132 



DEFLECTION OF A BEAM. 



Art. 85. 



y at C = 



ZEIL 



but 2/ m ax occurs in the longer segment 



hh 



where - = 0. From equation (a) i/ 2 P a; 2 = P 



and 



a: = j/J^i 2 + 2/i/ 2 ) where y is a maximum. 

 Fig. 95 shows a special case of the above (Z 1 = i 2 ) > but the 

 equation of the elastic line may easily be deduced independently. 

 The elastic line is evidently horizontal at the middle of the beam. 



85. Deflection of a Beam Carrying a Number of Loads 1 . 



It is evident from the preceding case that the evaluation of 

 the constants of integration in the equation of the elastic line 

 would become increasingly burdensome as the number of loads 

 increased. Equation (39) must be written for each segment. 

 Finding the location of the section at which the maximum 

 deflection occurs might be practically impossible by this method, 

 but the deflection at a particular section may be obtained by 

 taking the sum of those calculated for each load separately. 



The deduction of the equation of the elastic line for simple 

 cases of combined loading does not become very involved, par- 

 ticularly if the loading is symmetrical about the middle of a 

 beam, whose end conditions are alike. Thus the cases of Arts. &3 

 and 84 might be combined, or a uniform load might be combined 

 with that given in Art. 81. 



Fig. 90. 



Fig. 90 shows a cantilever beam- carrying four loads. The 

 deflection at the end consists of four parts ; y is due to the uni- 



J For a complete general discussion of this subject, with numerical 

 examples, see Mueller-Breslau's Oraphische Statik, Vol. II, Part 2. 



