EXTERNAL FORCES 49 



The uniformly loaded beam restrained at the ends is shown in 

 Fig. 44. The reasoning follows that for the beam carrying one 

 center concentrated load. The bending moment diagram, however, 



WL 



is a parabola with height, Z = - > the area of which is equal to 



o 



the product of the base times two- 

 thirds the height ; then 



2ACZy 

 ACxy = 5 - 



Eliminate like quantities from the 

 two sides of the equation and 



2Z 



Then x = negative moment = 



2 WL WL 

 ~ o x ~~o~ = To~> at each end. 



o o I - 



1 WL 

 The center positive moment = 5 X - 



o o 



Now take unit load per lineal foot = w. 



wP wL* wL 2 I? 



Let - -JTJ-; then wP = -5 and P = -5- (eliminating M>). 



O - 1 O o 



/ /1 s L 



3 >/3 1.732 

 When L = 1, 1 = t s = 0.5773L. 



Since / - 0.5773L and I + 2a = L, 

 L-l 1.0000 - 0.5773 



fl ;; jc = U.Zllo Li. 



Continuous Beams 



Continuous beams, that is beams running over a number of 

 supports, are designed by methods which are an extension of the 

 principles used for overhanging beams and restrained beams. 

 The only instance of continuous beams in wood construction ap- 

 pears in the placing of floors over joists or closely spaced beams. 

 On account of the excessive deflection of wood this is not justifi- 

 able, for the theory underlying continuous and restrained In-ams 



