Modelling a Frame Subjected to Multiple Loading Conditions Essay

In this experiment the main aim was to modelling a frame subjected to multiple loading conditions and record how the force and strain vary to different loads. The frame represented a simple roof trusses and the loading conditions are similar to what a typical roof would undergo. In this experiment a universal fame was used with load cells to provide the load and digital force and strain instruments to record the data. As the load was increased the strain went up linear showing a linear relationship between loading and strain. After analysing results it was found that the results for experimental forces compared to theoretical forces were very close showing that this experiment was very accurate, with very small uncertainty, the reason for this is due to very sensitive equipment as a change of 1 µ? is equivalent to change of 6 N (using young’s modulus) and other factors described in detail in the report. Table of Contents Summary 1 Introduction Pg 4 2 Theory Pg. 4 3. 1 Apparatus Pg 6 3. 2 Experimental procedures Pg 8 4 Observation and results Pg 8 4. 1 Results Pg8 4. 2 Observations Pg11 4. 3 Discussion Pg11 4. 4 Sources of error Pg11 5 Conclusions Pg12 References Pg13 Appendices Pg13 Introduction The aim of this laboratory was to carry out an experiment to measure the strain in members of a frame, where load was being applied in different loading conditions. This experiment was carried out to put to use the theory learnt in lectures and see how they actually perform in a real life model. By doing this it is possible to appreciate the limit of theoretical approach to these loading conditions and compare the errors. The model used in the experiment was that of an idealised roof truss, a roof must withstand a lot of force over a long time during its lifetime. Three 3 different loading scenarios will be modelled and the strain forces are expected to be within the range of the calculated theoretical forces. Main aims were: 1. Measure the strain in each member and record results 2. Calculate theoretical values for the experiment 3. Compare theoretical values with experimental results and calculate percentage error Theory In a frame model where there is a load being applied members of the frame will feel a compressive or tensional force. The value of the force can be worked out by resolving the forces in horizontal and vertical directions and taking moments. This is done by analysing each of the joints of Fig 1 separately. In a rigid static frame the sum of the vector forces add up to zero Fig 1 model of experiment The first loading model has is simulated with a load of 500N. First work out the value for the reaction force at the supports. Then use these values to calculate the tension in each member of the truss. Hand written theory in appendix (1) Apparatus The apparatus used in this experiment are by Tecquipment STR8 Pin-jointed Frameworks Digital force display -500N to 500 N Digital strain display- 1Ãâ€"10-9 ? Load cell – 0-500N range Screwdriver Experimental procedures Test 1 1. Calibrate the load reading instruments to measure zero on channel 1 on the digital load display, if the display shows load being applied then adjust the appropriate load cell W1 by rotating the appropriate knob. Test 2 1. Carefully remove the pin that is holding load W1 and reinstate load W2 2. When no load is being applied to the members check the digital strain display, there are 13 channels one for each gauge. Each gauge must be reading zero if not use adjust the reading to read zero as close by using a small screw driver. 3. Make sure the load cell W2 does not interfere with the frame. 4. In table 1 record the strain values of each member from the digital strain display. 5. Next apply a load of 100N to the load cell W1 by turning the handle anti clockwise then read the digital strain display for channels 1 to13 and record in the table. 6. Repeat steps 5 for loads 200N, 300N, 400N and 500N 7. After recording all values reduce the load to zero by rotating clockwise. 8. Using the values of strain for 500N load calculate their equivalent member forces and record them in table 3 using the following equations : Test 3 1. For this model both load cells must be loaded on to the frame 2. In table record the strain values of each member from the digital strain display when no load is being applied 3. Next apply a load of 500N to the load cell W1 by turning the handle anti clockwise then read the digital strain display for channels 1 to13 and record in the table. 4. Switching to channel 2 on the digital force display apply a load of 100N then read the digital strain display for channels 1 to13 and record in the table 5. Repeat steps 4 for loads 200N, 300N, 400N and 500N on load cell W2 6. After recording all values reduce the load to zero by rotating clockwise. 7. Using the values of strain for 500N load calculate their equivalent member forces How to use the strain to convert into force is described in the appendix (2) 4. Results and observations 4. 1 Results CENTRAL LOADING Angled loading Multiple loading The sum of experimental forces for loading of 500 N in loading 1 and 2 4. 2 Observation Allow the equipment to stabilise by waiting 5 minutes in order to eliminate and uncertainty due to heat affecting resistance values. There are no significant health and safety risks in this experiment. 4. 3Discussion A way in which to improve the results of the experiment would be to take repeat readings of the strain for each gauge at least three times in order to eliminate any anomalous results. Another addition would be having different loading conditions on the frame and see how they affect the two gauges EF and IJ as they experience any strain which could lead to the question are these members required and do they make any difference. In loading condition 3 by having 2 load cells you create a model where there are members which are superimposed. When analysing table 8 and looking at the sum of the experimental values are larger than the theoretical value, when looking at member AH the values are notably are different when superimposed. 4. 4 sources of error The main sources of uncertainty will come from the calibration of the device as the digital strain reading instrument has an accuracy of  ± 0. 5Ãâ€"10-10 ? and the digital force display has an accuracy of 0. 5 N. These are very small values; it is difficult to zero the strain display which lead to a poor accuracy. The strain values is calculated by the change in resistance of the wire when it is under tension or compression, however change in temperature would affect the length of the wire therefore giving a different value of resistance leading to inaccurate strain reading. 5. Conclusion After analysing the results in detail it is shown that the difference in theoretical and experimental results is not significantly different and therefore using the theory of resolving forces it is possible to gain an accurate value of true member forces and equally important to simulate and model the situation in real life scenario to gain a true understanding of what is going on. Also analysing table 3 shows that is also possible to calculate the force on a complex load by adding the forces individually. References Mechanics structures and thermo dynamics –university of Warwick Mechanics lectures by Dr. T. Karavasilis http://www. tecquipment. com/Datasheets/STR8_0213. pdf 29/12/2013 Appendices Pin jointed lab briefing sheets Theory (1. ) (2). Stress strain thoery