Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Torsion shear
13.438 MPa
Beam shear
3.659 MPa
z
Hoop stress
11.000 MPa
x
H
Longitudinal stress
5.500 MPa
Bending stress
34.351 MPa
Combined Stresses at H
The normal and shear stresses acting at point H are summarized
on a stress element. Note that, at point H, the torsion
shear stress acts in the −x direction on the +z face of the stress
element. The shear stress associated with the 13 kN shear
force acts in the opposite direction.
9.78 MPa
z
x
11.00 MPa
H
39.85 MPa
17.1°
17.43 MPa
25.4 MPa
Stress transformation Results at H
The principal stresses and the maximum shear stress at H can
be determined from the stress transformation equations and
procedures detailed in Chapter 12. The results of these calculations
are shown in the accompanying figure.
The absolute maximum shear stress at H is 21.43 MPa.
42.9 MPa
8.00 MPa
y
Stresses at K
Although shear stresses are associated with the 13 kN shear force that
acts in the −y direction, the shear stress at point K is zero.
z
2.533 MPa
9 kN
H
K
x
Transverse shear stress is associated with the 9 kN shear force acting
in the −y direction at the section of interest. The shear stress formula
[Equation (9.2)] is used to calculate the shear stress:
3
VQ (9 kN)(212,352 mm )(1, 000 N/kN)
τ = =
= 2.533 MPa
4
It (31, 439,853 mm )(200 mm − 176 mm)
y
y
34.351 MPa
z
H
K
x
The 10.8 kN · m bending moment about the x axis creates bending
stresses at the section of interest. Point K, however, is located on the
neutral axis for this bending moment, and consequently, the bending
stress at K is zero.
10.8 kN·m
15.6 kN·m
y
z
49.619 MPa
H
K
x
The 15.6 kN · m (i.e., 15.6 × 10 6 N · mm) bending moment about the
y axis creates compressive normal stress at K:
6
Mc x
(15.6 × 10 Nmm)(100 ⋅ mm)
s z = =
= 49.619 MPa (C)
4
I 31,439,853 mm
x
650