This question requires the analysis of data
presented Below. For this demonstration a rectangular bar is clamped at
one end and is subjected to a state of
combined loading %u2013 torsion and bending.
Three strain gauges are positioned on the bar and the direct strains in
the directions of the three gauges
are to be deduced and analysed.

E=72GPa

G=27GPa

a (width of bar) = 30mm

b (heigh of bar) = 5.0mm

mass of weight = 2.0kg

g = 9.81 m/s^2

L_bend = 435mm

L-torque = 300mm

The grade resistance for loaded R_(in degrees) also note that measured in ohms

R_0 = 120.47

R_45 = 120.31

R_90 = 120.33

Grade Resistance loaded R

R_0 = 120.72

R_45 = 120.53

R_90 = 120.25

NOTE shape of bar is a L shape with gauges on top of L an weight on lower end of L.

The strain registered on a strain gauge can be
calculated from the change of resistance of the gauge ( ? R) provided the gauge factor (GF) and unstrained resistance of the gauge (R) are known.

?=1GF*?RR

The manufacturer of the strain gauges provides the following value:

GF = 2.055 (dimensionless).

Required analysis tasks:

(a) Determine the direct strains on each of the 3 gauges.

(b) Obtain the following strains from the strain gauge measurements: ? x
? y and ? xy

(c) Calculate the values of s x s y and t xy corresponding to the strains
obtained in part (b) using the specified material properties.

(d) Based on the loading the given geometry
and Stress Analysis expressions calculate the bending moment and the
direct stress due to bending at the
strain gauge location.

(e) Based on the loading the given geometry
and Stress Analysis expressions calculate the torque (twisting moment)
and the shear stress due to torsion
at the strain gauge location.

(f) Compare results from parts (d) and (e) with those of part (c) and discuss any differences.

(g) Sketch a square element aligned with the x
and y directions and show the direct and shear stresses acting on each
edge of the square.

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