dr. mustafa y. al-mandil department of civil engineering
DESCRIPTION
Dr. Mustafa Y. Al-Mandil Department of Civil Engineering. Chapter 9. Centroid of Area. Centroid of Volume. z. y. dV. y. dA. x. x. Dr. Mustafa Y. Al-Mandil Department of Civil Engineering. Chapter 9. Example. Find Centroid of area ?. y. m. dy. h. y. x. b. - PowerPoint PPT PresentationTRANSCRIPT
CE 201 - STATICSDr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
Centroid of AreaCentroid of Area
dA
dAy~y
dA
dAx~x
Centroid of VolumeCentroid of Volume
dv
dvz~z
dv
dvy~y
dv
dvx~x
x
z
y
y
x
dV
zyxC ,,
,, yxC
dA
CE 201 - STATICS
3
h
h2y
hy
3y
2y
h
dyyhhb
dyyyhhb
dyhb
yh
dyhb
yhy
dΑ
dΑy~y
dyh
byhmdydΑ
h
byhm
h
yh
b
m
o
2
h
o
32
ho
2ho
ho
ho
A
A
Dr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
Find Centroid of area ?
Example
y
mh
dy
b
y
x
CE 201 - STATICSDr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
+
7cm 7cm 3cm 4cm
6cm
r =2cm
r =2c
m
0
6cm
2
1
y
x
4
1 +
33
2
4
+0.85cm
2cm 2cm
0.85cm
0.85cm
2cm
+
2cm
3cm
FIND CENTROID ?
+
2cm 1cm
CE 201 - STATICSDr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
TOTAL
S.N.
1
2
3
4
Shape
36.14 41.67 130.35
Areacm2 cm
~x~ y
cm
~~ xAcm3
yAcm3
Semi-Circle
Rectangle
Triangle
Quarter-Circle
6.28
24
9
-3.14
2
2
-1
3.15
6.85
3
2
0.85
12.56
48
-9
-9.89
43.02
72
18
-2.67
cm
i
ii 1.1536.14
41.67
A
Ax~X
cm
i
ii 3.6036.14
130.35
A
Ay~Y
CE 201 - STATICSDr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
+
7cm 7cm
r =2cm
r =2c
m
0
6cm
2
1
y
x
3
4
FIND MOMENTOF INERTIAIxx & Iyy ?
2yyyy
2xxxx
AdxII
AdyII
Parallel - Axis Theorem
CE 201 - STATICSDr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
TOTAL
S.N.
1
2
3
4
Shape
36.14 674.24 544.4
Semi-Circle
Rectangle
Triangle
Quarter-Circle
5
5
2
6.15
6.85
3
2
0.85
157
600
36
-118.76
294.67
216
36
-2.67
6.28
24
9
-3.14
Areacm2
dxcm
dycm
Adx2
cm4Ady2
cm4
Ixx
cm2Iyy
cm2
90.87 41.91
1.74
72
18
-0.87
6.24
32
4.5
-0.87
2yyyy
2xxxx
AdxII
AdyII 90.87 + 544.4 = 635.27 cm4
41.91 + 674.24 = 716.15 cm4
CE 201 - STATICSDr. Mustafa Y. Al-MandilDepartment of
Civil Engineering
Example 1:
h
o
h
o
bdy
ybdy
dA
dAyy
yy
h
o
h
o
dyb
ydyb
ho
h
o
y
y
2
2
222
2
hy
y
dy
y
x
h
b