Stress and StrainDeforming SolidsLinearly ElasticStressStiletto HeelsStrainShear ForceVolume StressStress and StrainStress and StrainDeforming SolidsDeforming SolidsSolids deform when they are subject to forces.Solids deform when they are subject to forces.•Compressed, stretched, bent, twistedCompressed, stretched, bent, twisted•They can maintain or lose their shapeThey can maintain or lose their shapeLinearly ElasticLinearly ElasticFor small deformations, For small deformations, solids follow Hooke’s law.solids follow Hooke’s law.The ratio of the force to the The ratio of the force to the displacement is the spring displacement is the spring constant (constant (kk).).xF xkF xFStressStressA force on a solid acts on an A force on a solid acts on an area.area.For compression or tension, For compression or tension, the stress the stress is the ratio of the is the ratio of the force to the cross sectional force to the cross sectional area.area.Units are Pa, like pressure.Units are Pa, like pressure.AFFAStiletto HeelsStiletto HeelsA 60 kg woman takes off a A 60 kg woman takes off a shoe with an area of 130 cmshoe with an area of 130 cm22 and puts on a spiked heel and puts on a spiked heel with an area of 0.8 cmwith an area of 0.8 cm22..What stress is placed on the What stress is placed on the floor?floor?The force is due to weight, The force is due to weight, about 600 N.about 600 N.The stress with regular The stress with regular shoes is 600 N / 0.013 mshoes is 600 N / 0.013 m22 = = 46 kN/m46 kN/m22..The stress with spiked heels The stress with spiked heels is 600 N/0.00008 mis 600 N/0.00008 m22 = 7.5 = 7.5 MN/mMN/m22..For comparison that is an For comparison that is an increase of from about 7 psi increase of from about 7 psi to over 1000 psi!to over 1000 psi!StrainStrainDeformation is relative to the Deformation is relative to the size of an object.size of an object.The displacement compared The displacement compared to the length is the to the length is the strainstrain ..LLLLShear ForceShear ForceDisplacement of a solid can Displacement of a solid can follow the surface of a solid.follow the surface of a solid.This is due a shear force.This is due a shear force.One can measure a shear One can measure a shear stress stress ss and a shear strain and a shear strain ss..F xA (goes into screen)LLxsAFsVolume StressVolume StressPressure from all sides can Pressure from all sides can change the volume of a change the volume of a solid.solid.There is a volume stress and There is a volume stress and volume strain.volume strain.nextPVVPAFVA (surface
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