32.3 An Example of Using the Birger Method
419
Fig. 32.10 Distribution of
axial normal stress
Fig. 32.11 Plot of shearing
stresses
2.0
1.0
0
-1.0
-2.0
P
F
=
σ t + αkσ s
1 + αk
,
α =
l p
l 0
, k =
E
E 1
− 1
.
(32.28)
To eliminate the incompatibility of deformations, a uniform pressure p was
applied to the side surface of the beam. Equating the radial movement (32.19) to
the incompatible strain (32.18), we receive
p =
k(σ 0 − σ σ s )
2(1 − ν)
.
(32.29)
Given formula (32.28), we get the second of the required dependencies
419
Fig. 32.10 Distribution of
axial normal stress
Fig. 32.11 Plot of shearing
stresses
2.0
1.0
0
-1.0
-2.0
P
F
=
σ t + αkσ s
1 + αk
,
α =
l p
l 0
, k =
E
E 1
− 1
.
(32.28)
To eliminate the incompatibility of deformations, a uniform pressure p was
applied to the side surface of the beam. Equating the radial movement (32.19) to
the incompatible strain (32.18), we receive
p =
k(σ 0 − σ σ s )
2(1 − ν)
.
(32.29)
Given formula (32.28), we get the second of the required dependencies