STRESSES IN CONTINUOUS BEAMS. 



S9.Comif1UOU5 B4M5,COfiCff17KATDLOAD5 t COfl5JAmriOf1[fiT Of /flfffriAAfiO MODULUS Off LA5TICITY. 



if. .rjj* 



Load, | 4 l||! 



' , v' \y g 



l ! i __ i 4' 4 



I 1 



Span, ^ I 

 length, ^_ I, 



Support, / 

 Reaction, R, 

 tlomenk, M t 



n-span 



(fltljSfspan 



*; 



n \ 



p 



K n 



M n \M, 



ntl 



ml 



Relation between moments at supports for n ^andfnti) % spans, 



Ml 4-?M ,/7 *7 )iM ,7 .=ffPl l fl(-Jf})l--4rPjt/?Je -Mr* Air* l7 

 i '17 1 (j ril >f}f/( if) rlntljri ifH? (-/it/ '/ / /7V>l /r /7 "n'J Zl r nt/intl(t "fitt '"ntt + "nt/sj i 



Shear to the right of n^> support, Shear to left offntlj^ support, 



t / 



Shear to riqhtof(ntl) support, Reaction at (n+i) support, 



, CI 



(C) 



ft+ 



Shear at any point in n&span, 



K tt fS& where ff> n equals (f) 

 the sum oF the loads between 

 n& support and point considered. 



Point of max. positive moment in n^spar), 

 The max. positive moment occurs 

 where shear,as calculated From(F) 

 passes through zero. This point is 

 afwaysatoneoF the loads. (h) 



Ex PL AflAT/Ofl OF FORMULAS: (See under 56.) 



Moment at any point in n^span, 



lP n (x-k n ?) equals the sum of the 

 moments of the loads, between 

 the n*-$ support and the point con- 

 s/dered, about the point 

 Maximum positive moment in the n t!?$pan, 

 After the point of man positive 

 moment has be/ocatedas de scribed 

 infh} the value oFx thus de6er mined 

 is substituted in(q) and M x determined. 



SPECIAL CASE, 



fora beam of two unequal spans with unequal concentrated toads and with ends 

 simply supported, fi, =0, M s =C 



A/ - 



V> 



60. CONTINUOUS BEAMS OFTNO AND THREE EQmSPAHS: Uniform load, w, per unit length or load f?in center oFone span 



i p 



foment, 0, -1/16, 0, 0, -1/15. +1/60, 0, 0, -1/10, +1/40, 0. 

 faction, +7/16, +5/8, -I//6, +11/30, +/fiO, -1/10, +1/60, +4/10, +29/40, -1/ZO, +1/40, 



Moment, 0, -3/H, 0, 0, -IfiO, -1/20, 0, 0, -3/40, -3/40, 0, 

 Reaction, +U/3Z, +///I6, -3/32, -1/20, +II/ZO, +l//?0, -1/20, -3/40, +21/40, +13/40, -3/40, 

 CoeFFicients of w2*dndPl', for moments at supports, andofwt and f? for reactions at supports. 

 By add/tionofprope r cases any beam maybe solved. For shears and moments between supports se(56&59. 



36 



