C05_stationary potential energy

Chapter 5 Applications of

Energy Methods

5.1 Principle of stationary potential energy

1 1 UEME2163 Solid Mechanics II

5.1 Principle of stationary

potential energy


Vanish: System is in

equilibrium

5.1 Principle of stationary potential energy


Example 5.1 Equilibrium of a linear elastic two-bar

system



Solution

5.2 Castiglinos theorem on deflections


Example 5.2 Equilibrium of a nonlinear elastic two-

bar system



Solution

5.2 Castiglianos theorem on deflections for linear load-deflection

relations


5.3.1 Strain energy UN for axial

loading


5.3.1 Strain energy UN for axial loading


5.3.1 Strain energy for axial loading Spring


5.3.2 Strain energies UM and US for Beams




k: Correction coefficient

Shear stress component

5.3.3 Strain energy UT for torsion


Example 5.3 Linear spring-weight system




Solution

5.4 Deflections of statically determinate


Example 5.5 End load on a cantilever Beam


Solution

Example 5.5 End load on a cantilever Beam


Example 5.6 Cantilever beam loaded in its

plane



plane


Solution


plane


Example 5.7 A shaft-beam mechanism


Example 5.7 A shaft-beam

mechanism


Solution

Example 5.8 Uniformly loaded cantilever

beam


Example 5.8 Uniformly loaded cantilever

beam


Solution

Example 5.9 Curved beam loaded in its

plane


Example 5.9 Curved beam loaded in its

plane


Solution

Example 5.10 Semicircular cantilever beam


Example 5.10 Semicircular cantilever beam


Solution

5.4.2 Dummy load method and dummy unit load




Normal method

Dummy load method

Example 5.11 Cantilever beam deflections and

rotations



Solution

Example 5.12 Pin-connected truss



Solution

5.5 Statically indeterminate structures


Redundant supports



Redundant members

Example 5.15 Uniformly loaded propped cantilever beam




Solution

Example 5.16 Statically indeterminate system




Solution

Example 5.18 Spring supported I-beam




Solution

C05_stationary potential energy

Documents

ueme2163 solid mechanics

solution example

loaded cantilever beam

strain energy ut

linear springweight

strain energies um

axial loading spring

bar system