Trial version. Thermal Expansion of Solids. How can an engineer assess the expansion characteristics of a rail to produce an optimal design?

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1 Thermal Expansion of Solids How can an engineer assess the expansion characteristics of a rail to produce an optimal design? Thermal Expansion of Solids page: 1 of 10 Contents Initial Problem Statement 2 Narrative 3-7 Notes 8 Appendices 9-10

2 Thermal Expansion of Solids Initial Problem Statement Figure 1. The joint has a clear gap between the rails. This is to allow for expansion of the rails on hot days. If this gap were not present the rails would press against each other as they expanded and buckle. When the rails cool they contract and slightly increase the gap size. How can the engineer assess the expansion characteristics of the rail to produce an optimal design? Thermal Expansion of Solids page: 2 of 10

3 Narrative Introduction Many engineering materials respond to a change in temperature with a change in physical characteristics. One such change is in the physical dimensions of an object. This can be very apparent in metals which form an important class of commonly used engineering materials. The photo below shows a gap between two rails to allow for expansion in hot weather. Figure 1. Why do you think the gap between long rails has to be larger than the gaps for short rails? How could you assess the thermal expansion properties of the rail material? Multimedia What problems might a large gap in the rails cause for a train? The resource Thermal Expansion Interactive is available to demonstrate the motion of a train wheel over a gap between rails. Thermal Expansion of Solids page: 3 of 10

4 2. Experimental measurement of thermal expansion An experiment to measure the thermal expansion of a metal bar that has a length of 1 m long at 20 C produced the following results. Temperature ( C) Length (m) Why are some lengths less than 1 m while others are greater than 1 m? Are you sure the bar is 1 m long at 20 C? Activity 1 Plot these data. What do you notice about the y-axis? Activity 2 Would you expect to get the same results for a different type of metal? The gradient of the graph gives the thermal expansion coefficient of the material. This tells an engineer the change in length in metres that occurs per metre of material initially present per C change in temperature. What is the gradient of the graph you have just plotted? Give your answer in standard form. Thermal Expansion of Solids page: 4 of 10

5 3. A better representation of the data The previous section gave the following results from an experiment to measure the thermal expansion of a metal bar that has a length of 1 m long at 20 C. Temperature ( C) Length (m) Activity 3 How could the data be better presented to make plotting easier? When you have found a better way of representing the data make another plot and determine the gradient. Does it agree with the previous value? Thermal Expansion of Solids page: 5 of 10

6 4. Calculating a suitable gap Activity 4 A standard rail is made of the same material as used the previous analyses and has a length of 18 m at 15 C. By how much does it expand if the temperature rises to 30 C? Give your answer in mm. Activity 5 A welded rail has a length of 2 km at 15 C. By how much does it expand if the temperature rises to 30 C? Give your answer in m. The gap in tracks is the reason people associate a clickety-clack sound with trains. However, a modern train runs smoothly without this characteristic sound. Why is this? How could you prevent a long continuously welded rail from buckling in high temperatures? Thermal Expansion of Solids page: 6 of 10

7 5. Pre-stressed rails Long, welded rails are usually laid in cooler conditions, usually at night, so that they have contracted slightly below expected ambient temperatures. They are then either artificially heated or stretched hydraulically so that they attain the maximum expected length under hot-day conditions. At this point the rail is securely fixed to the sleepers (which are securely embedded in the ground). When the heating, or hydraulic pressure, is removed the rails want to shrink back to their original size but cannot as they are now firmly fixed. In this situation, under normal operating temperatures the rails are like slightly stretched elastic and are stressed. However, the steel used to make the rails has a high tensile strength so is in no danger or breaking. When the temperature rises the rail expands, reducing the stress in the rail. However, because the rail is pre-stressed to an extended length this does not cause buckling as the rail is merely catching up to the conditions under which it was fixed to the sleepers. What would happen if the temperature was higher than the pre-stressing temperature? Thermal Expansion of Solids page: 7 of 10

8 Notes Pre-stressed materials Pre-stressed materials are common in engineering and they allow for designs and structures to be made that would otherwise be weak, unstable or unsuitable using the material in its unstressed state. The example given in the main text is the pre-stressing of rails to prevent buckling in hot conditions. Another example is the use of pre-stressed sheets of metal in an aircraft skin. Having the skin under tension adds greatly to the strength of the construction and means that the number and size of internal spars can be reduced, thus reducing the aircraft s weight. A third well known use of pre-stressing is in the production of concrete elements for a structure. Concrete is much stronger under compression than it is under tension. If concrete is used as a loadsupporting material, the floor of a multi-story car park or bridge for example, the dimensions must be such that the load does not lead to cracking and failure: Figure 2. Pre-stressing with a tensioned metal tendon near the bottom of the concrete will tend to force a curve upwards under no load (exaggerated in the diagram!). When a load is applied the concrete block will flatten into a block that is almost entirely under compression. As concrete is strong under compression this does not lead to structural weakness. Thermal Expansion of Solids page: 8 of 10 Figure 3.

9 Appendix 1 using the interactive resources Thermal Expansion Interactive This resource is available to demonstrate the motion of a train wheel over a gap between rails. Figure 6. The display shows a wheel moving from left to right. The path of the centre of the wheel is shown with a red trace. You can move the right-hand section of track by clicking and dragging the section. The path of the wheel centre will show a dip as the wheel runs over the gap. The wider the gap the more pronounced the dip, as demonstrated below. Thermal Expansion of Solids page: 9 of 10 Figure 7.

10 Appendix 2 mathematical coverage Use and apply mathematical modelling to solve engineering problems The engineering problem is quantified using mathematical expressions Use algebra to solve engineering problems Be able to use standard form Be able to use appropriate units Be able to convert from one set of units to another Be able to draw a graph by constructing a table of values Plot a straight line graph from given data and use it to deduce the gradient, intercept and equation of the line Thermal Expansion of Solids page: 10 of 10