Concentration Factors for Slender Beams

For slender beams, concentration factors can be defined respectively for normal, bending and torsion stress, as [8]:

II

05 f

where

: S —

F

or

A

: S —

Ml

W

Kt

Tmax

— T

where

: T —

Mt

Wp

with the following meaning for the symbols (referred to the notched cross-section):

omax — maximum stress (by the theory of elasticity)

Подпись: Fig. 6.20 Stress states at the root of the notch in slender beams in pure tension, bending and torsion
Concentration Factors for Slender Beams

S — nominal stress (by Saint Venant theory in the notched section)

F = applied load

Mf = applied bending moment

W = bending section modulus of inertia

Mt = applied torsion moment

Wp = polar section modulus of inertia

t = maximum shear stress

Both stresses obtained by the theory of elasticity and by the elementary Saint Venant theory must fulfill the equilibrium relationships with external loads. In the first case of Fig.6.20, the equilibrium condition is:

Concentration Factors for Slender Beams(6.46)

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