RESULTS OF TESTING AUSTRALIAN TIMBERS. 



141 



Method of Sections. 



The method of sections which has been mentioned may be briefly 

 described as follows. If we consider an ideal section cutting any 

 three bars of the truss illustrated in Plate 9, and separating it 

 into two portions, and if we apply stresses to the three bars equal 

 to those developed in the structure, we may consider the portion 

 cut off to be removed as the stresses balance the external forces. 

 In order to obtain the stress in one of the three bars it is conveni- 

 ent to take moments about the point where the other two meet 

 and forming the equations with the unknown stress and the known 

 reaction at abutment and loads at apices of triangulation, we 

 readily determine the unknown force. It is generally very con- 

 venient to draw the truss to a sufficiently large scale, and measure 

 off the lengths of the lever arms to the same scale. The details 

 of the method are fully illustrated in the following equations in 

 which the letters X V Z &c. correspond with the letters on Plate 5. 





sh. 



&.-.-: :::: 



2 / "3 4 S & 7 Q' 9 10 II /3M2 



4— -100- 



-yt 



■t- 



"$" 



Section. 

 1 

 9 



3 



4 

 5 



Stresses due to Dead Load. 

 - X x x 10-5 + 14. | x 20 = 



x 9-1 + 14. £ x 20-0 



+ Z ± 



-X 2 y 10-5 + 14. f x 20 = 



+ Z 2 x 18-5 + 14 (£ 40 - 20 = 



+ Y, x 18-5 + 14 x 20 = 



- V 9 x 40 + 14 x 20 = 



-X s x21 +14(f x 40-20)+ 14. 



f x 40 = 

 + Z, x23-5 + 14{(i + £)60-(20 



+ 40)}=0 

 + Y s x 116 -U{£(6 + 7)100- 



(120+140)} = 





Tons. 



x x = 



+ 23-33 



v x = 



+ 14-00 



z x ~ 



- 26-92 



x 2 = 



+ 23-33 



z^ 



- 11-35 



r* = 



-15-14 



v 2 = 



+ 7 



X 3 = 



+ 30 



z 3 = 



-22-34 



r s = 



-11-77 



