CAMBEIA STEEL. 75 



THRUST OF ARCHES. 



The horizontal thrust of segmental floor arches, on the assump- 

 tion of uniform loading, may be found by the following formula: 



3WL* 

 ~ 



in which 



T = pressure or thrust in pounds per lineal foot of arch. 



W = load on arch in pounds per square foot, uniformly distributed. 



L = span of arch in feet. 



R = rise of segmental arch in inches. 



For a concentrated load at the center, of weight P, the thrust 

 3PL 



T = 



R 



For arches with flat tops and bottoms, such as are used in floors, 

 the voussoir joints on each side of the central key are usually laid 

 out on parallel lines, and in these cases the thrust may be deter- 

 mined approximately by using for R, in the above formula, the 

 effective depth of the arch, which is somewhat less than the 

 nominal depth, as indicated on page 77. 



For segmental arches the rise R is the vertical distance from the 

 highest part of the intrados to the plane of the springing line. If 

 the radius of the intrados for segmental arches is r, the rise may 

 be obtained from the following formula: 



conversely,r =+ 



TIE RODS. 



Although in the completed structure the horizontal thrusts of 

 adjoining arches may counterbalance each other, the tie rods 

 should be so proportioned and spaced as to withstand the entire 

 thrust of the arches, thus tying the structure together and facili- 

 tating the construction. 



