Consider a 2-dimensional cantilever beam made of stainless steel and with dimensions L, b and h, and subjected to a vertical load of 2P exerted at its free tip:

(a) Design a configuration (location and alignment) of four single strain gauges at the root of the beam that could be used to determine the maximum load the beam could carry before breaking. Include all derivations and specify that load P.

(b) Using the Micro-Measurements catalog, select one or more strain gauges to use in

(a) and justify.

(c) Derive the expression of the gauge factor from the resistance change as a function of resistivity equation.

(d) Draw a schematic of a quarter Wheatstone bridge and explain how the strain gauges can read the data. Derive the formula to determine the strain. Specify all the equipment that is needed to measure the strain gauge data.

(e) If metallic foil strain gauges were not used, indicate what other means could be used to measure the strain. Compare the different solutions and justify.

(f) Create a Matlab code to determine the axial strain at any position of the surface of the beam in terms of the load using Euler-Bernoulli beam theory.

(g) Create a Matlab code to determine the axial strain at any position of the surface of the beam in terms of the load using a first order shear beam theory.