Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

(nextflipdebug5) #1
9.7Tension Field Beams 307

Now,resolvingforceshorizontally,


FB−FT+σztd= 0

whichgives,onsubstitutingforσzandFTfromEqs.(9.18)and(9.19),


FB=

Wz
d


W

2tanα

(9.20)

Thediagonaltensionstressσtinducesadirectstressσyonhorizontalplanesatanypointintheweb.
Then, on a horizontal plane HC in the element ABCD of Fig. 9.8, there is a direct stressσyand a
complementaryshearstressτ,asshowninFig.9.10.
FromaconsiderationoftheverticalequilibriumoftheelementHDC,wehave


σyHCt=σtCDtsinα

whichgives


σy=σtsin^2 α

SubstitutingforσtfromEq.(9.15),


σy=τtanα (9.21)

or,fromEq.(9.14),inwhichS=W


σy=

W

td

tanα (9.22)

Thetensilestressesσyonhorizontalplanesinthewebofthebeamcausecompressioninthevertical
stiffeners.Eachstiffenermaybeassumedtosupporthalfofeachadjacentpanelinthebeamsothatthe


Fig.9.10


Stress system on a horizontal plane in the beam web.

Free download pdf