CE472 - KSUfac.ksu.edu.sa/sites/default/files/one way solid slab_1.pdfย ยท CE472 Eng.ALI ALQARNI...
Transcript of CE472 - KSUfac.ksu.edu.sa/sites/default/files/one way solid slab_1.pdfย ยท CE472 Eng.ALI ALQARNI...
CE472
Eng.ALI ALQARNI Page 1
CE472
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One way Solid Slab formula:
๐ ๐ =๐๐ข 0.9
1000 โ ๐2โ 106 = ___๐๐๐ , ๐ = ๐ โ 20โ
๐๐2
= ___๐๐
๐ =๐๐ฆ
0.85 โ ๐๐= __ , ๐ =
1
๐ 1โ 1โ
2 โ ๐ ๐ โ ๐
๐๐ฆ = __
๐ด๐ = ๐ โ 1000 โ ๐ = __ ๐๐2 , ๐ด๐ ๐๐๐ = 0.0018 โ 1000 โ ๐ = __ ๐๐2
๐๐๐๐ฅ = min ๐ด๐๐ด๐ โ 1000 , 300๐๐ , 2 โ ๐ = __ ๐๐
๐๐๐ ๐๐๐๐ฅ๐ข๐๐๐ โ ๐ข๐ ๐ โ ๐๐@๐๐๐๐ฅ
๐ด๐ ๐๐๐ = 0.0018 โ 1000 โ ๐ = ___ ๐๐2
๐๐๐๐ฅ = min ๐ด๐๐ด๐ โ 1000 , 300๐๐ , 4 โ ๐ = __๐๐
๐๐๐ ๐ ๐๐๐๐๐๐๐๐ โ ๐ข๐ ๐ โ ๐๐@๐๐๐๐ฅ
Beam formula:-
๐ ๐ =๐๐ข 0.9
1000 โ ๐2โ 106 = ___๐๐๐
๐ = 600โ 40โ ๐๐ โ๐๐2
= ___ ๐๐ ๐๐๐ ๐๐๐ฆ๐๐
๐ = 600โ 40โ ๐๐ โ 25โ๐
2= ___ ๐๐ ๐ก๐ค๐ ๐๐๐ฆ๐๐
๐ =๐๐ฆ
0.85 โ ๐๐= ___ , ๐ =
1
๐ 1โ 1โ
2 โ ๐ ๐ โ ๐
๐๐ฆ = ___
๐ด๐ = ๐ โ ๐ โ ๐ = __ ๐๐2 ,
๐ด๐ ๐๐๐ (1) =1.4
420โ ๐๐ค โ ๐ = __๐๐2
๐ด๐ ๐๐๐ (2) = ๐๐
4 โ 420โ ๐๐ค โ ๐ = ___ ๐๐2
๐ด๐ ๐๐๐ = max ๐ด๐ ๐๐๐ 1 ,๐ด๐ ๐๐๐ 2 = __๐๐2
๐๐๐๐๐ ๐ด๐ > ๐ด๐ ๐๐๐ ๐๐
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Eng.ALI ALQARNI Page 5
๐ =๐ด๐
๐ด๐ = ๐๐๐๐ ๐๐ข๐๐๐๐
๐๐๐๐๐ ๐๐๐๐ = 80 + 60 + ๐ โ 1 ๐๐ + 25 > ๐ ๐๐
๐๐ ๐๐๐
= ๐ฝ1 600
600 + ๐๐ฆ >
๐
๐ โด ๐๐ =๐๐ฆ
๐๐ ๐๐๐ถ๐ฟ๐๐ก
= 0.375 ๐ฝ1 >๐
๐๐ก โด ๐๐๐๐ ๐๐๐ โ ๐๐๐๐ก๐๐๐๐๐๐ ๐ ๐๐๐ก๐๐๐
โ ๐๐ = 0.75 โ ๐๐
6โ ๐๐ค โ ๐ โ 10โ3 = ___๐๐
๐๐ =๐๐ข โ โ ๐๐
0.75= __๐๐
๐ด๐ฃ = 2 โ ๐๐๐
2
4= ___ ๐๐2 (๐ก๐ค๐ ๐๐๐)
๐ =๐ด๐ฃ โ ๐๐ฆ โ ๐
๐๐ โ 10โ3___๐๐
๐๐ ๐๐ โค 2๐๐
๐๐๐๐ฅ = min(600 ,๐
2 )
๐๐ 2๐๐ < ๐๐ โค 4๐๐
๐๐๐๐ฅ = min 300 ,๐
4
๐๐ ๐๐ > 4๐๐
๐๐๐๐ ๐ก๐ ๐๐๐๐๐๐ ๐ ๐ก๐๐ ๐ ๐๐๐ก๐๐๐
๐๐ ๐๐ข <1
2โ ๐๐
๐๐ ๐๐๐๐ ๐๐๐ ๐ ๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐๐ก
