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- 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
- 28. Thank You