RESISTANCE OF MATERIALS 67 



and that the values of y in the latter system are deduced from 

 G by the equation : 



Y = G X 0-963 X 10 7 . 



The application of these three laws of torsion lead to the 

 use of hollow shafts in machinery, by which weight is reduced and 

 material economised without prejudice to strength. 



47. Shearing. The name of shearing is given to the action 

 produced when a body is broken at any section by causing the 

 two portions of the body to slide past one another. It is seen 

 in the effect of shears cutting a bar, the two parts separating by 

 sliding transversely. The effort of shearing is called the shear 

 stress. The shearing due to the action of a punch, or a fly-press, 

 can also be cited. There is therefore a transverse resistance of 

 the matter, laterally and tangential! y, which opposes the sliding. 

 It is that which prevents the threads of screws from breaking. 

 The deformation by torsion is a shear strain. The shear stress 

 which will produce fracture in pinewood is estimated at 23 kilo- 

 grammes per square centimetre. 



48. Alterations of Elasticity. The fatigue already discussed 

 in connection with elasticity is the result of various causes : 



1. The former state of the substance, the work that it has had 

 to perform, the duration of the action of the stresses endured, and 

 the age of the substance. 



2. The real nature of the material, whether the deformation 

 causes temporary or permanent internal frictions., or whether 

 there is viscosity, as in the case of the majority of organic 

 substances. 



3. Sharp variations of temperature. 



4. Shocks and vibrations whose effects are cumulative and 

 frequently cause its rupture. 



49. Role of Elasticity and Work or Elastic Energy. A funda- 

 mental property of the elasticity of bodies is to store and accumu- 

 late in them short impulses, those of shock and vibration : a few 

 small items of energy will add together and form a very appreci- 

 able quantity of energy. First of all, the work of deformation 

 or elastic energy, that is to say, the product of stress and defor- 

 mation must be estimated. These are : 



1. Work of traction or of compression : 



(equations that are deducted from the formula of elongations (1) 

 and easily established directly). 



