Module 5 : Force Method - Introduction and applications
Lecture 1 : Analysis of Statically Indeterminate Beams
  Example 5.3 Determine the support reactions of the fixed beam with one end fixed and other supported on spring as shown in Figure 5.4(a). The stiffness of spring is .   
 
   
 

Solution: The static indeterminacy of the beam is = 3–2 =1. Let the force in the spring be R . The free body diagram of the beam along with the M/EI diagram and spring are shown in Figure 5.4(b) and (c), respectively. The unknown R can be obtained with the condition that the vertical deflection of the free end of the beam and spring is identical.   
 
                          
 

Using moment area theorem, the deflection of free end A of the beam is

 

                                     

                                       
   
   
1