a) Locate the X' centroidal axes for the areas shown with the respect to the reference axis shown below. b) Calculate the moment of inertia around the X'-Centroidal axis found in part a. Make sure you show all the shapes used, locate their local centroidal axis and show the X' centroidal axis on the sketch below. Solve part a and b using tables on the following page as shown in class. Axis of Reference. 30 mm 15 mm 50 mm

a) Locate the X' centroidal axes for the areas shown with the respect to the reference axis shown below. b) Calculate the moment of inertia around the X'-Centroidal axis found in part a. Make sure you show all the shapes used, locate their local centroidal axis and show the X' centroidal axis on the sketch below. Solve part a and b using tables on the following page as shown in class. Axis of Reference. 30 mm 15 mm 50 mm

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

Control Survey and Geodetic reductions

Control surveys or survey controls are used to establish reference points as a basis for various construction activities. Vertical and horizontal control points are to be established in a control survey to increase accuracy. After establishing the control points, all other types of surveys such as topographic, right-of-way, aerial mapping, construction layout, boundary surveys, and utility mapping can be worked upon so that control networks can be formed. The place from which the observations are made is called a survey station.

Question

Use the chart method to solve and show work in organized mannner. write out steps

a) Locate the X' centroidal axes for the areas shown with the respect to the reference axis
shown below.
b) Calculate the moment of inertia around the X'-Centroidal axis found in part a.
Make sure you show all the shapes used, locate their local centroidal axis and show the X'
centroidal axis on the sketch below. Solve part a and b using tables on the following page as
shown in class.
Axis of Reference.
30 mm
15 mm
50 mm

Centroids locations and Moment of Inertia for simple geometric shape
a
CG
b
A=bh
I₁=
bh³
12
hb³
12
h
x
x=y=4
лd²
4
A=
1,-1,-10²
64
CG
b k
A=
bh
2
bh³
36
I₂ =
h
y=
3
b +
X=
A=
CG
a+b
3
bh
2
I₂ =
bh³
36
h
y=
y=
2 d
3r
CG
πd²
8
Jd4
I₂ = 1
128
d
лdª
128
145.78
HEL
8
3π
x
d/2
A=
x=p=-
πα
2d
3π
16
I₁=I₂
➜
d4
291.4

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Step 1: Introducing given data

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Step 2: Calculation of y-centroid (Location of X' centroidal axis)

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Step 3: Calculate moment of inertia about X' centroidal axis

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