BEAMS AND STRUCTURES 



87 



The shearing stress /» in any part of the box is shear per inch divided by thickness, 



or 



fs 



h 

 t 



When any of the sides buckle to form diagonal tension fields, the wrinkles being 

 assumed to make an angle of 45 deg., the tensUe stress St is 



2/1 



Torsional deflection in 6 radians per in. of length is 



T 



e 



GJ 



(15) 



where J is the torsion constant of the section corresponding to the moment of inertia I 

 as commonly used in the formulas for beams under flexure. The equations for 6 and 

 for the shear loads per inch are strictly true only for shear resisting panels. If sides 

 buckle to form diagonal tension fields, the values of t used in the equations for bi, fe,, 

 and &3 should be multiplied by H. That is, use Ht instead of t. But for the stress 

 calculations for fs and St, always use for t, the 

 actual thickness. However, if allowable buckling 

 stress of tension field sides is high compared with 

 actual stress, the use of an effective thickness 

 te = Ht wiU not be accurate. For reasonable 

 accuracy, proceed as follows: 



Assume that the torsional moment causing 

 buckling is 50,000 in. -lb. and the total applied 

 torsional moment is 120,000 in. -lb. Calculate aU 

 stresses and deflections under a load of 50,000 

 in. -lb. as in a shear resisting section. Then calcu- 

 late stresses and deflections under a load of 70,000 

 in.-lb. for the section as a tension field. Add the 

 stresses and the deflections. 



In a design as in Fig. 16, the front and rear spars are designed to resist all bending 

 whereas the box is assumed to resist all torsional moments. To accomphsh this, the 

 proportion of the total bending moment resisted by each spar is proportional to the 

 ratios of the moments of inertia of the respective spars, to the total moment of inertia., 

 or 



MEph 



Fig. 16. — Front and rear spars are 

 designed to resist all the bending, whereas 

 the box is designed on the assumption that 

 it resists all the torsion. 



Mpi = 



M«i = 



where M = total applied bending moment 



Mpi and Mri = bending moments in front and 

 rear spars 



Eplf + ErIr 



MEJb 

 Eplp + ErIr 



Ef and Er 



(16) 

 (17) 



= modulus of elasticity of material 

 of the spars 

 If and Ir = moment of inertia of front and 

 rear spars 



