82 



HANDBOOK OF MECHANICAL DESIGN 



M^ and My are obtained by resolving the applied bending moment, which may 

 be at any angle to the XX axis, into its components about the XX axis and YY axis, 

 respectively. 



H is the summation of the product of each elemental area times both of its coordi- 

 nates, i.e., H = XAxy, the values of x and y being the distances from the centroid of 

 the elemental areas to the YY axis and XX axis, respectively. Distances above the 

 XX axis and distances to the right of the YY axis are positive. 

 XX axis and distances to the left of the YY axis are negative. 

 are principal axes, H is equal to zero. 



9 10 



Distances below the 

 Hence if XX and YY 



-^--0.05/--A 

 -. j Corrugofiom\ 



12 13 14 '\I5 

 ^'-Verfica/ reference 



Horizon -tal 

 reference 



Fig. 11.- 



-0. 032 "smoofh sheet 

 Unsymmetrical box beam. 



From the preceding equation, the normal stress /^ at any point in the cross sec- 

 tion can be calculated. When E is equal to zero, i.e., XX and YY are the principal 

 axes, 



(9) 



M,y MyX 



Further, if H is equal to zero and the section is synometrical about one axis, at 

 least, and the applied bending moment makes an angle of 90 deg. with the XX axis, 

 and the reference axis is in the plane of the resulting bending moment. 



h = 



My 



(10) 



As an example of the most general case of an unsymmetrical section such as 

 shown in the figure and with the apphed bending moment at an angle to the neutral 

 axis, assume that/b had been calculated from Eq. (8) and had been found to be 



/„ = -1,0862/ + 85x (11) 



For the elemental or elementary area 4 in. Fig. 8, 



X = -54.43 + 38.27 = -16.16 

 y = 31.63 - 6.81 = 24.82 



= 25.57 measured to extreme fiber of corrugation 



from which 



/, = -1,086 X 25.57 - 85 X 16.16 

 = -27,770 - 1,370 

 = —29,140 lb. per sq. in. compression 



