STRENGTH OF BEAMS 



53 



Section III. The section modulus Z is then calculated from the 

 given dimensions. For ordinary rolled shapes of structural steel 

 the section moduli are given in Tables III- VII. The stress in the 

 extreme fiber (or skin stress, as it is called) is then found by substi- 

 tuting these numerical values of M and Z in the equation 



M 

 P = ~Z' 



By comparing this calculated value of p with the allowable unit 

 stress for the material, it is determined whether or not the beam 

 is safe. 



For a beam of given size and shape the maximum external 

 moment it can carry safely is found by calculating its moment of 

 resistance. Thus, if p denotes the allowable, or working, stress for 

 the material in lb./in. 2 , and the section modulus Z is calculated 

 from the given dimensions of the cross section, the maximum 

 external moment M which this beam can carry with safety is found 

 by inserting these numerical values in the equation 



M=pZ. 



In designing a beam to carry a given loading, the maximum 

 external moment M due to this loading is first calculated. Then, 

 for any specified unit working stress p, the required section modulus 

 is found from the relation 1/r 



Z=- . 

 P' 



This section modulus Z may then be looked up in Tables III- VI, 

 thus determining the exact dimensions of the beam. 



APPLICATIONS 



101. Find the safe moment of resistance for an oak beam 8 in. deep and 

 4 in. wide. 



Solution. In this case I = 170.7 in.* and e = 4 in. Therefore the section modu- 

 lus is 



I 170.7 .__. , 



Z = = = 42.7 in. 1 



e 4 



From Table I the safe stress for timber may be assumed as p = 1000 lb./in, 2 

 Consequently, the moment of resistance for this beam is 

 M = pZ - 42,700 in.-lb. 