๐๐ โ ๐๐ > ๐๐ข >1
2โ ๐๐
๐๐๐๐ ๐ก๐ ๐๐๐๐ฃ๐๐๐ ๐๐๐๐๐ข๐๐
๐๐ฃ ๐๐๐ = max{ 1
16 ๐๐ โ ๐๐ค โ
๐
๐๐ฆ , (
๐๐ค โ ๐
3๐๐ฆ )}
CE472
Eng.ALI ALQARNI Page 6
Example 1:
The figure shown below shows the architectural plan for 3-story building. The slab will be designed to carry super imposed dead load (2.5KN/m2) and Live load (3KN/ m2) by compressive strength 25 Mpa and steel yield strength 420 Mpa.
Given data:
The one way solid slab is used.
Weight of Wall =15Kn/m
The slab thickness= 130mm
The beams dimensions = (300,600) mm
The columns dimensions= (300,500) mm
B
7m
7m
Strip strip
3m 3m 3m 3m A
C
1-m slab strip
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Eng.ALI ALQARNI Page 7
Determine the following:
1- Check if Slab thickness meets SBC304.
2- Design the slab for Max +Ve moment.
3- Design the slab for Max -Ve moment.
4- Check the slab for Shear reinforcement.
5- Draw the details and show all value.
6- Design the beam (A-B) for flexure and shear.
7- Calculate the axial load acting on column C.
Solution:
๐๐๐๐ =๐
28=
3000
28= 107.14 ๐๐
๐๐๐๐ =๐
24=
3000
24= 125 ๐๐
๐๐๐๐ = max(107.14,125) = 125 ๐๐
๐ > ๐๐๐๐ โ ๐๐
๐ท๐ฟ = ๐๐ค๐ ๐ค๐๐๐๐๐ก + ๐ ๐ข๐๐๐๐๐๐๐๐ ๐๐
๐ท๐ฟ = 0.13 โ 25 + 2.5 = 5.75 ๐๐ ๐2
๐ฟ๐ฟ = 3 ๐๐ ๐2
๐๐ข = 1.4๐ท๐ฟ + 1.7๐ฟ๐ฟ
๐๐ข = 1.4 5.75 + 1.7 3 = 13.15๐๐ ๐2
Lu (m) 3m 3m 3m 3m
Ln (m) 2.7m 2.7m 2.7m 2.7m
Cm 1/12 1/14 1/12 1/12 1/16 1/12 1/12 1/16 1/12 1/12 1/14 1/12
Wu(kn/m2) 13.15 13.15 13.15 13.15 13.15 13.15 13.15 13.15 13.15 13.15 13.15 13.15
Mu(kn.m) 7.99 6.85 7.99 7.99 5.99 7.99 7.99 5.99 7.99 7.99 6.85 7.99
D (mm) 104 104 104 104 104 104 104 104 104 104 104 104
Rn (Mpa) 0.821 0.704 0.821 0.821 0.615 0.821 0.821 0.615 0.821 0.821 0.704 0.821
ฮก 0.002 0.0017 0.002 0.002 0.0015 0.002 0.002 0.0015 0.002 0.002 0.0017 0.002
