Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate k = 45 W / m ⋅ K , ρ = 7800 k g / m 3 , c p = 500 J / k g ⋅ K that is initially at a uniform temperature of 300°C and is heated (on both sides) in a gas-fired furnace for which T ∞ = 700 ° C and h = 500 W / m 2 ⋅ K . How long will it take for a minimum temperature of 550°C to be reached in the plate?
Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate k = 45 W / m ⋅ K , ρ = 7800 k g / m 3 , c p = 500 J / k g ⋅ K that is initially at a uniform temperature of 300°C and is heated (on both sides) in a gas-fired furnace for which T ∞ = 700 ° C and h = 500 W / m 2 ⋅ K . How long will it take for a minimum temperature of 550°C to be reached in the plate?
Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate
k
=
45
W
/
m
⋅
K
,
ρ
=
7800
k
g
/
m
3
,
c
p
=
500
J
/
k
g
⋅
K
that is initially at a uniform temperature of 300°C and is heated (on both sides) in a gas-fired furnace for which
T
∞
=
700
°
C
and
h
=
500
W
/
m
2
⋅
K
. How long will it take for a minimum temperature of 550°C to be reached in the plate?
PROBLEM 3.23
3.23 Under normal operating condi-
tions a motor exerts a torque of
magnitude TF at F. The shafts
are made of a steel for which
the allowable shearing stress is
82 MPa and have diameters of
dCDE=24 mm and dFGH = 20
mm. Knowing that rp = 165
mm and rg114 mm, deter-
mine the largest torque TF
which may be exerted at F.
TF
F
rG-
rp
B
CH
TE
E
1. (16%) (a) If a ductile material fails under pure torsion, please explain the failure
mode and describe the observed plane of failure.
(b) Suppose a prismatic beam is subjected to equal and opposite couples as shown
in Fig. 1. Please sketch the deformation and the stress distribution of the cross
section.
M
M
Fig. 1
(c) Describe the definition of the neutral axis.
(d) Describe the definition of the modular ratio.
using the theorem of three moments, find all the moments, I only need concise calculations with minimal explanations. The correct answers are provided at the bottom
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