EARTHWORK 



201 



Therefore, 



F = 233.33+1.85 = 235.18, say 235, cu. yd. 



Correction for Curvature. Besides the prismoidal correction, 

 a correction for curvature is sometimes required in calcula- 

 tions of earthwork on a curve. 



In Fig. 6, let rn be the curved center line of the roadbed, 

 O the center of this circular curve, and R its radius. Let 

 Ai be the area of the cross-section mnpq, G its center of gravity, 

 and ei the horizontal distance from G to the center of the 

 roadbed, which distance is called the eccentricity of the section. 

 Similarly, let At be the area of the section mmipiqi, G\ its 



FIG. 6 



center of gravity, and ei the eccentricity of that section. 

 The general formula for curvature correction is, then, 



If G and Gi lie on the outside of the curved center line of 

 the roadbed, C c is to be added to the volume calculated as 

 for a straight track. If G and Gi are on the inside of this curved 

 center line, the correction C c is to be subtracted. 



The expression for C c shows that the larger the eccentricities 

 of the end sections, the larger C c will be, and that, if the 

 radius of the curve is very large, C e will be very small. For 

 curves of very large radii, the correction is usually so small 

 that it may be neglected. When the area of that part rpqt 

 of the end section lying on the inside of the center of the track 

 is approximately equal to the portion of the area rtmn lying 



