Tutorial 08
MECH 101 Spring 2009
M 30th
Mar-30
Tutor: LEO Mail-add: myleo@ust.hk
Contents
„
„
Homework 3 (remaining)
Solution to mid‐term exam
HW3- Prob.
HW3
Prob 1
A shaft is made of a steel alloy having an allowable shear stress of τallow =
120 N/mm2. If the diameter of the shaft is 15 mm, determine the
maximum
i
torque
t
T that
th t can be
b transmitted.
t
itt d What
Wh t would
ld be
b the
th maximum
i
torque T′ if a 10-mm-diameter hole is bored through the shaft? Sketch the
shear-stress distribution along a radial line in each case.
Solution:
Use the allowable shear stress to determine: maximum shear stress →
allowable torque: T and T’
Tc
T (7.5)
79 52kN ⋅ mm
; ⇒ 120 N / mm 2 =
; ⇒ T = 79.52
π
J
4
(7.5 )
2
T 'c
T (7.5)
(7 5)
τ max = τ allow =
;⇒
120 N / mm 2 =
; ⇒ T = 63.8kN ⋅ mm
π
J
(7.54 − 54 )
2
T 'ρ
τ inner =
= 80 N / mm 2
J'
Stress distribution:
τ max = τ allow =
HW3- Prob.
HW3
Prob 7
The A-36 steel assembly consists of a tube having an outer radius of 20 mm
and a wall thickness of 2.5 mm. Using a rigid plate at B, it is connected to
th solid
the
lid 20
20-mm-diameter
di
t shaft
h ft AB.
AB Determine
D t
i the
th rotation
t ti off the
th tube’s
t b ’
end C if a torque of 20 N · m is applied to the tube at this end. The end A
of the shaft is fixed-supported. G = 76 GPa.
Solution:
Twistingg angle
g @ point
p
C = (angle
( g from A → B)) + ((Angle
g from C → B))
TAB LAB
20 ⋅ (103 ) ⋅ 200
=
≈ 0.00335rad
φA / B =
π
JG
4
3
(10) × 76 ×10
2
TCB LBC
−20 ⋅103 ⋅ 80
=−
φC / B = −φB / C = −
≈ 0.0002024
0 0002024rad
π
J 'G
4
4
3
(20 − 17.5 ) × 76 ×10
2
φ A = φ A / B + φC / B = 0.00355rad = 0.204o
Mid-term
Mid
term Exam
Prob. 1
D t
Determine
i the
th forces
f
acting
ti in
i all
ll the
th members
b off the
th truss
t
as shown.
h
„
Solution
∑ Fx = 0; ∑ Fx = 0; ∑ M A = 0
Force analysis
F
l i (EoE):
(E E)
We have 3-unknowns here, i.e., FAx FAy FCy
„ →Free-body
→Free body diagram (FBD)
„ Force analysis @ Joint C:
„
FCD = 4.1 kN (T)
FCB = 5.02 kN (C)
Or else, we can rotate the coordinate sys to
simplify the equations: similarly.
Mid-term
Mid
term Exam
Prob. 1
Determine the forces acting in all the members of the truss as shown.
shown
„
Solution (continued)
„
Force analysis
y @ Joint D:
FBD as shown on the right:
„
L tl @ Joint
Lastly,
J i t B:.
B
∑ Fx = 0; FAB cos 45ο + 5.02 × cos 45ο − 3kN = 0
FAB = 0.776 kN (C)
5 02kN y
5.02kN
x
FAB
B 3kN
4.1kN
Mid-term
Mid
term Exam
Prob. 2
The th
Th
three A-36
A 36 steel
t l bars
b shown
h
in
i Fig.
Fi 10–14a
10 14 are pin
i connected
t d to
t a rigid
i id
member. If the applied load on the member is 15 kN, determine the force
developed in each bar. Bars AB and EF each have a cross-sectional area of 25 mm2,
and bar CD has a cross-sectional area of 15 mm2.
Solution
„
FBD→Force equilibrium:
„
Compatibility of the rigid member:
„
Recall the load-displacement
load displacement relation:
Prob. 2
Mid-term
Mid
term Exam
Prob. 2
The th
Th
three A-36
A 36 steel
t l bars
b shown
h
in
i Fig.
Fi 10–14a
10 14 are pin
i connected
t d to
t a rigid
i id
member. If the applied load on the member is 15 kN, determine the force
developed in each bar. Bars AB and EF each have a cross-sectional area of 25 mm2,
and bar CD has a cross-sectional area of 15 mm2.
Solution
„We
have:
Solving eq. (1), (2), (3):
Prob. 2
(3)
Mid-term
Mid
term Exam
Prob. 3
The two solid steel shafts shown here are coupled together using the meshed
gears. Determine the angle of twist of end A of shaft AB when the torque
T 45 N
m is applied. Take G
80 GPa. Shaft AB is free to rotate within bearings E and F, whereas shaft DC
is fixed at D. Each shaft has a diameter of 20mm.
Mid-term
Mid
term Exam
Prob. 3
The two solid steel shafts shown here are coupled together using the
meshed gears. Determine the angle of twist of end A of shaft AB
when the torque T 45 N
m is applied. Take G
80 GPa. Shaft AB is free to rotate within bearings E and F, whereas shaft
DC is fixed at D. Each shaft has a diameter of 20mm.
Mid-term
Mid
term Exam
Prob. 4
AT
T-beam
b
iis subjected
bj t d to
t the
th bending
b di momentt off 15 kNm
kN as shown
h
in Fig. 12–17a. Determine the maximum normal stress in the beam
and the orientation of the neutral axis.
Solution
(3)
=0.089 m
Mid-term
Mid
term Exam
Prob. 4
AT
T-beam
b
iis subjected
bj t d to
t the
th bending
b di momentt off 15 kNm
kN as shown
h
here. Determine the maximum normal stress in the beam and the
orientation of the neutral axis.
Solution
(3)
Mid-term
Mid
term Exam
Prob. 4
AT
T-beam
b
iis subjected
bj t d to
t the
th bending
b di momentt off 15 kNm
kN as shown
h
here. Determine the maximum normal stress in the beam and
the orientation of the neutral axis.
Mid-term
Mid
term Exam
Prob. 4
AT
T-beam
b
iis subjected
bj t d to
t the
th bending
b di momentt off 15 kNm
kN as shown
h
here. Determine the maximum normal stress in the beam and the
orientation of the neutral axis.
(3)