Module 5 : Force Method - Introduction and applications
Lecture
2 : The Force Method
Example 5.13 Determine the reaction of the propped cantilever beam 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 =1. Remove the support at B and allow the beam deflect freely under the temperature variation. The deflection of the free end of the beam due to temperature variation (from eqs 4.28 of Chapter 4).
(i)
Apply the force R at point B such that the deflection in the direction of R is equal to . Since deflection of a cantilever beam due to force R is equal , therefore
(ii)
Equating the
from two expressions of Eqs. (i) and (ii)
The vertical reaction and bending moment at A will be
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)
. Since deflection of a cantilever beam due to force R is equal 
, therefore
(ii) 
from two expressions of Eqs. (i) and (ii) 
