Seismic Design of R.C and Steel
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Transcript of Seismic Design of R.C and Steel
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External Mom. 143.73 kNm Internal Mom. 227.33 kNm
" 232.25 kNm " 82.72 kNm
External Mom. 33.73 kNm Internal Mom. 201.95 kNm
" 201.97 kNm " 33.75 kNm
External Mom. -180.34 kNm Internal Mom. 157.28 kNm
" 183.83 kNm " -164.6 kNm
External Mom. -61.59 kNm Internal Mom. -98.92 kNm
External Mom. -115.65 kNm Internal Mom. -115.61 kNm
External Mom. 2.78 kNm Internal Mom. -5.38 kNm
Linpro Analysis of Members to be designed
Combo 3 = 1.2D + 1.6LBeam Member #12 - AB
Beam Member #13 - BC
Column Member #3 - BE
Moments (kNm)
Combo 1 = 1.2D + 0.5L 1.0E
Beam Member #12 - AB
Beam Member #13 - BC
Column Member #3 - BE
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External Mom. 160.65 kNm Internal Mom. -200.16 kNm 781.89
" -231.8 kNm " 83.45 kNm 699.69
External Mom. 65.5 kNm Internal Mom. -170.18 kNm
" -170.2 kNm " 65.51 kNm
502.37
420.16
External Mom. -181.1 kNm Internal Mom. 158.76 kNm
" 183.07 kNm " -163.12 kNm
1017.38
Combo 2 = 0.9D 1.0E
Beam Member #12 - AB
Beam Member #13 - BC
Column Member #3 - BE
Column Member
Axial Loads (kN)
Column Member
Combo 1 = 1.2D + 0.
Combo 2 = 0.9D
Column Member
Combo 3 = 1.2D
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kN
KN
kN
KN
kN
3 - BE
3 - BE
5L 1.0E
1.0E
3 - BE
1.6L
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Column span (height) (mm); (m) 5000 5
Width, b (mm); (in) 450 18 OK
Depth, h (mm); (in) 450 18 OK
width/depth ratio 1 From Graph A7
width/depth ratio check OK
Ult. Axial load, Pu(kN); (kip) 1017.38 228.707
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Step 3 - Strong-Column-Weak-
Beam Check
Sidesway to left
0.30 Beam mom. strength M-
287.66
0.15 Beam mom. strength M+
188.50
Axial load due to beam at joint 699.69 kN
0.0105 0.0105
OK as psi values 0.21
1.05% From interaction graph
2126.25 hence find Mn 0.14
2272 Mn(kip-ft); (kNm) 246.65 334.41
506.25 Mnis the column's mom. strengthDesign As A Column Check
668.81 kNm
571.40 kNm
OK
OK
OK Sidesway to right
OK Beam mom. strength M-
287.66 kNm
OK Beam mom. strength M 188.50 kNm
Axial load due to beam at joint 781.89 kN
0.0105
as psi values 0.23
From interaction graph
= 0.14 (hence find Mn)
Mn(kip-ft); (kNm) 246.645 334.41
Check
668.81 kNm
571.40 kNmOK
mn Main Steel
olumn dimensions
the rebar
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tep - a c. e traverse re ar or
Confinement hoops
Confinement zone Lo
, max of
d 450 mm
h 450 mm
(col. Height - beam depth)/6 733 mm
450mm 450 mm
Lo= 733 mm
Det hc, cross section of column core not including cover
hc 364 mm
Consider hxas 250mm (10in)
Max hoop spacing "sx"is the smallest
out of (as shown below):
sx = 4 + (14 - hx)/3 in inches 5.33 in 133.33 mm
sx = depth/4 112.5 mm
sx = 6 x column rebar diameter 114 mm
hence max sx = 112.50 mm
Try a spacing of 50mm or 2 in
Achis the cross section of column core not including cover, but includes stirrups
for our column Ach= 139876 mm
hc= (total width h)-(concrete cover to centroid of stirrup)- (2 x stirrups half diameter)
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tep - a c. raverse e ar or
Shear
Lu 4.4 m
Since sidesway to left and right is the same we will do one calc
