Cable Tensions at points, help.

[gu3szwhoo]

Homework Statement

Compute the cable tension at the midpoint, (L/2), the quarterpoint (L/4), and support for a 1600 foot span with a sag at the midpoint of 100 feet, when the cable is loaded with 10 kips/foot spread uniformly along the horizontal line.

Homework Equations

The Attempt at a Solution

I have no clue what so ever, of what to do. I'm in an introductory engineering class.

 

[PhanthomJay]

I'd hardly call this an "Introduction to Engineering" question, but anyway, the cable loaded under an externally applied distributed load takes on the shape of a parabola. Are you given the formula for the horizontal tension at mid point? The tension acts horizontally at this point, and always in the direction of the tangent to the curve at other points. If not, you should calculate the horizontal tension at midpoint using a free body diagram cut through the midpoint and around one of the supports, to solve for it and the support reaction. Then you can proceed. Give it a try.

 

[gu3szwhoo]

seriously huh, intro to structural engineering is so hard here at ucsd. nope that's all they give us for that question, everything there is evedrything provide

 

[PhanthomJay]

Well, 'Intro to Structural Engineering' is different than 'Intro to Engineering', but usually cable problems are reserved for later studies. Nevertheless, the same concept applies when determining forces: You can easily determine the vertical component of the support reactions by looking at the entire system and summing forces in the y direction: due to symmetry, half of the vertical load from the distributed load will be supported at the left support, and the other half at the right support. But that won't give you wire tensions, or horizontal components of the reaction forces at those supports. To do so, isolate the cable in a free body diagram that encircles the left support and the left half of the cable, cutting thru the cable at midpoint. At the midpoint, only the tension force, T_h, acts horizontally; there is no vertical component at that point, because cables cannot support shear (cables tensions always act along their longitudinal axis, parallel to the tangent of the cable curve at that point). Now just sum moments about the left end to solve for T_h. That should get you started, at least.