EESULTS OF TESTING AUSTRALIAN TIMBERS. 



135 



The strength may be calculated from the equations given after 

 the manner already sufficiently explained. 



Plate 7, shows a timber viaduct for 24 feet spans designed to 

 carry a single line of railway. As the design of this class of 

 structure has not been investigated and does not appear to the 

 author to be generally understood, it has been thought desirable 

 to work out an example in detail. In the first place the stresses 

 in the wedges and bolts will be considered. Fig. 3 represents a 

 portion of a beam subjected to transverse stress. It is required 

 to find the intensity and distribution of the horizontal shearing 

 stress at any section of the beam. 



Fig 3 



Let M denote the bending moment at a section a c e g at a 

 distance x from the origin. 



Let M+ A M denote the bending moment at a section b dfh, at 

 a distance x + dx from the origin. 



Let /denote the intensity of direct horizontal stress at c. 



Then M = — and/ = j y where / denotes the moment of inertia 



of the section with reference to an axis passing through its centre 



of gravity. ^/ y , 



The total stress on the plane etc e g between a and c is : Av h ^ y 



The total stress on the plane b dfh between the same limits is : 

 — j — I yb&y 



h m 



The difference between these stresses equals the force with which 

 the portion of the beam b doi the section b dfh is pushed towards 



the section ace g — = 



~j I y b d y 



Jy 



This stress is distributed over an area b x d x } hence the 

 intensity of horizontal shearing stress is: — H = jy^l^^^^ 



