Analysis of deflection in structural and machine members is of great importance in machine and structural design. Youngs modulus for the cantilever material steel is determined from the observed frequencies of the fundamental mode for a series of. Exp 02 a determination of modulus of elasticity for the material of a cantilever version 2009 10 part 1. For 20 gauge copper wire the following experimental results produced a youngs modulus constant of 6063 mpa, or 6. An undergraduate experiment on the vibration of a cantilever. The paper presents a novel determination method based on cantilever resonance theory. Pdf this paper presents an analytical method for youngs modulus determination of an individual. Modulus of elasticity determination from cantilever. In this study, a new technique for evaluation of the elastic modulus of a vibrating cantilever beam was presented. The width, thickness, youngs modulus, poissons ratio, and density of the ith layer are w i, h i, e i, n i, and r i respectively. To determine the youngs modulus of the thin epicuticle, tensile tests were performed. It is the measure of elasticity and it is a very important characteristic of a material.
Youngs modulus determination using strong static bending of a cantilever. Exp 02 a determination of modulus of elasticity for the. Activityforces, elasticity, stress, strain and youngs modulus handout 2 elasticity and youngs modulus elasticity describes a material property in which the material returns to its original shape after stress has been applied and then removed. Youngs modulus determination using strong static bending. Elasticity of materials and youngs modulus description in this lab you will measure the youngs modulus of a metal wire.
Micromachines 2017, 8, 201 2 of 11 in this paper, a novel approach was proposed to extract the young s modulus of each layer with multilayer beams using resonance frequency measurement. The method is based on measuring the resonant frequency of flexural vibrations of a partially restrained rectangular beam. See the attached pictures for the diagram strobe is. Youngs modulus for the cantilever material steel is determined from the observed frequencies of the fundamental mode for a series of different lengths, and the result is. The deflection of microstructures have been previously measured using optical interferometry methods. Cnt as a cantilever beam subjected to uniform distributed. A novel determination method of ipmc youngs modulus based on. The tangent modulus of elasticity was calculated by drawing a tangent to the steepest initial straightline. Youngs modulus determination using strong static bending of a cantilever k turvey department of physics, napier polytechnic, edinburgh many textbooks of practical physics contain descrip tions of experiments for the determination of youngs modulus based on the bending of beams. Abstract experimental setup determining youngs modulus stress. Youngs modulus determination using strong static bending of. In the process, you will gain an understanding of the concepts of stress and strain. Equipment youngs modulus apparatus weights 4 2kg, 2 1kg, and 1kg of smaller weights micrometer laboratory.
See also matter glossary entry a cantilever beam is fixed at one end and free to move vertically at the other, as shown in. When compared to the accepted value this represents a percent difference of 94. The ruler used for finding the length has an uncertainty of 0. There is an experiment to determine the youngs modulus of the wood which involves bending it. Determination of youngs modulus of epoxy coated polyethylene. Nov 24, 2014 there is an experiment to determine the young s modulus of the wood which involves bending it.
Material testing, cantilever, youngs modulus, mechanical. In this experiment only two types of beam will be discussed one is simple supported beam and other is cantilever beam. Deflection measurement and determination of youngs. Pdf youngs modulus measurement of thinfilm materials using. Solid mechanics lab report experiment to determine the youngs modulus of an aluminium cantilever beam and the uncertainties in its measurement 1. This report contains the results of an experiment to determine the elastic. Experimental techniques to determine the youngs modulus of the trachea vera hermawan thesis submitted in partial fulfilment of the degree of the master of engineering auckland university of technology auckland new zealand september 2004. Youngs modulus experiment 1 beam structure youngs modulus. By hanging several different weights on the ends of the strips, and measuring the corresponding deflections, a graph can be can be plotted which allows the youngs modulus to be calculated. Determination of young modulus using the cantilever experiment.
Numerical and experimental analysis of a cantilever beam. Determining youngs modulus by bending a piece of wood. Measurement of youngs modulus using strain gauges cole c. The calculated values for the youngs modulus may be compared with the values in this properties table. Flexural vibration test of a beam elastically restrained at. What they are using is the equation derived from solid deformation mechanics for the downward displacement at the location were a force is applied to a cantilever. Experimental techniques to determine the youngs modulus. Determining the youngs modulus of wood along the grain using a. From the viewpoint of the experiment, however, it is very simple and. Pdf analytical method for determination of youngs modulus. Using that value we can find the value of young s modulus for the wire.
