1540
THEORY AND PRACTICE OF ENGINEERING. Book II.
Dimensions of the other parts of the Locks. — The chambers have also walls above streams,called shoulders of defence, shoulders below stream, or discharging walls, wing-wallsabove and below, and return walls. The thickness of the shoulders of defence should beless than those of the sides ofthe lock; 3 feet 2 inches willbe sufficient, or half the heightof the water; but on accountof the foundations, and aboveall, of the beton to be placedin the centre, it is better tomake them, as well as thewing-walls above stream, 4 feet3 inches: their length shouldbe at least equal to the widthof the gates; an additional1 foot 8 inches will form thenecessary projection for therecess, into which they willfall when opened.
The return walls of the wingsare necessary, to prevent thewater from working behind thebody of the lock, but as the back walls are furnished with a lining laid very low, it will besufficient to give 25\ inches of thickness to the return walls; their length must be pro-portionate to the quality of the soil with relation to its permeability to water or otherwise.The lining may be continued further than the length of the walls; this portion cannot be toowell protected both before and behind, nor can the wing, the shoulder wall, and the back ofthe fall.
The shoulders of discharge must not be regulated by the height of the water, as it seldomrises to half that of the walls, which should be regulated by the thrust of the earth, andconsequently the thickness may be equal to one-third their total height, if they areperpendicular on both sides; but it is better to make a retreat or set-off of 12| inches at theback, level with the water, and to give the lower part an increased thickness: it is notabsolutely necessary to use any beton, but it would be unquestionably advantageous. Thelength of the shoulders of discharge should be relative to the height of the water in thechamber of the lock, the gates down the canal supporting all the weight of water, which issent back against the heel-posts, which in their turn rest entirely on the shoulders ; con-sequently their length must depend on the resistance necessary for opposing this thrust.
To ascertain this resistance it must be remembered first, that if instead of gates a wall weresubstituted, it must have the same thickness as the longitudinal walls of the chamber of thelocks, that is to say, a third of the total height of the gates, for although the water of thelower interval resists the thrust of the upper, it must not be taken into account, theresistance being small with regard to the thrust, not only from the weight of water beingmuch less, but from the centre of impression being very near the point of support; there is,therefore, but little action to resist the centre of impression of the water on the chamber,which is much higher.
Secondly, the two gates may be regarded as a single inflexible sluice, resting against theheel-posts and the sills.
Thirdly, as the thrust is considerable, it is to be presumed that if the masses constructedbehind the heel-posts of the gates were not sufficiently strong to be in equilibrio with it, adisjunction would take place in the masonry, the tenacity of which alone is not capable ofvery great resistance, particularly if the masonry be lately constructed.
Fourthly, this disjunction will take place in the line of an angle more or less open,according as the stones are shorter or longer in the direction of the headers; if they wereabout as long again as wide, the angle would be one of 50°, and its base would be one-halfsmaller; if the lengths were equal to the widths, it might be even less, as the masonsusually bed the stone in the direction of the face of the wall; the filling-in being almostalways of small stones, so that the facing only would form a resistance.
Fifthly, in order to place the resistance above the equilibrium, the tenacity of the mortarmust not be taken into account, and the base of the angle of rupture must be considered asequal to half its height. When the weight of water, instead of acting against the gates,acts against the wall, it has been already shown that the thickness of this wall should beequal to half the height of the water. Let l be the width between the hanging-posts, hthe height of the water, the cube of this wall will be \ Ih 8 ; the arm of the lever will be\ h , thus its energy or momentum $lh*. Let the shoulder wall be A II D C ; draw A E insuch a manner that E B shall be equal to £ A B, naming B E a, BA will be equal to 2a ;let x be the length B C sought for. It is evident that the mass A E D C, and that which