THIRD LECTURE. 



BRIDGES-BEAMS. 



Bridges are the structures used by the engineer to carry a road over 

 streams or dry ravines. They are necessarily structures, with open- 

 ings beneath, of greater or less size, and portions of them at least 

 must be adapted to carry a load over a space. The solidity of such 

 structures depends upon the cohesion of the materials composing them, 

 or, in other words, upon the strength of the materials, their resistance 

 to compression or extension. When we extend a piece of any material, 

 we draw the particles of it further apart than they are in the normal 

 condition ; and when we crush it, we force them into closer contact. 

 These are direct strains, and can be readily made the subjects of experi- 

 ment. To determine the tensile strength of wrought-iron, we have 

 only to prepare a rod of any known section — say one square inch — and 

 fastening it by one end in a vertical position, hang weights to the 

 other end until it gives way. In this case all the fibres in it are equally 

 subjected to the strain, and if we double the section, we may double 

 the weight which it carried before. The strength is directly propor- 

 tional to the section', and the calculations for any weight are of the 

 simplest nature. The same remarks apply to the crushing weight 

 determined by subjecting a cube of the material of known section to 

 the action of a weight tending to crush it directly. 



When, however, we come to the consideration of the strength of 

 materials in other forms, and in positions where the direction of the 

 force does not coincide with the axis of symmetry, we shall find that the 

 investigations become much more complicated, and that direct experi- 

 ments must be applied through some general law to special cases. 



The most natural way to span an opening of moderate width is evi- 

 dently to throw across it a beam of such length that its extremities 

 will rest upon the sides of the opening. The rudest bridge is a tree 

 felled so as to lie across a stream. Now, in a beam in this position, 

 ,and of equal size throughout, we shall find that the fracture, from too 

 •great a load distributed over it, will be in the middle ; and that if the 

 section of the fracture be examined, it will give evidence of different 

 kinds of forces having been in action at that point. 



It is, perhaps, simpler in the beginning to consider half of the beam, 

 and to determine what are the strains which are caused by the appli- 

 cation of a load. 



If we have a beam firmly fixed at one end in 

 F an unyielding wall, and loaded at the other 

 i> end as in Fig. 10, we will find it first bend as 



©in Fig. 11 ; and then, as the load is increased, 

 break at or near the point of support A C. 

 Galileo, who investigated this, noticed that, 



