This document discusses analyzing statically indeterminate structures using the energy principle. It states that in beams and frames with rigid joints, both shear and bending stresses can occur at any section. The total strain energy stored depends on the magnitudes of direct forces, shear, and moments. When analyzing indeterminate structures, the work done by direct and shear forces is neglected compared to that done by bending. It also introduces Castiglione's first theorem relating the partial derivative of strain energy to displacements and forces/moments. It provides an example of using this method to determine the vertical deflection of a point on a rigid cantilever frame under a given load.

1. Government Engineering College, Bhavnagar.
Civil Engineering Department

2. Structure Analysis
2
Topic:- Indeterminate frame by
using energy principle

3.  In beams and frames having rigid joints ,
shear stress and bending stress may also
occur at any section.
 In such cases, the total strain energy
stored depends on the magnitudes of
direct force such cases, shear and
moment.
 While analyzing statically indeterminate
structures, the work done by direct and
shear force is neglected since it is very
small in comparison to that done by
bending.

4. Castiglione's first theorem
If there is any elastic system in equilibrium
under the action of a set of a force w1, w2,
w3………wn and corresponding
displacement
δ1, δ2, δ3…… δn and a set of moments
M1, M2, M3………Mn and corresponding
rotations
φ1, φ2, φ3……φn, then the partial derivative
of the strain energy with respect to any one
of the force or moments taken individually will
give its corresponding displaements in it’s
direction of action”.

6. Determine vertical deflection of point D for a rigid cantilever
frame shown in fig.take EI = 6 * 10¹³ n.mm²
Consider 50 kn load at D as p.
50kn
D
C
20
kn
3m
3m3m
A
B

7. 3
0
3
0
3
0

9. Thank youThank you

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