As (mm2) 208 176.8 208 208 156 208 208 156 208 208 176.8 208
3m
m
3m
m
3m
m
3m
m
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Eng.ALI ALQARNI Page 8
As min(mm2) 234 234 234 234 234 234 234 234 234 234 234 234
As (mm2) 234 234 234 234 234 234 234 234 234 234 234 234
S max (mm) 260 260 260 260 260 260 260 260 260 260 260 260
As rinkashge (mm2)
234 234 234 234 234 234 234 234 234 234 234 234
S max (mm) 300 300 300 300 300 300 300 300 300 300 300 300
Cv 1 1.15 1 1 1 1 1 1
Vu (kn) 17.75 20.42 17.75 17.75 17.75 17.75 20.42 17.75
ฯVc (kn) 65 65 65 65 65 65 65 65
๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐
๐ฟ๐ข = 3๐ , ๐ฟ๐ = 3 โ 0.15โ 0.15 = 2.7๐
๐ถ๐ =1
12 , ๐๐ข =
1
12โ 13.15 โ 2.72 = 7.99 ๐๐.๐
๐ = 130โ 20โ12
2= 104๐๐ , ๐ ๐ =
7.99 0.9
1000 โ 1042โ 106 = 0.821 ๐๐๐
๐ =420
0.85 โ 25= 19.765 , ๐ =
1
19.765 1โ 1 โ
2 โ 0.985 โ 19.765
420 = 0.002
๐ด๐ = 0.002 โ 1000 โ 104 = 208 ๐๐2 , ๐ด๐ ๐๐๐ = 0.0018 โ 1000 โ 130 = 234 ๐๐2
๐๐๐๐ฅ = min 113.04
234โ 1000 = 483.1 ๐๐, 300๐๐, 2 โ 130 = 260 = 260๐๐
๐๐๐ ๐๐๐๐ฅ๐ข๐๐๐ โ ๐ข๐ ๐ โ 12@260 ๐๐
๐ด๐ ๐ ๐๐๐๐๐๐๐๐ = 0.0018 โ 1000 โ 130 = 234 ๐๐2
๐๐๐๐ฅ = min 113.04
234โ 1000 = 483.1๐๐, 300๐๐, 4 โ 130 = 520 = 300๐๐
๐๐๐ ๐ ๐๐๐๐๐๐๐๐ โ ๐ข๐ ๐ โ 12@300 ๐๐
๐ถ๐ฃ = 1.15 , ๐๐ข =1.15 โ 13.15 โ 2.7
2= 20.42 ๐๐
โ ๐๐ = 0.75 โ 25
6โ 1000 โ 104 โ 10โ3 = 65 ๐๐
โ ๐๐ > ๐๐ข โ ๐ ๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐๐ก ๐๐ ๐๐๐ก ๐๐๐๐๐๐
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Eng.ALI ALQARNI Page 9
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Eng.ALI ALQARNI Page 10
Design of beam (A-B) :-
Load acting on the beam (A-B)
1- Dead load:
๐ท๐ฟ = 5.75 โ 1.5 + 1.5 + 15 + 0.47 โ 0.3 โ 25 = 35.775๐๐ ๐
2- Live load
๐ฟ๐ฟ = 3 โ 1.5 + 1.5 = 9๐๐ ๐
