# C2_2 - S/No 1 2 3 CONTENTS Subject Introduction Objectives...

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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 I-Section 11 7.4.3 Hollow Box Section 8. Conclusion 12 Appendix 13

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1. 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 mid-span 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 (two-dimemsioned 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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## This note was uploaded on 10/18/2009 for the course ECONS 111 taught by Professor Yo during the Spring '09 term at Nassau CC.

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C2_2 - S/No 1 2 3 CONTENTS Subject Introduction Objectives...

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