The intent of this experiment was to find the value of Young ‘s Modulus for a rectangular subdivision of a stuff. The first phase was the adhesion of the strain gage to the mild steel beam, and soldering connexion wires onto these contacts. The beam was so arranged as shown in Image 1, such that, for two changing weights at either terminal of the beam, values of maximal warp and strain were measured for each certain weight. Using the equations of simple Beam Theory, and geometric analysis of the beam whilst under burden, the Elastic Modulus can be found by two methods as described in the theory subdivision, and an mean taken. Since the beam in inquiry is a mild steel beam, this experimental value of Young ‘s Modulus can be compared against the standard value for the stuff, taking to an analysis of the truth of the experiment.

### 2 Theory

The first phase of this bipartite experiment was the readying of the stuff for adhesion of the strain gage. The surface readying is indispensable to guarantee that the physical contact between the strain gage and the stuff under strain is accurate. This ensures that whatever strain is experienced by the stuff is replicated precisely in the strain gage. As such, the undermentioned procedures must be taken to guarantee a good adhesion:

- Degreasing – the surface was foremost degreased to take oils, lubricating oils and organic contaminations. This was performed with propanone and tissue paper.
- Surface corrading – the following procedure involved corrading the surface to take any slackly bonded contaminations, such as rust, graduated table or pigment. This was done with surface conditioner and all right class emery paper. Once the surface was bright, the stuff was cleaned with tissue paper.
- Layout lines – the stuff was marked with the terminal of a pen at the points where the strain gage was to be positioned. The place of the strain gage is imperative as if it is misaligned the displaced value of strain will non be the true strain in the stuff.
- Surface conditioning – the surface was so scrubbed with conditioner and cotton buds. This was repeated until the cotton buds were no longer discoloured when cleansing. The residuary conditioner was cleaned with tissue paper by pass overing from the Centre outwards in on gesture.
- Neutralizing – to guarantee good adhesion of the strain gage, the surface must be neutralised. This is done by using neutraliser liberally to the surface and cleansing with cotton buds. The extra neutraliser was wiped off with tissue paper. The surface should now be ready for strain gauge adhesion. For steel, this must be done within 45 proceedingss.

The strain gage and soldering contacts are now ready to be stuck to the stuff, which was performed as follows ;

- The strain gage and soldering contacts were placed on the glass surface and picked up with cellophane tape, with a spread of around 1.5mm, as shown in the image to the right.
- The strain gage and contacts are so positioned in the exact topographic point on the saloon and stuck down. The tape is pulled up and left stuck on one border, such that the adhesive country is exposed.
- The adhesive side of the strain gage and contact points are so applied with Catalyst solution, to guarantee a good adhesion with the adhesive solution.
- The base of the tape is so coated with the adhesive solution, and the tape is spread across the adhesive country with a tissue paper, such that a bed of adhesive is dispersed across.
- The strain gage and contact points are so held steadfastly in contact with the surface to put the adhesive.
- The tape is so removed to go forth the strain gage and contact points in the right place, steadfastly attached to the saloon.

The wires are prepared such that there is a long thin strand, to be soldered to the strain gage, and a thick short wire, soldered to the contact points to supply a good ground tackle. A diagram of this is shown below.

The steel beam is now ready to be tested for strain and warp, to cipher Young ‘s Modulus.

The experimental process to happen the strain and warp on the beam was as follows:

- The setup was set up as shown in Image 1, guaranting that the distance between the warp metre and simple support was the same on each side, and that the distance between the simple support and hanging weight was the same on each side. These distances were measured to be 12.7cm and 14.1cm severally. The strain gage is on the tenseness side such that the strain is given as a positive value.
- The initial weight is 1lb on each side, which gives a certain warp and strain. However, the strain metre and warp gage were adjusted such that at this weight the strain and warp indicated was 0.
- The weight on each side is increased by 1lb, which gave a certain warp and strain. These values were recorded.
- The beam is loaded in increases of 1lb until the weight on each side is 5lbs, with the strain and warp being recorded at each phase.
- The beam was so unloaded in decreases of 1lb until merely the initial weight was left. The consequences for droping mirrored the consequences of strain and warp for burden, turn outing the snap of the beam.

The recorded consequences were tabulated, and taken off from the initial value of strain and warp at Weight = 1lb, to give values of weight, strain and warp difference. These values were so input into a graph such that the gradient of ( weight / strain ) and ( weight / warp ) lines could be obtained.

As proven in Appendix 1 at the terminal of this study, the value of Young ‘s Modulus for this stuff can be calculated by the Equation 1:

Where

Equation 1: Young ‘s Modulus when given gradient of Weight Strain graph.

In the above equation, a was the distance between the simple support and the point where the weight hung, ( W/e ) was the gradient of the Weight Strain graph, B was the breadth of the beam and T was the thickness.

When sing the warp of the stuff, the 2nd value of Young ‘s Modulus can be found in the undermentioned equation, Equation 2, as proven in Appendix 2:

Equation 1: Young ‘s Modulus when given gradient of Weight Deflection graph.

The variables in the above equation are the same as Equation 1, nevertheless cubic decimeter is the length from the simple support to the distortion gage and ( W/d ) is the gradient of the line on the Weight Deformation Graph.

Using the two experimental values for Young ‘s Modulus, an norm can be taken and compared against the published value.

### 3 Consequences

The following tabular array, Table 1, shows the numerical consequences of the experiment, in the signifier of difference between the measured value and the initial value for each.

Weight difference ( lb 's ) Weight Difference ( N ) Strain Difference Deflection Difference ( m )0 0 0 0 1 4.448 7.20E-05 0.000375 2 8.896 1.50E-04 0.000755 3 13.344 2.25E-04 0.00113 4 17.792 2.99E-04 0.00149

Table 1: Valuess of strain and warp for a given weight on beam.

Therefore, the first value for Young ‘s Modulus is 211.4GPa.

The same can be done for Graph 2, which shows the reverse gradient, which is equal to r, is 11940.9. Using this value for R in equation 2, the 2nd value of Young ‘s Modulus E2 can be found:

Therefore the 2nd value for Young ‘s Modulus is 217.2GPa.

### 4 Discussion

As shown in the consequences subdivision, the experimental values for Young ‘s Modulus of the stuff were 211.4GPa and 217.2GPa.

Therefore, the mean value was found to be 214.3GPa.

The by and large accepted value of Young ‘s Modulus for mild steel is about 200GPa, which gives and mistake value of 6.7 % . This mistake can be accounted for by the followers:

- When ab initio puting up the beam such that the beam and its tonss were symmetrical, the lengths were measured by a swayer. The mistake involved in this, as a general human reading mistake, is around one half of the smallest division, so around 0.5mm. The largest mistake will ensue from the smallest length, measured to be 12.7cm, which resulted in a measurement mistake of around 4 % .
- The warp of the beam was read off an parallel gage, which had a graduated table of 0.01mm/division. As such, the mistake is ? a division, i.e. 0.005mm. At the minimal warp, the maximal mistake is about 1.3 % .
- There was besides an mistake associated with the weights themselves. Since they have been in usage for some clip, the indicated weight of each, 1lb, may non hold been the existent weight during the experiment. This mistake, nevertheless, can non be quantified.

### 5 Decisions

By manner of the method outlined by this study, the experimental value for Young ‘s Modulus was 214.3GPa. The mistake associated with this measuring was 6.7 % , which is comparatively low. As such, the experiment can be considered successful in finding the value of Young ‘s Modulus for the given beam.