BEAMS AND STRUCTURES 85 



Allowable j = ^^ 



= 8.35^?0.032 = ^'^^0 ^^- P^' ^^- ^^- 



This sheet value will not be realized unless the rivets are spaced closely enough 

 so that the sheet cannot buclde between rivets. A rivet pitch not greater than forty 

 times the sheet thickness is suggested as a safe limit. 



Neutral axis and moment of inertia of the section are calculated in the usual 

 manner except that a reduced area is used for the portion of the curved sheet which is 

 under compression. 



r^nc .■ A .. sheet allowable , D 



i^nective area = A X -r^ v^ r-r X —f 



stmener allowable a 



where D = distance from neutral axis to ex- d = distance from centroid of the portion of 

 treme fiber of section sheet to neutral axis. 



or 



Use K = \ \i K calculates greater than one. 



Because a sheet on the compression side is only partly effective, the neutral axis 

 shifts to shghtly below the center of the circular section (Fig. 12) . The error resulting 

 therefrom is negligible. 



For a bending moment of 3,300,000 in. -lb. in the preceding example, the maximum 

 compression in the fibers is 



, -3,300,000X45.9 on onn ii 



jb = ^^gQ = 20,200 lb. per sq. m. 



This is equal to the allowable P/A calculated above ; hence it is satisfactory. 



BOX SECTIONS SUBJECTED TO TORSION 



Closed tubular or box sections are the most efficient and hence most generally 

 used. For a single-cell thin- walled box, 



f- = 2-3i (12) 



where /s = shearing stress, in lb. per sq. in. A = inclosed cross-sectional area in box, in sq. in. 



T = applied torsional moment, in in. lb. t = thickness of skin or covering 



where 8 = deflection in radians per in. of length J = torsion constant of the section 



G = torsional modulus of elasticity, gen- 1 _ 1 t' ds 



erally taken as OAE for aluminum J ~ iA- J t 

 alloy 



