Results
Deflection per Unit Load (mm/kN)
The following method is used to calculate the deflection per unit load in mm/kN from the slope of the graph.
Slope=y2-y1x2-x1=6.41-1.2820.19-0.03=32.05kNmm
Deflection=132.05=0.0312mmkN
Strain per Unit Load (µƐ/kN)
The following method is used to calculate the strain per unit load in µƐ/kN from the slope of the graph.
For Strain (positive)
Slope=y2-y1x2-x1=6.41-1.28242-6=0.142kNμε
Strain=1slope=10.142=7.042μεkN
For Strain (negative)
Slope=y2-y1x2-x1=6.41-1.28246-8=0.135kNμε
Strain=1slope=10.135=7.407μεkN
Calculations and Discussion
Stress
The following method is used to calculate stress per unit load in N/mm2/kN from the strain measurements.
Stress=StressLoad=8.61×106-1.23×1066.41-1.282=1.439×106N/mm2kN
Stress=StressLoad=9.43×106-1.64×1066.41-1.282=1.519×106N/mm2kN
The following method is used to calculate the theoretical value of maximum stress.
Maximum stress=MomentElastic Modulus
Moment=Load×Distance=1kN×378.5mm=378.5 kN.mm
Maximum stress=MomentElastic Modulus=378.574.94×10-6=5.05×106N/mm2kN
The values of the above calculated stresses from the strain measurements are within the range of the maximum stress. This is the endorsement of the correctness of the experimental methods.
Deflection
The position at which the maximum loading occurs is calculated using the Macaulay’s method in the following steps.
The maximum deflection is 0.19 mm which occurs at a load of 6.41 kN.
Solve using the Macaulay’s method to get the below equation for the beam.
EIw=18Px3-7128PL2x
Plug in the known values and solve for x, the point at which the maximum loading occurs is found to be x=480.979 mm which is fairly close to 492 mm.
Plug in the values to calculate the maximum theoretical deflection for a load of 1 kN. The value is found to be 0.192 mm.
A comparison between the theoretical and experimental values shows that the experimental values are well in agreement with the theoretical values, thereby endorsing the correctness of the experiment.
Experimental Errors
The difference in experimental and theoretical values is due to the possible inaccuracy in measuring strain in the experiment. The induction of other human errors in the experiment will also cause a difference in the theoretical and practical values. It was observed that the pressure gauge was leaking, this could lead to inaccurate pressure readings on the gauge and cause the difference. There might be other factors as well which contribute to the difference.
Maximum load per unit length
The following method is used to calculate the maximum load that the beam can carry per unit length.
Plug in the known values in the above equation to find out the maximum load. The maximum load is calculated to be 13.99 kN/m.
