Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

44 CHAPTER 1 Basic Elasticity

P.1.11 The simply supported rectangular beam shown in Fig. P.1.11 is subjected to two symmetrically placed
transverse loads each of magnitudeQ. A rectangular strain gauge rosette located at a pointPon the centroidal
axisononeverticalfaceofthebeamgavestrainreadingsasfollows:εa=− 222 × 10 −^6 ,εb=− 213 × 10 −^6 ,and
εc=+ 45 × 10 −^6. The longitudinal stressσxat the pointPdue to an external compressive force is 7N/mm^2.
CalculatetheshearstressτatthepointPintheverticalplaneandhencethetransverseloadQ:

(Q= 2 bdτ/3 whereb=breadth,d=depthofbeam)

E=31000N/mm^2 ν=0.2

Ans. τ=3.17N/mm^2 Q=95.1kN.

Fig. P.1.11