198 PRACTICAL STRUCTURAL DESIGN 



27 68 



of Inertia for the braces is 6.8. Dividing, ^75 = 2.25, and - - = 



I - O 



0.85. Suppose the 8 and the 12 are divided by 2, to get the half- 

 length, and then multiplied by 12 to reduce the half-length to 

 inches, it is plain to see that this is equivalent to multiplying the 

 8 and 12 by 6, so the result of the division in each case will be 

 one-sixth as large as before, but the proportion is unaltered. 

 This illustration has been worked out because it explains the 

 appearance of many expressions which often cause the amateur 

 considerable trouble. A man accustomed to reasoning as he 

 figures will often introduce many short cuts into formulas and 

 expressions which he alone will understand, but the reasons for 

 which can be readily worked out by any other equally competent 

 man. 



Returning to Fig. 115, add together the values of y for the 



I 



two chord members and the two web members, the sum being 

 (2 X 2.25) + (2 x 0.85) = 6.19. The moments are now distributed 

 as follows: 



2.25 x 267,000 



6.19 

 0.85 x 267,000 



= 97,000 in. Ibs. for the chord. 



= 36,700 in. Ibs. for the web members. 



6.19 



The maximum fiber stress in the members induced by these 

 moments is as follows : 



, , , My 97,000 x 4 

 For chords, / = -~ = ^=- = 14,400 Ibs. per sq. in. The 



/ i 



4 in. is the distance from the top of the angles of the chord mem- 

 bers to the center of gravity axis, parallel to it, of the rivets. 



v TO v ** v f My 36,700 x 2.25 



For Web Members, / = f = - -^ = 12,300 Ibs. per 



1 O.o 



sq. in. The 2.25 ins. is the distance from the back of the angle 

 to the center line of the rivets. 



Compare the stresses due to the eccentricity caused by failing 

 to have the lines through the center of gravity of the members 

 meet at a common po nt, with the stresses used in the design and 

 marked on Fig. 115. It will be seen that the secondary stresses 

 are about fifty per cent greater than the direct stresses and will 

 cause the failure of the joint ultimately, for the effect of the direct 

 and eccentric stresses is the sum of the two. 



