mm222 lec 19-20
TRANSCRIPT
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
The actual value of T is 420 lb.ft
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.
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Example
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Problem 3.70
• Use T/τmax = J/c2
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
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Chapter 4
Pure Bending
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
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
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.
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
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Tensile and Compression
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
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
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.