A 250 g mass hangs from the end of an aluminum cantilever be

A 250 g mass hangs from the end of an aluminum cantilever beam fixed at the opposite end. Determine the strain measured at a gage mounted 15 cm from the free end, given a beam thickness of 2.3 mm and beam width 2.5 cm. Is this a measureable value? Wheatstone bridges are used to record very small changes in resistance encountered in strain gage measurements. What is the difference between quarter-, half-, and full-bridge circuits? How many strain gages are required for each circuit? Can you measure axial and bending strain in each configuration?

Solution

Bending stress at a location 15 cm from free end = (My/I) = (mg*x)*y/I = (0.25*9.81*0.15)*(0.023/2)/(1/12)*0.025*0.023^3 = 166900 N/m^2 = 0.1669 MPa

So, the induced strain = 0.1669/(70000) = 2.384*10^-6 = 2.384 micron