Solid Mechanics Lab Report
Experiment to determine the Young’s modulus of an aluminium cantilever beam and the uncertainties in its measurement 1. Abstarct: The young’s modulus E, is a measure of the stiffness and is therefore one of the most important properties in engineering design. It is a materials ratio between stress and strain: E=σε

Young’s modulus is a unique value for each material and indicates the strength of that material as well as how it will deform when a load is applied.

2. Introduction: The Young’s Modulus can only be derived experimentally, there are no theoretical methods by which the young’s Modulus of a material can be calculated therefore in this experiment our aims were: * To calculate the Young’s modulus ,E of Aluminium from measurement of the end deflection of cantilever beam of aluminium loaded at its free end * To assess the accuracy and precision of this method by comparing the calculated value of E to the known value Eal=72.6 GPa * To measure the deflected shape of the aluminium beam for one loading condition (15N) and to compare this with the theoretical prediction of the beam bending theory for deflection of a cantilever

yx= PL32EIxL2-13xL3

3. Materials and Methods
The apparatus shown below was set up and the following equipments were used: * Dial gauge was used to measure deflection of the beam
* Magnetic clamp stand (not to affect the bending of the beam) * Solid Aluminium Beam
* 15 Weights(1N each)
* Clamp to keep it still at one end.
* Steel base

4.Results
1. Load/Deflection behaviour :Equation to calculate the young’s Modulus from the slope of deflection vs. load graph E= 4L3bd3(slope)

We measured the length (L) the width (d) and the breadth (b) of the beam 5 times and then calculated the average: Average Length/mm| Average width/mm| Average breadth/mm| 998| 25.28| 15.73|

The uncertainties of the slope, length, breadth and width were estimated using the rage...

...Anil Shrestha
IB Physics Labwork
FINDING YOUNG’SMODULUS OF WOODEN METRE RULER
INTRODUCTION:
Young’smodulus is also known as tensile modulus. It is the measure of elasticity and it is a very important characteristic of a material. The formula of young’smodulus is stress by strain.
In this experiment I am going to determine the young’smodulus (E) of wood from the period of oscillation of a loaded wooden ruler. Equation relating the period of oscillation t to the overhanging length l of the ruler is;
T2=kl3/E
DESIGN:
To do this experiment I will following equipments; g-clamp,1metre wooden ruler, 50 gram of mass, tape, stop watch and materials to write. After getting all the required materials I will start to fix the materials. I will clamp the wooden ruler with the help of g-clamp. Using the tape I will attach the 50g mass at the end of the ruler.
I will start the oscillations with the length of 95cm of the ruler and then 90cm, 85cm and gradually decreasing. I will then make a angle less than 150 by the ruler and release it. With the help of stop watch I will measure the time period required to complete 20 oscillations.
I will use the same wooden ruler for doing the whole experiment so that the elasticity in my experiment does not change. I will measure the time period for 20 oscillations for every lengths and also use the 50...

...
Bending of a Beam
Senior Freshman Engineering Laboratories
Lab: 2E4A
Coordinator: Asst. Prof. Bidisha Ghosh
Demonstrator:
Concept
A transverse load is applied to a beam. The beam changes its shape and experiences bending moment. Internal stresses (bending stress) develop in the beam.
In the bent or curved shape, the material on the inside of the curve experiences compression and material on the outside of the curve experiences tension. In pure bending, the transverse planes in the material remain plane and parallel during bending.
Objectives
1. To measure deflections and strains in a simply supported steel beam.
2. To compare the analytical and experimental values of strains in the beam.
3. To use measured deflections and theory to evaluate the Young’smodulus of the material.
4. To note the source of errors in a typical simply supported beam experiment.
Theory
Please refer to the beam bending lecture notes as provided by Dr A. O’Connor in 2E4 class.
A steel I-beam is subjected to a point load in the middle. The beam is loaded within the elastic limit.
Figure 1: Bending of a BeamBeam deflection :
The deflection, can be computed for general loading situation by integrating the moment curvature equation. For Fig. 1, the theoretical value of...

...construction beam and find lightest weight material that can be used as an construction beam , currently we are taking strength of material course that helping us to learn more about construction beam’s design , we will be going over types of beams , types of loads and beams design , on our own we will research about the materials of beams and try to find the lightest beam’s material that we can use in construction according to our knowledge so far.
Introduction:
The universally and traditionally descriptions of civil engineering structural elements or buildings And one of the building’s principles, this is what they call beam, so basically beam is a long thick piece structural element of wood or metal or concrete, etc., that has an ability to withstanding stress ,some people they defined Beam is structural member designed to support loadings perpendicular to their longitudinal axis, but simply we say it’s the pole of a carriage in the building , as you see in the picture (# of pic ) these are beams of woods attached to each other to make the primal structure , I think this picture is an good example of construction beams,
in this project we going to talk about several things are related to construction beams, First of all we going to talk separately about types of beams, and then we will...

