A cantilever beam is subject to a constant normal force Fn

A cantilever beam is subject to a constant normal force F_n = 500 N and an unknown constant axial force F_a. Two identical strain gauges with gauge factors of 2 are attached to the top and bottom of the beam as shown in the figure. When the forces are applied, the bridge circuit\'s voltage increases by 20 mu V. Determine the magnitude and direction of the axial force F_a.

Solution

The bending strain can be calculated from given expression and is constant before axial strain from axial force is applied, by linear superposition, the change in strain is due to the axial force only.

DR/R = DE = strain*GF

Strain between gages is 2*20 * 10^{-6 =} 40 * 10^-6

From the bending strain expressions, a total of .0429 results

Hence the difference is due to the eaxial force and is compresive since it reduces by (.0429-4*10^-5 )

Compressive strain = .04286

From the modulus : stress = 3 Gpa

taking cross sectional area .01*.03 m^2

F=9*10^5 N