162 



CAMBBIA STEEL. 



BENDING MOMENTS AND DEFLECTIONS FOR 

 BEAMS OF UNIFORM SECTION. 



W = Total Load, in Ibs., uniformly 

 distributed, ncluding the weight of 

 beam. 



Wi =Total Superimposed or Live 

 Load, in Ibs., uniformly distributed, 



W 2 = Total Weight of Beam or 

 Dead Load, in Ibs., uniformly dis- 

 tributed. 



P, Pi, P2, Ps = Loads, in Ibs., con- 

 centrated at any points. 



M =Total BendingMoment.in inch-lbs. 

 M w i,Mp=BendingMoments,ininch-lbs. t 

 due toWeights Wi and P respectively. 

 I = Moment of Inertia, in inches*. 

 1 = Length of Span, in inches. 

 E= Modulus of Elasticity, in Ibs. per 



square inch =29 000 000 for steel. 



W s = Total Safe Load, in Ibs., uni- 

 formly distributed, including weight of 



i = Total Safe Load of Tables. 

 The ordinates in diagrams give the bending moments for corresponding points 

 on beam. For superimposed load only, make W in formulae equal to zero. 



(1) Beam Supported at both ends 

 and Uniformly Loaded. 



Diagram for Total Load:- 



Wl 



Draw parabola having M = -3- 

 o 



Safe Superimposed Load, in Ibs., uni- 

 formly distributed, W' 8 =W B -Wj. 



Maximum Bending Moment at middle 

 Wl_ (Wi +W 2 )1 

 8 ~ ~~~8~~ 

 Maximum Shear at points of support 

 W_ WH-Wi 

 = 2 " 2 



of beam = M 



Maximum deflection 



5 (\ 



384 El 



384 El 



(2) Beam Supported at both ends 

 with Load Concentrated 

 at the Middle. 



Safe Superimposed Load, in Ibs., con- 

 centrated, P a = *= 



Maximum Bending Moment at middle 

 oftaun-M-5 + WjL. 



Maximum Shear at points of support = 

 P+W, 



Diagram for Superimposed Load: 



Draw triangle having M p = 

 Diagram, Dead Load.similar to Case(l) 



Max. Deflection = ^ + 



W 2 1 J 



(3) Beam fixed at one end, Unsup- 

 ported at the other and 

 Uniformly Loaded. 



Diagram for Total Load 



iiri 



Draw Parabola having M = 



Safe Superimposed Load, in Ibs., uni- 

 formly distributed, W' B = ^' - W. 



Maximum Bending Moment at point of 



WI (Wi+W 2 )l 

 support = = s ^ ^~ 



Maximum Shear at point of support 



W = Wl -t- VV2. 