Mpr1 + Mpr2 476.16 kNm
Vu 108.2182 kN
0.75
in psi units
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Step 1 - Beam Dimensions
Span (m); (mm) 5.2 5200
Width, b (mm); (in) 400 16
Depth, D (mm); (in) 600 24
Effective depth, d (mm); (in) 560 22.4
Clear Span (mm); (in) 4750 190
4d (mm); (in) 2240 89.6
OK
OK
OK
OK
Step 2 --As(Top Main Rebar) Internal Support
Substitute "a" in eqn above; solve As
phi, 0.9
fy(Mpa or Nmm-2); (ksi) 414 60.03
f'c(Mpa or Nmm-2); (ksi) 25 3.625
Quadratic formed below
a 9073905.882b -208656c = Mu 227.33
As + (m ); (mm ) 0.021848492 21848.49
As - (m ); (mm ) 0.001146677 1146.677
Area of steel to choose (mm ) 1146.68 mm
Assume No. 25mm rebars 2.33 3 Bars
Steel Provided 1473 mm2
71.74 mm
Step 3 - Check limits on As(Int. Supp)
0.006575893
0.003381643
OK
OK
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Step - 4-Asat external supports
Substitute "a" in eqn above; solve As
phi, 0.9
fy(Mpa or Nmm-2); (ksi) 414 60.03
f'c(Mpa or Nmm-2); (ksi) 25 3.625
Quadratic formed below
a 9073905.88
b -208656
c = Mu 232.25
As + (m ); (mm ) 0.02182227 21822.27
As - (m ); (mm ) 0.0011729 1172.902
Area of steel to choose (mm ) 1172.90 mm
Assume No. 25mm rebars 2.39 3 Bars
Steel Provided 1473 mm2
71.74 mm
Check limits on As(Ext. Supp)
0.00657589
0.00338164OK
OK
Step 5 - Calc. min +ve Mom. strength
Internal Supports+Mn
287.66 kNm
OK
Therefore+Mn= Mn/2 143.83 kNm
External Supports+Mn
287.66 kNm
OK
Therefore+Mn= Mn/2 143.83 kNm
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Step 6 - Calc.+AsBottom Main Bars
Substitute "a" in eqn above; solve As
phi, 0.9
fy(Mpa or Nmm-2); (ksi) 414 60.03
f'c(Mpa or Nmm-2); (ksi) 25 3.625
Quadratic formed below
a 9073906
b -208656
c = Mu 160.65
As + (m ); (mm ) 0.022198 22197.58
As - (m ); (mm ) 0.000798 797.5922
Area of steel to choose (mm ) 797.59 mm
Assume No. 20mm rebars 2.54 3 Bars
Steel Provided 942 mm2
45.88 mm
Check limits on As(Ext. Supp)
0.004205
0.003382OK
OK
Therefore+Mn, midspan
188.50 kNm
Mn =+Mn, midspan 188.50 kNm
Empirical Rules
71.92 kNm
OK
143.83 kNm
Extend bottom mid span rebars to internal and external su
Top Part of beam only
Top Part of beam only
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Since the bottom midspan rebars are extended to the
outer column as calculated for +Mn, mid-span then
143.83kNm is ok. If not, additional steel would be needed
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Top Steel
383.5 mm
200 mm OK
150 mm OK
Bottom Steel
306.8 mm
160 mm OK
150 mm OK
span rebars to internal and external supports
Step 7 - Calc. and check anchorage lengths for
main rebars that end in the ext. column
Note that the space referred to is the straight line from the inner column
face to the outer face of the hook = 500 > 383.5mm: OK
Rationale: Since I have 3 bars on the top external beam, I (multiply 3 bars
by 25mm)+(383.50mm) and round it off by the nearest 50mm. This gives
me the ditance I need for each of the 3 bars I designed for.
Note that the space referred to is the straight line from the inner column
face to the outer face of the hook = 400 > 306.80mm: OK
Rationale: Since I have 3 bars at the bottom external beam, I (multiply 3
bars by 20mm)+(383.50mm) and round it off by the nearest 50mm. This
gives me the distance I need for each of the 3 bars I designed for.
