RADIUS OF GYRATION. By definition, the radius of gyra tion is equal to the square root of the quotient of the moment of inertia divided by the area of the section ; therefore, if and correspond to radii of gyration about the axes 1-1 and 2-2 respectively, 7.1.1/2,087.548 = 9.46 23.323 /42.538 1.35 r2-2 = V 93.323 M — f I ; M I Or, f The proper section of beam could be determined by this formula, using the moment of inertia, the distance from the neutral axis to the extreme fibre, and the allowable fibre stress. It is more convenient, however, to have the constant I expressed in y the tables, and this constant is called the "Section Modulus." In the above case, therefore, s 1- = 2 2,087.548 — 173.96 1 The section modulus about the axis 2-2 is not given in the tables, because the beam is rarely used in this position. It can, however, be readily obtained : This also is a constant employed to express the relations of certain values used in the calculation of stresses in beams. As stated before, M y Also M = 2 for a load uniformly distributed, where p = the load per linear foot, and 1 = the length of span in feet. As
the value of Min the first equation is in inch-pounds, in the second also it must be in inch-pounds in order to equate them.
This value of C is convenient to use, because from it the total load that a beam can safely carry on a given span is readily obtained.
To derive the value of C in the case of the beam above, if we use f = 16,000, which is the value for buildings, then If the value of 1 given in the table of Carnegie's Handbook be used, the value of C will check with that above.
The value of C, however, varies as much as or more than this in the different books, because a slight variation in I is multiplied to such an extent. The variation, however, is of no practical importance in deducing the value of L, as the variation here is slight.
C', the coefficient derived by using the value of f = 12,500, becomes