The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. Determine the displacement of end A with respect to end D and the normal stress in each section. The cross-sectional area and modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C.
CHAPTER 1 CONCEPT OF ENERGY Macroscopic: Things we can see - (Classical Thermodynamics) Microscopic: Statistical Thermodynamics – (Energy being quantized) A Microscopic amount of mass can present energy in the following forms: - Internal – internal structure - Kinetic Energy-Related to motion - Potential Energy-External forces acting on this mass - Rotational Energy-Rotational force TotalEnergy=I+KE+PE+ℜ=U+KE+PE+ℜ Dividingbymassgivesus:e=E /m=u+ke+pe+ℜ=u+1/2v +gh+1/2I ꙍ 2 ¿ Internal Energy (macroscale)-similar set of energies (associated with macroscale motion of individual molecules .U=U external molectranslatio∫molecule Where: U externalmoleculeermolecular forces (PE sum) U translationKE of molecule) U molecule Internal/atomic structure ∫ But there is a difference between intermolecular forces High Density (ρ) =close spacing = high Low Density (ρ) =loose spacing = weak molecular interaction molecular interaction U ≈0 In the limit of a very low ρ (rarified gas) => ext - No external forces, molecules are too far apart, so the forces are little between them - Ex: leaving the earth’s atmosphere Translated Energy depends only on mass & velocity of center of mass of the molecule Internal Energy depends on the molecules internal structure We rewrite the energy eqn: .U=U molecule rotationvibrationatoms ∫ There are three principal vibration modes of the H2O molecule While we ev