i 7 8 THE IMPROVEMENT Of RIVERS. 



The proportion of the pressure on a between CD and F' which is carried to CD is 



X 



Ibs. 



- J 3 (H + d) + .| X 67* Ibs. - S. 



Similarly the proportion of pressure on c is 



c X \'' (H + * + g j X 6,J Ibs. - ? j 3 (// + </) + * j X 6a| Ibs. - T. 



The proportion of the uniform load between E and CD, extending the length of th 

 beam, which is carried to CD is 



The reaction at C is therefore 20 + 



The bending moment at the center is then 



7 7 



- + - = R, 



R- 1 - -Q(b + c) ~s( : + b\- J X 12 inch-pounds. 



From this we can find as before the section required. As the center of the beam is the 



point of maximum moment, it should be seen 

 that it is not too much reduced by notching 

 out for the gate-straps which are usually 

 placed there for the purposes of construction- 

 Where more than two valves are used 

 the process of analysis is similar to that given 

 above. 



In a metal gate where cover-plates are 

 used it will of course be necessary to find 

 the moment at one or two other points to 

 determine the length of plate required. 



The calculations for the upper beams 



FjG I0 of a gate are the same as used for beams 



with uniformly distributed loads as given in the first example. 



In the foregoing calculations we have not taken into account the support afforded 

 to the beam through its being connected with those above and below. Such support 

 exists, but its amount is uncertain, as it depends on theoretical perfection of jointing 

 which may or may not exist, and which in any case is liable to change as the gate 

 wears. It is best therefore to proportion each beam so that it will carry its load inde- 

 pendently. 



