Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

5.4Application to the Solution of Statically Indeterminate Systems 131

Atwo-dimensionalringhasredundanciesofdirectload,bendingmoment,andshearatanysection,
as shown in Fig. 5.13. However, in some special cases of loading, the number of redundancies may
bereduced.Forexample,onaplaneofsymmetry,theshearloadsandsometimesthenormalordirect
loadsarezero,whileonaplaneofantisymmetry,thedirectloadsandbendingmomentsarezero.Letus
considerthesimplecaseofadoublysymmetricalringshowninFig.5.14(a).Atasectioninthevertical
plane of symmetry, the internal shear and direct loads vanish, leaving one redundancy, the bending
momentMA(Fig.5.14(b)).Notethatinthehorizontalplaneofsymmetry,theinternalshearsarezero,

Fig.5.13

Internal force system in a two-dimensional ring.

Fig.5.14

Doubly symmetric ring.