LOCK GATES AND VALVES. 179 



It is frequently necessary in wooden gates where valves are used to reinforce the 

 valve beams so they will carry the total load with safety. This is done by framing a 

 metal girder between them, with diaphragm or vertical plates to which the valve 

 journals are attached; the metal and the 

 beam combined thus furnish the strength 

 required. 



The bottom beam of a gate which rests 

 against the miter-sill can be considered 

 as partly or wholly supported by it, and B K 

 will therefore require no unusual section. 



End Reactions. In addition to the FlG- "' 



water pressure on its face, each beam is subject to end pressure from the opposite 

 gate and from the hollow quoin. Thus if P' (Fig. n) be the total water pressure on 

 a beam inclined at an angle , and T the reaction at the toe, we have, by moments 

 about B, 



A ~R 

 P' X ~ - = r X AB sin a, 



2 



The reaction R at the quoin will be found to be of the same value as T, and inclined 

 to AB at the same angle. 



The component of T which acts along and produces compression in AB is equal to 



pi p, 



T cos at = r - V cos a = - cot a. 

 2 sin a 2 



This compression is distributed over the section of the beam, and produces a stress 



P' 

 per square inch equal to cot a -* a, where a = the area of section in square inches. 



On the upper or compression side of the beam this stress increases that due to the water 

 load ; on the lower or tension side it decreases it. 



It will usually be found that the section required for bending will be sufficient to 

 carry this additional compression without undue strain, since the point of maximum 

 stress occurs only at the edges of the middle of the beam; the material near the axis 

 of the beam thus receives very little strain from bending, and in all ordinary cases it 

 will be found sufficient to carry the load from the end reactions as well. 



Vertical Framing. Where the beams are placed vertically, as in a certain class 

 of metal gates, they are supported at the bottom by the miter-sill and at the top by a 

 horizontal girder. The strains in the latter are those from the concentrated loads of 

 the verticals, while the strains in the beams themselves are found as follows : 



Let H (Fig. 12) be the head of water, and d the distance from the top support to the 



