- Compute the tension at the supports
Use the relation T=[H^2 + (wL/2)^2 ]^05 , where T= tension at supports, kips (kN), and the
other symbols are as before. Thus, T= [(2765^2 + (1.2 x 48O^2 ]^0 -^5 = 2824 kips (12,561 kN). - Compute the length of the cable
When dlL is 1/20 or less, the cable length can be approximated from S = L + 8</^2 /(3L),
where S = cable length, ft (m). Thus, S = 960 + 8(50)^2 /[3(960)] = 966.94 ft (294.72 m).
CATENARY CABLE SAG AND DISTANCE
BETWEEN SUPPORTSA cable 500 ft (152.4 m) long and weighing 3 pounds per linear foot (Ib/lin ft) (43.8
N/m) is supported at two points lying in the same horizontal plane. If the tension at the
supports is 1800 Ib (8006 N), find the sag of the cable and the distance between the
supports.
Calculation Procedure:
- Compute the catenary parameter
A cable of uniform cross section carrying only its own weight assumes the form of a cate-
nary. Using the notation of the previous procedure, we find the catenary parameter c from
d+C = TJw= 1800/3 = 600 ft (182.9 m). Then c = [(d + c)2 - (S/2)
2
]
0 5
= [(60O)
2
]
0 5
- (25O)
2
]
05
= 545.4 ft (166.2m).
- Compute the cable sag
Since d + c = 600 ft (182.9 m) and c = 545.4 ft (166.2 m), we know d= 600 - 545.4 = 54.6
ft (16.6 m). - Compute the span length
Use the relation L = 2c In (d + c + 0.55)/c, or L = 2(545.5) In (600 + 250) 545.4 = 484.3 ft
(147.6 m).
STABILITY OFA RETAINING WALLDetermine the factor of safety (FS) against sliding and overturning of the concrete retain-
ing wall in Fig 10. The concrete weighs 150 lb/ft^3 (23.56 kN/m^3 , the earth weighs 100
lb/ft^3 (15.71 kN/m^3 ), the coefficient of friction is 0.6, and the coefficient of active earth
pressure is 0.333.
Calculation Procedure:- Compute the vertical loads on the wall
Select a 1-ft (304.8-mm) length of wall as typical of the entire structure. The horizontal
pressure of the confined soil varies linearly with the depth and is represented by the trian-
gle BGF in Fig. 10
Resolve the wall into the elements AECD and AEB; pass the vertical plane BF through
the soil. Calculate the vertical loads, and locate their resultants with respect to the toe C.