Question

ME 370 Spring 2020 Problem 1 (10 points): The cantilever bar in figure below has a vertical force applied, creating bending in the bar, and a horizontal force along the bar axis, creating axial strain. All strain gages are identical and experiencing the same strain caused by temperature fluctuation. Is the given configuration sensitive to axial strain? Bending strain? Temperature? Why or why not? nn Strain gages of the same kind placed in the environment and connected to Wheatstone bridge circuit 3

Answer 1

This is a simple configuration to find the bending strain of the cantilever bar. The electrical configuration is Wheatstone Bridge.

For Wheatstone Bridge shown in the figure,

if

$\frac{R_1}{R_2}=\frac{R_3}{R_4}$

the bridge is balanced and $e_0$ will read zero value

i) If the temperature of the environment changes, all four strain gauges will experience same temperature fluctuation. So that the ratios
and RA
is maintained constant. There won't be any change in $e_0$ reading. Hence the system is not sensitive to temperature fluctuations.

ii) If the cantilever is applied with axial strain, both $R_1$ and $R_2$ will experience the same strain so that the ratio $\frac{R_1}{R_2}$ is maintained constant. As a result, there will not be any variation in $e_0$ value. Hence the system is not sensitive to axial strain forces.

iii) If the cantilever is subjected to bending, the strain experienced by $R_1$ and $R_2$ won't be the same. The ratio $\frac{R_1}{R_2}$ is changed. This will cause the unbalancing of Wheatstone Bridge and $e_0$ will display some value which will be related to the bending strain. Hence this configuration is used to measure the bending strain applied to the cantilever bridge.