mm222 lec 19-20
TRANSCRIPT
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Hafiz Kabeer Raza Research Associate
Faculty of Materials Science and Engineering, GIK Institute Contact: Office G13, Faculty Lobby
[email protected], [email protected], 03344025392
MM222
Strength of Materials
Lecture – 19
Spring 2015
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The actual value of T is 420 lb.ft
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Design of Transmission Shafts • Principal transmission shaft
performance specifications are:
- power
- speed
• Determine torque applied to shaft at
specified power and speed,
f
PPT
fTTP
2
2
• Find shaft cross-section which will not
exceed the maximum allowable
shearing stress,
shafts hollow2
shafts solid2
max
41
42
22
max
3
max
Tcc
cc
J
Tc
c
J
J
Tc
• Designer must select shaft
material and cross-section to
meet performance specifications
without exceeding allowable
shearing stress.
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Example
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Problem 3.70
• Use T/τmax = J/c2
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Hafiz Kabeer Raza Research Associate
Faculty of Materials Science and Engineering, GIK Institute Contact: Office G13, Faculty Lobby
[email protected], [email protected], 03344025392
MM222
Strength of Materials
Lecture – 20
Spring 2015
![Page 7: MM222 Lec 19-20](https://reader034.vdocuments.us/reader034/viewer/2022042717/55cf8fe7550346703ba1151f/html5/thumbnails/7.jpg)
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Chapter 4
Pure Bending
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Pure Bending
Pure Bending: Prismatic members
subjected to equal and opposite couples
acting in the same longitudinal plane
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Other Loading Types
• Eccentric Loading: Axial loading which
does not pass through section centroid
produces internal forces equivalent to an
axial force and a couple
• Transverse Loading: Concentrated or
distributed transverse load produces
internal forces equivalent to a shear
force and a couple
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Symmetric Member in Pure Bending
• Internal forces in any cross section are equivalent
to a couple. The moment of the couple is equal
to the bending moment of the section.
• From statics, a couple M consists of two equal
and opposite forces.
• The sum of the components of the forces in any
direction is zero.
• The moment is the same about any axis
perpendicular to the plane of the couple and
zero about any axis contained in the plane.
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Bending Deformations Beam with a plane of symmetry in pure
bending:
• member remains symmetric
• bends uniformly to form a circular arc
• cross-sectional plane passes through arc center
and remains planar
• length of top decreases and length of bottom
increases
• a neutral surface must exist that is parallel to the
upper and lower surfaces and for which the length
does not change
• stresses and strains are negative (compressive)
above the neutral plane and positive (tension)
below it
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Tensile and Compression
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Strain Due to Bending Consider a beam segment of length L.
Where:
ρ = radius of curvature (length from center of
curvature to the neutral axis)
θ = the angle subtended by the entire length after
bending
y = the distance of the point where stress/strain is to
be computed from neutral axis (0, c)
After deformation, the length of the neutral surface
remains L. Length at other sections above or below,
mx
m
m
x
c
y
cρ
c
yy
L
yyLL
yL
or
linearly) ries(strain va
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Stress Due to Bending • For a linearly elastic material,
linearly) varies(stressm
mxx
c
y
Ec
yE
I
My
c
y
inertiaofmomenttionII
Mc
c
IdAy
cM
dAc
yydAyM
x
mx
m
mm
mx
ngSubstituti
sec,
2
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Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Beam Section Properties • The maximum normal stress due to bending,
modulussection
inertia ofmoment section
c
IS
I
S
M
I
Mcm
A beam section with a larger section modulus
will have a lower maximum stress
• Consider a rectangular beam cross section,
Ahbhh
bh
c
IS
613
61
3
121
2
Between two beams with the same cross
sectional area, the beam with the greater depth
will be more effective in resisting bending.
• Structural steel beams are designed to have a
large section modulus.