Design And Development Of A Bending Moment Apparatus

ABSTRACT

This study is on bending moment apparatus. Bending moment apparatus is an analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam. The aim of the report is to understand the concept of structural engineering and how it is applied in laboratory exercises. The experiments carried out help to explain the stress, shear, axial forces, bending and deflection properties.

TABLE OF CONTENTS

COVER PAGE

TITLE PAGE

APPROVAL PAGE

DEDICATION

ACKNOWLEDGEMENT

ABSTRACT

CHAPTER ONE

1.0      INTRODUCTION

• BACKGROUND OF THE STUDY
• AIM AND OBJECTIVES OF THE STUDY
• SIGNIFICANCE OF THE STUDY
• SCOPE OF THE STUDY
• DEFINITION OF TERMS

CHAPTER TWO

LITERATURE REVIEW

• REVIEW OF THE STUDY
• REVIEW OF RELATED STUDIES
• BENDING MOMENT OF BEAMS
• TYPES OF STRESS THAT CAUSES BENDING

2.4        BEAMS

2.4.1 Classification of beams

• TYPES OF LOADING

CHAPTER THREE

3.0      METHODOLOGY

• BENDING MOMENT TEST
• APPARATUS
• PROCEDURE

CHAPTER FOUR

4.0      DIMENSION AND CALCULATIONS AND DISCUSSION

4.1      DIMENSION AND CALCULATIONS

4.2      DISCUSSION

4.3      PRECAUSION

CHAPTER FIVE

• CONCLUSION
• RECOMMNDATION

CHAPTER ONE

• INTRODUCTION

Bending Moments are rotational forces within the beam that cause bending. At any point within a beam, the Bending Moment is the sum of: each external force multiplied by the distance that is perpendicular to the direction of the force. Bending Moment apparatus is used for measurement of bending moment on a section of a beam from which comparison with theoretical values can be made. For measurement of bending moment at a section in a beam. The beam has two parts with a ball bearing hinge at the joint. An underhung spring balance with an adjustable length holds the hinge in compression, hence resists bending moment. The beam is simply supported on two end bearings, one with an adjustable height.

This work is aimed at carrying out a study on a bending moment apparatus which will also involve setting up the experiment.

1.1                                    BACKGROUND OF THE STUDY

A bending moment (BM) is a measure of the bending effect that can occur when an external force (or moment) is applied to a structural element. This concept is important in structural engineering as it is can be used to calculate where, and how much bending may occur when forces are applied.

The most common structural element that is subject to bending moments is the beam, which may bend when loaded at any point along its length.

Failure can occur due to bending when the tensile stress exerted by a force is equivalent to or greater than the ultimate strength (or yield stress) of the element. However, although the mechanisms are different, a beam may fail due to shear forces before failure in bending (Gere et al., 2016).

The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple (Gere et al., 2016).  For equilibrium, the moment created by external forces/moments must be balanced by the couple induced by the internal loads. The resultant internal couple is called the bending moment while the resultant internal force is called the shear force (if it is transverse to the plane of element) or the normal force (if it is along the plane of the element). Normal force is also termed as axial force.

The bending moment at a section through a structural element may be defined as the sum of the moments about that section of all external forces acting to one side of that section. The forces and moments on either side of the section must be equal in order to counteract each other and maintain a state of equilibrium so the same bending moment will result from summing the moments, regardless of which side of the section is selected. If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause “hogging”, and a positive moment will cause “sagging”. It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is, the point of transition from hogging to sagging or vice versa.

1.2    AIM AND OBJECTIVES OF THE STUDY

The aim of this study is to develop a bending moment apparatus. The objectives of the study are:

1. To carry out an experiment on the bending moment apparatus.
2. To examine how the bending moment varies with an increasing load. .

• To examine how bending moment varies at the cut position of the beam for various loading conditions.

1.4    SCOPE OF THE STUDY

The scope of this study covers studying development of a bending moment apparatus. It is performed by using the Bending Moment in a Beam apparatus and loaders. Bending Moment in a Beam apparatus consists of a beam, which is ‘cut’ by a pivot. To stop the beam collapsing a moment arm bridges cut onto a load cell thus reacting (and measuring) the bending moment force.

1.5      SIGNIFICANCE OF THE STUDY

This study serves as a means of demonstrating the principle involved and gives practical support in engineering study. This study will help to explain the stress, shear, axial forces, bending and deflection properties.

1.6    DEFINITION OF TERMS

Terms frequently used in this study are defined as below:

1. Compression:Particles of a material are pushed against each other, causing them to shorten, or compress. In a building, compression usually comes from the top.
2. Tension:The opposite of compression, in which a pulling force is working to lengthen the material. If a beam is being compressed from the top, it will be in tension at the bottom.

• Torsion:A structural element is subject to torque—or a twisting force.

1. Shear:Opposing structural forces cause slippage on a plane. In other words, a shearing force that causes layers to slide across each other in opposite directions. Buildings need shear walls to resist lateral, or shear, forces.

CHAPTER FIVE

5.1    Conclusion

I reach to the conclusion that the tests carried out has proved the thesis which states that ‘ the shear force at a cut section of a beam is equal to the algebraic sum of the forces acting to the left or right of the section’.

5.2    Recommendation

Recommendations for fellow students who are going to do this experiment are to repeat the experiment more than once so that the average reading can be taken which is more accurate. Ask more than one class mate to record the readings to avoid errors. Also, while performing the experiment, more than one class mate should carry out the tasks so that the different approaches will show the results observed and the variables recorded.

Noise should be kept to a minimum while in a laboratory and always listen to the instructor. If any guide lines are needed, then refer to the supervisor.