For the cable structure shown in figure below determine the

For the cable structure shown in figure below, determine the forces of reaction, the tension in each segment of the cable, and the sag in the cable. The total Ir····h of the cable is 65 ft. Hp 10 ft 50 kips 35 ft

Solution

S₁+S₂ =65ft

S1/15 =65/50

S1=19.5ft , S2=45.5ft

therefore Sag =(45.5²-35²)^1/2 =29ft

Tan =29/35        tan 2 =19/15    

=39.35                2 =51.7

using Lami ‘s theorem

F_CA/sin (129.35) =F_CB/ sin (141.7) =50/sin (88.85)

F_CA=38.66 Kips F_CB=30.98Kips

H_A=H_B

Taking moment about c

-V_B X35+H_B X 29 =0

Taking moment @a

-V_B X 50 +10H_B =-750

Solving both equations simultaneously

H_B =23.86kip, V_B=19.77Kip

VA=50-19.77=30.23Kip