๐๐ข = 1.4 35.775 + 1.7 9 = 65.385 ๐๐ ๐
B
7m
7m
Strip strip
3m 3m 3m 3m A
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Eng.ALI ALQARNI Page 11
๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐
๐ฟ๐ข = 7๐ , ๐ฟ๐ = 7 โ 0.15โ 0.15 = 6.7๐
๐ถ๐ =1
9 , ๐๐ข =
1
9โ 65.385 โ 6.72 = 326.13 ๐๐.๐
๐ = 600โ 40โ 10โ20
2= 540 ๐๐ ๐๐๐ ๐๐๐ฆ๐๐
๐ ๐ =326.13 0.9
300 โ 5402โ 106 = 4.14 ๐๐๐
๐ =420
0.85 โ 25= 19.765 , ๐ =
1
19.765 1โ 1 โ
2 โ 4.41 โ 19.765
420 = 0.0111
๐ด๐ = 0.0111 โ 300 โ 540 = 1798.2 ๐๐2 ,
Lu (m) 7m 7m
Ln(m) 6.7m 6.7m
Wu(kn/m) 65.385
Cm 1/16 1/14 1/9 1/9 1/14 1/16
Mu (kn.m) 210 326.13 326.13 210
d(mm) 540 (one layer) 517.5(two layer) 517.5(two layer) 540 (one layer)
Rn(Mpa) 2.667 4.51 4.51 2.667
ฮก 0.00681 0.01221 0.01221 0.00681
As(mm2) 1103.2 1896 1896 1103.2
As min (mm2) 540 517.5 517.5 540
n 3.51โ4 6.03โ7 6.03โ7 3.51โ4
Fs=Fy Ok Ok Ok Ok
TCL Ok Ok Ok Ok
b min (mm) 275 275 275 275
Use 4โ 20 7โ 20 7โ 20 4โ 20
Cv 1 1.15 1.15 1
Vu (kn) 219.04 252 252 219.04
ฯVc (kn) 101.25 97.03 97.03 101.25
Vs (kn) 157.05 206.67 206.67 157.05
Av (mm2) 157 157 157 157
S (mm) 226.72 165.1 165.1 226.72
S max (mm) 270 258.75 258.75 270
Use โ 10@270 โ 10@160 โ 10@160 โ 10@270
CE472
Eng.ALI ALQARNI Page 12
๐ด๐ ๐๐๐ =1.4
420โ 300 โ 540 = 540 ๐๐2
๐ด๐ ๐๐๐ = 25
4 โ 420โ 300 โ 540 = 483 ๐๐2
๐ด๐ ๐๐๐ = max 540,483 = 540๐๐2
๐ =1798.2
314= 5.72 โ 6
๐๐๐๐ = 80 + 60 + 5 20 + 25 = 365๐๐ > ๐ = 300 โด ๐ข๐ ๐ ๐ก๐ค๐ ๐๐๐ฆ๐๐
๐ = 600โ 40โ 10โ 20โ25
2= 517.5 ๐๐ ๐ก๐ค๐ ๐๐๐ฆ๐๐
๐ ๐ =326.65 0.9
300 โ 517.52โ 106 = 4.51 ๐๐๐
๐ =420
0.85 โ 25= 19.765 , ๐ =
1
19.765 1โ 1โ
2 โ 4.51 โ 19.765
420 = 0.01221
๐ด๐ = 0.01224 โ 300 โ 517.5 = 1896 ๐๐2 ,
๐ด๐ ๐๐๐ =1.4
420โ 300 โ 517.5 = 517 ๐๐2
๐ด๐ ๐๐๐ = 25
4 โ 420โ 300 โ 517.5 = 462.1 ๐๐2
