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 22
Spring 2015
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Section moment of inertia General Formula
Where = section moment of inertia of area component A = area of area component = vertical distance (along the plane of moment) of
centroid of area component from a reference point
= vertical distance (along the plane of moment) of overall centroid
d =
2dAII x
A
AyY
Section moment of inertia, also called area moment of inertia
Distance of centroid from a reference point
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Exercise
b h A d Ad2 +Ad2
1 30 40 1200 20 24000 18 388800 160000
2 90 20 1800 50 90000 12 259200 60000
= 3000 = 114000
38 =
General Formula Where = section moment of inertia of area component A = area of area component = vertical distance (along the plane of moment) of centroid of area component from a reference point = vertical distance (along the plane of moment) of overall centroid d =
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Sample Problem 4.2
A cast-iron machine part is acted upon
by a 3 kN-m couple. Knowing E = 165
GPa and neglecting the effects of
fillets, determine (a) the maximum
tensile and compressive stresses, (b)
the radius of curvature.
SOLUTION:
Based on the cross section geometry,
calculate the location of the section
centroid and moment of inertia.
2dAIIA
AyY x
Apply the elastic flexural formula to
find the maximum tensile and
compressive stresses.
I
Mcm
Calculate the curvature
EI
M
1
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Sample Problem 4.2 SOLUTION:
Based on the cross section geometry, calculate
the location of the section centroid and
moment of inertia.
mm 383000
10114 3
A
AyY
3
3
3
32
101143000
104220120030402
109050180090201
mm ,mm ,mm Area,
AyA
Ayy
49-3
23
12123
121
23
1212
m10868 mm10868
18120040301218002090
I
dAbhdAIIx
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Sample Problem 4.2 Apply the elastic flexural formula to find the
maximum tensile and compressive stresses.
49
49
mm10868
m038.0mkN 3
mm10868
m022.0mkN 3
I
cM
I
cM
I
Mc
BB
AA
m
MPa 0.76A
MPa 3.131B
Calculate the curvature
49- m10868GPa 165mkN 3
1
EI
M
m 7.47
m1095.201 1-3
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
=
1
=
We can also compute the radius of curvature by first calculating maximum strain
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Home work Problems 3.56, 3.69, 3.73, 3.74
Problems 4.2, 4.5, 4.9, 4.10, 4.18
Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials
Problem 4.3
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