Answer:
x = 8 ft
Step-by-step explanation:
Given:
- Length of beam L = 20 ft = 240 in
- Left cable: E = 30,000,000 psi, Area = 2 in2
- Right Cable: E = 10,000,000 psi, Area = 4in2
- Force P = 10,000 lb
- distance from left cable = x
- distance from right cable = 240 - x
- Length of both cables h = 15 ft
Find:
Distance x that would ensure the beam remains horizontal.
Solution:
- Compute forces in right and left cables P_1 and P_2, respectively:
Sum of vertical forces
P = P_1 + P_2
Sum of Moments about left point
P_1*240 = P*x
P_1 = P*x / 240
Hence, P_2 = P*(240 - x) / 240
- Compute deflections in right and left cables Δk and Δm, respectively
Δk = P_1*h / A_1*E_1
Δm = P_2*h / A_2*E_2
- Since, deflection are same equate the above two Δk = Δm :
P_1*h / A_1*E_1 = P_2*h / A_2*E_2
P*x/ 240*4*10,000,000 = P*(240-x) /240*2*30,000,000
(x / 2) = (240-x) / 3
- Compute for x:
3x = 480 - 2x
5 x = 480
x = 96 in = 8 ft
