INTERNAL FORCES 67 



and this divided by the distance from the neutral axis to the 

 most distant fiber gives the section modulus, as follows: 

 W _ ft _ W 2 6^ 

 12 : 2 ~ 12 X n ~ 6 " 

 the distance from the neutral axis to the skin being h -5- 2. 



The section modulus is dependent entirely upon the shape and 

 is independent of the weight of a beam and of the strength of the 

 material in the beam. Tables giving the section modulus when 

 once computed are good for all time. In steel manufacturers' 

 handbooks tables are given of the section moduli for every shape 

 rolled, so the proper beam may be selected when the bending 

 moment is known and the fiber stress is known. 



Let M = moment (bending moment = resisting moment) in inch 



pounds. 



S = section modulus in inches. 



/ = allowable maximum fiber stress in pounds per square 

 inch. 



then M = S/andS = j- 



In many books the expression / = =- is encountered. The 

 moment divided by the section modulus gives the fiber stress. The 



section modulus = -, in which 

 c 



I = moment of inertia. 



c = distance from the neutral axis to the most stressed fiber. 

 Sometimes y is used instead of c. 



t M Me 

 Therefore / = j-j- = -j 



One method for finding the Moment of Inertia and the Section 

 Modulus for T-sections, L's, etc., is to first assume a rectangular 

 section having dimensions equal to the extreme outside dimen- 

 sions of the shape. Find the properties (i.e., / and <S) for this 

 rectangular section. Next take each hollow portion considered 

 as a smaller rectangular section and find the properties. Adding 

 the results for each of the pieces cut away and subtracting the 

 sum from the properties for the entire section, the properties arc 

 found for the remainder. 



Example. - What is the section modulus for a hollow rec- 

 tangular section having an outside width of 8 ins. and an outside 



