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Strengths Chapter 11 Mechanical Properties of Materials

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Tension Test Most common used test for metals and ductile materials Universal testing machine used Can also test compression Shear Bending Round specimen made to ASTM spec clamp into machine The tensile force P acting on the specimen at any time during the test is indicated The corresponding change in length between two marks is recorded Corresponding values of stress versus strain can be calculated.

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Stress – Strain diagram Graphical representation of the tension test Elastic Stage – straight line to the proportional limit (stress proportional to strain) Deformation is consider elastic in this range – means specimen will return to its initial size and shape Beyond elastic limit only part of the deformation can be recovered – deformation after becomes permanent – called plastic deformation. Yield Stage – curve becomes horizontal – specimen continues to elongate without any significant increase in load Strain hardening stage – ability of the material to resist deformation is regained after the yield stage has passed Modulus of elasticity – figure 11-5 page 389 Example 11-1 page 390

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Mechanical Properties of Materials Strength – greatest stress that it can withstand without failure Stiffness – ability of material to resist deformation Elasticity – property of material that enables it to regain its original unreformed length once the load is removed Ductility – ability of material to undergo a lot of plastic deformation before rupture Brittleness – undergoes very little plastic deformation before rupture is said to be brittle Hardness – the resistance of a material to penetration Machinability – the ease with which a material can be machined Resilience – capacity of a material to absorb energy within the elastic range Toughness – capacity of a material to absorb energy without fracture

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Allowable stresses and factor of safety To provide margin of safety in design, machine and structural members are designed for a limited stress level – called the allowable stress – which is the maximum stress considered to be safe when a member made of a given material is subjected to a known loading condition Formula = 11-5, 11-6 Elastic design with ductile materials significant deformation may occur and render the structural element unusable when the yield strength is reached A factor of safety of 2 means that the member can withstand a maximum load equal to twice the load for which the member is designed before failure Choosing appropriate value for the factor of safety depends on Variation in material properties Uncertainty in the method of analysis Problems in manufacturing Environmental conditions Uncertainty in loading conditions Risk and liability

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Allowable stresses and factor of safety Example 11-2 Example 11-3

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Stress Concentrations When an axially loaded subjected to central axial tension or compression the normal stress is unifromly distributed in the cross section Stress raisers in flat axially loaded members and the resulting stress distributions can change this equation Stress is concentration adjacent to the stress raiser Stress may be several times greater then the average stress over the net cross sectional area The max stress is called the stress concentration The max stress vs the average stress is called the stress concentration factor Examples –figure 398 11-10 Examples 11-4 Examples 11-5

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Elastic Design Versus Plastic Design Up to this point design of axially loaded members based on allowable stress – allowable stress design Elastic design – assumes that once a material starts to yield it can no longer carry any additional load Elastoplastic materials – highly ductile metals – hooke law is valid up to the yield point – once yield point is reached the stress and the stress strain diagram can be modeled – a material is considered elastoplastic Maximum plastic load is reached when every point in the section has yield Another design approach assumes that failure will not occur until every point in a critical section has yielded – called ultimate strength design Example 11-6 Example 11-7

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