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Lecture 24: Finite Element Method: Beams and Frames

This document discusses the finite element method for analyzing beams and frames. It covers the beam element, including its nodal variables, degrees of freedom, potential energy from bending and axial loads, kinetic energy from distributed and concentrated masses, and work done by external loads. The document also provides an example of applying the beam element method to a three-element structure and defining the corresponding boundary conditions. Finally, it briefly introduces the plane frame element.

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65 views8 pages

Lecture 24: Finite Element Method: Beams and Frames

This document discusses the finite element method for analyzing beams and frames. It covers the beam element, including its nodal variables, degrees of freedom, potential energy from bending and axial loads, kinetic energy from distributed and concentrated masses, and work done by external loads. The document also provides an example of applying the beam element method to a three-element structure and defining the corresponding boundary conditions. Finally, it briefly introduces the plane frame element.

Uploaded by

ali381
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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53/58:153 Lecture 24 Fundamental of Vibration

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Lecture 24: Finite element method: Beams and Frames


Reading materials: Section 9.3

1. Beam element

Nodal variables

Nodal loads: vertical loads and moments

Nodal degree of freedom: vertical displacements and rotations

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Potential

Kinetic energy

Kinetic energy due to the distributed mass

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Kinetic energy due to the concentrated masses at nodes

work done by external loads

work done by the distributed load

work done by the concentrated loads and moments

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Equations of motion

Example

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Element 1

Element 2

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Element 3

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Boundary conditions

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53/58:153 Lecture 24 Fundamental of Vibration
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2. Plane Frame element

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