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state will be provided if the largest tangential stresses does not
exceed the allowable determined in linear stress state.
The conditions of strength by the third theory are:
  
  1 3    .
max
2
The largest tangential stresses under uniaxial tensile or
compression equal to half of the largest normal stress    5 , 0   ,
thus
 Й       . (3.35)

eqv 1 3
The third theory has good strength convergence with the
experimental data for plastic materials.
The fourth or the energy theory of strength - the hypothesis that
the strength of the material in difficult stress state will be provided
if the specific potential energy of deformation does not exceed the
allowable values established experimentally in linear stress state.
The conditions of strength by the fourth theory has the form
u   u .
n n
Taking into account the relations (2.35) and (3.31), we obtain:

2
2
2

 ЙV        2 (         )    . (3.36)
eqv 1 2 3 1 2 1 3 2 3

Experimental studies show that the fourth theory gives a true
result, if we take into account only the potential energy in
deformation and neglect the energy of volume change. To do this,
analyzing the relation (3.29), we assume   5 , 0 then the
expression (3.36) takes the form

2
2
2

 ЙV                   ,
eqv 1 2 3 1 2 1 3 2 3
or
1 2 2 2

 ЙV                   (3.37)
eqv  1 2 2 3 3 1 
2
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