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

20.05 MPa
c
b
y
M z = 3.85 kN·m
20.05 MPa
a
distance x = ± 60 mm from the neutral axis (which is the z centroidal axis for M z ).
The maximum bending stress magnitude is
Mx z (3.85 kN⋅ m)( ± 60mm)(1,000 N/kN)(1, 000 mm/m)
s bend = =
6 4
I
11.52 × 10 mm
z
=± 20.05 MPa
z
d
x
Normal Stresses at Corners a, b, c, and d
The normal stresses acting at each of the four corners of the post can be determined
by superimposing the preceding results. In all instances, the normal
stresses act in the vertical direction—that is, the y direction. The sense of the
stress, either tension or compression, can be determined by inspection.
Corner a:
s = 7.29 MPa(C) + 16.41 MPa(T) + 20.05 MPa(C)
a
=− 7.29 MPa + 16.41 MPa − 20.05 MPa
=− 10.93 MPa = 10.93 MPa(C)
Ans.
Corner b:
σ = 7.29 MPa(C) + 16.41 MPa(T) + 20.05 MPa(T)
b
=− 7.29 MPa + 16.41 MPa + 20.05 MPa
= 29.17 MPa = 29.17 MPa(T)
Ans.
Corner c:
σ = 7.29 MPa(C) + 16.41 MPa(C) + 20.05 MPa(T)
c
=−7.29 MPa − 16.41 MPa + 20.05 MPa
=− 3.65 MPa = 3.65 MPa(C)
Ans.
Corner d:
σ = 7.29 MPa(C) + 16.41 MPa(C) + 20.05 MPa(C)
d
=−7.29 MPa −16.41 MPa − 20.05 MPa
=− 43.75 MPa = 43.75 MPa(C)
Ans.
mecmovies
ExAmpLES
m15.5 Two loads are applied as shown to the 80 mm by
45 mm cantilever beam. Determine the normal and shear
stresses at point H.
638