Sewerage and Sewage Treatment

by Harold E. Babbitt

4. Size of Cross Braces.—The cross braces act as columns. The dimensions of the cross braces are determined by trial in such a manner that the vertical dimension of the brace is equal to the vertical dimension of the ranger and the compressive stress in pounds per square inch is computed from the expression,

S ⪙ S₁(1 − l
60d),[^[94]]

TABLE 60
Computations for Sheeting and Bracing for Trench Shown in Fig. 111
Material is moist sand weighing 110 pounds per cubic foot, with an angle of repose of 30°. Lumber is yellow pine, with working stress as given in Table 59. Working stresses for columns given as S(1 − l 60d).
Sheeting 2 inches × 12 Inches			Cross Braces
Depth	Maximum Bending Moment, Inch-Pounds	Maximum Fiber Stress, Pounds per Square Inch	Depth and Description	Total Load, Pounds	Size, Inches	Actual Intensity, Pounds per Square Inch	Allowable Intensity, Pounds per Square Inch
23′–26.75′	9100	1140	end at 26′ 9″	6,445	4 × 8	202	784
19′–23′	8800	1100	int. at 26′ 9″	12,890	4 × 8	403	784
13′–17.5′	8550	1070	end at 23′ 0″	6,393	4 × 8	200	784
8′–13′	7160	900	int. at 23′ 0″	12,785	4 × 8	400	784
0′–6′	3000	375	end at 19′ 0″	3,930	4 × 8	123	784
			int. at 19′ 0″	7,860	4 × 8	240	784
			end at 17′ 6″	3,566	4 × 8	112	684
			int. at 17′ 6″	7,132	4 × 8	224	684
			end at 13′ 0″	4,385	4 × 8	137	684
			int. at 13′ 0″	8,770	4 × 8	274	684
			end at 8′ 0″	2,270	4 × 6	96	687
			int. at 8′ 0″	4,540	4 × 6	189	667
			end at 6′ 0″	1,344	4 × 6	60	584
			int. at 6′ 0″	2,687	4 × 6	112	584
			end at 0′ 0″	432	4 × 6	18	584
			int. at 0′ 0″	863	4 × 6	36	584

Rangers
Depth	Area of Panel Below this Depth, Square Feet	Intensity of Pressure, Pounds per Square Inch	Total Load in Pounds	Load Transmitted to the Ranger from the			Size, Inches	Maximum Bending Moment in Thousand Inch-Pounds	Maximum Stress Pounds per Square Inch
				Panel Below	Panel Above	Both Panels
26′ 9″	24	508.5	12,200	6000	6890	12,890	8 × 10	155	1160
23′ 0″	30	448	13,440	6545	6240	12,785	8 × 10	153	1150
19′ 0″	32	378	12,100	5860	2000	7,860	8 × 10	94.3	708
17′ 6″	12	328.5	3,942	1942	5190	7,132	8 × 10	85.6	636
13′ 0″	36	274.5	9,880	4690	4080	8,770	8 × 10	105	790
8′ 0″	40	189	7,560	3480	1060	4,540	6 × 8	54.4	850
6′ 0″	16	126	2,020	960	1727	2,687	6 × 8	32.2	503
0′ 0″	48	54	2,590	863	0	863	6 × 8	10.4	161

in which S = permissible crushing across the grain in a column whose length is greater than 15 diameters; S₁ = unit working compressive strength of wood; l = length of the column; d = smallest dimension of the column; l and d are in the same units.

The lower intermediate cross brace supports a length of 8 feet of the lower ranger on which the load has been found to be 12,890 pounds. The load on the end cross brace for the same ranger is one-half of this or 6,445 pounds. The length of each brace is 4 feet 4 inches. From Table 59, S₁ is 1,000 pounds per square inch. From the column formula, S is 784 pounds per square inch.

A 4 × 8 inch cross brace is the smallest that is feasible. This is stressed only 12,890 pounds or 403 pounds per square inch, which is well within the permissible limits. The results of the other computations for cross braces are shown in Table 60.

158. Steel Sheet Piling.—This is coming into more general use with the increased cost of lumber and better acquaintance with its superiority over wood under many conditions. Although its first cost is higher than that of wood, the fact that with proper care it can be used almost an indefinite number of times renders it economical to contractors who may have an opportunity to make repeated use of it. The life of good yellow pine sheeting with the best of care may be as much as three or four seasons. With no particular care it will be destroyed at the first using. Fig. 112 shows various sections of steel piling used for trench sheeting. These forms are practically water-tight and aid materially in maintaining dry trenches. The piling can be made water tight by slipping a piece of soft wood between the steel sections when they are being driven, or by pouring in between the piles some dry material which will swell when wet. The piling is generally driven by a steam hammer and is pulled by attaching a ring through a bolt hole in the pile, or by grasping the pile with a clutch that tightens its grasp as the pull increases. An inverted steam hammer attached to the pile is sometimes used in pulling it. The impulses of the hammer together with a steady pull on the cable serve to drag out the most stubborn piece of piling.

Fig. 112.—Sections of Lackawanna Steel Sheet Piling.