INTERNAL FORCES 83 



ing moment as we have seen being 131,880 in. Ibs. It is cheaper to 

 use a commercial beam with a resisting moment larger than the 

 bending moment than to trim the beam down to the theoretically 

 exact size. This happens with rolled steel beams also. When a 

 built-up plate girder or a latticed girder (truss) is used the differ- 

 ence between the bending moment and resisting moment can be 

 cut to a smaller amount. Reinforced concrete is a material which 

 permits of closer designing than rolled shapes, hence the differ- 

 ences in design shown by equally competent designers tackling 

 the same problem when using reinforced concrete. 



A formula to find the limiting span when bending and shear 

 are considered is developed as follows for wood : M in inch pounds. 



8M M 3M M 



~ 12W " = 1.5x46/18 " Gbhs ~ 2bhs' 



3 

 Find the deflection on the limiting span. 



Q fi7 v 12 



The allowable deflection = ' * - - 0.323 in. 



ooU 



L 2 9 67 x 9 67 



The actual deflection = 777 - - -^-=- = 0.184 in. 

 44n 44 x 11.5 



Find the allowable safe uniformly distributed load the beam 

 will carry on a span of 20 ft. 



8M_ 143,500 

 12L 1.5 x 20 



10 v 9ft 



Allowable deflection = * = 0.667 in. 



ouU 



20 X 20 

 Actual deflection = rr r-r-= = 0.79 in. 



%rt. X * 1 O 



The deflection is too great if the lower side of the beam is to be 

 plastered, or the beam is to carry a plastered ceiling. 



NOTE. When a wooden beam has a depth in inches less than 

 two-thirds the span in feet the deflection is apt to cause plaster to 

 crack. Try a beam 14 ins. deep, the actual depth being 13.5 ins. 



M r 143,500 

 " I6W - 167 x 13.5 " 



Try a commercial 6 ins. x 14 ins. - 5.5 ins. x 13.5 ins. 



M r - 167 X 5.5 x 13.5 8 - 167,500 in. Ibs. 

 This beam is seen to be excessively strong, but a beam 4.5 ins. x 13.5 



