Question

The horizontal distance from A at one end of the river to frame C at the other end is 20 m. The cable carries a load W=50 kN.

a.) At what distance from A is the load W such that the tension in segment AD of the cable is equal to that in segment CD?

b.) When the load W is at distance x1= 5m from A, the sag in the cable is 1m. Calculate the tension in segment DC of the cable

c.) If the sag in the cable is 1m at a distance x1= 5m, what is the total length of the cable?

FIGURE SIT. CC: 20. m D W-50 KN SIT. CC: The horizontal distance from A at one end of the river to frame C at the other end is 20 m. The cable carries a load W = 50 kN. 79. At what distance from A is the load W such that the tension in segment AD of the cable is equal to that in segment CD? A. 6.67 m B. 12 m C. 10 m D. 15 m 80. When the load W is at the distance x1 = 5 m from A, the sag in the cable is 1m. Calculate the tension in segment DC of the cable. A. 184.58 kN B. 187.90 KN C. 181.31 kN D. 191.26 kN 81. If the sag in the cable is 1 m at a distance x1 = 5m, what is the total length of the cable? A. 20.09 m B. 20.26 m C. 20.42 m D. 20.13 m 11

Answer 1

Solution :- Criven that i- Vc 2om Rc re * HA А. He ac 'AD XCO Н. W WEBORN 6 Criven, Tension in AD = Tension in CD TAD Teo RA Rc Sunt the = Juz+HE Sң со -HA & He=0 HA=He = H (Say) TV+ H² Vu+M? The Left hand side term and Right Hand Side term of above equation will be equal only when VA=Vc = 50 = 25kN t

and we know that VA and No will be canal When load. 'W' is at Cender of Span. that is at ild =lom=H= And (6) Whem, x=5m and Sag, y=im X2=20-5= 15m Evro V-50+ Vero VA TVC = 50KN EM=0 V* 20 * 20 – 50*(20-81)=0 50*120-5) = 0 20 V 50AIS 20 = 37.5KN (^) A from equation ② V=50-VA= 50-37.5=12:5KN Ve=12.5KN EH=0 -HA theo THA= H = H (say)

Moment is too we know that everywhere in the Cable Hence EMD=0 V* Hq - Henyo 12-5*15 = 187.5km He = H = 12:5*15 He=H= 187.5KN () Now, Tension to 12 + H2 112.98+187 Tco=187.916 KN C Whem, Sag, y=1m and H=5m H₂=20-5=15m Total length of Cable = length of As a length of De L E552 + 1152 12 =20.1323m) Ane Any