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stationary potential energy
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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
2 2 UEME2163 Solid Mechanics II
Vanish: System is in
equilibrium
5.1 Principle of stationary potential energy
3 3 UEME2163 Solid Mechanics II
Example 5.1 Equilibrium of a linear elastic two-bar
system
4 4 UEME2163 Solid Mechanics II
Example 5.1 Equilibrium of a linear elastic two-bar
system
5 5 UEME2163 Solid Mechanics II
6 6 UEME2163 Solid Mechanics II
Solution
7 7 UEME2163 Solid Mechanics II
8 8 UEME2163 Solid Mechanics II
5.2 Castiglinos theorem on deflections
9 9 UEME2163 Solid Mechanics II
5.2 Castiglinos theorem on deflections
10 10 UEME2163 Solid Mechanics II
5.2 Castiglinos theorem on deflections
11 11 UEME2163 Solid Mechanics II
Example 5.2 Equilibrium of a nonlinear elastic two-
bar system
12 12 UEME2163 Solid Mechanics II
13 13 UEME2163 Solid Mechanics II
Solution
14 14 UEME2163 Solid Mechanics II
Solution
5.2 Castiglianos theorem on deflections for linear load-deflection
relations
15 15 UEME2163 Solid Mechanics II
5.2 Castiglianos theorem on deflections for linear load-deflection
relations
16 16 UEME2163 Solid Mechanics II
5.3.1 Strain energy UN for axial
loading
17 17 UEME2163 Solid Mechanics II
5.3.1 Strain energy UN for axial loading
18 18 UEME2163 Solid Mechanics II
5.3.1 Strain energy UN for axial loading
19 19 UEME2163 Solid Mechanics II
5.3.1 Strain energy for axial loading Spring
20 20 UEME2163 Solid Mechanics II
5.3.1 Strain energy for axial loading Spring
21 21 UEME2163 Solid Mechanics II
5.3.2 Strain energies UM and US for Beams
22 22 UEME2163 Solid Mechanics II
5.3.2 Strain energies UM and US for Beams
23 23 UEME2163 Solid Mechanics II
5.3.2 Strain energies UM and US for Beams
24 24 UEME2163 Solid Mechanics II
k: Correction coefficient
Shear stress component
5.3.3 Strain energy UT for torsion
25 25 UEME2163 Solid Mechanics II
Example 5.3 Linear spring-weight system
26 26 UEME2163 Solid Mechanics II
Example 5.3 Linear spring-weight system
27 27 UEME2163 Solid Mechanics II
Solution
Example 5.3 Linear spring-weight system
28 28 UEME2163 Solid Mechanics II
Solution
5.4 Deflections of statically determinate
29 29 UEME2163 Solid Mechanics II
5.4 Deflections of statically determinate
30 30 UEME2163 Solid Mechanics II
31 31 UEME2163 Solid Mechanics II
32 32 UEME2163 Solid Mechanics II
Example 5.5 End load on a cantilever Beam
33 33 UEME2163 Solid Mechanics II
Solution
Example 5.5 End load on a cantilever Beam
34 34 UEME2163 Solid Mechanics II
Example 5.6 Cantilever beam loaded in its
plane
35 35 UEME2163 Solid Mechanics II
Example 5.6 Cantilever beam loaded in its
plane
36 36 UEME2163 Solid Mechanics II
Solution
Example 5.6 Cantilever beam loaded in its
plane
37 37 UEME2163 Solid Mechanics II
Example 5.6 Cantilever beam loaded in its
plane
38 38 UEME2163 Solid Mechanics II
Example 5.7 A shaft-beam mechanism
39 39 UEME2163 Solid Mechanics II
Example 5.7 A shaft-beam
mechanism
40 40 UEME2163 Solid Mechanics II
Solution
Example 5.8 Uniformly loaded cantilever
beam
41 41 UEME2163 Solid Mechanics II
Example 5.8 Uniformly loaded cantilever
beam
42 42 UEME2163 Solid Mechanics II
Solution
Example 5.9 Curved beam loaded in its
plane
43 43 UEME2163 Solid Mechanics II
Example 5.9 Curved beam loaded in its
plane
44 44 UEME2163 Solid Mechanics II
Solution
45 45 UEME2163 Solid Mechanics II
Example 5.10 Semicircular cantilever beam
46 46 UEME2163 Solid Mechanics II
Example 5.10 Semicircular cantilever beam
47 47 UEME2163 Solid Mechanics II
Solution
48 48 UEME2163 Solid Mechanics II
5.4.2 Dummy load method and dummy unit load
49 49 UEME2163 Solid Mechanics II
5.4.2 Dummy load method and dummy unit load
50 50 UEME2163 Solid Mechanics II
5.4.2 Dummy load method and dummy unit load
51 51 UEME2163 Solid Mechanics II
Normal method
Dummy load method
Example 5.11 Cantilever beam deflections and
rotations
52 52 UEME2163 Solid Mechanics II
53 53 UEME2163 Solid Mechanics II
Solution
54 54 UEME2163 Solid Mechanics II
Solution
55 55 UEME2163 Solid Mechanics II
Solution
56 56 UEME2163 Solid Mechanics II
Solution
Example 5.12 Pin-connected truss
57 57 UEME2163 Solid Mechanics II
58 58 UEME2163 Solid Mechanics II
Solution
59 59 UEME2163 Solid Mechanics II
Solution
5.5 Statically indeterminate structures
60 60 UEME2163 Solid Mechanics II
Redundant supports
5.5 Statically indeterminate structures
61 61 UEME2163 Solid Mechanics II
Redundant members
5.5 Statically indeterminate structures
62 62 UEME2163 Solid Mechanics II
Example 5.15 Uniformly loaded propped cantilever beam
63 63 UEME2163 Solid Mechanics II
Example 5.15 Uniformly loaded propped cantilever beam
64 64 UEME2163 Solid Mechanics II
Solution
Example 5.15 Uniformly loaded propped cantilever beam
65 65 UEME2163 Solid Mechanics II
Solution
Example 5.16 Statically indeterminate system
66 66 UEME2163 Solid Mechanics II
Example 5.16 Statically indeterminate system
67 67 UEME2163 Solid Mechanics II
Solution
Example 5.16 Statically indeterminate system
68 68 UEME2163 Solid Mechanics II
Solution
Example 5.18 Spring supported I-beam
69 69 UEME2163 Solid Mechanics II
Example 5.18 Spring supported I-beam
70 70 UEME2163 Solid Mechanics II
Solution
Example 5.18 Spring supported I-beam
71 71 UEME2163 Solid Mechanics II
Solution
Example 5.18 Spring supported I-beam
72 72 UEME2163 Solid Mechanics II
Solution
Example 5.18 Spring supported I-beam
73 73 UEME2163 Solid Mechanics II
Solution