๐ด๐ ๐๐๐ = max 517,462.1 = 517๐๐2
๐ =1900.3
314= 6.03 โ 7
๐ =7 โ 314 โ 420
0.85 โ 25 โ 300= 144.81 ๐๐
๐๐๐
= 0.5 >๐
๐= 0.28 โด ๐๐ =๐๐ฆ
๐๐๐ถ๐ฟ๐๐ก
= 0.31875 >๐
๐๐ก= 0.268 โด ๐๐๐๐ ๐๐๐ โ ๐๐๐๐ก๐๐๐๐๐๐ ๐ ๐๐๐ก๐๐๐
๐๐๐ ๐๐๐๐ฅ๐ข๐๐ ๐ข๐ ๐ 7โ 20
๐ถ๐ฃ = 1.15 , ๐๐ข =1.15 โ 65.385 โ 6.7
2= 252 ๐๐
CE472
Eng.ALI ALQARNI Page 13
โ ๐๐ = 0.75 โ 25
6โ 300 โ 517.5 โ 10โ3 = 97.03๐๐
๐๐ =252.3โ 97.03
0.75= 206.67๐๐
๐ด๐ฃ = 2 โ ๐102
4= 157 ๐๐2 (๐ก๐ค๐ ๐๐๐)
๐ =157 โ 420 โ 517.5
206.67โ 10โ3 = 165.1 ๐๐
๐๐ โค 2๐๐
๐๐๐๐ฅ = ๐๐๐ 300,517.5
2= 258.75 = 258.75 ๐๐
๐ข๐ ๐ โ 10@160๐๐
Axial load on column C:-
Beam s in x- direction:
๐ท๐ฟ = 0.3 โ 0.47 โ 25 + 15 โ3
2 + 0.3 โ 0.47 โ 25 + 15 โ
3
2 = 55.575 ๐๐
๐ฟ๐ฟ = 0 + 0 = 0 ๐๐
Beams in y- direction:
๐ท๐ฟ = 0.3 โ 0.47 โ 25 + (15) + 5.75 โ 3 โ7
2 + 0.3 โ 0.47 โ 25 + (15) + 5.75 โ 3 โ
7
2
= 250.425 ๐๐
๐ฟ๐ฟ = 3 โ 3 โ7
2 + 3 โ 3 โ
7
2 = 63 ๐๐
๐๐ข = 1.4 55.575 + 250.425 + 1.7 63 = 388.5 ๐๐
CE472
Eng.ALI ALQARNI Page 14
Example 2:
Given data:-
๐๐ = 30 ๐๐๐ ,๐๐ฆ = 420 ๐๐๐
๐ ๐ข๐๐๐ ๐๐๐๐๐ ๐๐ = 2.5๐๐/๐2 , ๐ฟ๐ฟ = 3๐๐/๐2
๐ค๐๐๐๐๐ก ๐๐ ๐ค๐๐๐ = 12๐๐/๐
๐๐ = 170๐๐ , ๐๐๐๐ ๐ ๐๐ง๐ = 700,400 , ๐๐๐๐ข๐๐๐ ๐ ๐๐ง๐ (500,400)
Required:-
Design the one way solid slab for flexure and shear.
Design the beam (A-D) for flexure and shear.
Compute the axial load on column C.
B
4.4m 4.4m 4.4m 4.4m
C
9 m
9 m
9 m
A
CE472
Eng.ALI ALQARNI Page 15
๐๐๐๐ =๐
28=
4400
28= 157.14 ๐๐
๐๐๐๐ =๐
24=
4400
24= 183.33 ๐๐
๐๐๐๐ = max(157.14 , 183.33) = 183.33 ๐๐
๐ < ๐๐๐๐ โ ๐๐๐ก ๐ ๐๐ก๐๐ ๐๐๐๐ ๐๐๐๐๐๐๐ก๐๐๐ ๐๐๐๐ข๐๐๐๐๐๐ก
๐ท๐ฟ = ๐๐ค๐ ๐ค๐๐๐๐๐ก + ๐ ๐ข๐๐๐๐๐๐๐๐ ๐๐
๐ท๐ฟ = 0.17 โ 25 + 2.5 = 6.75 ๐๐ ๐2
๐ฟ๐ฟ = 3 ๐๐ ๐2
๐๐ข = 1.4๐ท๐ฟ + 1.7๐ฟ๐ฟ
๐๐ข = 1.4 6.75 + 1.7 3 = 14.55๐๐ ๐2
Lu (m) 4.4m 4.4m 4.4m 4.4m
Ln (m) 4m 4m 4m 4m
