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BELL SYSTEM TECHNICAL JOURNAL 



apparent. Therefore, a sample calculation follows showing the method of 

 finding the section modulus of the brace bolt hole section containing a | 

 inch knot. 



Sample Calculation 



Referring to Fig. 2, it will be noted that the knot and bolt hole divide the section into 

 three parts: the top segment (D and two rectangular portions {R\ and R2). The moment 

 of inertia (/) of such a compound section about its neutral axis (at a distance c from M-M) 

 is equal to the sum of the moments of inertia {IT, IR\ and IR2) of the component parts 

 T, R\ and R2 about axes through their own centers of gravity, plus the areas of the com- 

 ponent parts multipilied by the squares of the distances of their own centers of gravity from 

 the neutral axis of the comi)ound section. The section modulus {S) of this section is found, 

 of course, by dividing its moment of inertia l)y the distance (y) from the neutral axis of the 

 section to the most remote fiber. 



Dimensions: 



Areas: 



Moments about M — M: 



b = 3.1875" (Width of Section) 



k = 0.7500" (Diameter of Knot) 



d = 3.7625" (See Computation I in Appendix) 

 //I = 0.7000" (d - 2.125" - 0.1875" - k) 

 hi = 1.9375" (2.125" - 0.1875") 



g = 0.1330" (See Computation I) 



/ = 3.8955" {d + ?) 

 n = 2.6625" (I hi '+ 2.3125") 

 r2 = 0.96875" (^ //2) 

 D = 4.09375" (Depth of Section) 



T = 0.7099 sq. ins. (See Computation I) 

 Rl = 2.2313 " (bhl) 

 R2 = 6.1758 " {bh2) 



Tt 

 Rlrl 

 R2r2 



9.1170 sq. ins. 



2.7654 

 5.9408 

 5.9828 



Moments of Inertia: 



14.6890 = 9.1170 c; and hence 

 = 1.6112 



IT = 0.0053 (See Computation I) 

 IRl = 0.0911 (MP -4- 12) 

 IR2 = 1.9319 (W/23 -=- 12) 

 T{t - c)2 = 3.7043 

 Rl{rl - c)2 = 2.4661 

 R2ic - r2Y = 2.5490 



Section Modulus: 



I = 10.7477 



y = 2.48255 (D - c) 



S = 4.3293 



y 



The same general procedure shown in this sample calculation was fol- 

 lowed in dealing with the other cross-sectional shapes. For this reason, 

 only the final results of the several calculations are presented; although, for 



