ON BRIDGES — BEAMS. 145 



and put vertical ties in the place of the posts, the resistance of both 

 sets of braces serving the purpose of the posts. 



We must always bear the principle, however, carefully in mind, and 

 not make the mistake of causing a strut to be exposed to a tensile 

 strain, or a tie to a strain of compression. 



It will be seen in Figs. 33 and 34 that the braces are always dis- 

 posed to support a weight at the central point of the truss, and it is 

 evident that if we cut a girder of this sort into two pieces, they will 

 not serve as two shorter beams, since in each one half of the braces 

 will be in the wrong diagonal of the rectangles. Although this seems 

 simple enough, it is sometimes not understood in practice. In the 

 lecturer's practice he has seen an iron roof which was in such a posi- 

 tion that it could only be sloped one way ; that is, it was a lean-to 

 roof, and the builder had copied one half of a very good iron roof truss 

 for his half span, the consequence being that the tie rods near the 

 high side of the roof became struts, and being too flexible to resist a 

 a compressive strain they gave way under a weight of snow, and the 

 roof sank in. 



The story is also told of a certain double-pitched roof of an English 

 railway station, that, during the absence of the chief engineer of the 

 road, some wise man connected with the management proposed to 

 strengthen it by putting a row of columns under it down the centre. 

 His advice was adopted, and in the act of wedging the columns up to 

 sustain the weight the roof fell in, much to the astonishment of the 

 sagacious designer. 



It is evident that by means of the braces and ties we have consid- 

 erable control over the form of the beam, even after it is up, and it is 

 usual to give a bridge a slight cumber or curvature upwards, to insure 

 that it shall not settle in time or under a passing load below the hori- 

 zontal line. For this reason iron ties in at least one direction are 

 convenient, since the screws and nuts by which they are fastened pro- 

 vide a simple means of adjustment, while the wedges that must be 

 used in a structure entirely of wood are less easily managed. 



Care must be taken in designing a beam that there is no more 

 material used than is necessary, such excess being worse than a waste, 

 since it increases the load which the beam has to bear. 



Dr. Young called attention to the fact that, besides the tensional 

 strain below the neutral surface and the compressive strain above it, 

 there was a vertical strain existing near the ends, and diminishing 

 towards the middle, which he called the shearing strain. The weight 

 of the beam tends to shear off the fibres immediately over the point of 

 support just as a bar of metal is cut in a shearing machine. Before 

 this was understood, engineers were astonished to find that bridges, 

 the parts of which had been carefully calculated, sometimes failed uear 

 the abutments while retaining their form towards the centre, and now 

 the posts aud braces are made stronger near the abutments, or addi- 

 tional struts, called arch braces, are inserted. In cast-iron beams 

 with a plate web, it is proper to thicken the web near the points of 

 support to resist this strain. 



Care must be taken in deciding upon the proportions of the posts 

 and braces that their section is not only great enough to enable them 

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