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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, load...
Failure of machine partsThere are two types:Functional   failureFracture   failure
Failure of machine parts Functional     failure   e.g. Excessive deflection of shaft   Noise, decrease in efficiency, inc...
Fracture failure Excessive   stress  –Tensile  –Shear  –Combined stress  –Fatigue  –Crack  –Stress concentration  Excessi...
Load: A component subjected to a single  load implies: • A transverse force in the case of a   beam component, • A longitu...
Expressions of the load:   The actual load, extrinsic,:    is the load exerted on the component by its    surrounds, andT...
Factor of safety • Uncertainty about the actual   load. • Uncertainty about the   maximum allowable load
Uncertainty about the actual loadThe inherent variability of the load  (e.g. in practice the mass of a "ten tonne truck" ...
Inherited Variability of Actual Load            25Frequency            20            15            10            5        ...
Dynamic magnification factor Elementary energy methods give    dmf = [ 1+ ( 1 + 2hk/W)1/2 ]                              ...
Uncertainity about the maximum allowable                   load  dimensions   differing from their   nominal or expected ...
Factor of safety (fs)=                          Maximum   allowable   load                               Actual loadIt fol...
Suggested Safety (design) Factors for Elementary Work           For exceptionally reliable materials used under controllab...
Impact forces : the factors given in items 3 to 6 areacceptable, but an impact factor (the above dynamicmagnification fact...
Important points :Loads    not known for certainty : Increase factor of safety e.g for shock loads; obtain a realistic dm...
Stress concentration  Sudden change of cross-section        F                            F Presence of a hole           ...
Stress concentration on gears                                 Low                                stress               High...
Stress concentration near a hole                                     So                                          o        ...
Hole            F                             F    Stresses are low where the streamlines are widely    spaced.   Stress...
Estimation of Stress Concentration Factor:Form factor (K)                                           S =F/(b          - d)h...
The stress concentration factor (K’).                         K  = 1 + q(K -1)     Where q: index of sensitivity of the m...
For repeated loads                                                      Index of sensitivity               Material       ...
Theories of Failures  Failureof a tensile member occurs   when the stress reaches the stress   limit  How  can we correl...
Theories of failure1. Maximum Normal Stress theory (Rankine):      S1= Sy    Hold well for brittle materials2. Maximum str...
Theories of failure  1. Shear energy theory (Von Mises):                      2        2                  S       3S   s  ...
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CHAPTER #1 Load stress and_failure
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CHAPTER #1 Load stress and_failure

CHAPTER #1 Load stress and_failure

  1. 1. Load, Stress and Failure
  2. 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. 3. Failure of machine partsThere are two types:Functional failureFracture failure
  4. 4. Failure of machine parts Functional failure e.g. Excessive deflection of shaft Noise, decrease in efficiency, increase in heat generationFunctional failure could be as a result of: Deformation Wear corrosion
  5. 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. 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. 7. Expressions of the load: The actual load, extrinsic,: is the load exerted on the component by its surrounds, andThe 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. 8. Factor of safety • Uncertainty about the actual load. • Uncertainty about the maximum allowable load
  9. 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 its 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. 10. Inherited Variability of Actual Load 25Frequency 20 15 10 5 0 900 925 950 975 1000 1025 Actual Load
  11. 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. 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. 13. Factor of safety (fs)= Maximum allowable load Actual loadIt follows that :if fs = 1 then the component is on the point of failureif fs < 1 then the component is in a failed stateif fs > 1 then the component is safe
  14. 14. Suggested Safety (design) Factors for Elementary Work For exceptionally reliable materials used under controllable1.25 - 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 mustbe applied to the endurance limit rather than to the yield strength of thematerial.
  15. 15. Impact forces : the factors given in items 3 to 6 areacceptable, but an impact factor (the above dynamicmagnification factor) should be included.Brittle materials : where the ultimate strength is usedas the theoretical maximum, the factors presented initems 1 to 6 should be approximately doubled.Where higher factors might appear desirable, a morethorough analysis of the problem should beundertaken before deciding on their use.
  16. 16. 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
  17. 17. Stress concentration Sudden change of cross-section F F Presence of a hole Hole F F
  18. 18. Stress concentration on gears Low stress High stress
  19. 19. Stress concentration near a hole So o 3So So 1 2 3 4d d
  20. 20. 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
  21. 21. 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
  22. 22. 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 sensitivityDuctile material 0 Ductile and very soft 0.4 materialBrittle material, hardened 0.1 steel Ductile material 0.61Very brittle material, 0.2 Brittle material, hardened 1quenched steel steel Cast iron 0.5Cast iron 0
  23. 23. For repeated loads Index of sensitivity Material Heat treated Heat treated Annealed and drawn at and drawn at or soft 12000 F 9000 FArmco 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 0.450.30% C 0.26 0.40 0.500.50% C ….. 0.45 0.570.85% CSpring 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 ….. …..
  24. 24. 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
  25. 25. Theories of failure1. Maximum Normal Stress theory (Rankine): S1= Sy Hold well for brittle materials2. 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 five3. Maximum Shear Stress Theory (Guest-Tresca): ½(S1 – S2) = ½ Sy Sy= S1-S2 Holds well for ductile materials
  26. 26. Theories of failure 1. Shear energy theory (Von Mises): 2 2 S 3S s Se Hold well for ductile materials
  27. 27. Thank You

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