Strengths

1. Strengths Chapter 11 Mechanical Properties of Materials

2. 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.

3. 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

4. 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

5. 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

6. Allowable stresses and factor of safety • Example 11-2 • Example 11-3

7. 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

8. 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