C • Power transmission methods & devices • Stresses & strains • Section-D • Introduction to manufacturing system(NC & CNC Machining) For more info. : www.goodwisher.com

3. Topics • Introduction, Concept & types of Stresses and strains, • Poison’s ratio • Stresses and strains in simple and compound bars • Stress- strain diagrams, • Hooks law, • Elastic constants & their relationships. For more info. : www.goodwisher.com

4. Section-C(ii) • Strength:-Maximum Resistance that a material can offer to externally applied forces. • Stress:-when some external forces are applied to the body, then the body offers resistance to forces. This internal resisting force per unit area is called stress. For more info. : www.goodwisher.com

5. Types of stresses ENGG. stress TRUE stress Tensile stress compressive stress SHEAR stress For more info. : www.goodwisher.com

6. TENSILE STRESS • A Structural member is said to be in tension, when it is subjected to two equal & opposite pulls & member tends to increase its length. • Where, is the tensile stress P is the pull or force A is the area of crossection. • Example)Hoisting ropes used in cranes & passenger elevators are elements subjected to tensile stress. P P For more info. : www.goodwisher.com

7. COMPRESSIVE STRESS • A Structural member is said to be in compression, when it is subjected to two equal & opposite pushes & member tends to decrease its length. • Where, • is the compressive stress P is the push or force A is the area of crossection. P P For more info. : www.goodwisher.com

8. Shear stress • When a body is subjected to the type of forces such that it shear off the section is called shear stress.It is denoted by Ԏ • Ԏ= For more info. : www.goodwisher.com

9. CONVENTIONAL OR ENGG. STRESS • IT Can be defined as the ratio of load to origionalcrosssection. • = • Where is the conventional or engg. Stress • P is the load • Ao is the origional area of crossection. For more info. : www.goodwisher.com

10. True Stress • It is the ratio of load to the instantaneous area of crossection. • Where P is the load A is the instantaneous area. For more info. : www.goodwisher.com

11. Problem • To prove that :- = SOLUTION:- X= For more info. : www.goodwisher.com

12. STRAIN • Whenever a body is acted upon by tensile or compressive loading,its dimensions will increase or decrease. • This deformation (change in dimension) per origional dimension is called strain. • If deformation is change in length,then it is called primary strain or longitudnal strain. • £== For more info. : www.goodwisher.com

13. Types of strain ENGG. strain TRUE strain Tensile strain compressive strain SHEAR strain VOLUMETRIC strain For more info. : www.goodwisher.com

14. Tensile strain • Strain produced due to tensile stress is called tensile strain. • £= For more info. : www.goodwisher.com

15. Compressive strain • Strain produced due to compressive stress is called tensile strain. • £= For more info. : www.goodwisher.com

16. Shear strain • Strain produced under the action of shear stress,Measured by change of angle. For more info. : www.goodwisher.com

17. Volumetric strain • If A Uniform stress is applied on all 3 faces ,then it changes its volume.Thus,it changes its volume. • £= For more info. : www.goodwisher.com

18. CONVENTIONAL OR ENGG.STRAIN • IT can be defined as change in length per unit length. • £=⨜ For more info. : www.goodwisher.com

19. Natural STRAIN • IT can be defined as change in length per unit Instantaneous length. For more info. : www.goodwisher.com

20. 2.Poisson’s Ratio • The strain in the direction of applied load is calledlongitudnal or primary strain. • The strain produced in the perpendicular direction to the applied load is called lateral or secondary strain. • When the deformation of the bar is within elastic limit, the ratio of lateral strain to longitudnal strain. • It is denoted by µ. • µ = For more info. : www.goodwisher.com

21. HOOKE’S LAW • The loading limit under which the deformation entirely dissapears on removal of load is called ELASTIC LIMIT. • Hooke’s law states that, when a material is loaded within the elastic limit , Stress is directly proportional to Strain. • Stress ἀ strain • ἀἐ • ἐ • Where, E is a constant known as modulus of elasticity or young’s modulus. For more info. : www.goodwisher.com

22. Stress-Strain Diagram/Curve • Stress-Strain Curve is a graphical plot of stress-versus-strain. • These quantities are experimentally obtained by subjecting a metallic bar of uniform crossection to a gradually increasing tensile load till failure of bar occurs. • The test is conducted on a tensile testing machine on a test specimen as shown. P P Gauge length For more info. : www.goodwisher.com

23. Stress-Strain Curve(Contd…) E STRESS C B F A A:Proptional limit B:Elastic limit C,D:Upper & lower yield Point. E:Ultimate stress Point F:Breaking Point D O STRAIN For more info. : www.goodwisher.com

24. Stress-Strain Curve(Contd….) • Propotional limit:-Stress is a linear function of srain & material obeys hooke’slaw.Theproportionality extends upto point A & this point is called proportional limit. O-A is a straight line portin of the curve. • Elastic limit:-Beyond proportional limit,sress & strain departs from straight line.Material remains elastic upto state ‘B’. Upto point B,deformation is recoverable.Stress at point B represents is called elastic limit stress. • Yield Point:- Beyond point B, material shows consideral strain; the strain is not fully recoverable i.e there is no tendency to return to origionalposition.Point C is called upper yield point & Point D is called lower yield point. For more info. : www.goodwisher.com

