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

The 10.8 kN · m (i.e., 10.8 × 10 6 N · mm) bending moment about the
x axis creates tensile normal stress at H:
y
6
Mc x
(10.8 × 10 Nmm)(100 ⋅ mm)
s z = =
= 34.351 MPa ( T)
4
I 31,439,853 mm
x
34.351 MPa
H
z
K
x
10.8 kN·m
The 15.6 kN · m bending moment about the y axis creates bending
stresses at the section of interest. Point H, however, is located on the
neutral axis for this bending moment, and consequently, the bending
stress at H is zero.
15.6 kN·m
H
y
z
K
x
49.619 MPa
The 8.45 kN · m (i.e., 8.45 × 10 6 N · mm) torque acting about the
z axis creates shear stress at H. The magnitude of this shear stress can be
calculated from the elastic torsion formula:
y
Tc
τ = =
J
6
(8.45 × 10 Nmm)(100 ⋅ mm)
62,879,706 mm
4
= 13.438 MPa
13.438 MPa
H
13.438 MPa
K
x
8.45 kN·m
The 1,500 kPa internal fluid pressure creates tensile normal stresses
in the 12 mm thick wall of the pipe. The longitudinal stress in the pipe
wall is
y
pd (1,500 kPa)(176 mm)
s long = = = 5,500 kPa = 5.500 MPa (T)
4t 4(12 mm)
and the circumferential stress is
pd (1,500 kPa)(176 mm)
s hoop = = = 11,000 kPa = 11.000 MPa (T)
2t 2(12 mm)
H
5.50 MPa 11.00 MPa
z
5.50 MPa
K
x
Observe that the longitudinal stress acts in the z direction. At point H, the
circumferential direction is the x direction.
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