66 RESISTANCE OF MATERIALS 



Also, the total angular deflection for half the beam is found to be 



A 



(53) 



tan = = 



El 16 El 



r- i 



The deflection may also be obtained by considering the moment 

 diagram as representing the load on the beam, and then taking 



moments about the 

 point at which the 

 deflection is meas- 

 ured, say the center 

 C (Fig. 67). Since 

 the total area of the 

 moment diagram is 

 1 PI . PI 2 ., .. 



2'T-' =: T' lflt 



is regarded as the 

 load on the beam 

 each reaction will be 



PI 2 



Then, taking 





moments about the center, the result is 



PT 



2 16 6/ 48^7 



pi PI 



From the relation ^ = M = -, the deflection at the center may 

 e 4 



be expressed in terms of the 

 maximum fiber stress p. Thus, 



replacing - - by its equal * 



A C- 



in the expression for d, the 

 result is 



(55) 



12 Ee 



16 



FIG. 68 



If the concentrated load P is not at the center but divides the 

 span I into two unequal segments a and 5, the reactions are , 



i I 



