TRANSACTIONS OF SECTION G. 649 



The new system of traction for limber-coupled wagons is one which causes 

 the limber and the carriage to constitute two mechanica levers which at such 

 times as the resistance to traction is small, carry a part of the weight ot t e 

 animal, while when it is great, they cause an automatic transterence ot weight 

 from the wheels to the animal ; thus securing an ever-varying virtual angle ot 

 traction. The same effect is automatically brought about to the advantage ot 

 the horse by each of the inventor's new appliances. 



The same conditions are obtained in the case of man-hauled vehicles. 



The paper was illustrated by working models and diagrams. 



2. Ecporl on Complex Stress DiRtrihulion.—See Eeports, p. 159. 



3. The Slrenglh of Iron, Steel, and Cast-iron Struts. 

 By A.NDREW Egbert SON, M.Sc. 



A series of experiments on solid free-ended centrally-loaded struts has been 

 carried out in the Engineering Laboratories of the Manchester University during 

 the last two ye-ars. They lead to the following conclusions : 



1. For all the struts tested the collapsing load was in accordance with the 

 values calculated from Euler's formula, except for struts so short that the 

 average stress produced by the theoretical load was above the elastic limit ot 



the material. i- -j j • 4 



2. In the case of the shorter struts the material tested may be divided into 



two classes : i i / ■ j 



(rt) Materials having no appreciable drop of stress at yield (cast iron and 

 bright-rolled steel). For such materials, Southwell's formula— of which Euler's 

 is the particular case for wholly elastic material— gives the collapsing load for all 

 lengths. 



{h) Materials having a decided drop of stress at yield (mild steel, wrought 

 iron, and high tensile steel). For such materials Euler's or Southwell's formula 

 applies for all lengths for which the average stress calculated is less than the 

 elastic limit. Southwell's formula applies between the elastic limit and the 

 yield jMiiit, and for the shortest struts the collapsing load is equal to the yield 

 stress multiplied by the area. 



4. The Calculation of Torsion Stresses in Framed Structures and Thin- 

 u-ttlled Prisms. By Professor Cymi. Batho, M.Sc, B. Eng.* 



In designing a double track cantilever bridge with suspended span, it is 

 necessary to calculate the stresses arising in the suspended span due to unsym- 

 metrical live loads on the cantilever and anchor arms. It is also .sometimes of 

 importance to determine the stresses in an ordinary truss-bridge, braced arch 

 or other framed structure on four supports due to unequal settlement of the 

 supports. Similar problems arise in connection with erection travellers carry- 

 ing un.symmetrical loads, &c. The .«tresses arising under such conditions may be 

 termed \orsion stresses. Tlie calculation of these may be considerably shortened 

 by the upl> of the following thieorenis : 



If a framed structure consisting of two parallel trusses, similar in outline 

 and connected by lateral bracing, be subjected to unit forces at the corners 

 forming a pair of equal and opposite couples in the planes of the two trusses 

 respectively, the shear perpendicular to the plane of the trusses is constant 

 throughout the lateral system and equal to the area of the base of the frame- 

 work divided bv twice the area of one of the trusses. The theorem may be 

 extended to inehide thin-walled prisms, and in its most general form may be 

 stated thus : 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 everywhere constant and equal to the twisting moment multiplied by 



* See Eixjinecrlr.fi. October 1.5, 1915, p. 392. 



