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 L. The Torsicn of Closed and Open Tubes. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



THE formulae for closed and open tubes under torsion 

 given by Dr. Prescott in the November number of 

 the Philosophical Magazine have already been published 

 by me in two papers : (A) " The Calculation of Torsion 

 Stresses in Framed Structures and Thin-walied Prisms" 

 (Brit. Assoc. Report, 1915, and ' Engineering,' October 15th, 

 1915), and (B) "The Torsion of Solid and Hollow Prisms 

 and Cylinders " (' Engineering/ Nov. 24th and Dec. 1st, 

 1916). 



Formula (32) of Dr. Prescott's paper, giving the stress in 

 a thin tube, is stated in § 2 of paper B, and is a particular 

 case of the theorem which forms the main subject of paper A, 

 viz. : — If a hollow cylinder or prism, either continuous- 

 walled or of framework, and having plane ends perpendicular 

 to its length, be subjected to a twisting moment by couples 

 in the planes of its ends, the total longitudinal shear is every- 

 where constant and equal to the twisting moment multiplied 

 by the length of the cylinder and divided by twice the area 

 of one of its ends. 



This theorem was proved very simply from elementary 

 considerations without using the equations of elasticity. As 

 applied to frameworks, it was used in the calculation of the 

 torsion stresses in the suspended span of the Quebec Bridge, 

 and has also been applied to aeroplane fuselages. 



The formula (35) for the angle of twist of a tube given 

 by Dr. Prescott is also stated in § 2 of paper B, and is 

 deduced there from the work stored in the tube during 

 torsion. 



The formula (56) for the angle of twist of a thin strip 

 (called an " unclosed tube " by Dr. Prescott) is slightly 

 more general than my formula in paper B § 6 eq. 24, which 

 is only true when the strip is of uniform width, but equa- 

 tion (25) of paper B § 6 gives the extension of (24) to rolled 

 sections. 



Dr. Prescott does not give explicitly a formula for the 

 shear stress in a thin strip in terms of the torque, but, by 

 combining his equations (53) and (56), it follows that 



which is the formula given by me in B § 5 and extended to 

 structural steel sections in § 6. 



