134 W. H. WARREN. SOME APPLICATIONS OF THE 



* 



The modulus of rupture is taken at 13000 pounds per square 

 inch in consequence of the larger section of the main beam. 



Hence the factor of safety is ^ - =7*7. 



In the design for timber viaducts which has been used exten- 

 sively in Victoria for spans of 1 5 feet, the superstructure consists 

 of 4 main beams arranged so that there are two under each of the 

 rails with a space of 7 inches. Upon the beams is laid a close timber 

 deck from 3 inches to 4 inches thick, and there is a kerb 12 inches 

 deep by 4 inches wide for retaining the ballast. The rails, sleepers 

 and ballast are laid in the ordinary way upon the timber deck, 

 and are maintained as on other parts of the line. The piers are 

 somewhat similar to those illustrated on Plate 5. The main beams 

 are made 18 inches deep by 7 inches wide when red gum timber 

 is used. The strength may be calculated as follows : — The dead 

 weight of the structure including the permanent way is half a ton 

 per foot run, and produces a bending moment in the centre thus : 



ir=lJ-W =14 foot tons. 



For the live load assume one of the heaviest of the Victorian 

 engines with a pair of driving wheels carrying 14 tons load exactly 

 at mid span, the leading and trailing wheels would be off the span 



and would not affect the bending moment which is : , -'== — £— = 



& 4 4 



53 foot tons. Total bending moment is therefore 67 foot tons. 



The moment of resistance of the four beams each 7 inches wide 

 by 18 inches deep is taking the modulus of rupture of red gum as 

 7,000 pounds per square inch :— 7Q0Qx4x7xi8x i8 = 10584000 inch 

 pounds. 39375 =393 '75 foot tons. 



Hence the factor of safety is _ e 7 = 6 \. 



These viaducts are very economical in timber and are much 

 appreciated in Victoria, they are clearly not too strong, but ex- 

 perience has shown that they are strong enough. They would not 

 carry our Consolidation engines with the same factor of safety as 

 may be seen from the following calculations : — The equivalent 

 distributed load produced on a span of 15 feet, see fig. 2, is 2*8 

 tons producing a bending moment of 78*7 foot tons. The total 

 bending moment would therefore be 78-7 + 14 =92 foot tons, and 



the factor of safety = 92 = 4 J, which is not sufficient for rail- 

 way practice. If however iron bark timber was substituted for 

 the red gum the factor of safety would be about 8 which is ample, 

 hence the design adopted in Victoria might be advantageously 

 used in New South Wales for spans of 15 feet, with iron bark, 

 and a few of our strongest timbers. 



Plate 6, illustrates completely the practice of the Roads and 

 Bridges Department, New South Wales for ordinary beam bridges. 