Youngs modulus of the material of a beam by method of. The experiment should be repeated twice and any anomalous results repeated and checked. To determine the youngs modulus of the material of the bar subjected to nonuniform bending by measuring the depression at the center. Talking about the material of the beam, in this lab experiment three materials brass, aluminum and steel will be discussed. Determining the youngs modulus of wood along the grain. The result obtained for the youngs modulus of the steel comprising the cantilever is in good agreement with two.
Evaluation of elastic modulus of cantilever beam by taespi. It is bent by the action a force acting at its centre. Good agreement between experiment and theory is obtained. Try the data analysis yourself, download a free works. Without changing the major dimensions of the microcantilever, young. It defines the relationship between stress force per unit area and strain proportional deformation in a material in the linear elasticity regime of a uniaxial deformation. Determination of the ultimate strength of 1018 steel. Users may need to adapt the risk assessment information to local circumstances.
As the shown in figure 1 the sample was never taken past the elastic region. Youngs modulus is named after thomas young,19th century,british scientist. In this experiment i am going to determine the youngs modulus e of wood from the period of oscillation of a loaded wooden ruler. Experimental techniques to determine the youngs modulus of. Comparison of cantilever resonance, static threepoint bending and ultrasonic tests for the determination of young s modulus for douglasfir was reported by sinclair and farshad 1987. This report contains the results of an experiment to determine the elastic modulus, yield point, and ultimate strength of 1018 steel. A new vibration beam technique for the fast determination of the dynamic young modulus is developed. Dec 15, 2017 video of the experiment to determine the young s modulus of a metal wire using a travelling microscope. An undergraduate experiment on the vibration of a cantilever and its application to the determination of youngs modulus.
Excessive deflection of structural member results in geometric distortion of the whole structure whereas in a machine excessive deflection may result in interference between. Determination of youngs modulus of pzt and co80ni20 thin. Pdf analytical method for determination of youngs modulus of. Iintroduction manyattemptshavebeanmadetodeterminetheexactrela tionbetweenthestressandstrainofabody. When the two values agree with each other, the deformed shape is determined ultimately. N2 this paper presents a technique to determine the youngs modulus and residual stress of thin films using a simple micromachined silicon cantilever as the test structure. Comparison of youngs modulus calculated from freefree resonance. Using the pullin force and large deflection solution of.
In this experiment we shall measure this depression against different weight to calculate the youngs modulus of the material of the beam. Youngs modulus, or the young modulus, is a mechanical property that measures the stiffness of a solid material. This method would fill up some deficiencies, such as damaging the tested ipmc strip, having low precision and so on, in the traditional method like tensile test and bending test. Principle and task a flat bar is supported at two points. This method adopts eulerbernoulli beam to build a vibration differential equation of the beam.
The method utilized time average electronic speckle pattern interferometry taespi, which can extract directly the resonance frequencies, and its elastic modulus can be readily determined from classical beam theory. Determination of the youngs modulus of the epicuticle of. A graph of extension yaxis against load xaxis is plotted. Experiment 3 modulus of elasticity related topics youngs modulus, modulus of elasticity, stress, deformation, poissons ratio, hookes law. There were some limitations which affected my experiment. An undergraduate experiment on the vibration of a cantilever and its application to the determination of youngs modulus american journal of physics 58, 483 1990.
A novel determination method of ipmc youngs modulus based. The determination of youngs modulus was achieved with an instron 3367 testing machine using the threepoint bending test. Youngs modulus of a cantilever, help please physics forums. Doitpoms tlp library thermal expansion and the bimaterial. In solid mechanics, youngs modulus is defines as the ratio of the longitudinal stress over longitudinal strain, in the range of elasticity the hooks law holds stress is directly proportional to strain. Notes on experiments related content youngs modulus. Theory when forces are applied to materials, they deform in reaction to those forces. If we consider the beam in the position given in the. Forces, elasticity, stress, strain and youngs modulus. Young s modulus for the cantilever material steel is determined from the observed frequencies of the fundamental mode for a series of. The uncertainty on devices used is the major limitation. Flexural vibration test of a beam elastically restrained.
