86 HANDBOOK OF MECHANICAL DESIGN 



For the section in Fig. 14, 



J 



ds Si Si So S2 



t El ti ts 14 



(13) 



When the sides of the box act as tension field members, in the preceding equation 

 for 6 the value of t used should be five-eighths the actual thickness, which will give a 

 reasonably accurate value for 6, the angular deflection. 



In the preceding equation for stress fs the torsional moment is assumed to be 

 applied so as to be distributed uniformly around the perimeter, an ideal condition 



which is approached by placing bulkheads or ribs 

 at aU points of application of load so as to transfer 

 external loads directly to the walls of the box. 



For a multiceU section such as the wing 

 section in Fig. 15 wherein sheets of different 

 thicknesses are used, and if the trailing edge 



h S2 



Fig. 14. — Single-cell thin-walled box section. 



Fig. 15. — Unsymmetrical box beam wherein 

 sheets of different thicknesses are used. 



portion which resists only a small part of the torque is neglected, 



T = 2{AJn + ^2/12) 



(14) 



where hi = shear factor, in lb. per in. of portion /12 = shear force, in lb. per in. of portion of per- 

 of perimeter bounding area ..4i but imeter, bounding area yl 2 but not including 



not including front spar web front spar web 



Note that the portion of the perimeter S4 is omitted, i.e., the front spar web, the 

 shear per inch of which is given by 



/13 = hi — hi 



Shear per inch of the three sides of thickness ii, ^0, and ^.3 is 



hi = ^[h^{Ai + A.^) + AM 



K = h{Ai + A.y + A'2bi + A\b2 

 wliere 63 = st/ti 62 = s-^/U 



Shear per inch for leading edge covering 



ho 



2K 



-Abs{Ai + A,) +Aobi] 



wherein 



Si 



7 01 „i „;, 

 bi = 7- + r + T 



Sj 



U 



