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1、When external force is applied on object made of elastic material, there will be a change of size and shape of the object.（R1） Strain, represented by the Greek letter , is a term used to measure the deformation or extension of a body due to externally-applied forces.（R2） It can be classified as norm

2、al strain and shear strain. Normal strain is generally defined as the change in length divided by the initial length. =L/LIn this experiment, only normal strain will be measured. Stress is the internal force associated with strain. According to the Figure 1. below, it can found that there is a linea

3、r relationship between stress and strain when elastic deformation happens. And the equation = E can be got, where E is the material property that represents the stiffness of the material called Youngs Modulus.Figure 1.In engineering, its important to measure strain as it can represent the hardness o

4、f material. It helps engineers to choose appropriate material while designing. In this experiment, normal stress will be measured. And the measured stress value will be compared to the theoretical values and the error calculated.BackgroundStrain gauge is a metal strip that can be used as a measuring

5、 element for physical force if the stress is kept within its elastic limit. If the strip is stretched, it will become skinner and longer leading to an increasing of its resistance. On the contrary, if it is placed under a compressive force, it will broaden and shorten and its resistance will decreas

6、e.（R6） Thus applied force can be inferred from its resistance.In 1856, the relationship between strain and resistance of wire conductor was first reported by Lord Kelvin. And in early 1930s, bonded resistance strain gauge was first used to measure vibratory strain. Then a discovery that small diamet

7、er wires made of electrical resistance alloys could be bonded to a structure to measure surface strain was made in 1937. Its a break though that from then on strain gauge measurements were adopted for use in aircraft development programmes. Later on, the idea of making a strain gauge by etching the

8、pattern for the gauge from a thin foil was developed by Saunders-Roe in 1952. （R7）The types of strain gauge materials are various including piezoresistive or semiconductor gauge, carbon-resistive gauge, bonded-metallic-wire, and foil-resistance gauges. And the most common type of strain gauge is the

9、 bonded-wire strain gauge which is often used in pressure sensor. （R8） It looks like this:Figure 2Its usually resistances range from 30 to 3 k. This resistance may change only a fraction of a percent for the full force range of the gauge. So a quarter-bridge strain gauge circuit is designed consider

10、ing precision demanding. The circuit is shown in Figure 3.Figure 3.Normally, the rheostat arm of the bridge R2 is set at a value equal to the strain gauge resistance with no force applied. To ensure the bridge will be symmetrically balances and the voltmeter will indicate zero volts which representi

11、ng no force on the strain gauge, R1 and R3 are set equal to each other. When there is a force applied on the strain gauge making it either compressed or tended, its resistance will decrease or increase. As a result, it will produce a change in the voltmeter which has the relation with applied force.

12、 TheoryA straight bar of homogeneous material is symmetrical about Y-Y as the following figure shows. Figure 4.Assume that the traverse plane sections remain plane and normal to the longitudinal fibres after bending. If the bar is subjected to a moment at one end and an equal but opposite moment at

13、the other end, the very close section AB and CD will no longer be parallel. AC will have extended to AC and BD will have compressed to BD as the Figure 5. shows.Figure 5.The line EF will be located such that it will not change its length.This surface is called neutral surface and its intersection wi

14、th Z-Z is called the neutral axis. The development lines of AB and C intersect at a point o with an angle of radians and the radius of the curve EF = R. If y （EG） is the distance of any layer （H） originally parallel to EF. Then two equations can be got H/E =（R+y） /R = （R+y）/R Eq.1And the strain at l

15、ayer H is = （H- HG） / HG = （H- HG） / EF = （R+y） - R /R = y /R Eq.2The accepted relationship between stress and strain is = E . （E is elastic modulus）Therefore = E. = E. y /R Eq.3 / E = y / R Eq.4As the beam is in static equilibrium and is only subject to moments, the forces across the section （AB） a

16、re entirely longitudinal and the total compressive forces must balance the total tensile forces.So the internal couple resulting from the sum of （.dA .y） over the whole section must equal the externally applied moment The force on each area element = .&A =. z &y. Eq.5The resulting moment = y.&A =y.

17、z &y. Eq.6The total moment M = （y.&A） = （y. z &y.） Eq.7Using = E. y /RM =E/R.（y2.&A） = E/R （y2. z &y.） Eq.8（y2.&A） is the Moment of Inertia of the cross section.From the above the following important simple beam bending relationship results Eq.9（R9）Equipment1. A bending beam experimental device It i

18、s used to produce a force applied on the beam.2. YJ-4501A static digital strain gaugeIt is used to measure the strain.3. A strain gauge output deviceIt is used to display the results of strain.Experimental Procedure1. Set a load of 0.5KN on the beam.2. Reset the strain gauge output device to make st

19、rain gauge readings to zero3. Increase the load by 1KN and record the reading.4. Repeat this for a total 4 sets of strain gauges. （ 1KN, 2KN, 3KN, 4KNResultsTable 1. The measured dataStrain GaugeDistance From Neutral Axis（mm）Strain Gauge Readings For Applied Load（u）1KN2KN3KN4KN1y1=02y2=10-37-73-110-

20、1463y3=-1036711071414y4=15-55-109-163-2165y5=-15561091622156y6=20-72-144-215-2867y7=-2074146218288The table shows the reading data recorded from the experiment. As = E, experimental stresses for different loads can be got. Table 2. Experimental data （106Pa）Stress-7.77-15.33-23.1-30.667.5614.9122.472

21、9.61-11.55-22.89-34.23-45.3611.7622.8934.0245.15-15.12-30.24-45.15-60.0615.5430.6645.7860.48 I = bh3/12=0.02x（0.04）3/12 = 32/3 x 10-8m4 M = （F/2）.C, where C=150mm. So M1 = 75 N.m M2 = 150N.m M3 = 225N.m M4=300N.m = （M/I）yTable 3. Theoretical stress （106Pa）-7.03 -14.06 -21.09 -28.13 7.03 14.06 21.09

22、28.13 -10.55 -31.64 -42.19 10.55 31.64 42.19 -56.25 56.25 According to the equations above, theoretical stresses can be calculated.Figure 6.Figure 6. shows the diagram of stress distribution against distance from the neutral axis for experimental and theoretical values with a load 1KN. The equation

23、for the theoretical value is y = - 1.42x, and the equation for the experimental value is y = - 1.3xFigure 7.Figure 7. shows the diagram of stress distribution against distance from the neutral axis for experimental and theoretical values with a load 2KN. The equation for the theoretical value is y =

24、 - 0.71x, and the equation for the experimental value is y = - 0.66xFigure 8.Figure 8. shows the diagram of stress distribution against distance from the neutral axis for experimental and theoretical values with a load 3KN. The equation for the theoretical value is y = - 0.47x, and the equation for

25、the experimental value is y = - 0.44xFigure 9.Figure 9. shows the diagram of stress distribution against distance from the neutral axis for experimental and theoretical values with a load 4KN. The equation for the theoretical value is y = - 0.36x, and the equation for the experimental value is y = -

26、 0.33xDiscussion By using the bending beam testing device to produce a load on the beam, strains for different bending moments can be got. According to the equation = E. , the experimental normal stress distribution across the cross section of a rectangular beam can be calculated. Also, according to

27、 the equation = （M/I）y, the theoretical values can be obtained. Compare the theoretical values with experimental values, the %errors can be calculated out. Here the slope of the line representing the deformability will be made as the comparison object. The %error for load 1KN %error=8.45%The %error for load 2KN%error=7.04%