Indeterminate frame by using energy principle
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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.
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1) Shear force and bending moment diagrams show the variation of shear force V and bending moment M over the length of a beam, which is necessary for design analysis.
2) The maximum bending moment is the primary consideration in design, and its value and position must be determined.
3) The procedure for drawing shear force and bending moment diagrams involves first calculating support reactions, then plotting the shear diagram with slope equal to loading, and finally the moment diagram with slope equal to shear.
11 energy methods
This document discusses energy methods for analyzing deformation and stress in engineering structures. It covers concepts like strain energy, strain energy density, elastic strain energy for normal and shearing stresses, impact loading, work and energy under single and multiple loads, and Castigliano's theorem. Sample problems demonstrate applying these concepts to determine deflections in beams and trusses due to applied loads.
2.Dynamic stability of beams with damping under periodic loads
My project is on dynamic stability of beams with damping. We are going to find out the dynamic instability region for a beam with and without damping cases. So that we can able to find whether a beam can undergo any response within its boundary limits and we are going to find upto what extent it can be minimised by introducing damping.
Bending wikipedia
The document discusses bending, which refers to the behavior of a structural element subjected to an external load applied perpendicularly to its longitudinal axis. It describes Euler-Bernoulli beam theory, which assumes plane sections remain plane, and Timoshenko beam theory, which accounts for shear deformation. It also covers bending of plates, plastic bending, large bending deformations, and extensions of bending theories.
Welcome to International Journal of Engineering Research and Development (IJERD)
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Stress strain curve
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Elastic beams
The use of Calculus is very important in every aspects of engineering.
The use of Differential equation is very much applied in the concept of Elastic beams.
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Collapse propagation in bridge structures. A semi-analytical model
Collapse propagation in bridge structures. A semi-analytical model
Shear Force And Bending Moment Diagram For Beam And Frame
Shear Force And Bending Moment Diagram For Beam And Frame
2.Dynamic stability of beams with damping under periodic loads
2.Dynamic stability of beams with damping under periodic loads
Welcome to International Journal of Engineering Research and Development (IJERD)
Welcome to International Journal of Engineering Research and Development (IJERD)
On the Vibration Characteristicsof Electrostatically Actuated Micro\nanoReson...
On the Vibration Characteristicsof Electrostatically Actuated Micro\nanoReson...
Seismic protection variable stiffness part 2 poster
Seismic protection variable stiffness part 2 poster
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Indeterminate frame by using energy principle
- 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