A cable has a weight density γ and is supported at points that are a distance d apart and at the same elevation. If it has a length L, determine the sag. Given: γ = 3 Ib/ft d = 500 ft L = 600 ft

Question

A cable has a weight density [latex]\gamma[/latex] and is supported at points that are a distance [latex]d[/latex] apart and at the same elevation. If it has a length [latex]L[/latex], determine the sag.

Given:

[latex]\gamma[/latex] = [latex]3[/latex] [latex]\frac { Ib }{ ft } \quad \quad d[/latex] = [latex]500[/latex] [latex]ft\quad \quad L[/latex] = [latex]600[/latex] [latex]ft[/latex]

Accepted Answer

Guess [latex]\quad { F }_{ H }=100Ib[/latex]

Given [latex]\frac { L }{ 2 } -\left[ \frac { { F }_{ H } }{ \gamma } \sinh { \left[ \frac { \gamma }{ { F }_{ H } } \left( \frac { d }{ 2 } \right) \right] } \right] =0\quad \quad { F }_{ H }=Find\left( { F }_{ H } \right) \quad \quad { F }_{ H }=704.3Ib[/latex]

[latex]\quad \quad h=\frac { { F }_{ H } }{ \gamma } \left[ \cosh { \left( \frac { 1 }{ 2 } \frac { \gamma }{ { F }_{ H } } d \right) } -1 \right] \quad \quad \quad \quad h=146ft[/latex]

Question : A cable has a weight density γ and is supported at points th...

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