68 PRACTICAL STRUCTURAL DESIGN 



depth of 12 ins., the thickness of the shell being 1 in.? Axis 

 horizontal. 



6/i 2 8 X 12 x 12 

 S (for entire section) = = =192 



, bh 2 6 x 10 x 10 

 S (for interior section) = = =100 



S (for metal section of hollow shape) = 92 ins. 



Example. What is the section modulus for a T-section 12 ins. 

 deep over-all with an extreme width of 8 ins. and with stem and 

 flanges each \ in. thick? Axis horizontal. 



,. , 6/i 2 8 x 12 x 12 

 S (for entire section) = -^- = ^ = 192 ins. 



S (for section on one side) = - - = 75.625 ins., and 



2 X 75.625 = 151.25 ins. 



The S for the section = 192 - 151.25 = 40.75 ins. The fiber 

 stress is called by some writers the " skin stress," a very good 

 term, for it is actually the stress in the outer skin, which is assumed 

 to have no thickness, or has an infinitesimal thickness. The 

 stress, within the elastic limit, varies uniformly as a straight line 

 to zero at the neutral axis. Therefore on each layer between the 

 skin and the neutral axis the stress is less than that assumed 

 in the computations. The total stress is equal to the average 

 stress multiplied by the distance from the neutral axis to the 

 skin. 



In Fig. 55 two beam sections are shown with the axes at right 

 angles and the respective moments of inertia and section moduli 

 are also given. The moment of resistance depends upon the square 

 of the depth, so that for two rectangular beams of homogeneous 

 material, having the same breadth, the beam having a depth 

 twice as great as that of the other beam has a resisting moment 

 four times as great. It will also be much stiffer, so there will 

 be less deflection with a deep beam. The most economical 

 beam, considering stiffness and strength, with a rectangular 

 cross section, has a breadth between two-thirds and three-fourths 

 the depth. 



A beam of /-section is possible in steel and iron because of the 



