CHAMBERS'S INFORMATION FOR THE PEOPLE. 



Fig. 33- 



beam of ash, diameter 10 inches, and length 12 

 feet? Here 2030 X 10 X io 2 -r- 144 = 14097 Ibs. 

 the strength of a square beam of 10 inches in the 

 side. But a cylindrical beam of 10 inches diameter 

 has less area by about one-third, and therefore its 

 strength will be 14097 X f = 9398 Ibs. More 

 exactly, the square is to the circle as I to -7854 ; 

 and 14097 X -7854 = 11071 Ibs. 



The most frequent case of transverse strain is 

 that of a beam resting freely on supports at the 

 two ends, with a weight or weights pressing some- 

 where between. If the weight rests on the middle 

 point, as in fig. 33, each of the supports sustains a 

 pressure equal to W. 

 We may therefore con- 

 sider the reaction of 

 either of the supports, 

 B, as a force acting up- 

 wards, and tending to 

 break the beam at C, 

 while the two forces at 

 A and C merely hold 

 the end of the beam fixed, as the wall does in fig. 

 34. The moment of the force of rupture is thus 

 W X CB = W X AB = i W X AB. But if 

 the beam were fixed in a wall at A, with a force W 

 acting at B, the moment would be W X AB. 

 That is, a beam supported freely at both ends will 

 support four times as much weight at its middle 

 Point, as it would if fixed at one end, with the 

 weight resting on the other. 



Ex. A bar of cast-iron, 2 inches square and 15 

 feet long, is supported at both ends, what weight 

 applied at its middle will break it ? Such a bar, 

 if fixed and loaded as in fig. 31, would support, by 

 the former rule, 8iooX 2 X 2 2 -j-i8o= 360 Ibs. 

 The breaking-weight in the present case is, there- 

 fore, 360 X 4 = 1440 Ibs. 



The strain of W is greater when applied at C, 

 the middle point, than when applied at any other 

 point, D. 



Form of Greatest Strength. It is evident (see 

 fig. 31) that the fibres of a beam near the neu- 

 tral axis on both sides, have little efficacy in resist- 

 ing rupture, and might be removed without much 

 affecting its strength ; and this principle is largely 

 applied in constructing metal beams or girders, in 

 order to produce the greatest strength with the least 

 material. For girders of cast-iron, resting on both 

 ends, and loaded in the middle, the form of section 

 adopted is that of an in- 

 ., , verted T (fig. 34). Cast- 



iron has much less power 

 of resisting extension than 

 compression, and there- 

 fore the lower flange is 

 made much greater than 

 the upper, so as to throw 

 the neutral axis as nearly 

 as possible in the middle 

 of the beam ; for the sum 

 of the moments of the two 



Fig. 34- 



sets of resistances is greater when the axis is in 

 the middle than when it is anywhere else. With 

 wrought-iron, which resists extension better than 

 compression, the upper flange is made the larger. 

 The advantage of the T-form is, that the great 

 mass of the material being collected on the two 

 flanges, acts at the greatest possible leverage. In 

 a series of experiments with cast-iron beams, the 

 strongest form was found to be that represented 



218 



A 



Fig- 35- 



\ in fig. 34, in which the lower flange, cd, is six 

 times the area of the upper, ab. With this pro- 

 portion, the strength per square inch of section of 



i the whole beam was 4075 pounds, whereas 'in 

 the best form of girder used before these experi- 



I ments, there was never attained a strength of 

 more than 2885 pounds. There was, therefore, 

 by this form a gain of 1190 pounds per square 

 inch of the section, or of \ the strength of the 



: beam.' 



Hollow or Tubular Structure. Another way of 



! throwing the great body of the material at a 

 distance from the neutral axis is, to make it into 



; the shape of a tube or 

 hollow cylinder. Let B 

 be the section of a hol- 



, low cylinder, the thick- 



, ness of whose walls 



I is represented by the 



1 shaded ring; and A be 



I the section of a solid 



: cylinder of the same 



| material. If the area 

 of A is equal to that of the ring in B, the two 

 cylinders will contain the same quantity of matter, 

 but B will be stronger than A, in proportion as eg 

 is longer than dg. 



The principle of hollow structure prevails both 

 in nature and art, wherever strength and lightness 

 have to be combined. It is seen in the stems of 

 plants, especially of the grasses ; the bones of 

 animals are also hollow, and those of birds, where 

 great lightness is required, are most so. A feather, 

 with its hollow stem, is perhaps the best instance 

 of the union of strength and lightness that could 

 be given. In art, again, we have hollow metal 

 pillars ; and sheet-iron for 

 roofing and other purposes is 

 corrugated, or bent into ridges 

 and furrows, to give it depth. 

 Each ridge or furrow is, as it 

 were, half a tube, and resists 

 bending with twice or thrice 

 the energy it would if flat 



The most striking applica- 

 tion of the principle of hollow 

 structure is seen in Tubular 

 Bridges. Fig. 36 represents a 

 section of the tube of the 

 Conway Bridge. The object 

 being to resist a vertical strain, 

 the form is made rectangular, 

 and the chief mass of the 

 material is thrown into the 

 top and bottom. The tube 

 may, in fact, be considered as an immense beam 

 or girder constructed on the principle of fig. 34, 

 the top and bottom being the two flanges, and the 

 two sides serving to connect them, instead of the 

 one rib in the middle. As it is constructed of 

 plate-iron, the top requires more metal than the 

 bottom, in order to resist the compression ; but 

 instead of putting the metal into one thick plate, 

 or into several plates laid the one on the other, it 

 is made to form a set of minor tubes or cells, 

 which gives additional stiffness and strength to 

 the whole tube. The floor, in like manner, con- 

 tains cells. Each of the tubes over the Conway is 

 24 feet high, 14 feet wide (outside), and 420 feet 

 long, and weighs 1300 tons; yet these enormous 

 hollow beams sustain not only their own weight, 



u 





Fig. 36. 





