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Find internal axial force for cable

Jonathan Ochshorn

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Directions: Enter values for loads and their horizontal positions along the cable, using any consistent units. To eliminate a load, set its magnitude to zero. Refer to the diagram for variable names. For example, use ft for distances; use either lb/ft and lb units, or kips/ft and kip units for loads; the reactions will be in either lb or kips, depending on your choice. Loads are assumed to act in a downward direction, with vertical reactions acting in an upward direction and horizontal reactions acting away from the cable supports. Upward-acting loads (negative numbers) cannot be used. The vertical sag of the cable (A) must be entered; however, the sag point (C), measured along the horizontal length of the cable, is calculated based on the magnitude and position of the various loads, and cannot be entered.

Enter distance measured horizontally from left reaction to the point where axial force(s) are to be calculated (distance J; see Fig. 1 below). All such internal forces are positive (tension). In cases where the FBD is cut under a concentrated load, there will be two values for axial forces, one just to the left, and one just to the right of the concentrated load.

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More detailed explanations and examples can be found in my text.

cable dimensions and load magnitudes
Fig. 1. Cable geometry (lengths) and magnitude of loads
 

Positions of loads and reactions (ft)  
Sag Span Sag point Uniform load position Point load positions FBD
A B C D E F G H J
  Loads (use kips/ft and kips or lb/ft and lb)  
  w   P1 P2 P3  
     
 
Vert reaction at "a" Vert reaction at "b" Horiz reaction at "a,b" Axial force(s) at FBD FBD Height
     
 
 
 
 
 
Checks:    
errors:  
A>0  
B>0  
D<B  
D>=0  
D<E  
E<=B  
F<B  
F>0  
G<B  
G>0  
H<B  
H>0  
F<G  
G<H  
w>=0  
P1>=0  
P2>=0  
P3>=0  
J>=0  
J<=B