98 



MOMENT OF RESISTANCE OF A BEAM. Art. 70. 

 ^ QSSJ&SSB "-CSMlpSSft " ~ N 1 N 



I i _L_ 



Fig. 70. 



beam, and the manner in which the strength is increased Dy 

 moving the area away from the neutral axis, .VA r . 



Equation (10) is perhaps the most valuable in the entire 

 subject of stresses, and the student should be as familiar with 

 its use as with the use of the ordinary multiplication table. 



If v i is greater than v. 2 , $! will be the maximum unit fiber 

 stress (working stress) and vice versa. The extreme fiber gov- 

 erns the section. 



Perhaps the most convenient form in which to remember 

 equation (10) is, since M K =M, 



(12) 



= or === = section modulus. 



This is most frequently written in the form (dropping the 

 subscripts) , s = ^ 



In any case this equation must be solved by trial, because 

 both 7 and v depend upon the section, unless a table of section 



moduli is available. 



I . 



is called the section modulus because it 



is a measure of the sections value in resisting bending. The 

 tables for rolled shapes given in the rolling-mill handbooks give 

 the section moduli and for these, equation (12) furnishes a di- 

 rect solution as the following example shows. 



A beam of 20 ft. span carries a total uniform load of 9000 

 Ibs. The maximum moment will evidently be at mid-span and 



is equal to 9QQO >< 20 =22500 ft. Ibs. (64). If the maximum 

 allowed fiber stress is 16000 Ibs. per sq. in., the required section 

 modulus 225 ^Q 12 =16. 9 in. 3 (The moment must be in 



in. Ibs. in order to divide it by Ibs. per sq. in.). According to 

 column 8, Cambria p. 158, this requires a 9"X21.0 Ib. I beam. 1 

 An 8"X25.25 Ib. beam has nearly the required section modulus 

 but it weighs more; while it meets the requirements, the 9" I is 

 not only more economical but stronger and stiffer. Stiffness is 

 A The beam must be properly stayed against transverse buckling (68). 



