Question 1: Cross-Sectional Properties For the cross-sectional shape shown below, we wish to determine a series of important section properties. The dimensions of the cross-section, as labelled on the below Figure, are given as: • b₁ = 80.0 mm, b₂ = 430.0 mm, • b3 = 110.0 mm, • b4 = 220.0 mm, h₁ = 500 mm, h₂ = 220.0 mm, • h3 = 90.0 mm, • h4 = 500 mm, • 1 =90.0 mm. Note: The diagram below is not drawn to scale. y t y 1 b₁ 2 b₂ 3 4 b₁ h₁=h4
Question 1: Cross-Sectional Properties For the cross-sectional shape shown below, we wish to determine a series of important section properties. The dimensions of the cross-section, as labelled on the below Figure, are given as: • b₁ = 80.0 mm, b₂ = 430.0 mm, • b3 = 110.0 mm, • b4 = 220.0 mm, h₁ = 500 mm, h₂ = 220.0 mm, • h3 = 90.0 mm, • h4 = 500 mm, • 1 =90.0 mm. Note: The diagram below is not drawn to scale. y t y 1 b₁ 2 b₂ 3 4 b₁ h₁=h4
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![Question 1: Cross-Sectional Properties
For the cross-sectional shape shown below, we wish to determine a series of important section properties. The dimensions of the cross-section, as
labelled on the below Figure, are given as:
• b₁ = 80.0 mm,
b₂ = 430.0 mm,
• b3 = 110.0 mm,
• b4 = 220.0 mm,
●
h₁ = 500 mm,
h₂ = 220.0 mm,
• h3 = 90.0 mm,
• h4 = 500 mm,
• t = 90.0 mm.
Note: The diagram below is not drawn to scale.
h₂
t
y' 1
b₁
2
b₂
3
b3
4
b
X
h₁=h4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6312c2ba-3ddd-4e1a-91e2-a12af60ced38%2F346a485a-3f1a-4484-a19f-bac98503af88%2Fulrrjl_processed.png&w=3840&q=75)
Transcribed Image Text:Question 1: Cross-Sectional Properties
For the cross-sectional shape shown below, we wish to determine a series of important section properties. The dimensions of the cross-section, as
labelled on the below Figure, are given as:
• b₁ = 80.0 mm,
b₂ = 430.0 mm,
• b3 = 110.0 mm,
• b4 = 220.0 mm,
●
h₁ = 500 mm,
h₂ = 220.0 mm,
• h3 = 90.0 mm,
• h4 = 500 mm,
• t = 90.0 mm.
Note: The diagram below is not drawn to scale.
h₂
t
y' 1
b₁
2
b₂
3
b3
4
b
X
h₁=h4
![Part 1: Second Moment of Area about the Centroid
With respect to the origin at O, the centroid of the cross-section C is located at:
a) x =
mm
b) y =
The second-moment of area about the centroidal axes (x - y) are given by:
c) Ixx =
mm4
d) Iyy =
mmª
e) Ixy =
mm
Imin
mm
Part 3: Principal Second Moment of Area
For the cross-sectional shape, what are the principal second moment of area about the centroid?
a) Imax=
mmª
b) Imin =
mm
Part 3: Mohr's Circle
An example of the Mohr's circle for this cross-section is shown below (not to scale)
For the cross-section given, what is the:
a) Radius of Mohr's Circle, R =
b) Coordinate of Centre, X =
R
C (X,0)
mm
mm
max
Ily](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6312c2ba-3ddd-4e1a-91e2-a12af60ced38%2F346a485a-3f1a-4484-a19f-bac98503af88%2Fvceol3d_processed.png&w=3840&q=75)
Transcribed Image Text:Part 1: Second Moment of Area about the Centroid
With respect to the origin at O, the centroid of the cross-section C is located at:
a) x =
mm
b) y =
The second-moment of area about the centroidal axes (x - y) are given by:
c) Ixx =
mm4
d) Iyy =
mmª
e) Ixy =
mm
Imin
mm
Part 3: Principal Second Moment of Area
For the cross-sectional shape, what are the principal second moment of area about the centroid?
a) Imax=
mmª
b) Imin =
mm
Part 3: Mohr's Circle
An example of the Mohr's circle for this cross-section is shown below (not to scale)
For the cross-section given, what is the:
a) Radius of Mohr's Circle, R =
b) Coordinate of Centre, X =
R
C (X,0)
mm
mm
max
Ily
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