NOTE TO ART. 128. [APPENDIX. 



For the shears, then, we have 



Mj wl 7 7 a , 9 , 



s '= + = w '' S = w '> 



7 18 7 



Hence, R! = ^ w> Z, Rj = ^- w> Z, Kg = 



Ex. 2. J70w> rat&^ mw$ w>0 lower the second support in the 

 above example, in order that the reaction at the centre support 

 may be just zero f 



In this case we have 



2M 3 7 w>^ G/^EI , 5 

 ',= -^+^^:--. J^-. +w l = - 



If this is to be zero, we have 



, 5 W I* 



and R! i^ I, I^ = 0, R 3 = w I, 



or precisely as for a beam of single span and length 2 I. 



Ex. 3. A beam of four equal spans is unloaded, and the 



wl* 

 third support is lowered l)y an amount h% = _ . What are 



the reactions f 



An*. R = ^? R,. 



^4 = Rgj 1*6 = R!' 



Ex. 4. A beam of five equal spans rests as a continuous gir- 

 der over six suppovts. Having given the dimensions of the 

 beam, length of spans, and coefficient of elasticity ; to deter- 

 mine the reactions due to a sinking of the third support one- 

 eighth of an inch. 



Let the beam be of wood, 1 foot wide, 1.5 deep, 

 I = 20 feet, 8 = 5, r = 3, E = 288,000,000 Ibs. per sq. ft., 

 A, = in. = 0.010417 ft. 



