Moment Of Inertia.docx
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- Pages: 9
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK DGDGDFDFDFDGFDFDFDGGDFDFDG
Moment of Inertia for an Area or Second Moment of Area for typical cross section profiles Area Moment of Inertia or Moment of Inertia for an Area - also known as Second Moment of Area - I, is a property of shape that is used to predict deflection, bending and stress in beams.
Area Moment of Inertia - Imperial units
inches4
Area Moment of Inertia - Metric units
mm4 cm4 m4
Converting between Units
1 cm4 = 10-8 m4 = 104 mm4 1 in4 = 4.16x105 mm4 = 41.6 cm4
Example - Convert between Area Moment of Inertia Units 9240 cm4 can be converted to mm4 by multiplying with 104 (9240 cm4) 104 = 9.24 107 mm4
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK
Area Moment of Inertia (Moment of Inertia for an Area or Second Moment of Area)
for bending around the x axis can be expressed as Ix = ∫ y2 dA
(1)
where Ix = Area Moment of Inertia related to the x axis (m4, mm4, inches4) y = the perpendicular distance from axis x to the element dA (m, mm, inches) dA = an elemental area (m2, mm2, inches2) The Moment of Inertia for bending around the y axis can be expressed as Iy = ∫ x2 dA
(2)
where Ix = Area Moment of Inertia related to the y axis (m4, mm4, inches4) x = the perpendicular distance from axis y to the element dA (m, mm, inches)
Area Moment of Inertia for typical Cross Sections I
Area Moment of Inertia for typical Cross Sections II
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK Solid Square Cross Section
The Area Moment of Inertia for a solid square section can be calculated as Ix = a4 / 12
(2)
where
a = side (mm, m, in..)
Iy = a4 / 12
(2b)
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK Solid Rectangular Cross Section
The Area Moment of Ineria for a rectangular section can be calculated as Ix = b h3 / 12
(3)
where b = width h = height
Iy = b3 h / 12
(3b)
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK
Solid Circular Cross Section
The Area Moment of Inertia for a solid cylindrical section can be calculated as Ix = π r4 / 4 = π d4 / 64
(4)
where r = radius d = diameter
Iy = π r 4 / 4 = π d4 / 64
(4b)
Hollow Cylindrical Cross Section
The Area Moment of Inertia for a hollow cylindrical section can be calculated as
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
INSTRUCTOR :
STEEL AND TIMBER DESIGN
ENG.JERSON CONTIC
RESEARCH WORK Ix = π (do4 - di4) / 64
(5)
where do = cylinder outside diameter di = cylinder inside diameter
Iy = π (do4 - di4) / 64
(5b)
Square Section - Diagonal Moments
The diagonal Area Moments of Inertia for a square section can be calculated as Ix = Iy = a4 / 12
(6)
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
INSTRUCTOR :
STEEL AND TIMBER DESIGN
ENG.JERSON CONTIC
RESEARCH WORK Rectangular Section - Area Moments on any line through Center of Gravity
Rectangular section and Area of Moment on line through Center of Gravity can be calculated as Ix = (b h / 12) (h2 cos2 a + b2 sin2 a)
(7)Symmetrical Shape
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
INSTRUCTOR :
STEEL AND TIMBER DESIGN
ENG.JERSON CONTIC
RESEARCH WORK Area Moment of Inertia for a symmetrical shaped section can be calculated as Ix = (a h3 / 12) + (b / 12) (H3 - h3)
(8)
Iy = (a3 h / 12) + (b3 / 12) (H - h)
(8b)
Nonsymmetrical Shape
Area Moment of Inertia for a non symmetrical shaped section can be calculated as Ix = (1 / 3) (B yb3 - B1 hb3 + b yt3 - b1 ht3)
(9)
Area Moment of Inertia for typical Cross Sections II
Area Moment of Inertia vs. Polar Moment of Inertia vs. Moment of Inertia
"Area Moment of Inertia" is a property of shape that is used to predict deflection, bending and stress in beams "Polar Moment of Inertia" as a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque "Moment of Inertia" is a measure of an object's resistance to change in rotation direction.
Section Modulus
the "Section Modulus" is defined as W = I / y, where I is Area Moment of Inertia and y is the distance from the neutral axis to any given fiber
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
RESEARCH WORK
INSTRUCTOR :
ENG.JERSON CONTIC
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK DGDGDFDFDFDGFDFDFDGGDFDFDG
Moment of Inertia for an Area or Second Moment of Area for typical cross section profiles Area Moment of Inertia or Moment of Inertia for an Area - also known as Second Moment of Area - I, is a property of shape that is used to predict deflection, bending and stress in beams.
