Question $1$

A$.$ simple load cell is constructed by a light and uniform beam $50$ mm long and a resistive strain gauge

as shown in Figure Q$1.$ The thickness $t,$ the elastic modulus $E$ and the second moment of area I of the

beam are $0\mathrm{.}5mm,200$GPa and $50{10}^{-12}{m}^4,$ respectively. The load cell is used for measuring a

downward force $F(N)$ applying at the mid span of the beam.

is bonded

of the

Figure Q$1.$ The Construction of the Load Cell

At the mid span of the beam, the strain on the lower surface is given by

$=\frac{Flt}{8EI}$

where $F$ is the force in N and $l$ is the length of the beam in m $.$

$($a$)$ Calculate the strain $$ per unit force $F(N).$

$($b$)$ The maximum allowable stress of the beam is $100$ MPa $.$ Determine the measurement range of the

load cell.