References
75
y
1
2
=
2
3
0.5 2 + 0.5 2 + 1 ≈ 0.82; y(1) =
2
3
√
2 ≈ 0.94,
as the argument x grows, the function y grows monotonously (y > 0 when
1
2 < x < 1). Consequently, as the middle tangential stress grows, the intensity
of tangential stresses grows within
0.82
τ o
τ max
0.94.
(7.25)
The determination of the maximum tangential stresses and the intensity of
(tangential) stress is required to formulate the conditions for the occurrence of
plastic strain described below (Chap. 13).
References
1. M. Leonov, Osnovy mekhaniki uprugogo tela [Fundamentals of elastic body mechanics] (Izd-vo
AS Kirg. SSR, Frunze, 1963)
2. M. Leonov, Mekhanika deformatsii i razrusheniya [Deformation and fracture mechanics] (Izdvo Ilim Publ., Frunze, 1981)
3. V. Molotnikov, Kurs soprotivleniya materialov [The course of strength of materials] (SPb.,
Moscow/Lan’ Publ., Krasnodar, 2006)
4. V. Molotnikov, Mekhanika konstruktsii [Mechanics of structures] (SPb., Moscow/Lan’ Publ.,
Krasnodar, 2012)
75
y
1
2
=
2
3
0.5 2 + 0.5 2 + 1 ≈ 0.82; y(1) =
2
3
√
2 ≈ 0.94,
as the argument x grows, the function y grows monotonously (y > 0 when
1
2 < x < 1). Consequently, as the middle tangential stress grows, the intensity
of tangential stresses grows within
0.82
τ o
τ max
0.94.
(7.25)
The determination of the maximum tangential stresses and the intensity of
(tangential) stress is required to formulate the conditions for the occurrence of
plastic strain described below (Chap. 13).
References
1. M. Leonov, Osnovy mekhaniki uprugogo tela [Fundamentals of elastic body mechanics] (Izd-vo
AS Kirg. SSR, Frunze, 1963)
2. M. Leonov, Mekhanika deformatsii i razrusheniya [Deformation and fracture mechanics] (Izdvo Ilim Publ., Frunze, 1981)
3. V. Molotnikov, Kurs soprotivleniya materialov [The course of strength of materials] (SPb.,
Moscow/Lan’ Publ., Krasnodar, 2006)
4. V. Molotnikov, Mekhanika konstruktsii [Mechanics of structures] (SPb., Moscow/Lan’ Publ.,
Krasnodar, 2012)