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strength calculations, the verification must be performed to
calculate beam hardness. The hardness condition of a beam can be
written in the form
y    f , (6.43)
max
where y – the largest beam deflection, which is found in
max
building its elastic line;
  f – the allowable deflection arrow, depending on the

purpose and construction varies in quite wide limits. For example,
the required hardness of shaft bending is determined by the terms
of the correct gears and bearings. Thus, for shaft bearing gear
wheels,

 1 1 
  f     l ;
 3000 5000 

for axes and shafts that do not require high hardness,
 1 1 
  f     l ;
 300 1000 
for building constructions
 1 1 
  f     l ,
 150 400 
where l – the length of the span (distance between supports) or
console parts of a beam.

6.11 Potential energy of deformation under bending

Consider the case of pure bend of a beam (see. fig. 6.6, a).
Following the formula (2.33), the expression of elementary works
of internal bending moments shown in fig. 6.7, b, is written as
1
dA dU  M d . (6.44)
п z
2
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