The equation used to calculate it is like this ewx34zdy3 where damount of bending wforce n which causes the bending zwidth of the wood ythickness of the wood xhorizontal distance between the. The determination of young s modulus was achieved with an instron 3367 testing machine using the threepoint bending test. The tangent modulus of elasticity was calculated by drawing a tangent to the steepest initial straightline portion of the loaddeflection curve. Introduction in this experiment we try to measure the elasticity modulus of scales made of di. Youngs modulus of a cantilever, help please 1 background. Video of the experiment to determine the young s modulus of a metal wire using a travelling microscope. Youngs modulus experiment 1 free download as word doc. Apr 04, 2010 exp 02 a determination of modulus of elasticity for the material of a cantilever version 2009 10 part 1. A simple extraction method of youngs modulus for multilayer. An analytical relation was developed based on the shift in resonance frequency caused by the addition of a thin film on the cantilever.
Testing of methods for the determination of youngs. The youngs modulus e, is a measure of the stiffness and is therefore one of the most important properties in engineering design. The ratio of stress to strain is a consistent physical property of the material the elastic modulus or youngs modulus. An analytical relation was developed based on the shift in resonance frequency caused by the addition of a. This is the working formula of the experiment, and is valid so long as the slope of the bar at any point with respect to the unstrained position is much less than unity. To achieve this, stick insects were allowed to adhere onto a thin latex membrane, which was stretched while simultaneously observing the elongation of latex membrane and arolium contact area under a microscope. Using that value we can find the value of youngs modulus for the wire. Determination of young modulus using the cantilever. Youngs modulus, a measure of the deformation of a material in.
The technique was validated in experiments on thin film specimens of silicon nitride deposited on a silicon substrate see figure3. The result obtained for the young s modulus of the steel comprising the cantilever is in good agreement with two other methods used the same specimen. From my experiment i got the youngs modulus value as 1. Determining the youngs modulus of wood along the grain using a cantilever alep. Video of the experiment to determine the youngs modulus of a metal wire using a travelling microscope. Youngs modulus of a metre ruler 1076 words bartleby.
The modulus of elasticity is determined from the bending and the geometric data of the. Evaluation of elastic modulus of cantilever beam by ta. Determination of youngs modulus for spruce, fir and. Determination of youngs modulus from static deflection data a technique for extracting youngs modulus from static deflection data was presented 1. Using the modulus of elasticity previously obtained, and with the help of the ansys program 10, students can obtain the elastic curves of the cantilever beam for different external loads and compare these curves with the experimental ones. Youngs modulus experiment appliedstatics eme1016 mmu. The stripshaped specimen fixed at one end to a force sensor and free at the other forms the euler bernoulli cantilever beam with linear and torsion spring on the fixed end. When thinking about elasticity, think about a coiled metal spring or a rubber band.
In a properly posed experiment, the frequency of the strongest resonance. Comparison of young s modulus calculated from freefree resonance. Example long laboratory report mechanical properties. This paper presents an analytical method for young s modulus determination of an individual carbon nanotube under electrostatic loading.
Jul 11, 2008 youngs modulus of a cantilever, help please 1 background. Example long laboratory report mechanical properties of 1018 steel in tension i. Comparison of cantilever resonance, static threepoint bending and ultrasonic tests for the determination of youngs modulus for douglasfir was reported by sinclair and farshad 1987. Young s modulus, or the young modulus, is a mechanical property that measures the stiffness of a solid material. The technique was validated in experiments on thin film specimens of silicon nitride deposited on a silicon. To determine the value of young s modulus of the material of a beam by method of bending of beam supported at its ends and loaded in the middle. The atomic force microscope acquires any information about a surface because of the.
This paper presents an analytical method for youngs modulus determination of an individual carbon nanotube under electrostatic loading. However,beingalittle lateinpublication,honorandtitleofthediscoveriesofthelaw mustbegiventohooke. Vibrationbased technique for youngs modulus determination. Cantilever resonance theory is one of the methods to determinate the youngs modulus of metal wire and metal strip. Describes an experiment which is unusual in that it not only allows for large angle bending but specifically requires that such bending occurs. Example long laboratory report mechanical properties of 1018.
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