CEPE2S BSCE 4B
JEREMIAH JAMES M. ZABALA
Instructions:
Provide a complete and orderly solution to the given problem. Redraw the figure with the
corresponding locations of the centroid and center of rigidity. Submit your answers using the
submission format from the previous assignments.
A section of a reinforced concrete elevator shaft is shown in the figure. Compute the following:
a. Centroid of the section;
b. Center of Rigidity from the given reference axis. Consider the effect of shear deflection.
Assume h = 15m, P= 1000 kN, and f'c = 24 MPa.(Elevator dimensions are in meters.)
Hint: Break the composite shape into several rectangular sections.
ANSWER:
Material Properties:
4700
′
0.40
0.4
a Centroid of the section
Figure:
4700√24 23025.20358
23025.20358 9210.08143
3.24
#
0.40
1.296
0.4
0.20
2
3.24
1.62
2
2.83
0.40! 0.40
0.812
2.03
0.4 "
1.415
2
0.40
3.24
3.04
2
2.83
2
#
2
0.40! 0.40
0.812
2.03
0.4 "
1.415
2
0.40
0.20
#
2
1.12!
$
$
$
0.40
0.4
2.83
2
1.12
3.24
2
1.12!
%
%
0.448
2.63
2.68
0.40
0.448
0.4
2.83
2.63
2
1.12
0.56
%
2
i
1
2
3
4
5
Total
Ai
1.296
0.812
0.812
0.448
0.448
3.816
xi
Aixi
0.2592
1.149
1.149
1.1782
1.1782
4.9136
0.2
1.415
1.415
2.63
2.63
yi
1.62
3.04
0.2
2.68
0.56
∑
&
∑
&
Aiyi
2.09952
2.46848
0.1624
1.20064
0.25088
6.18192
4.91364
3.816
6.18192
3.816
( (
(
( (
(
1.288
1.62
b. Center of Rigidity from the given reference axis
)*
))*
))*#
)-#
)*$
)-$
)*%
)-%
Elements
b
+ℎ#
12
ℎ+ #
12
3.24#
12
3.24 0.4#
12
+ℎ#
12
ℎ+ #
12
2.03 0.4#
12
0.4 2.03#
12
+ℎ#
12
ℎ+ #
12
2.03 0.4#
12
0.4 2.03#
12
+ℎ#
12
ℎ+ #
12
1.12#
12
1.12 0.4#
12
+ℎ#
12
ℎ+ #
12
1.12#
12
1.12 0.4#
12
w
H
A
0.4
0.4
0.4
E
G
1.13374
$
0.01728
$
0.01083
$
0.27885
$
0.01083
$
0.27885
$
0.04683
$
0.00597
$
0.04683
$
0.00597
$
P
1
0.4
3.24
15
1.296
23025.2
9210.081
1000
2
2.03
0.4
15
0.812
23025.2
9210.081
1000
3
2.03
0.4
15
0.812
23025.2
9210.081
1000
4
0.4
1.12
15
0.448
23025.2
9210.081
1000
5
0.4
1.12
15
0.448
23025.2
9210.081
1000
Xr
Ix
Ph^3/(3EI)
1.2Ph/AG
Ry
x
x(Ry)
1.13374
43.0958622
1.50800935
0.022419578
0.2
0.004483916
0.01803
2709.90032
2.40687206
0.00036869
1.415
0.000521696
0.01803
2709.90032
2.40687206
0.00036869
1.415
0.000521696
0.04683
1043.33767
4.36245561
0.000954472
2.63
0.00251026
0.04683
1043.33767
4.36245561
0.000954472
2.63
0.00251026
SUM
0.025065901
0.010547828
Yr
Iy
Ph^3/(3EI)
1.2Ph/AG
Rx
y
y(Rx)
0.01728
2827.51753
1.50800935
0.000353479
1.62
5.726353E-04
0.27885
175.217869
2.40687206
0.005629846
3.04
1.711473E-02
0.27885
175.217869
2.40687206
0.005629846
0.2
1.125969E-03
0.00597
8184.17133
4.36245561
0.000122122
2.68
3.272869E-04
0.00597
8184.17133
4.36245561
0.000122122
0.56
6.838831E-05
SUM
0.011857415
x/
y/
Figure:
∑ R - x(
R∑ R * y(
R*
0.02507
0.01055
0.01921
0.01186
0.019209013
2.376
1.620