Point Load On Cable
Point Load On Cable
(OP)
Hello everyone.
The problem:
I need a way by hand the calculate the tension in a cable due to a central lateral point load neglecting any intial sagging effects and intial tensioning. So basically the intial stiffness is zero.
I have looked at many iterative solutions for similar cable problems but have not found any for this case.
Any help would be much appreciated.
The problem:
I need a way by hand the calculate the tension in a cable due to a central lateral point load neglecting any intial sagging effects and intial tensioning. So basically the intial stiffness is zero.
I have looked at many iterative solutions for similar cable problems but have not found any for this case.
Any help would be much appreciated.






RE: Point Load On Cable
Anyway this is a simple statics problem: the cable elongates under load and it takes the shape of a broken line. The displacement of the load is calculated from geometry and equilibrium.
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RE: Point Load On Cable
If it deflects sideways by y then the strain in each half of the cable is (sqrt((L/2)^2+y^2)-L/2)/(L/2). This produces a tension T, and you know that T*sin(theta)=F/2, and you know that tan(theta)=y/(L/2)
There is a missing step in there.
Cheers
Greg Locock
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RE: Point Load On Cable
T*cos(theta) = P/2 ... T = (P/2)/cos(theta)
and (of course) T/A = stress
and (of course) the deflected length is L/cos(theta)
so that the strain is 1/cos(theta)-1
and (of course) stress/strain = E
so (P/2)/A/cos(theta)/(1/cos(theta)-1) = E
(P/2)/A/(1-cos(theta)) = E
cos(theta) = 1-(P/2)/(A*E)
no?
RE: Point Load On Cable
The supports will need to react the point load applied, so this is an iterative solution until you can get the rotation of the cable away from the horizotal and tension due to the elongation to be equal.
I'm sure it's not impossible to write a spreadsheet that converges the two with goalseek.
RE: Point Load On Cable
the tension in the cable is constant ...
a parabola has a changing slope, which implies that the vertical component of the cable tension is changing ...
but the only load is a central point load (so that the cable tension vertical component needs to be constant)
no ?
RE: Point Load On Cable
RE: Point Load On Cable
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RE: Point Load On Cable
RE: Point Load On Cable
If were ignoring mass of cable and any initial sag wouldn't this case just become a triangle of forces ie imagine a piece of string pinned to a board at each end of the string, then a central load is applied and the string deflects to a triangular shape and the tension in the string can be calculated depending on the angle of the string to the horizontal.
I believe rb1957 as done the maths relating to what I am describing.
desertfox
RE: Point Load On Cable
with all those simplifications you state you would get zero deflection and therefore infinite tension.
Generally the simplest way is to assume a cable size and then calculate deflection based on this and therefore axial load. Unfortunately the iterative method is the only option here.
RE: Point Load On Cable
RE: Point Load On Cable
You said: "T*cos(theta) = P/2 ... T = (P/2)/cos(theta)"
Shouldn't that be T*sin(theta) = P/2?
BA
RE: Point Load On Cable
RE: Point Load On Cable
T.sin(theta) = P/2
delta = T.a/AE where a is the half length between supports
T = (L - a)AE/a where L is the slope length of half cable.
T = (1/cos(theta) - 1)AE = P/2sin(theta)
So tan(theta) - sin(theta) = P/2AE.
Solve for theta, then T.
BA
RE: Point Load On Cable
yeah, that looks better