132 



W. H. WARREN. SOME APPLICATIONS OF THE 



Where W= total load uniformly distributed in pounds or tons. 



f— modulus of rupture per square inch in pounds or tons. 

 I = length, b = breadth, d = depth of beams. 

 F=the deflection at the centre. 



E = modulus of Elasticity in pounds or tons per square inch. 

 F= Shearing stress. 



It is necessary to state that the same units should be used 

 throughout, viz. inches, square inches, and pounds or tons. 



If the load is not uniformly distributed the maximum bending 

 moment must be found and equated with the moment of resistance. 

 Plate 1 shows an ordinary timber viaduct designed to carry a 

 single line of railway, consisting of two beams each 10 feet long 

 by 1 2 inches by 1 2 inches. The deck is formed with cross sleepers 

 each 1 feet long by 8 inches by 8 inches, spaced 1 6 inches centre 

 to centre, bolted to the main beams with bolts f inch in diameter. 

 There is a timber guard rail on each side. The piers consist of 

 three piles, with two horizontal walings at the top, and diagonal 

 bracing. As this deck appears to the author to be very suitable 

 for timber railway viaducts, and as it has been very largely used 

 in America, and in a few cases in this colony it is thought desirable 

 to investigate its strength and to consider its advantages some- 

 what in detail. The maximum weight on the driving wheels of 

 the locomotives on the New South Wales Railways does not 

 exceed 16 tons for a pair of wheels, therefore the weight on each 

 rail is say 8 tons, but since this may be increased from a variety 

 of causes such as the oscillation and plunging of the engine, defects 

 in the balancing of the rotating parts, it is assumed that the 

 total maximum effect will not exceed 10 tons on each rail. At 

 least three sleepers will take part in carrying the weight brought 

 on any one of them from the driving wheels, therefore the maximum 

 weight on a sleeper is taken at 5 tons for each rail, so that W— 

 5 tons in the sketch fig. 1. 



<- 





7-0 



1-0 



Fig I 



v 



W-5 



y, I'O > 



Max. Bending moment = 5 foot tons 

 Moment of Resistance 



60 inch tons. 



U 2 / 8x8x8x 14000 



= 1194600 inch pounds. 

 = 533 inch tons. 



533 



Therefore the factor of safety = — = 8*8. 



The author is indebted to Mr. W. Shellshear, A.M.inst.c.E., 

 District Engineer, for particulars of this deck as applied in the 



