A cable of length L is suspended between two points a distance d apart and at the same elevation.If the minimum tension in the cable is Tmin, determine the total weight of the cable and the maximum tension developed in the cable. Units Used: kip = 10^3 Ib Given: L = 50 ft d = 15 ft Tmin = 200 Ib

Question

A cable of length [latex]L[/latex] is suspended between two points a distance [latex]d[/latex] apart and at the same elevation.If the minimum tension in the cable is [latex]{ T }_{ min }[/latex], determine the total weight of the cable and the maximum tension developed in the cable.

Units Used:

[latex]kip[/latex] = [latex]{ 10 }^{ 3 }[/latex] [latex]Ib[/latex]

Given:

[latex]L[/latex] = [latex]50[/latex] [latex]ft\quad \quad d[/latex] = [latex]15[/latex] [latex]ft\quad \quad { T }_{ min }[/latex] = [latex]200[/latex] [latex]Ib[/latex]

Accepted Answer

[latex]{ T }_{ min }={ F }_{ H }\quad \quad \quad { F }_{ H }={ T }_{ min }\quad \quad \quad { F }_{ H }=200Ib[/latex]

From Example 7-15: [latex]\quad \quad s=\left( \frac { { F }_{ H } }{ { w }_{ 0 } } ight) \sinh { \left( \frac { { w }_{ 0 }x }{ { F }_{ H } } ight) } [/latex]

Guess [latex]\quad { w }_{ 0 }=1\frac { Ib }{ ft } [/latex]

Given [latex]\quad \frac { L }{ 2 } =\left( \frac { { F }_{ H } }{ { w }_{ 0 } } ight) \sinh { \left( \frac { { w }_{ 0 } }{ { F }_{ H } } \frac { d }{ 2 } ight) } \quad \quad { w }_{ 0 }=Find\left( { w }_{ 0 } ight) \quad \quad { w }_{ 0 }=79.93\frac { Ib }{ ft } [/latex]

[latex]Totalweight={ w }_{ 0 }L\quad \quad \quad \quad Totalweight=4.00kip[/latex]

[latex] an { \left( { heta }_{ max } ight) } =\frac { { w }_{ 0 } }{ { F }_{ H } } \frac { L }{ 2 } \quad \quad \quad \quad { heta }_{ max }=a an { \left[ \frac { { w }_{ 0 }\left( \frac { L }{ 2 } ight) }{ { F }_{ H } } ight] } \quad \quad \quad { heta }_{ max }=84.28deg[/latex]

Then,

[latex]{ T }_{ max }=\quad \frac { { F }_{ H } }{ \cos { \left( { heta }_{ max } ight) } } \quad \quad \quad \quad { T }_{ max }=2.01kip[/latex]

Question : A cable of length L is suspended between two points a distan...

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