Results
Deflection per Unit Load (mm/kN)
The deflection per unit load in mm/kN is calculated from the slope of the graph as follows.
Slope=RiseRun=y2-y1x2-x1=6.4113-1.282260.2-0.04=32.0565kNmm
Deflection per unit load=1slope=132.0565=0.031195mmkN
Strain per Unit Load (µƐ/kN)
The strain per unit load in µƐ/kN is calculated from the slope of the graph as follows.
For Strain (+)
Slope=RiseRun=y2-y1x2-x1=6.4113-1.2822642-7=0.146544kNμε
Strain per unit load=1slope=10.146544=6.8239μεkN
For Strain (-)
Slope=RiseRun=y2-y1x2-x1=6.4113-1.28226-48-(-8)=-0.128226kNμε
Strain per unit load=1slope=1-0.128226=7.799μεkN
Calculations and Discussion
Stress
The stress per unit load in N/mm2/kN is calculated from the strain measurements as follows.
Stress per unit load=StressLoad=8.61×106-1.435×1066.4113-1.28226=1.399×106N/mm2kN
Stress per unit load=StressLoad=-9.84×106--1.64×1066.4113-1.28226=-1.599×106N/mm2kN
The theoretical value of maximum stress is calculated as follows.
Theoretical maximum stress=MomentElastic Modulus
Moment=Load×Distance=1kN×657.5mm=279 kN.mm
Theoretical maximum stress=MomentElastic Modulus=378.574.94×10-6=5.05×106N/mm2kN
The value of stresses calculated from the strain measurements are less than the calculated theoretical maximum stress. This means that the measured stresses are within the range of the theoretical maximum stress. This validates the stress and the strain measurements.
Deflection
According to the Macaulay’s method, the position at which the maximum loading occurs is calculated as follows.
The maximum deflection of 0.2 mm occurs at a load of 6.4113 kN.
Solving with Macaulay’s method, the equation for the point of maximum deflection is given as follows.
EIw=18Px3-7128PL2x
Plugging in the known values and solving for x, we get x=493.425 mm which is approximately equal to 492 mm.
Plugging in the values in the above equation, the maximum theoretical deflection for a load of 1 kN is found to be 1.5 mm.
Comparing the theoretical and experimental values, it may be seen that the two are fairly close and the experimental value is justified.
Experimental Errors
The difference in experimental and theoretical values may be due to the inaccuracy in strain measurement during the experiment. Any difference in strain will cause a noticeable difference in the resulting values. Other factors that might contribute include the human and/or systematic errors during the experiment.
The maximum load that the beam can carry per unit length is calculated by plugging the above conditions in the equation.
The maximum load per unit length is found to be 7.079 kN/m.
