CONTENTS
S/No
Subject
Page
1.
Introduction
1
2.
Objectives
1
3.
Theory
3.1
Statically Determinate Structure
1
3.2
Statically Indeterminate Structure
2
3.3
Principle Of
Superposition
2
3.4
Maxwell’s Reciprocal Theorem
3
4.
Equipment
3
5.
Procedure
5.1
Verification Of The Principle Of Superposition
Using A Cantilever Beam
4
5.2
Verification Of Maxwell’s Reciprocal Theorem
5.2.1
Using A Cantilever Beam
4
5.2.2
Using A Propped Cantilever Beam
4
5.3
Determination Of The Unknown R
b
Experimentally
4
5.4
Deflection Shape Of A Propped Cantilever Beam
5
6.
Results And Calculations
5
7.
Discussion
7
7.1
Deflected Shapes of Beams
7.1.1
Simply Supported Beam
7
7.1.2
Cantilever Beam
8
7.1.3
Fixed End Beam
8
7.1.4
Propped Cantilever Beam
8
7.2
Test Results And Sources Of Errors
7.2.1 Verification Of The Principle Of Superposition
Using A Cantilever Beam
9
7.2.2 Verification Of Maxwell’s Reciprocal Theorem
9
7.2.3 Determination Of The Unknown R
b
Experimentally
9
7.2.4 Deflection Shape Of A Propped Cantilever
Beam
9
7.2.5 Sources Of Errors
10
7.3
The Compatibility Equations Required In The Case
Of
A Fixed End Beam
10
7.4
Advantages And Disadvantages of Different Types Of
Sections For A Bridge Grider
10
7.4.1
Rectangular Section
11
7.4.2
ISection
11
7.4.3
Hollow Box Section
8.
Conclusion
12
Appendix
13
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Introdution
A structure is made op of one or more members joined together and supported
by its foundation. These members are made up of various materials such as steel,
timber, reinforced concrete and aluminum etc. These members can be of different types
and shapes. For the purpose of analysis and construction, they can be grouped into a
number of common element types. Examples are beams, trusses, frames, cables, plates
and shells. These element types are then combined to build structures such as buildings
and bridges.
Beams are one of the most common structural components used. A beam is a
long bar which carries its loads by developing bending moments and shear forces at
diffferent sections due to lateral forces along its length. There are various types of
beams, classified according to how they are supported. An example is the cantilever,
shown in Fig.1 below.In this experiment, the cantilever is used extensively.
Fig.1
A Cantilever.
2.
Objectives
The objectives of this experiment are:
I. To verify the principle of superposition and Maxwell’s reciprocal theorem.
II. To analyse a propped cantilever which is a statically indeterminate beam by using
the principle of superposition and compatibility equation.
III.To readily obtain the deflected shape of a propped cantilever beam under a midspan
load by using Maxwell’s reciprocal theorem.
3.
Theory
3.1
Statically Determined Structure
For rigid bodies, the static equations may be used to determine the reactions of
the structures. For plane structures (twodimemsioned structures) to be in equilibrium,
the three equations of statics must be satisfied. They are:
a) The sum of horizontal forces must be zero.
F
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