...of Young’sModulus
Sherin Joseph
00549618
Measurement of Young’sModulus of Aluminium using Cantilever loading
Abstract
The Young’smodulus of Aluminium was calculated using the measurements of the cantilever deflections. A beam of aluminium was clamped on one end and the other end was loaded with different weights, ranging from 1 to 15N. The deflection was then measured using a dial gauge. The slope of a load (abscissa) vs. deflection (ordinate) graph was then substituted into,
E=4L3bd3(Slope). The Young’smodulus was calculated to be 67.3 GPa. The results were then compared with known Young’sModulus value of Aluminium, 72.6 GPa.
A supplementary experiment was carried out to measure the deflection of a cantilever at different distances along the beam (from the origin) using a constant load. Measures were taken at regular intervals of 100mm from the origin when loaded with 15N. A deflection (ordinate) vs distance from origin (absicca) graph was then plotted. The known values of Young’smodulus and dimensions of the beam were used to deflection values at each interval, using the following formula
yx= PL32EI xL2- 13xL3 .Both the curves were then plotted on the same graph to compare the...

...Laboratory Three: Parallam Beam Deflection
Lab Group - 1st Mondays, Late: Jesse Bertrand, Ryan Carmichael, Anne Krikorian, Noah Marks, Ann Murray Report by Ryan Carmichael and Anne Krikorian
E6 Laboratory Report – Submitted 12 May 2008 Department of Engineering, Swarthmore College
Abstract:
In this laboratory, we determined six different values for the Elastic Flexural Modulus of a 4-by10 (100” x 3.50” x 9.46”) Parallam wood-composite testbeam. To accomplish this, we loaded the beam at 1/3 span with 1200 psi in five load increments in both the upright (9.46 inch side vertical) and flat (9.46 inch side horizontal) orientations. We then used three different leastsquare methods (utilizing Matlab and Kaleidagraph) on the data for each orientation to fit the data, resulting in the following:
E: Upright Orientation Units Method One Method Two Method Three
E: Flat Orientation 10 ksi 103 ksi
3
0.981 ± 0.100 1.253 ± 0.198 1.065 ± 0.247
1.880 ± 0.046 2.080 ± 0.083 1.881 ± 0.106
1
Purpose:
The purpose of this lab is to determine the flexural elastic modulus of a Parallam woodcomposite beam by examining its behavior when simply supported and under flexural stress, and to analyze deflection data using different least-squares methods to fit theoretical deflection curves.
Theory:
In theory, a beam’s deflection can be mapped by the governing equation of beam...

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ALUMINIUM ALLOY 1
OVERVIEW 2
TEMPER DESIGNATION 3
WROUGHT ALUMINIUM ALLOYS 4
CAST ALUMINIUM ALLOYS 5
ALUMINIUM ALLOY
-Aluminium alloys are alloys in which aluminium (Al) is the predominant metal.
-The typical alloying elements are copper, magnesium, manganese, silicon and zinc.
-Two principal classifications, namely casting alloys and wrought alloys , both of which are further subdivided into the categories heat-treatable and non-heat-treatable.
-Alloys composed mostly of aluminium have been very important in aerospace manufacturing since the introduction of metal skinned aircraft.
-Aluminium alloy surfaces will keep their apparent shine in a dry environment due to the formation of a clear, protective layer of aluminium oxide.
Overview
Aluminium alloys with a wide range of properties are used in engineering structures.
Alloy systems are classified by a number system (ANSI) or by names indicating their main alloying constituents (DIN and ISO).
Selecting the right alloy for a given application entails considerations of...

...Aluminium is the most abundant metal in the world; however it can be quite expensive due to the extraction method, electrolysis. Aluminium ore is called bauxite, it is then purified into a white powder (aluminium oxide) then the aluminium can be extracted.
To turn it into aluminium they heat the powder till it’s molten so electricity can pass through it. Its melting point is over 2,000 Celsius, so it would therefore be quite expensive. One way of cutting costs is by dissolving it in molten cryolite. Which has a lower melting point.
Current price £1.53 for a kilo of aluminium.
Iron is the second most common metal in the world and cheaper to extract than aluminium. It is extracted by using a blast furnace. Iron ores such as haematite contain iron oxide, the oxygen must be removed which then leaves the iron behind. This reaction is called a reduction reaction.
Carbon is more reactiuve than iron so it can displace the iron and join with the oxide
2Fe2O3 + 3C → 4Fe + 3CO2
Above you can see the iron oxide has been separated into iron and carbon dioxide.
Current price £1.03 for a kilo of iron ore.
Gold extraction or recovery from its ores may require a combination of comminution, mineral processing, hydrometallurgical, and pyro-metallurgical processes to be performed on the ore. Gold is not hard to extract as it is found as elements. However finding it is...