# In this project I am going to investigate the factors which affect how a bridge bends, and how its sag varies because of the input factors.

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Introduction

Introduction

In this project I am going to investigate the factors which affect how a bridge bends, and how its sag varies because of the input factors.

In general, sags can vary because of a series of input factors, such as the difference in mass, i.e. the load, applying on the bridge, also the difference of its position; the material the bridge made of, in terms of the differences of density; the type the bridge has been designed, such as an arch bridge and a beam bridge are only being supported at two points; a cantilever bridge is being supported by three or more points. The length, width and the thickness of the bridge (i.e. difference in volume).

The bridge bends under a mass, which can be a static force, less likely to break the bridge, or a dynamic force, more likely to break a bridge. The sag depends the compression (Fig. 1) and, the tension being made to the bonds between atoms of the bridge material.

Fig. 1 A force being exterted onto a bridge

Aim

This investigation focuses on only: -

- how sag changes when mass varies when distance between load and pivot is constant;

Middle

Graphically, I predict that the sag increased constantly would be directly-proportional to the increase of mass, i.e. a straight slope on the graph heading to the top right-hand corner, until it reaches its elastic limit (the yield point).

Varying distance

The sag of a bridge also affected by the change in length. The length is the distance between one of the two pivots and the load in the middle, which means there are two sets of identical rotations, one is clockwise and one is anti-clockwise, are taking place at the same time, this is because of moments.

Fig. 3 The motions when a sag occurs

The moment of force or the turning effect depends on both the size of force and how far it is applied from the fulcrum. It is measured by multiplying the force by the perpendicular distance from the pivot, i.e. Moment = F × d.

Ignoring one of the two identical turning effects, we are going to investigate how sag is affected by the distance from the pivot to the load.

Fig. 4 The moment acting on the left half of a bending bridge

As Moment = F × d

Conclusion

I predicted that Sαm, sag of a bridge is directly proportional to the mass applied on it, which this idea was taken from Hooke’s Law focusing on the extension of a spring, is directly proportional to the stretching force. After doing the “varying mass” experiment, I found that Sαm. I predicted correctly.

I also predicted that sag is the moment, multiplying force and distance; as

I predict that sag, which is the moment (= F × d) of the turning effect would vary proportionally when distance varies. Same for the sag of a bridge, which would vary proportionally as distance varies. After doing the “varying distance experiment, I discovered that my prediction is only partly correct. Sag is not directly proportional to distance, in fact, sag is directly proportional to distance3, Sαd3.

Evaluation

This investigation of the sag of a bridge has been done smoothly. Inaccuracy of results could be made by many factors. It was difficult to make an accurate point M (the middle point) and keep both sides absolutely identical to each other. It was in fact impossible to sellotape the needle and apply a mass at the same point, M. Therefore, measurements could not be read accurately and formed errors.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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