Stress and Strain. Deforming Solids  Solids deform when they are subject to forces. Compressed, stretched, bent, twistedCompressed, stretched, bent,

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Presentation transcript:

Stress and Strain

Deforming Solids  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 shape

Linearly Elastic  For small deformations, solids follow Hooke’s law.  The ratio of the force to the displacement is the spring constant (k). xx F

Stress  A force on a solid acts on an area.  For compression or tension, the stress  is the ratio of the force to the cross sectional area.  Units are Pa, like pressure. F A

Stiletto Heels  A 60 kg woman takes off a shoe with an area of 130 cm 2 and puts on a spiked heel with an area of 0.8 cm 2.  What stress is placed on the floor?  The force is due to weight, about 600 N.  The stress with regular shoes is 600 N / m 2 = 46 kN/m 2.  The stress with spiked heels is 600 N/ m 2 = 7.5 MN/m 2.  For comparison that is an increase of from about 7 psi to over 1000 psi!

Strain  Deformation is relative to the size of an object.  The displacement compared to the length is the strain . LL L

Shear Force  Displacement of a solid can follow the surface of a solid.  This is due a shear force.  One can measure a shear stress  s and a shear strain  s. F xx A (goes into screen) L

Volume Stress  Pressure from all sides can change the volume of a solid.  There is a volume stress and volume strain. next P VV V A (surface area)