Ki4 MERRIMAN— DEPTH OF BRIDGE TRUSS. [April 



THE RELATION BETWEEN THE ECONOMIC DEPTH 



OF A BRIDGE TRUSS AND THE DEPTH 



THAT GIVES GREATEST STIFFNESS. 



BY MANSFIELD MERRIMAN. 



( Read April 14, 1Q05. ) 



The fact that there is a certain depth for a bridge truss which 

 renders the quantity of material a minimum has long been known, 

 and the marked increase in the depth of bridge trusses which has 

 occurred during the past quarter of a century is due to the efforts 

 of manufacturers to use the least possible amount of material. It 

 has generally been supposed that the vertical deflection of a bridge 

 under a moving load decreases with the depth, and this is true for 

 plate girders. For a truss, however, investigations made by the 

 author show that the least deflection and hence the greatest stiffness 

 increases up to a certain limit, as the depth increases, and then 

 decreases, so that there is a depth which gives the truss its greatest 

 vertical stiffness. 



The following are the results obtained by the author for the type 

 known as the deck Pratt truss. Let / be the span, d the depth, p 

 the panel length, and n the number of panels, so that /= np. 

 The economic depth was obtained by forming an algebraic expres- 

 sion for the amount of material in the truss in terms of its dimen- 

 sions, given loads and allowable unit-stresses, and then finding the 

 value of d/p which renders that expression a minimum. There 

 were found, 



2.65 3.21 



0.13 O.I I 



which shows that djp increases with length of span while ^///decreases 

 with length of span. To determine the depth that gives greatest 

 stiffness, an algebraic expression for the stored energy in the truss 

 due to the deformation of its members was formed and this equated 

 to the deflection due to the given loads. Then the values of djp 

 that render this expression a minimum were deduced for different 

 values of n, as follows : 



