Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

10.7 Properties of Materials 337

Fig.10.4

Bending test on a beam, single load.

beam, producing zero shear force and constant bending moment in the central span of the beam
(Fig.10.3(b)and(c)).Theconditionofpurebendingisthereforeachievedinthecentralspan.
Thesecondformofloadingsystemconsistsofasingleconcentratedloadatmidspan(Fig.10.4(a))
whichproducestheshearforceandbendingmomentdiagramsshowninFig.10.4(b)and(c).
The loads may be applied manually by hanging weights on the beam or by a testing machine.
Deflections are measured by a dial gauge placed underneath the beam. From the recorded results, a
load–deflectiondiagramisplotted.
Formostductilematerials,thetestbeamscontinuetodeformwithoutfailureandfracturedoesnot
occur.Thus,plasticproperties—forexample,theultimatestrengthinbending—cannotbedetermined
for such materials. In the case of brittle materials, including cast iron, timber, and various plastics,
failuredoesoccursothatplasticpropertiescanbeevaluated.Forsuchmaterials,theultimatestrength
in bending is defined by themodulus of rupture.This is taken to be the maximum direct stress in
bending,σx,u, corresponding to the ultimate momentMu, and is assumed to be related toMuby the
elasticrelationship

σx,u=

Mu

I

ymax