STRAINS ON GATES. 



415 



must pass through the intersection of the lines of action of the two 

 other forces. 



Resolving the two latter forces in directions parallel and per- 

 pendicular to the line A B, it follows by the ordinary conditions 

 of equilibrium that the reaction at either end perpendicular to A B 



w I 

 = , and that the reaction parallel to the gate, or the corapressivc 



ivls 

 strain along the gate = 



The longitudinal strain will be the same whether the gates be 

 straight or curved. 



For all practical purposes the compression on any cross-section 

 of the horizontal curved members may be found by the formula 

 t=pr; t being the horizontal compression, p the intensity of water 

 pressure per unit of surface, and r the radius of the gate. 1 



It has been pointed out 2 "that this formula is only rigidly 

 and accurately true in the case of an indefinitely thin cylinder of 

 perfectly homogeneous material under an uniform external pressure 

 normal to the surface." On the other hand, it is remarked 8 : " It 

 was undoubtedly true that when the formula t = pr was applied to 

 dock gates, it was assumed that the centres of pressure coincided with 

 the centre line of the cross-sections of the gate ; but in a gate con- 

 structed of such material as Memel or pitch-pine, the factor of safety 

 was necessarily so large, owing to the variations in the strength of 

 the timber, and to the fact that to some extent in practice the dimen- 

 sions have to be regulated by the scantlings obtainable in the market, 

 that the formula is ample to cover any deviation from the ideal 

 condition," and therefore gives as good a practical result as more 

 complicated methods. 



Theoretically, the stresses on the front and back flanges of the 

 horizontal beams in iron gates vary somewhat, but it has been 

 shown * that in ordinary cases the difference is so slight that prac- 

 tically it may be disregarded. 



The following investigation of the stresses under normal condi- 

 tions is taken from Mr. Blendy's paper on '* Dock Gates.*' 6 



Let Fig. 362 be a plan of a pair of dock gates, A A' being the 

 centre of the heel-posts, B the centre of the meeting-faces of the 

 mitre-posts. Considering the left-hand gate A B, the primary forces 

 acting on this are P = water pressure, M = the reaction of the other 

 gate on the mitre-post, and H = the reaction of the hollow quoin 

 on the heel-post. 



1 M.P.I.C.E., vol. Iv. p. 12. 



3 Ibid., p. 93. 



6 Hid., vol. Iviii. p. 159. 



76tW., p. 56. 



4 /Mrf., vol. xxxi. p. 349. 



UNiVER: 



OKON1 



PtaG 



