Question 1: Cross-Sectional PropertiesFor the cross-sectional shape shown below, we wish to determine a series of important section properties. The dimensions of the cross-section, aslabelled 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.h₂ty' 1b₁2b₂3b34bXh₁=h4 Part 1: Second Moment of Area about the CentroidWith respect to the origin at O, the centroid of the cross-section C is located at:a) x =mmb) y =The second-moment of area about the centroidal axes (x - y) are given by:c) Ixx =mm4d) Iyy =mmªe) Ixy =mmIminmmPart 3: Principal Second Moment of AreaFor the cross-sectional shape, what are the principal second moment of area about the centroid?a) Imax=mmªb) Imin =mmPart 3: Mohr's CircleAn 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 =RC (X,0)mmmmmaxIly

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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, • 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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Length and Length related Variables

Length can de defined as the measurement or extent of physical quantities or objects from one terminal to another terminal. Stone age humans used finger length, step length, and so on to measure the size or displacement of an object. Nowadays, depending on how precise the measurement requires to be and the object’s size is measured, we use measuring devices for measurements like rulers and steel tape. Most people have used a ruler or tape measure to measure a particular distance or the size of an object. For more precise measurements of tiny objects, the development of measurement tools such as the Vernier caliper, which permits us to measure dimensions within 1/1000 of an inch. In the last few decades, electronic distance measuring instruments (EDMI) have been implemented that permit us to measure distances from a few feet to many miles with reasonable accuracy.

Question

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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