32 BENDING. 



cast-iron IH I UIII. The modus operandi of finding the 

 modulus figure of a section of any shape is as follows : The 

 figure of the section should be drawn to scale, and this 

 figure should next be cut out in thin cardboard. This 

 ranlboanl tiii'iire can now be balanced on some kind of 

 knife edge in order that the position of its centre of 

 gravity may be found. Through this point a line is placed 

 upon the drawing to represent the neutral axis. Two base 

 lines are now drawn parallel to the neutral axis ; if the 

 figure is symmetrical about the neutral axis, the base lines 

 are equidistant from it, and are drawn through that 

 portion of the figure farthest from the axis. If the figure 

 is not symmetrical, the base lines should be still drawn 

 equidistant from the axis, and either at a distance equal to 

 that of the farthest point on one side or the other, as will 

 afterwards be explained. The modulus figure may now be 

 drawn. 



A number of lines should be drawn parallel to the 

 neutral axis, intersecting the boundary lines of the figure 

 in a number of isolated points. In (a) one of such points 

 is A. To get the corresponding point on the modulus 

 figure, draw AB perpendicular to the base line LM; join 

 B to the centre 0, cutting the horizontal line through A in 

 C ; then C is the required point on the modulus figure. In 

 this way, by taking in a number of points on the original 

 figure, a number of corresponding points on the modulus 

 figure may be obtained, by a precisely similar construction. 



Where the beam section is unsymmetrical, as at (6), the 

 distance of the base lines has to be decided according to 

 whether the stress considered is the maximum in tension or 

 the maximum in compression. Thus, if the section is to be 

 that of a beam loaded upon the top side, and supported at 

 both ends, the beam will be carried downwards by the load, 

 and the portion of the section above the neutral axis will be in 

 compression, while that below is in tension. If it is desired 

 to work on the maximum stress allowable in the metal in 

 compression, then the base lines must be drawn at a 

 distance from the neutral axis = C A ; if the stress in tension 

 is to be used, as is usually done, the base line distance will 

 be B C .= C D. The construction is the same as before. 



When the modulus figure has been obtained in the way 

 just described, the two portions, upper and lower, should 

 be cut out in cardboard, balanced about a knife edge in 

 two positions, and the centres of gravity of the areas found 

 in this way. In addition to this, their areas should also be 

 found, and the modulus of the section will easily follow. 



