84 



RESISTANCE OF MATERIALS 



47. Single eccentric load. For a beam fixed at both ends and 

 bearing a single concentrated eccentric load the simplest method 

 of computing the unknown reactions and moments at the sup- 

 ports is as follows: 



Consider the beam as 

 fixed at one end E only 

 (Fig. 75) and carrying, in 

 addition to the concen- 

 trated load P, the shear R^ 

 at the left support and the 

 restraining moment M l at 

 this point. Then, from (50) 

 and (51), article 39, the de- 

 flection from the tangent at 



E due to the moment M l is 



Mf 



tan <f>. = 



El 



From (38) and (40), article 37, that due to the shear R l is 



Rf 



tan</> = 



_ Rf . 



2 El 



and from (42) and (44), article 37, that due to the load P is 



d = - 



Since the total vertical deflection of the point A with respect to 

 the point E is zero, and since the total angular deflection is also 

 zero, these two conditions furnish the equations 



(96) 

 From the second equation, 



1EI 



+ 



2m 



MJ RJ* Pit _ Q 

 2 El " 



