Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

212 CHAPTER 6 Matrix Methods

P.6.2 UsethestiffnessmethodtofindtheratioH/Pforwhichthedisplacementofnode4oftheplanepin-jointed
frameshownloadedinFig.P.6.2iszero,andforthatcasegivethedisplacementsofnodes2and3.
AllmembershaveequalaxialrigidityEA.
Ans. H/P=0.449,v 2 =− 4 Pl/( 9 + 2

√

3 )AE,

v 3 =− 6 PL/( 9 + 2

√

3 )AE.

Fig. P.6.2

P.6.3 FormthematricesrequiredtosolvecompletelytheplanetrussshowninFig.P.6.3anddeterminetheforce
inmember24.Allmembershaveequalaxialrigidity.

Ans. S 24 =0.

Fig. P.6.3

P.6.4 Thesymmetrical planerigid-jointed frame1234567, as shown in Fig. P.6.4, is fixed to rigid supports at
1and5andsupportedbyrollersinclinedat45◦tothehorizontalatnodes3and7.Itcarriesaverticalpointload
Pat node 4 and a uniformly distributed loadwper unit length on the span 26. Assuming the same flexural
rigidityEIforallmembers,setupthestiffnessequationswhich,whensolved,givethenodaldisplacementsofthe
frame.