124 Description of a Frame Bridge. 



ual strength is directly as the square of the depth, and inversely as 

 the rectangle of the distances from the supports ; which will be con- 

 stant when the beam is a semi-ellipse. A similar shape I have adopt- 

 ed for the frame bridge, as being of the most convenient construc- 

 tion, and of good appearance, although the actual strength will be as 

 the depth of the frame divided by the above rectangle, which would 

 give a curve differing not greatly from the ellipse : for instance, let 

 the depth of beam be 2 and the length be 12; let the ordinate \ 

 from either end be y, then the weight at the centre is to the weight 



J.2 _ 4(2x2) 



on the ordinate as -^ — is to , or the weights being equal 



3X9 6X6 ^ * ^ 



2/— ■\/3 = 1.7 nearly; and in the other instance the weights are as 



v 2 



— ^— to or y=l-5 a difference of .2 only. 



3X9 6x6 ^ ^ 



How these advantages are secured by this invention, will be seen 

 in the arrangement of the timbers in the following plan, which is a 

 complete draft of a model constructed at this place. The draft is on 

 a scale of -^^ of the model, which was of cypress timbers 1 \ inch 

 square. The model, ten feet long, eighteen inches high, and two 

 feet in width, was loaded with fourteen men, whose weight amounted 

 to 2,140 lbs. and yielded or sayed less than f of an inch. This ex- 

 periment is deemed conclusive as regards the superior strength of a 

 bridge of this construction. 



I will be further seen, that the stress arising from a weight placed 

 on the bridge, on each timber, will be in the strongest direction of 

 that piece. Let a weight W be placed on the center of the bridge, 

 it is immediately received on the middle posts, which are supported 

 by the main braces B, in the plan, and all the downward force is 

 transferred to tlie next outer posts, and thus continued to the abut- 

 ments A A. By this the strain on the string S is only in a hori- 

 zontal direction, and is in tension ; that on the posts P P is also in 

 tension in a vertical direction. The strain on the braces B B, and 

 on the timbers T T, is of an opposite kind or in thrust, either of 

 which is the strongest and most economical method of arranging 

 timbers in structures of the kind. The advantages of such a bridge 

 are too obvious to need particular discussion. The carpentry is of 

 the plainest kind, and the saving in piers and abutments, such as are 

 necessary to support arches, Sic, is of no inconsiderable account. 

 The abutments necessary for this bridge have merely to support the 

 weight of it, and its load in a vertical direction^ 



