ANALYSIS OF STRESS IN BEAMS 



37 



p denotes the stress on the extreme fiber and e denotes the distance 

 of this fiber from the neutral axis, then, from (17), 



(18) 



Me 



I 



Equation (18) gives the maximum normal stress on any cross section 

 of a beam, and is the fundamental formula in the common theory of 

 flexure. 



Problem 35. Find the moment of inertia of a rectangle of height h and breadth 

 6 about a gravity axis * parallel to its base. . 



* - 



Solution. I x l(bdy)y* = / = 



~5 "- 



Problem 36. Find the moment of inertia of a triangle of base 6 and altitude h 

 about a gravity axis parallel to its base. y i 



Problem 37. Find the moment of inertia of 

 a circle of diameter d about a gravity axis. 



Problem 38. The external moment acting 

 on a rectangular section 12 in. deep and 4 in. 

 wide is 30,000 ft. Ib. Find the stress on the 

 extreme fiber. 



Solution. M = 80,000 ft Ib. = 300,000 in. Ib., 

 I. = = 676 in.*. 



p = ^ = 8760 Ib./inA 





I 

 Fio. 21 



44, Moment of resistance. The moment of resistance is defined as 

 tin- ii n>ii ini t <f the internal stresses which balances the external moment 

 M. According to this definition the moment of resistance is simply 



si, 



e 



EL 



since = M. Therefore, if p is the maximum allowable unit stress 



for any material, the moment of resistance 



determines the 



maximum external bending moment which can be safely carried by 

 a beam of this material. 



In what follows, "gravity axis" will be used as an abbreviation for "axis through 

 the center of gravity." 



