328
DOCK ENGINEERING.
Connecting Pièces—Timber gates of the voussoir type are generally
stiffened by horizontal connecting pièces (vide tig. 288) on the front of the
gate, forming chords to the arc of the gate. The total moment of resistance
in such cases is compounded of the separate moments due to the voussoir
and the connecting piece, and since the angle of deflection producing the
moment of resistance is the same in both members, it is evident that the
distribution of stress due to bending will be similar, the amount and
maximum intensity being determined by the relative breadths of the
voussoir and connecting piece.
To draw the diagram of stress, find first the stress area, LPORM
(fig. 263), for the voussoir, considered as acting alone. Then through C the
neutral axis of connecting piece draw Q S parallel
to P R. The area MQOSN represents the
proportionate stress in the connecting piece. We
must now reduce both areas in the same propor-
tion until their sum is equal to the area of stress
caused by the bending moment—that is, LPORM.
To do this, divide LP in the point X such that
LX: XP : : O L2 : C M2. Draw XX'through the
Fig. 263. point O and Y Y' parallel to it through the point
C. Then the etched portion, L X O X'M Y CY' N,
is the required stress diagram as regards bending moment only. The direct
compressive stress is taken by the voussoir as before.
The proof of the diagram is as follows .■—The triangles, O X P and
CM Y, must be equal to fulfil the required conditions. Hence
XP x LO = MY x CM
MY-Xf x LO
OM '
Also, since X X' and Y Y' are to be parallel,
MY : OM : .•X'M : M0
: : L X : LO
CMxL X
MY - LO '
Equating the two values of M Y,
XPx LO _ CMxLX
CM LO
XP = CM2
LX L O2'
So delicate an adjustment of stress depends upon conditions which
cannot be obtained in practice, and it is certainly advisable to construct the
voussoirs of a gate so that they may be able to take the whole of the stress
unaided by the connecting pieces.