Work and Energy under a Single Load: Strain energy may be found from the work of other types ofsingle concentrated loadsTransverseload: Bending Moment: Twisting MomentPIy1BB01PANdy=PyW=[Mde=}M,NTdp=ToMLPLML()T2LU=IMU=PU=TGI.EI2EI2GI6EI16
• Strain energy may be found from the work of other types of single concentrated loads. • Transverse load 1 1 2 1 1 0 3 2 3 1 1 1 2 1 3 6 y W P dy P y PL P L U P EI EI • Bending Moment 1 1 2 1 1 0 2 1 1 1 2 1 2 W M d M M L M L U M EI EI 1 1 2 1 1 0 2 1 1 1 2 1 2 p p W T d T T L T L U T GI GI • Twisting Moment 16 Work and Energy under a Single Load
Strain Energy cannot be Superposed·Asolid circularbar isfixed at oneendandfreeatBTtheother.Threedifferentloading conditionsaretobe considered.For each case of loading, obtain aformula for the strain energy stored in the bar.(a)T?LU2GI,CThBT? (L/2) ,_T?L2GI,4GI,(T. +T, ) (L/2)_T?LT,T,LT,LT (L/2)(b)2GI,2GI,2GI,2GI,4GI,. The strain energy produced by the two loadsThCBTacting simultaneously is not equal to the sumof the strain energies produced by the loadsL22acting separately(C). Strain energy is a quadratic function of theloads, not a linear function17
• The strain energy produced by the two loads acting simultaneously is not equal to the sum of the strain energies produced by the loads acting separately. • Strain energy is a quadratic function of the loads, not a linear function. • A solid circular bar is fixed at one end and free at the other. Three different loading conditions are to be considered. For each case of loading, obtain a formula for the strain energy stored in the bar. Strain Energy cannot be Superposed 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 4 2 a a p b b b p p a a b a b a c p p p p p b T L U GI T L T L U GI GI T L T T L T L T L U GI GI GI T T L GI GI 17