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CHAPTER #1 Load stress and_failure

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Load, Stress and Failure
Design Basic Selection
 Mechanism
 Depends on the purposes of the machine

 Materials
 Depends on the shape of the part, loading and operation
 (corrosion & wear resistance … etc)

 Stresses
  Requires a working knowledge of the materials

 Cost
 Is always an important factor
Failure of machine parts

There are two types:
Functional   failure
Fracture   failure
Failure of machine parts
 Functional     failure
   e.g. Excessive deflection of shaft
   Noise, decrease in efficiency, increase in
   heat generation
Functional failure could be as a result of:
     Deformation
     Wear
     corrosion
Fracture failure
 Excessive   stress
  –Tensile
  –Shear
  –Combined stress
  –Fatigue
  –Crack
  –Stress concentration
  Excessive stress results of high load
  or low allowable material properties
  or dimensions
Load:
 A component subjected to a single
  load implies:
 • A transverse force in the case of a
   beam component,
 • A longitudinal compressive force in
   a column,
 • A torque in the case of a shaft,
 • A pressure in a fluid containment
   vessel, and so on
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CHAPTER #1 Load stress and_failure

  • 2. Design Basic Selection  Mechanism Depends on the purposes of the machine  Materials Depends on the shape of the part, loading and operation (corrosion & wear resistance … etc)  Stresses Requires a working knowledge of the materials  Cost Is always an important factor
  • 3. Failure of machine parts There are two types: Functional failure Fracture failure
  • 4. Failure of machine parts  Functional failure e.g. Excessive deflection of shaft Noise, decrease in efficiency, increase in heat generation Functional failure could be as a result of: Deformation Wear corrosion
  • 5. Fracture failure  Excessive stress –Tensile –Shear –Combined stress –Fatigue –Crack –Stress concentration Excessive stress results of high load or low allowable material properties or dimensions
  • 6. Load: A component subjected to a single load implies: • A transverse force in the case of a beam component, • A longitudinal compressive force in a column, • A torque in the case of a shaft, • A pressure in a fluid containment vessel, and so on
  • 7. Expressions of the load:  The actual load, extrinsic,: is the load exerted on the component by its surrounds, and The maximum load, intrinsic,: is the largest load that the component can withstand without failure;  The maximum load is a property of the component, a function of its dimensions and material properties
  • 8. Factor of safety • Uncertainty about the actual load. • Uncertainty about the maximum allowable load
  • 9. Uncertainty about the actual load The inherent variability of the load (e.g. in practice the mass of a "ten tonne truck" will depend on the load it's carrying), Static indeterminacy (when components share the load in proportion to their elastic responses), Dynamic (or shock) effects If a weight W is dropped from a height h onto an elastic component of stiffness k, , then the peak force in the component is = dynamic magnification factor (dmf) * W
  • 10. Inherited Variability of Actual Load 25 Frequency 20 15 10 5 0 900 925 950 975 1000 1025 Actual Load
  • 11. Dynamic magnification factor  Elementary energy methods give dmf = [ 1+ ( 1 + 2hk/W)1/2 ] W The effective actual load is h at least twice its nominal or supposed value k
  • 12. Uncertainity about the maximum allowable load  dimensions differing from their nominal or expected values  material strength differing from its nominal value due in turn to – variations in material composition – variation in heat treatment, – unsuspected flaws
  • 13. Factor of safety (fs)= Maximum allowable load Actual load It follows that : if fs = 1 then the component is on the point of failure if fs < 1 then the component is in a failed state if fs > 1 then the component is safe
