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.