Cm 1/24 1/14 1/10 1/11 1/16 1/11 1/11 1/16 1/11 1/10 1/14 1/24
Wu(kn/m2) 14.55 14.55 14.55 14.55 14.55 14.55
Mu(kn.m) 16.63 23.28 23.28 16.63
d (mm) 144 144 144 144
Rn (Mpa) 0.891 1.25 1.25 0.891
ฮก 0.00216 0.0031 0.0031 0.00216
As (mm2) 311 446.4 446.4 311
As min(mm2) 306 306 306 306
As (mm2) 311 446.9 446.9 311
S max (mm) 300 253 253 300
As rinkashge (mm2)
306 306 306 306
S max (mm) 300 300 300 300
Cv 1.15 1.15
Vu (kn) 33.465 33.465
ฯVc (kn) 98.59 98.59
CE472
Eng.ALI ALQARNI Page 16
๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐
๐ฟ๐ข = 4.4๐ , ๐ฟ๐ = 4.4โ 0.2โ 0.2 = 4๐
๐ถ๐ =1
10 , ๐๐ข =
1
10โ 14.55 โ 42 = 23.28๐๐.๐
๐ = 170โ 20โ12
2= 144๐๐ , ๐ ๐ =
23.28 0.9
1000 โ 1442โ 106 = 1.25 ๐๐๐ ,
๐ =420
0.85 โ 30= 16.471 , ๐ =
1
16.471 1โ 1 โ
2 โ 1.25 โ 16.471
420 = 0.0031
๐ด๐ = 0.0031 โ 1000 โ 144 = 446.4 ๐๐2 , ๐ด๐ ๐๐๐ = 0.0018 โ 1000 โ 170 = 306 ๐๐2
๐๐๐๐ฅ = min 113.04
446.4โ 1000 = 253.22๐๐, 300๐๐, 2 โ 170 = 340 = 253.22๐๐
๐๐๐ ๐๐๐๐ฅ๐ข๐๐๐ โ ๐ข๐ ๐ โ 12@250 ๐๐
๐ด๐ ๐ ๐๐๐๐๐๐๐๐ = 0.0018 โ 1000 โ 170 = 306 ๐๐2
๐๐๐๐ฅ = min 113.04
306โ 1000 = 452.88๐๐, 300๐๐, 4 โ 170 = 680 = 300๐๐
๐๐๐ ๐ ๐๐๐๐๐๐๐๐ โ ๐ข๐ ๐ โ 12@300 ๐๐
๐ถ๐ฃ = 1.15 , ๐๐ข =1.15 โ 14.55 โ 4
2= 33.465 ๐๐
โ ๐๐ = 0.75 โ 30
6โ 1000 โ 144 โ 10โ3 = 98.59 ๐๐
โ ๐๐ > ๐๐ข โ ๐ ๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐๐ก ๐๐ ๐๐๐ก ๐๐๐๐๐๐
CE472
Eng.ALI ALQARNI Page 17
Load acting on the beam (A-B)
1- Dead load:
๐ท๐ฟ = 6.75 โ 2.2 + 2.2 + 12 + 0.53 โ 0.4 โ 25 = 47๐๐ ๐
2- Live load
๐ฟ๐ฟ = 3 โ 2.2 + 2.2 = 13.2๐๐ ๐
๐๐ข = 1.4 47 + 1.7 13.2 = 88.24 ๐๐ ๐
Lu (m) 9m 9m 9m
Ln(m) 8.6m 8.6m 8.6m
Wu(kn/m) 88.24
Cm 1/16 1/14 1/10 1/11 1/16 1/11 1/10 1/16 1/11
Mu (kn.m) 466.2 652.6 652.6 466.2
d(mm) 615.5 615.5 615.5 615.5
Rn(Mpa) 3.4 4.8 4.8 3.4
ฮก 0. 009 0.0128 0.0128 0. 009