25. Stress-Strain Curve(Contd….) • Ultimate Strength or tensile strength:-After Yielding has taken place, the material becomes strain hardened & an increase in load is required to take the material to its maximum stress at a point E . • Breaking Stress:-In the portion EF, there is a falling off the load from maximum until fracture takes place at F. For more info. : www.goodwisher.com

26. Stress-Strain curve for material other than mild steel, ex:Aluminium,copper stress strain For more info. : www.goodwisher.com

27. Stress-strain curve for brittle materialex: CAST IRON stress BREAKING POINT strain For more info. : www.goodwisher.com

28. Elastic Constants • Modulus of elasticity(E) • Modulus of Rigidity(G) • BULK Modulus (K) The above three are called ELASTIC CONSTANTS. For more info. : www.goodwisher.com

29. Modulus of elasticity(E) • It is the ratio of stress to the strain. • E= • It’s unit is N/m2 For more info. : www.goodwisher.com

30. Modulus of Rigidity(G or C) • It is the ratio of shear stress & shear strain. • G or C = • UNITS-N/m2 For more info. : www.goodwisher.com

31. BULK MODULUS(K) • It is the ratio of stress to the volumetric strain. • K= For more info. : www.goodwisher.com

32. Relations between elastic constants • E=3K(1-2 µ) (Relation b/n E & K) • E=2G(1+ µ) (Relation b/n E & G) • E= (Relation b/n E,K & G) For more info. : www.goodwisher.com

33. Relation b/n E & K Y X Z For more info. : www.goodwisher.com

34. Relation b/n E& K(Contd…..) • Strain in x-direction= Strain in x-direction-strain in x direction due to –strain in x-direction due to = µ µ But,== = µ µ For more info. : www.goodwisher.com

35. Relation b/n E& K(Contd…..) = 2µ) Similarly,= 2µ) = 2µ) Volumetric strain=++=3 2µ) For more info. : www.goodwisher.com

36. Relation b/n E& K(Contd…..) • BULK MODULUS(K)= • K= K= E=3K(1-2) For more info. : www.goodwisher.com

37. Relation b/n E & G D D’ C C’ E 45 45 A B For more info. : www.goodwisher.com

38. Relation b/n E & G(Contd….) • Longitudinal strain in the diagonal AC = == Since, the extension CC’ is small,<AC’B can be assumed to be equal to <ACB,which is 45o. EC’=CC’cos45= 1 2 For more info. : www.goodwisher.com

39. Relation b/n E & G(Contd….) • From 2,put in 1 • Longitudinal strain in the diagonal AC == But, AC=BC • Longitudinal strain in the diagonal AC ==== 3 For more info. : www.goodwisher.com

40. Relation b/n E & G(Contd….) • From traingle, BCC’: • tan= • Put in eq-3: • Longitudinal strain in diagonal AC= • But, tan(deformation is very small) • Longitudinal strain in diagonal AC= For more info. : www.goodwisher.com

41. Relation b/n E & G(Contd….) • According to defination of shear strain: • = • Longitudinal Strain in diagonal AC= 4 For more info. : www.goodwisher.com

42. Relation b/n E & G(Contd….) • Strain in diagonal AC is also given by: =Strain due to tensile stress in AC-Strain due to compressive stress in BD. =) =(1+) 5 For more info. : www.goodwisher.com

43. Relation b/n E & G(Contd….) • From 4 & 5: • =(1+) • E=2G(1+) For more info. : www.goodwisher.com

44. Relation b/n E,K & G • E=3K(1-2 µ)--------------------(i) • E=2G(1+ µ)--------------------(ii) • From (ii) • µ=) • Put in (i) • E=3K[1-2 ()] For more info. : www.goodwisher.com

45. Relation b/n E,K & G(Contd….) • E=3K[1-2 ()] • E=3K(1- • E=3K(3 - ) • E=9K- • E+=9K For more info. : www.goodwisher.com

46. Relation b/n E,K & G(Contd….) • E+K • =9K • =9K • E(G+3K)=9KG • E= For more info. : www.goodwisher.com

47. Stresses & strains in Simple Bars • Extension of uniform section. • Extension of conical bar(Assignment) • Stresses in the bars of varying cross-section. • Stresses in the composite bars. For more info. : www.goodwisher.com

48. Extension of bar due to self weight Let w be the weight per unit volume. LOAD is given by: P=wAy ==dy = =x= dy l y For more info. : www.goodwisher.com

49. Stresses in the bars of varying cross-section. A1E1 A2E2 A3E3 P P l2 l3 l1 For more info. : www.goodwisher.com

50. Stresses in the bars of varying cross-section.(Contd….) • For such bar, the following condition applies:- • Each section is subjected to same external pull • Total change in length is equal to the sum of changes of individual lengths • P1=P2=P3=P For more info. : www.goodwisher.com