Area Moment of Inertia - Imperial units
inches4
Area Moment of Inertia - Metric units
mm4 cm4 m4
Converting between Units
1 cm4 = 10-8 m4 = 104 mm4 1 in4 = 4.16x105 mm4 = 41.6 cm4
Example - Convert between Area Moment of Inertia Units 9240 cm4 can be converted to mm4 by multiplying with 104 (9240 cm4) 104 = 9.24 107 mm4
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK
Area Moment of Inertia (Moment of Inertia for an Area or Second Moment of Area)
for bending around the x axis can be expressed as Ix = ∫ y2 dA
(1)
where Ix = Area Moment of Inertia related to the x axis (m4, mm4, inches4) y = the perpendicular distance from axis x to the element dA (m, mm, inches) dA = an elemental area (m2, mm2, inches2) The Moment of Inertia for bending around the y axis can be expressed as Iy = ∫ x2 dA
(2)
where Ix = Area Moment of Inertia related to the y axis (m4, mm4, inches4) x = the perpendicular distance from axis y to the element dA (m, mm, inches)
Area Moment of Inertia for typical Cross Sections I
Area Moment of Inertia for typical Cross Sections II
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK Solid Square Cross Section
The Area Moment of Inertia for a solid square section can be calculated as Ix = a4 / 12
(2)
where
a = side (mm, m, in..)
Iy = a4 / 12
(2b)
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK Solid Rectangular Cross Section
The Area Moment of Ineria for a rectangular section can be calculated as Ix = b h3 / 12
(3)
where b = width h = height
Iy = b3 h / 12
(3b)
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
INSTRUCTOR :
ENG.JERSON CONTIC
RESEARCH WORK
Solid Circular Cross Section
The Area Moment of Inertia for a solid cylindrical section can be calculated as Ix = π r4 / 4 = π d4 / 64
(4)
where r = radius d = diameter
Iy = π r 4 / 4 = π d4 / 64
(4b)
Hollow Cylindrical Cross Section
The Area Moment of Inertia for a hollow cylindrical section can be calculated as
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
INSTRUCTOR :
STEEL AND TIMBER DESIGN
ENG.JERSON CONTIC
RESEARCH WORK Ix = π (do4 - di4) / 64
(5)
where do = cylinder outside diameter di = cylinder inside diameter
Iy = π (do4 - di4) / 64
(5b)
Square Section - Diagonal Moments
The diagonal Area Moments of Inertia for a square section can be calculated as Ix = Iy = a4 / 12
(6)
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
INSTRUCTOR :
STEEL AND TIMBER DESIGN
ENG.JERSON CONTIC
RESEARCH WORK Rectangular Section - Area Moments on any line through Center of Gravity
Rectangular section and Area of Moment on line through Center of Gravity can be calculated as Ix = (b h / 12) (h2 cos2 a + b2 sin2 a)
(7)Symmetrical Shape
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
INSTRUCTOR :
STEEL AND TIMBER DESIGN
ENG.JERSON CONTIC
RESEARCH WORK Area Moment of Inertia for a symmetrical shaped section can be calculated as Ix = (a h3 / 12) + (b / 12) (H3 - h3)
(8)
Iy = (a3 h / 12) + (b3 / 12) (H - h)
(8b)
Nonsymmetrical Shape
Area Moment of Inertia for a non symmetrical shaped section can be calculated as Ix = (1 / 3) (B yb3 - B1 hb3 + b yt3 - b1 ht3)
(9)
Area Moment of Inertia for typical Cross Sections II
Area Moment of Inertia vs. Polar Moment of Inertia vs. Moment of Inertia
"Area Moment of Inertia" is a property of shape that is used to predict deflection, bending and stress in beams "Polar Moment of Inertia" as a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque "Moment of Inertia" is a measure of an object's resistance to change in rotation direction.
Section Modulus
the "Section Modulus" is defined as W = I / y, where I is Area Moment of Inertia and y is the distance from the neutral axis to any given fiber
NAME:
DATE SUBMITTED : MARCH 11, 2019
MALICDAN, JUNNIELE B.
SUBJECT :
STEEL AND TIMBER DESIGN
RESEARCH WORK
INSTRUCTOR :
ENG.JERSON CONTIC
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