As(mm2) 2215.8 3151.4 3151.4 2215.8
As min (mm2) 821 821 821 821
N 7.05โ8 10.03โ11 7.05โ8 10.03โ11
b min (mm)
Fs =Fy Ok Ok Ok Ok
TCL Ok Ok Ok Ok
Use 8ั20 11ั20 8ั20 11ั20
Cv 1.15 1.15
Vu (kn) 436.35 436.35
ฯVc (kn) 168.56 168.56
Vs (kn) 357.1 357.1
Av (mm2) 226.08 226.08
S (mm) 163.7 163.7
S max (mm) 307.75 307.75
Use ะค12@160 ะค12@160
CE472
Eng.ALI ALQARNI Page 18
๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐
๐ฟ๐ข = 9๐ , ๐ฟ๐ = 9โ 0.2โ 0.2 = 8.6๐
๐ถ๐ =1
10 , ๐๐ข =
1
10โ 88.24 โ 8.62 = 652.6 ๐๐.๐
๐ = 600โ 40โ 12โ 20โ25
2= 615.5 ๐๐ ๐ก๐ค๐ ๐๐๐ฆ๐๐
๐ ๐ =652.6/0.9
400 โ 615.52โ 106 = 4.8 ๐๐๐
๐ =420
0.85 โ 30= 16.471 , ๐ =
1
16.471 1โ 1โ
2 โ 4.8 โ 16.471
420 = 0.0128
๐ด๐ = 0.0128 โ 400 โ 615.5 = 3151.4 ๐๐2 ,
๐ด๐ ๐๐๐ =1.4
420โ 400 โ 615.5 = 821 ๐๐2
๐ด๐ ๐๐๐ = 30
4 โ 420โ 400 โ 615 = 803 ๐๐2
๐ด๐ ๐๐๐ = max 821,803 = 821๐๐2
๐ =3151.4
314= 10.03 โ 11
๐ =11 โ 314 โ 420
0.85 โ 30 โ 400= 142.22 ๐๐
๐๐๐
= 0.5 >๐
๐= 0.23 โด ๐๐ =๐๐ฆ
๐๐๐ถ๐ฟ๐๐ก
= 0.31875 >๐
๐๐ก= 0.222 โด ๐๐๐๐ ๐๐๐ โ ๐๐๐๐ก๐๐๐๐๐๐ ๐ ๐๐๐ก๐๐๐
๐๐๐ ๐๐๐๐ฅ๐ข๐๐ ๐ข๐ ๐ 11โ 20
๐ถ๐ฃ = 1.15 , ๐๐ข =1.15 โ 88.24 โ 8.6
2= 436.35 ๐๐
โ ๐๐ = 0.75 โ 30
6โ 400 โ 615.5 โ 10โ3 = 168.56 ๐๐
๐๐ =436.35โ 168.56
0.75= 357.1๐๐
CE472
Eng.ALI ALQARNI Page 19
๐ด๐ฃ = 2 โ ๐122
4= 226.08๐๐2 (๐ก๐ค๐ ๐๐๐)
๐ =226.08 โ 420 โ 615.5
357.1โ 10โ3 = 163.7๐๐
๐๐ < 2๐๐
๐๐๐๐ฅ = ๐๐๐ 300,615.5
2= 307.75 = 300 ๐๐
๐ข๐ ๐ โ 12@160๐๐
Axial load on column C:-
Beams in x- direction:
๐ท๐ฟ = 0.4 โ 0.53 โ 25 + 12 โ4.4
2 + 0.4 โ 0.53 โ 25 + 12 โ
4.4
2 = 76.12 ๐๐
๐ฟ๐ฟ = 0 + 0 = 0 ๐๐
Beams in y- direction:
๐ท๐ฟ = 0.4 โ 0.53 โ 25 + 12 + 6.75 โ 4.4 โ9
2 + 0.4 โ 0.53 โ 25 + 12 + 6.75 โ 4.4 โ
9
2
= 423 ๐๐
๐ฟ๐ฟ = 3 โ 4.4 โ9
2 + 3 โ 4.4 โ
9
2 = 118.8๐๐
๐๐ข = 1.4 76.12 + 423 + 1.7 118.8 = 900.728 ๐๐