  • 15. Suggested Safety (design) Factors for Elementary Work For exceptionally reliable materials used under controllable 1.25 - 1.5 conditions and subjected to loads and stresses that can be determined with certainty - used where low weight is very important consideration 1.5 - 2 For well-known materials under reasonably constant environmental conditions, subjected to loads and stresses that can be determined readily. 2 - 2.5 For average materials operated in ordinary environments and subjected to loads and stresses that can be determined. 2.5 - 3 For less tried materials or for brittle materials under average conditions of environment, load and stress. 3-4 For untried materials used under average conditions of environment, load and stress. 3-4 Should also be used with better-known materials that are to be used in uncertain environments or subject to uncertain stresses. Repeated loads : the factors established in items 1 to 6 are acceptable but must be applied to the endurance limit rather than to the yield strength of the material.
  • 16. Impact forces : the factors given in items 3 to 6 are acceptable, but an impact factor (the above dynamic magnification factor) should be included. Brittle materials : where the ultimate strength is used as the theoretical maximum, the factors presented in items 1 to 6 should be approximately doubled. Where higher factors might appear desirable, a more thorough analysis of the problem should be undertaken before deciding on their use.
  • 17. Important points : Loads not known for certainty : Increase factor of safety e.g for shock loads; obtain a realistic dmf .. search internet, other sources Employ reasonable accurate mathematical models rather than using simple models Design factors are increased also when the consequences of failure are serious Economic, social, environmental or political e.g. the headwaters of a remote River, doubled the size of every motor predicted
  • 18. Stress concentration Sudden change of cross-section F F Presence of a hole Hole F F
  • 19. Stress concentration on gears Low stress High stress
  • 20. Stress concentration near a hole So o 3So So 1 2 3 4d d
  • 21. Hole F F  Stresses are low where the streamlines are widely spaced.  Stresses are high where the streamlines are bunched together due to geometric shape variations  The more sudden these variations, the higher the local stresses.  This last is known as stress concentration.  Geometric irregularities give rise to non-uniform stresses
  • 22. Estimation of Stress Concentration Factor: Form factor (K) S =F/(b - d)h 3 F F factor K b d 2.5 o h Form stress 2 1.5 1 0 0.2 0.4 0.6 0.8 Ratio d/b Form stress factor due to hole in narrow plate
  • 23. The stress concentration factor (K’). K ' = 1 + q(K -1)  Where q: index of sensitivity of the material Static loads: Impact load Material Index of Material Index of sensitivity sensitivity Ductile material 0 Ductile and very soft 0.4 material Brittle material, hardened 0.1 steel Ductile material 0.61 Very brittle material, 0.2 Brittle material, hardened 1 quenched steel steel Cast iron 0.5 Cast iron 0
  • 24. For repeated loads Index of sensitivity Material Heat treated Heat treated Annealed and drawn at and drawn at or soft 12000 F 9000 F Armco iron, 0.02% C 0.15 0.20 ….. ….. Carbon steel 0.05 – 0.10 ….. ….. 0.10% C 0.10 ….. ….. 0.20% C (also cast steel) 0.18 0.35 0.45 0.30% C 0.26 0.40 0.50 0.50% C ….. 0.45 0.57 0.85% C Spring steel, 0.56% C, 2.3 Si rolled …. 0.38 …. SAE 3140, 0.37 C, 0.6 Cr, 1.3 Ni 0.25 0.45 …. Cr-Ni steel 0.8 Cr, 3.5 Ni ….. 0.25 ….. Stainless steel, 0.3 C, 8.3 cr, 19.7 Ni 0.16 ….. …… Cast iron 0 – 0.05 ….. ….. Copper, electrolite 0.07 ….. ….. Duraluminum 0.05 – 0.13 ….. …..
  • 25. Theories of Failures  Failureof a tensile member occurs when the stress reaches the stress limit  How can we correlate the triaxial stress state in a component –  Material strength(s) is measured in uniaxial tests
  • 26. Theories of failure 1. Maximum Normal Stress theory (Rankine): S1= Sy Hold well for brittle materials 2. Maximum strain Theory (Saint Venant ): 2 2 0 . 35 0 . 65 S 4S s Se It holds well for ductile materials. It is the best of five 3. Maximum Shear Stress Theory (Guest-Tresca): ½(S1 – S2) = ½ Sy Sy= S1-S2 Holds well for ductile materials
  • 27. Theories of failure 1. Shear energy theory (Von Mises): 2 2 S 3S s Se Hold well for ductile materials