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

Thus, to provide the necessary weld area, the minimum thickness is computed as
t
min
2
2,178.556 mm
≥ = 15.23 mm
Ans.
143.084 mm
(b) Solution Using Equations (1.8) and (1.9)
Determine the angle θ needed for Equations (1.8) and (1.9). The angle θ is defined as the
angle between the transverse cross section (i.e., the section perpendicular to the applied
load) and the inclined surface, with positive angles defined in a counterclockwise direction.
Although the butt-weld angle is labeled 57° in the problem sketch, that is not the
value needed for θ. For use in the equations, θ = −33°.
The normal and shear stresses on the inclined plane can be computed from
P
2
P
σn
= cos θ and τnt
= − sinθcosθ
A
A
According to the 80 MPa normal stress limit, the minimum cross-sectional area required
for the bar is
A
min
P (180 kN)(1, 000 N/kN)
cos
2
≥ θ = cos (33 − ° ) = 1,582.58 mm
2
σ
80 N/mm
n
2 2
Similarly, the minimum area required for the bar, on the basis of the 45 MPa shear stress
limit, is
P (180 kN)(1, 000 N/kN)
A sin cos min 2
≥− θ θ =− sin( − 33 ° )cos( − 33) ° = 1,827.09 mm
τ
45 N/mm
2
nt
Note: Here we are concerned with force and area magnitudes. If the area calculations had
produced a negative value, we would have considered only the absolute value.
To satisfy both stress limits, the larger of the two areas must be used. Since the steel
bar is 120 mm wide, the minimum bar thickness must be
t
min
2
1,827.09 mm
≥ = 15.23 mm
Ans.
120 mm
mecmovies
ExAmpLES
m1.12 The steel bar
shown has a 100 mm
by 25 mm rectangular
cross section. If an
axial force of P =
40 kN is applied to the bar, determine the normal and shear
stresses acting on the inclined surface a–a.
m1.13 The steel bar shown
has a 50 mm by 10 mm rectangular
cross section. The allowable
normal and shear stresses
on the inclined surface must be
limited to 40 MPa and 25 MPa,
respectively. Determine the
magnitude of the maximum
axial force of P that can be
applied to the bar.
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