Buckling of Deep Beams. 219 



assumption in this paper as to what Kn means except that 



torque 



Kn: 



angle of twist per unit length 



There is no assumption then that K has any particular form 

 such, for example, as is given by St. Venant/s theory of 

 torsion. The only assumption is that torque is proportional 

 to twist and that Kn is the constant expressing the quotient 

 obtained on dividing one by the other. Similar remarks 

 apply to EC, but there is no need to lay the same stress on 

 this as on the torsion coefficient because the bending 

 coefficient is better established, although even here G is not 

 rigorously the moment of inertia of the section if E is 

 Young's modulus. The point of the preceding argument 

 is this, that EC and Kn are a pair of coefficients which 

 should be obtained by experiment for any particular beam 

 that is to be used for testing the theory of this paper. It 

 would not be right to calculate EC and Kn, even if E and n 

 were known accurately, for that would be burdening the 

 theory of buckling beams with whatever errors are contained 

 in the theories of bending and of torsion. Of course, when 

 the buckling formulae have to be used in practice it will 

 usually be necessary to be content with calculated values of 

 C and K and assumed values of E and n, for that will be 

 the best that can be done. But, in the testing of the results 

 in the experiments carried out by Mr. Carrington, EC and 

 Kn are found experimentally and their values substituted in 

 the expressions for buckling loads, and these are compared 

 with the actual experimental buckling loads. 



In using the preceding results in practice, where it will 

 usually be necessary to calculate everything, the value of C 

 is the same as in the bending of beams and the best value 

 of K is the one given by St. Venant's theory of torsion. 

 For a beam of rectangular section, breadth b and depth d, 

 these values are 



c= T y,v, 



K=£W(l-0-630jV 



the latter being the approximate value of St. Venant's 

 torsion coefficient when b is less than ^d. 



