Handbook of Civil Engineering Calculations

2. State the equation for L when S > L
   Thus,

200(/zj/2 + h\/2)^2

L = 2S- l (47)

A

3. Assuming, tentatively, that S < L, compute L
   Thus /I 1 = 4.5 ft (1.37 m); h 2 = 4 in = 0.33 ft (0.1 m); A = 2.6 + 1.5 = 4.1 percent; L =
   4.1(450)
   2
   /(100(9
   1/2
   
   
   • 0.67
     172
     )
     2
     ] = 570 ft (173.7 m). Therefore, the assumption that S < L is
     valid because 450 < 570.
   
   
   
   

MINE SURVEYING: GRADE OF DRIFT

A vein of ore has a strike of S38°20'E and a northeasterly dip of 33°14'. What is the

grade of a drift having a bearing of S43°10'E?

Calculation Procedure:

1. Express ft as a function of a and O
   A vein of ore is generally assumed to have plane faces. The strike, or trend, of the vein is
   the bearing of any horizontal line in a face, and the dip is the angle of inclination of its
   face. A drift is a slightly sloping passage that follows the vein. Any line in a plane per-
   pendicular to the horizontal is a dip line. The dip line is the steepest line in a plane, and
   the dip of the plane equals the angle of inclination of this line. With reference to the in-
   clined plane ABCD in Fig. 24«, let a = dip of plane; /3 = angle of inclination of arbitrary
   line AG; 6 = angle between horizontal projections of AG and dip line.
   By expressing /3 as a function of a and O: tan ft = AF/GF; tan a = AF/DF; tan /3/tan a
   = DFIGF= cos 0.

tan j8 = tan a = cos 0 (48)

(Q) Isometric view of inclined plane (b) Strike-and-dip diagram (plan)

FIGURE 24

Horizontal