Flexion En Vigas

Mechanical Engineering
School of Engineering and Physical Sciences

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MODULE No:

B5.1PZ_2006-2007

MODULE TITLE:

Mechanical Engineering Science

ASSIGNMENT TITLE:

Laboratory Report 2: The Cantilever Beam

Lecturer:

Dr. X

Year: 2

Term: 2Grade:

Name:
Registration Number:

Marker’s Initials:

SZ

Session: 2

JKC@REC
XXXXXXXXX

Term Address:

Email:

XXXXXXXXX

Submission Date:

17/02/08

Group/Group Members:
(If applicable)

GROUP 1 X

Index

Page no.
Aim
Summary

3

1. Introduction

3

2. Theory/Aim

4

3. Experimental Methods

8

3.1 Procedure

8

3.2 Apparatus/Equipment

84. Results and Calculations

10

4.1 Data

10

4.2 Calculations

10

5. Discussion

11

6. Conclusion

15

7. References

15

Aim
The aim of the experiment is to investigate the relationships between load, bending moment, strain, deflection and slope in a
cantilever beam. The actual and theoretical strain and deflections will be measured and calculated. The resultswill be compared
by using graphics and tables. Equations for the deflection and slope of the cantilever beam will be derived.
Summary
The strain and deflection of a 500 mm aluminium cantilever beam are measured by the micro strain gauge and the dial gauge. To
evaluate the theoretical strain and deflection the derived formulae and the given data are used. After analyzing the experimental
results,it can be concluded that the strain and deflections are dependent on the load and proportional to each other. The values
obtained are analyzed and compared using tabulated data and graphs. The sensitivity of the strain and dial gauge will also be
tested. The values measured are almost the same from the predicted values. All of these values agreed within the estimated
experimental errors.
1.Introduction

A cantilever is a beam supported on only one end. The beam carries the load to the support where it it’s resisted by moment and
shear stress. Cantilever contraction allows for overhanging structures without external bracing. Cantilevers can also be
constructed with trusses or slabs [1].
Cantilever is widely found in construction, notably in cantilever bridges and balconies. Incantilever bridges the cantilevers are
usually built as pairs, with each cantilever used to support one end of a central section. The Forth Bridge in Scotland is a famous
example of a cantilever truss bridge [1].
A strain gauge is attached to the cantilever beam with a suitable adhesive. A strain gauge is a device used to measure the
deformation (strain) of an object [2]. As beam is deformed,the metallic foil pattern of the gauge is also deformed, causing its
electrical resistance to change. The resistance change is measured using the Wheatstone bridge. The dial gauge measures the
deflection of the beam.
A Wheatstone bridge is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of
which includes the unknown component. It is relatedto the strain by the quantity known as the gauge factor. Figure 1 and 2
shows the diagram of a strain gauge and the Wheatstone bridge [3].

Figure 1. A Strain gauge

Figure 2: A Schematic Diagram of the Wheatstone bridge.

In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by
the action of stress on a physicalbody.
In engineering mechanics, deflection is a term that is used to describe the degree to which a structural element is displaced under
a load. The deflection of a member under a load is directly related to the slope of the deflected shape of the member under the
load and can calculated by integrating the function that mathematically describes the slop of the member under that load [4]....