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Engineering Construction Plan and Materials Resistance Questions

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1/3
(4)
3 @ 5
000
Storey
Level i
Weight
W
i
(
kN
)
Mode
1
Mode
2
Mode
3
4
3,000
1.000
3,000
1.000
3,000
3,000
1.000
3,000
3,000
3
4,200
0.904
3,432
0.216
907
196
-0.831
-3,490
2,900
2
4,200
0.716
2,153
-0.701
-2,944
2,064
-0.574
-2,411
1,384
1
4,200
0.441
817
-0.921
-3,868
3,563
1.016
4,267
4,335
Σ
15,600
9,402
-2,905
8,822
1,366
11,620
M
=
[
w
i
φ
=
ik
]
g
w
i
φ
ik
11,656
2
14,450kN
=
9,402g g
= 14,45,000 kg
2,905
2
957kN
=
8,822g g
=95,700 kg
11,620g
=
g
= 16,100 kg
% of Total weight
92.6%
6.1%
1.0%
P
=
w
i
φ
ik
i ik
11,656
=
1.240
9,402
2,905
=
0.329
8,822
1,366
=
0.118
11,620
1.
y
(1)
(2)
(3)
(4)
(5)
(A)
(B)
(C)
4 @ 5000
PLAN
(D)
x
3200
3200
3200
4200
ELEVATION
2.
Solution:
2
1,366
2
k
2
161kN
k
w
φ
2

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2/3
3.
W
1
=W
2
=W
3
=300
×
(12+0.5
×
4)
= 4,200
kN
Roof:
W
4
=
300
×
10
= 3,000
kN
W = ΣW
i
=
3
×
4,200
+ 3,000
= 15,600
kN
4.
T
=
0.09
h d
=
0.09(13.8)
/ 15
=
0.32 sec
Sa
= 2.5;
g
A
h
= 0.09
5.
=
0.10(0.2 ×
otM
kN) 5.1(×
m)
= 30.0 kN-m
6. Total lateral forces in the walls:
FA = 50 - 21.92= 28.08 kN
FB = 50 +20.77= 71.92 kN
FC =-9+-5= -14.62 kN
FD = -5+-9=14.62 kN

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Unformatted Attachment Preview

1. (2) (3) y (4) (4) (5) (A) (1) (B) 3 @ 5000 (C) (D) x 4 @ 5000 PLAN 3200 3200 3200 4200 ELEVATION 2. Solution: Weight Storey Level i Wi (kN ) 4 3 2 1 3,000 4,200 4,200 4,200 15,600 Σ Mk = [∑ w φ= ] g i 2 ik i 2 ik ∑w φ % of Total weight P = k ∑w φ i ik ∑w φ i ik 2 Mode 1 1.000 0.904 0.716 0.441 3,000 3,797 3,007 1,852 11,656 Mode 2 3,000 3,432 2,153 817 9,402 11,656 2 14,450kN = 9,402g g 1.000 0.216 -0.701 -0.921 3,000 907 -2,944 -3,868 -2,905 2,9052 957kN = 8,822g g = 14,45,000 kg Mode 3 3,000 196 2,064 3,563 8,822 1.000 -0.831 -0.574 1.016 3,000 -3,490 -2,411 4,267 1,366 3,000 2,900 1,384 4,335 11,620 1,366 2 161kN = 11,620g g =95,700 kg = 16,100 kg 92.6% 6.1% 1.0% 11,656 = 1.240 9,402 −2,905 = −0.329 8,822 1,366 = 0.118 11,620 3. W1=W2 =W3 =300×(12+0.5×4) = 4,200 kN Roof: W4 = 300×10 = 3,000 kN W = ? ...
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