BEAMS AND STRUCTURES 89 



Cr approximates 0.70 at wing root for a trapezoidally loaded box wing, for which, 



Mf = 0.7Mf, + 0.3^^2 

 M„ = 0.7M«i + 0.3ilffl2 



(28) 

 (29) 



On the assumption that Cr increases hnearly from 0.70 at the root to 1.00 at 20 

 per cent of the half span of the wing, Eqs. (16) and (17) apply from the wing tip to 

 80 per cent of the way inboard, and from this point inward to the root, Eqs. (26) and 

 (27) wiU apply, mth C^ varying from 1.0 at the 80 per cent distance to 0.7 at the root. 



Allowable Stresses 



These must be based on the combined shear stress and direct compressive stress. 

 In the accompanying Fig. 17, /, and/,, are the allowable compressive stress and allow- 



1.0 



.9 08 



2 Q6 



J 0.4 



0.2 



S -0.Z 



4- 



-0.4 



J -Q6 



" -0.8 



-1.0 



-1.2 



Fig. 17. — The combined stresse.s for axial and shear loads are obtained through the use of this curve plotted from 



the equation 1 — (fca/fc) = (fsa/fsV- 



able shear stress, each acting alone. When shear stress oif.a is acting together with a 

 compressive or tensUe stress, f^a will be the allowable tensile or compressive stress. 

 Similarly, f^a will be the allowable shear stress when a compressive stress of f^a is 

 present. By means of the curve in Fig. 17, the allowable /,<, andf.a are readily obtained 

 for any ratio. This applies for curved sheet, flat sheet, or tubes and may be used for 

 combined bending and torsion or shear combined with axial tension or compression. 



