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Level Span Catenary Sag

The level span catenary sag describes the tensions and sagging curve, or catenary, of a cable connecting two points at the same elevation.

The sag increases with horizontal tension, and decreases with cable weight per unit length and span. The cable length increases with horizontal tension and span, and decreases with cable weight per unit length. The tension at the supports equals the horizontal tension plus the sag times the cable weight per unit length.

Formula

{QuantityVariable["D", "Length"] == ((-1 + Cosh[(QuantityVariable["S", "Length"]*QuantityVariable["w", "ForceGradient"])/(2*QuantityVariable["H", "Force"])])*QuantityVariable["H", "Force"])/QuantityVariable["w", "ForceGradient"], QuantityVariable["L", "Length"] == (2*QuantityVariable["H", "Force"]*Sinh[(QuantityVariable["S", "Length"]*QuantityVariable["w", "ForceGradient"])/(2*QuantityVariable["H", "Force"])])/QuantityVariable["w", "ForceGradient"], QuantityVariable["T", "Force"] == QuantityVariable["H", "Force"] + QuantityVariable["D", "Length"]*QuantityVariable["w", "ForceGradient"]}

symbol description physical quantity
D sag "Length"
H horizontal tension "Force"
S span "Length"
w cable weight per unit length "ForceGradient"
L cable length "Length"
T tension at supports "Force"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Level Span Catenary Sag"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Level Span Catenary Sag"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Level Span Catenary Sag"], {QuantityVariable["S","Length"] -> Quantity[1000, "Feet"], QuantityVariable["L","Length"] -> Quantity[1002.54`, "Feet"]}]
Out[3]=

Publisher Information