Unstiffened Roadway in a Suspension Bridge. 453 



400 feet, its weight 350 tons, and its deflection when suspended 

 at its two ends is 0*7 foot. It will have the same deflection as 

 this at its two ends if suspended in the middle. Moreover, if a 



Fig. 3. 



shorter girder of the same structure be used, the deflection will 

 be less in proportion to the square of the length*. Thus take 

 BC = AB : the curvature of the girder upheaved at P and resting 

 on that point will be the same as that of a shorter girder AC 

 resting on its middle point, and will therefore be less than 0*7 

 foot in the ratio of AC 2 : AD 2 . Making use, then, of the Table 

 deduced in the last paragraph, I obtain the following deflections 

 of the girder at P for different positions of the train on the 

 roadway : — 





Distance the train has passed along the roadway. 



40 

 feet. 



80 

 feet. 



125 



0-62 

 0-27 



120 



feet. 



121 



0-60 

 0-25 



160 



feet. 



112 



0-56 

 0-22 



200 

 feet. 



103 



0-51 

 0-18 



240 

 feet. 



91 



0-45 

 0-14 



280 

 feet. 



74 



0-37 

 0-10 



320 

 feet. 



58 



0-29 

 0*06 



360 

 feet. 



33 



0-16 

 0-02 



400 



feet. 









 



Distance of the greatest 1 

 elevation of the roadway 1 

 from the right-hand pier, j 

 infeet J 



Ratio of this to half-length 1 



129 



0-64 

 0-28 



Deflection of the girder AC 



As the train, therefore, occupies these successive positions, the 

 deflection of the girder at P, upheaved and subjected to its own 

 weight, would be continually diminishing, — beginning at the 

 first position with only 0*28 foot or 3*4 inches, lessening to 0*18 

 foot or 2*2 inches when the train is halfway across, and becoming 



* This is because the girder is a lattice-girder, in which the upper and 

 lower bars sustain the weight by compression and extension. Were the 

 girder a beam solid throughout, the deflection would vary as the cube of 

 the length. 



