Two strain gauges of gauge factor of $3$ and initial resistance of $120$ are used to monitor the

bending stress at the mid span of a simply supported beam of rectangular cross section subjected

to a uniformly distributed load. The beam is made of mild steel where the Young's Modulus

$E=210$GPa. A Wheatstone bridge circuit made of two resistors with resistance of $120$ each

and strain gauges were used for the measurement of strain. The bridge was excited using a $12V$

supply. At a particular load condition, unbalanced voltage of $1\mathrm{.}2mV$ was observed.

i$.$ Describe briefly with the aid of a sketch, how the two strain gauges were mounted on the

beam.

ii$.$ Draw the circuit diagram of the Wheatstone bridge circuit clearly indicating the location of

the strain gauges.

iii. Find the maximum bending stress at the mid span of the beam.

Note: In full bridge configuration with $R_1=R_2=R_3=R_4,$ the unbalanced voltage can be expressed

as follows with the change of resistance given as $dR.$

$V_o=\frac{V_s}{4}[\frac{d{R}_1}{R_1}-\frac{d{R}_2}{R_2}+\frac{d{R}_3}{R_3}-\frac{d{R}_4}{R_4}]$