Module 4 : Deflection of Structures
Lecture 3 : Principle of Virtual Work
  Example 4.11 Determine the slope and deflection of point A of the cantilever beam AB with length L and constant flexural rigidity EI.
 
 
  Solution: Deflection under the Load - Apply a vertical unit load at point A of the beam as shown in Figure 4.17(b). Consider any point X at a distance of x from A ,
 

 
 

         

 
 

The vertical deflection of point A is given by

 
 

 

 

Slope at the free end: Apply a unit couple at point A of the beam as shown in Figure 4.17(c). Consider any point X at a distance of x from A .

 
 
 
   
  The slope at A is given by