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Find reactions for 3-hinged arch

Jonathan Ochshorn

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Directions: Enter values for loads and their horizontal positions along the arch, 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 towards the arch. Upward-acting loads should be entered as negative numbers; a negative vertical reaction indicates that its direction is actually downward-acting rather than upward-acting; and negative horizontal reactions indicate that their direction is away from the arch.

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

3-hinge arch dimensions and load magnitudes
Fig. 1. Three-hinge arch geometry (lengths) and magnitude of loads
 

Positions of loads and reactions (ft)
Height Hinge locations Uniform load position Point load positions
A B C D E F G H
  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  
     
 
 
 
 
 
Checks:    
sum  
A>0  
B>C  
D<B  
D>=0  
D<E  
E<=B  
F<B  
F>0  
G<B  
G>0  
H<B  
H>0