7 g STRENGTH OF MATERIALS 



Putting x = - in this equation, the maximum deflection is found to be 



2 



384 El 



At the points of inflection -| = 0. Therefore 



whence 



x = - -4== .212Z or .788J, 

 2 Vl2 



which are the distances of the two points of inflection from the left support. 



Problem 83. A beam of length I is fixed at both ends and bears a single con- 

 centrated load P at a distance d from the left end. Find the deflection at th.- 

 point of application of the load. 



Problem 84. From the result of Problem 83, find the deflection at the point of 

 application of the load when the load is at the center. 



Problem 85. A concrete girder 10 ft. long, 18 in. drrp. and 12 in. \vidr i> 

 forced by two 1-in. twisted square steel rods near its lower face, si ml 

 a uniform load of 250 Ib. per linear inch. The moment of inertia of the equiv- 

 alent homogeneous section about its neutral axis (Article 48) is found to be 

 I c = 7230 in. 4 . Find the maximum deflection. 



70. Continuous beams. A continuous beam is one which is sup- 

 ported at several points of its length, and thus extends continuously 

 over several openings. If the reactions of the several supports \ 

 known, the distribution of stress in the beam and the IMJ nation of 

 the elastic curve could be found by the methods employ i*d in the 

 preceding articles. The first step, therefore, is to del en nine the 

 unknown reactions. General methods for determining these will be 

 explained in Articles 71, 77, 79, and 80. The two following prob- 

 lems illustrate special methods of treating the two simple cases 

 considered. 



Problem 86. A beam is simply supported at its center and ends. :in<l bears 

 a single concentrated load P at the center of each span. Assuming that tin- 

 supports are at the same level, find their reactions and the equation o: 

 elastic curve. 



Solution. Let each span be of length I, and assume the origin of coordinates 

 at O (Fig. 63). Consider the portion of the beam on the right of a sectioi. 



distant x from 0. Then, if x < - , 



