ON BRIDGES — BEAMS. 139 



In this case the lower side will be extended and the upper side com- 

 pressed, as in Fig. 14. 







Fig. 14. 



We found that while, if we added material to a beam, so as to increase 

 its breadth, we only gained so much strength as was due to the greater 

 number of particles ; if we added to the depth we not only increased 

 the number of particles, but also their moment, and thus gained a 

 double advantage. 



We should, therefore, in designing a beam, make it "as deep and as 

 thin as is practically possible, if we wish to economise material. The 

 importance of this may be tested by comparing the stiffness and strength 

 of an ordinary joist when laid on its side or on its edge across an 

 opening. 



Now, we cannot in practice reduce the breadth beyond a certain 

 limit, since our beam would twist and fail from that cause, but, since 

 the advantage is gained by disposing the material at a distance from 

 the neutral axis, we may make our beam with a flange at the top and 

 bottom, which will insure that result and give lateral stiffness at the 

 same time. 



Fig. 15 shows the cross section of a beam so made. c ^ 

 The material in the flanges A B and C D acts with a 

 moment due to its distance from the neutral axis G-, 

 and the material in the web, as it is called, serves 

 merely to keep the flanges together. A e^ ^ b 



In a beam made to bear pressure equally from all 

 sides as a straw, the material may be entirely withdrawn from the 

 centre and disposed in a circle around the neutral axis, forming a 

 tube or pipe, which is much stronger than it would be if the same 

 amount of material composing it were disposed in a solid cylinder. 



If the material of the beam resists extension and compression equally 

 well, the two flanges should be of the same size, but if not, they must 

 be unequal, to give each the share of the strain which it can bear. 



Thus, a cast-iron beam with equal flanges will break always upon 

 the lower or extended side, since the material resists com- 

 pression well but extension badly; and Mr. Eaton Hodg- ^ 

 lunson, who experimented largely on beams, succeeded, by 

 gradually increasing the lower flange, in making one 

 which was equally strong at the top and bottom. In this 

 the bottom flange had six times the area of the upper one, 

 (see Fig. 16,) and this is the form now adopted for cast-iron 

 beams. 



On the other hand, wrought iron does not resist a compressive strain 

 as well as it does one of extension, and in a beam of this material the 

 upper flange should have an area nearly twice that of the bottom 

 flange. 



