NEEDLE DAMS. 223 



In all ordinary cases, as in dams with trestles 4 to 8 feet apart, it will be found that 

 a considerable excess of metal must be used above that required for the direct strains, 

 in order to receive stiffness. Thus on the Louisa dam (Big Sandy River) the pass 

 trestles are 4 feet apart, and each leg is composed of one 4-inch 8-lb. channel. The 

 actual section needed for the direct strains is only about one-third of this. 



On the weir of the same dam the trestles support a head of 7 feet, but were made of 

 similar section, and are now used to carry a span of 8 feet, the 

 original span having been 4 feet. 



On the older needle dams of the Seine and of the Saone the 

 stresses in the main members varied from 2000 Ibs. to 2700 Ibs. per 

 square inch. 



The width of base is made from six- to eight-tenths of the 

 height. 



Needles. Suppose it is desired to design a needle to support a 

 head of water H, the lower pool being left out of the calculation 

 (Fig. 15). Let H = depth of water on the sill in feet; P= pressure 

 of water on the needle ; w = width of the needle in feet ; / = thickness 

 in inches required at the point of maximum moment. The length 

 of the needle is then H sec a. 



H iuH^ sec OL 



Then P = H sec a X w X X 6 2 Ibs. = X 6 2 Ibs. , of which one-third goes to A. 



2 2 



The bending moment M, at any point vertically distant x from the surface, is in inch- 

 pounds. 



/ H x sec a x x sec a\ 



M = ( wH. sec a X62^ Ibs. X -- wx sec a- -^62$ Ibs. -- I Xis 



\ O / 



. 



(/7 2 -* 2 )Xl2. 



wx sec 2 a. 62% Ibs. 



-- - 2 



IT 



This moment is a maximum at a point vertically distant 7= from the surface 



V3 

 of the water, in any beam supporting water level with its top and on one side only. 



17 



Putting x = :=., we find 



wH* sec 2 X 62* Ibs. X 12 . 

 M = - 7= inch-pounds. 



From the formulas for beams we have 



,, 57 



M = - and 7 = , 



c 12 ' 



where 5 = extreme fiber stress per square inch, 



c = distance of center of gravity of section from outside in inches, 



7 = moment of inertia of section, 

 M and / being as before stated and w t the width of the needle in inches. 



