Module 5 : Force Method - Introduction and applications
Lecture
3 : Analysis of Statically Indeterminate Structures by Energy Method
Example 5.21 Determine the support reactions of the continuous beam as shown in Figure 5.24(a) if the beam is assumed to be subjected to a linear temperature gradient such that the top surface of the beam is at temperature and lower at . The beam is uniform having flexural rigidity as EI and depth d . The coefficient of thermal expansion for beam material is .
Solution: The degree of static indeterminacy =2. Remove the supports at B and C and allow the beam to deflect freely under the temperature variation. The deflection of the points B and C of the beam due to temperature variation
(i)
(ii)
Apply the forces and at point B and C , respectively. According to Castigliano's theorem
and lower at 
. The beam is uniform having flexural rigidity as EI and depth d . The coefficient of thermal expansion for beam material is 
.
(i)
(ii) 
and 
at point B and C , respectively. According to Castigliano's theorem 
(iii)
(iv)
