Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

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.