Strength of Materials. 



333 



carry a much greater load than when lying flat-wise. If we 

 place a 2x4 and a 2x8, vvhicii differ onlv in thickness, on 

 edge their relative strengths are to each other as the squares 

 of 4 and 8, or as 16 to 64. That is the 2x8, containing only 

 twice the amount of lumber as the 2x4 will, under the con- 

 ditions named, sustain four times the load. The reason for 

 this is as follows : In Fig. 145 let A represent a 2x4 and B 

 a 2x8. In each of these cases the load draws lengthwise 

 upon the upper half of the joist, acting through a weight- 







FIG. 143. 







arm F, W, ten inches in length, to overcome the force of co- 

 hesion at the fixed ends, whose strength, according to (402) 

 is ten thousand pounds per square inch, or a total of 



2 X 2 X 10, 000 Ibs. = 40, 000 Ibs. in the 2 X 4 joist, 

 and of 2 X 4 XlO, 000 Ibs. = 80, 000 Ibs. in the 2 X 8 joist, 



These two total strengths become powers acting through 

 their respective power-arms F, P, whose mean lengths are, 

 in the 2x4 joist, one inch, and in the 2x8 joist, two inches. 



Now we have (531) 



PXP A = WX W A, 



and substituting the numerical values, in the 2x4 joist, 

 we get 



4X10,000X1 =WX10 

 or 4X10, 000 = IOW, 

 and W = 4,000. 



