Module 5 : Force Method - Introduction and applications
Lecture 2 : The Force Method

Example 5.12 Determine the horizontal thrust in a two-hinged trapezoidal arch. EI is constant.

 

 
             
            

         Figure 5.15(c) BMD due to applied loading

 
 
 

Solution: The degree of static indeterminacy = 4–3 = 1. Let H be the unknown horizontal reaction at A and B . Let and be the vertical reactions at support A and B respectively

 

Due to symmetry,   

 

Displacement in the direction of H due to applied loading is calculated by multiplication of two bending moment diagrams of Figure 5.15(c) and (e).

                  
                  
 

Displacement in the direction of H due to H obtained by multiplying diagram of Figure 5.10(d) and (e).

                  
                 
 

Since the net deflection in the direction of H is zero, therefore

                  
  or              
 
1