CAMBRIA STEEL. 



163 



BENDING MOMENTS AND DEFLECTIONS FOR 

 BEAMS OF UNIFORM SECTION. 



W = Total Load, in lbs. t uniformly 

 distributed, including the weight of 



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 Bending Moment.ih 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 9 = Total Safe Load, in Ibs., uni- 

 formly distributed, including weight of 

 beam = Total Safe Load of Tables. 



The ordinates in diagrams give the bending moments for corresponding points 

 >n beam. For superimposed load only, make Wg in formulae equal to zero. 



(4) Beam fixed at one end, and 

 Unsupported at other, with 

 Load Concentrated 



, -^_ at the free end. 



MI ^ 



Diagram for Superimposed Load : 



Draw triangle having M p = PI. 

 Diagram. Dead Load,similartoCase(3) 



Safe Superimposed Load, in Ibs., con- 

 centrated, P. = Wg " 4W> . 



Maximum Bending Moment at point of 



Wl 

 support = Pl + -^- 



Maximum Shear at point of support = 

 P+W*. 



Maximum Deflection ^ 



pis 



~ 



(5) Beam Supported at both ends 

 with Load Concentrated at 

 any point. 



Safe Superimposed Load, in Ibs., con- 



QP 



Diagram for Superimposed Load : 



Draw triangle having M p = -r 



Diagram, Dead Load,similar to Case(l 



Maximum Bending Moment under load 

 = a(2Pb+W2l-Wa) 



21 Pb W* 



Max. Shear at Sup. near a = H g~ ' 



Max. Shear at Sup. near b = -r- + - 

 Deflection at distance x from left sup- 

 = l f2al - an | 

 3EI1 L 3 J 



^/sP*, 



2al-i 



Distance, from left 



support,' of point of maximum deflection 

 for superimposed load. 



(6) Beam Supported atboth ends 

 with two Symmetrical Loads. 



M P 1 



Safe Superimposed Load, in Ibs., con- 



W,l - Wl 

 centrated, each, P g = g 



Maximum Bending Moment at center 

 of beam = Pa + ^p 

 Maximum Shear at points of support = 



2P+ Wj 



Diagram for Superimposed Load: 



Draw trapezoid having M p = Pa. 



Diagram,Dead Load, similar to Cased 



Maximum Deflection 



24 El 



384 



