ARCHES. 621 
ARCHES. 
By B. A. Suit, M.C.E. 
At the last meeting of the Association the writer con- 
tributed a Paper ou Circular Arches; a slight modifica- 
tion of the method followed in that paper enables us to 
obtain the formal solution for the general case, in which 
the intrados is any given curve. The method is applied 
in the present paper to obtain the solution for an Elliptic 
Arch under a uniform partial load with an additional 
concentrated load at the end of the partial load. 
The assumptions usually made in engineering text- 
books as to the position of the “line of pressure” are 
discarded, and instead we merely express the conditions 
that the ends of the arch are fixed in position and 
direction, and that at the point below the end of the 
partial load the arch remains unbroken, ?.e., the displace- 
ments of two points beside one another (one in each 
segment) at the end of the partial load are the same, and 
the tangents to the two segments at this point remain in 
the same straight line. The pressure at each point is 
assumed to be normal to the arch ring and the notation is 
the same as in the former paper. 
Considering the equilibrium of a small slamedie PR of 
the arch ring we have 
at 
pela: L=0 1 
dL w 
eae * —— = 0 
dM £ 
athe (3) 
where 7, L, M are the tension shear and bending 
moment at P 
w is the normal pressure at P due to the load, 
x is the curvature at P, 
and y is the inclination of the tangent at P to the 
horizon, 
