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Investigation in to the Variables, Length and Mass, to the Sag in a Bridge

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Introduction

                                                                                                                           Alex Aitchison

Investigation in to the Variables, Length and Mass, to the Sag in a Bridge

Aim: To investigate the effect that weight and length have on the sag of a bridge.

Introduction: This wholeexperiment is based on the elasticity of the molecules that make up the bridge. Springs were investigated about 300 years ago. They were investigated by a man called Hooke. Hooke found that the extension was proportional to the stretching force so long as the spring was not permanently stretched. This means that doubling the force doubles the extension.

Extension α Stretching Force

The bonds of the ability of a body to resist a distorting influence or stress and to return to its original size and shape when the stress is removed. All solids are elastic for small enough deformations or strains, but if the stress exceeds a certain amount known as the elastic limit, a permanent deformation is produced. Both the resistance to stress and the elastic limit depend on the composition of the solid. Some different kinds of stresses are tension, compression, torsion, and shearing. For each kind of stress and the corresponding strain there is a modulus, i.e.

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Middle

The material of the bridge.The height of the ruler off the desk. The point at which the weights are hung.The over lap at each end of the bridge.Heat must be kept constant. Size of the bridge.In the first experiment: MassIn the second experiment: length    

image01.png

Results: Length

Length(cm)

SAG

15

0.10

25

0.30

35

0.70

45

1.25

55

2.10

65

4.19

75

6.90

85image02.png

11.1

Analysis: Length: For the length experiment I predicted that the curve would be parabolic my prediction was right but some of the points are not were I would have expected them to be the final points. The points are where the length is 95, 85, 75 the gaps between these points is far greater than I predicted. At the beginning the gradient is approximately. On further investigation I found that this was due to the bonds in the bridge reaching their elastic limit. As the weight increased the bond’s expand when the length gets to 75cm some of the bonds have started to reach there elastic limit. When bonds reach their elastic limit and the weight is taken of they do not return to their original size. Making the weight being added have more effect on the structure.  Also the beams are supporting fewer bonds as the length increases.

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Conclusion

Results: Length³

length3

SAG

50625

0.10

390625

0.30

1500625

0.70

4100625

1.25

9150625

2.10

17850625

4.19

31640625

6.90

52200625image04.png

11.00

Evaluation

On the whole both my experiments went well.  The results in the first experiment were mainly good and they followed the Hookes law, which is what i predicted would happen. In the second one the results were worse than in the first but still fairly accurate under the circumstances. I think the main error came from the bridge slipping on the supports. This would have made the length larger and therefore changed the reading to a higher reading another error could have been me. My reading may not have been totally correct. To improve this experiment i would try different variables such as different materials or a different cross sectional area. It would be stupid to take this section of Hooke’s law in bridges any further because on the whole my results are accurate.            

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