CHAPTER 11 STRAIN ENERGY Summary The energy stored within a material when work has been done on it is termed the strain energy or resilience, i.e. strain energy work done In general there are four types of loading which can be applied to a material: 1.Direct load (tension or compression) CP2ds P2L Strain energy U= 2AE or 2AE o2AL a2 2E=2E :×volume of bar 2.Shear load fo2ds 02L Strain energy U= 2AG or 2AG 2G×AL= 2G x volume of bar 3.Bending M2ds M2L Strain energy U= or 2EI 2EI if M is constant 4.Torsion "T2ds T2L Strain energy U= or 2GJ 2GJ if T is constant From 1 above,the strain energy or resilience when the tensile stress reaches the proof stress p,i.e.the proof resilience,is x volume of bar 2E and the modulus of resilience is 2E The strain energy per unit volume of a three-dimensional principal stress system is 1 U=2E[oi+吃+号-2w(o102+a203+031】 254CHAPTER 11 STRAIN ENERGY Summary The energy stored within a material when work has been done on it is termed the strain energy or resilience, i.e. strain energy = work done In general there are four types of loading which can be applied to a material: 1. Direct load (tension or compression) 1% P2 L or - 2 AE Strain energy U = O~AL a2 =-- -- x volume of bar 2E 2E 2. Shear load j‘g or - QZL 2 AG Strain energy U = 72 T2 2G 2G Strain energy U = 1:; - or - if M is constant = - x AL = - x volume of bar 3. Bending M2L 2 EZ 4. Torsion if T is constant 1; T2L or - 2GJ Strain energy U = - From 1 above, the strain energy or resilience when the tensile stress reaches the proof stress ap, i.e. the proof resilience, is - 4 x volume of bar 2E and the modulus of resilience is - 0; 2E The strain energy per unit volume of a three-dimensional principal stress system is 1 2E U =--a:+a 254