CAMBBIA STEEL. 



165 



BENDING MOMENTS AND DEFLECTIONS FOR 

 BEAMS OF UNIFORM SECTION. 



W = Total Load, in Ibs., uniformly 

 distributed, including the weight of 

 beam. 



Wi = Total Superimposed or Live 

 Load, in Ibs., uniformly distributed. 



Wz = Total Weight of Beam or 

 Dead Load, in Ibs., uniformly dis- 

 tributed. 



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



M = Total Bending Moment in inch-lbs. 



M w i,M p =BendingMoments,ininch-lbs., 

 due to Weights Wi and P respectively. 



I = Moment of Inertia, in inches 4 . 



1 = Length of Span, in inches. 



E = Modulus of Elasticity, in Ibs., per 

 square inch = 29 000 000 for steel. 



W 3 = Total Safe Load, in Ibs., uni- 

 formly distributed, including the weight 

 of beam = Total Safe Load of Tables. 



centrated at any points. 



The ordinates in diagrams give the bending moments for corresponding points 

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



(8) 



m Fixed at both ends and 

 Uniformly Loaded. 



Diagram for Total Load: Draw 



WI 

 parabola having M = ~ Also A A' 



o 



parallel to base and at a distance 



WI 

 M' = The Vertical distances 



between the parabola and line A A' 

 are the moments for corresponding 

 points on beam. 



Safe Superimposed Load, in Ibs., uni- 

 formly distributed, W' a = f W 8 - Wj. 



Distance of points of contra-flexure 

 from supports = .21131. 



Maximum Bending Moment at points 



WI (Wi + W z ) 1 

 of support = = S -- l2~' 



Bendi 

 WI ( 



Moment at middle of beam = 



24 24 



Maximum Shear at points of support = 



2 



Maximum Deflection * 

 (Wi 



384EI 



384EI 



(9) Beam Fixed at both ends 

 with Load Concentrated at 

 the Middle. 



!M 

 V 



Diagram for Superimposed Load: 



PI 

 Draw triangle having M = Also 



A A' parallel to base and at a distance 

 M' = ~ The Vertical distances be- 

 tween the triangle and line A A' are 

 the moments f orcorresponding points 

 on beam. 



Diagram for Dead Load similar to 

 Case (8). 



Safe Superimposed Load, in Ibs., con- 

 centrated, P g = W. - 3 W z . 



Distance of points of contra-flexure 

 from supports = il. 



Maximum Bending Moment at points 



PI W*l 

 of support = - + --- 



Bending Moment at middle of beam 



PI wa 



8 "*" 24 ' 



Maximum Shear at points of support 

 P +W 2 



Maximum Deflection = 

 W 2 1. 



192EI 



384EI 