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Step - 8 Calculate the Seismic Shear Rebar
1.0
1.25fy(Mpa or Nmm-2
) 517.5
As1External Supports (mm2
) 1473
As2Internal Supports (mm2) 1473
a External Supports (mm) 71.74
a Internal Supports (mm) 71.74
d (mm) 560
Mpr1 Ext. Supp. (kNm) 399.53
Mpr2 Int. Supp. (kNm) 399.53
wu= 1.2wD+ 1.6wL (kN/m)
wD= Total Dead load from Frame Analysis 30.5 kN/m
wL= Total Live load from Frame Analysis 15 kN/m
Beam Span (m); (mm) 5.2 5200
wu 60.6 kN/m
Vu"+" 183.97 kN
Vu"-" -123.37 kN
Choose max. Vu 183.97 kN
Checks153.67 kN
91.98 kN
Pu(gravity load) taken from analysis 781.89 kN
300.00 kN
(lbs); (kN) use psi to calc. 43157.07 191.97
TRY ANOTHER CHECK
USE Calc. Vc in kN
40.0 kN
Vs 53.32 kN
Calc. stirrup spacing, s (mm)
Av= stirrup area for 2 legs (mm2) 157 (10 mm )
fyv= yield strength for stirrup (MPa) 275
454 mm
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Step - 9 Check stirrup spacing
d/4 (mm) 140 mm
160 mm
240 mm
possible smax 300 mm
Confinement zone = 2*600mm depth
s must be less than smax within the confinement zone
hence we choose the smallest = 140mm
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Step 1 - Beam Dimensions Step - 4-Asat external supports
Span (m); (mm) 5.8 5800
Width, b (mm); (in) 400 16
Depth, D (mm); (in) 600 24 Substitute "a" in eqn above; solve As
Effective depth, d (mm); (in) 560 22.4 phi,
Clear Span (mm); (in) 5350 214 fy(Mpa or Nmm-2); (ksi)
4d (mm); (in) 2240 89.6 f'c(Mpa or Nmm-2); (ksi)
OK Quadratic formed below
OK a
OK b
OK c = Mu
As + (m ); (mm )Step 2 -
-As(Top Main Rebar) Internal Support As - (m ); (mm )
Area of steel to choose (mm )
Assume No. 25mm rebars
Substitute "a" in eqn above; solve As Steel Provided
phi, 0.9
fy(Mpa or Nmm-2); (ksi) 414 60.03
f'c(Mpa or Nmm-2); (ksi) 25 3.625 Check limits on As(Ext. Supp)
Quadratic formed below
a 9073906b -208656c = Mu 201.95
As + (m ); (mm ) 0.021983 21982.73
As - (m ); (mm ) 0.001012 1012.437 Step 5 - Calc. min +ve Mom. strength
Area of steel to choose (mm ) 1012.44 mm Internal Supports+Mn
Assume No. 25mm rebars 2.06 3 Bars
Steel Provided 1473 mm2
71.74 mm Therefore+Mn= Mn/2
Step 3 - Check limits on As(Int. Supp) External Supports+Mn
0.006576
0.003382
OK Therefore+Mn= Mn/2
OK
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Step 6 - Calc.+AsBottom Main Bars
Substitute "a" in eqn above; solve As
0.9 phi, 0.9
414 60.03 fy(Mpa or Nmm-2); (ksi) 414 60.03
25 3.625 f'c(Mpa or Nmm-2); (ksi) 25 3.625
Quadratic formed below
9073906 a 9073906
-208656 b -208656
201.97 c = Mu 65.5
0.021983 21982.63 As + (m ); (mm ) 0.022677 22676.850.001013 1012.542 As - (m ); (mm ) 0.000318 318.3203
1012.54 mm Area of steel to choose (mm ) 318.32 mm
2.06 3 Bars Assume No. 20mm rebars 1.01 2 Bars
1473 mm2
Steel Provided 942 mm2
71.74 mm 45.88 mm
Check limits on As(Ext. Supp)
0.006576 0.004205
0.003382 0.003382OK OK
OK OK
Therefore+Mn, midspan
188.50 kNm
287.66 kNm Mn =+Mn, midspan 188.50 kNm
OK
143.83 kNm
287.66 kNm Empirical Rules
OK
143.83 kNm 71.92 kNm
OK
143.83 kNm
Extend bottom mid span
Top Part of beam only
Top Part of beam only
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Since the bottom midspan rebars are extended to the outer
column as calculated for +Mn, mid-span then 143.83kNm is ok. If
not, additional steel would be needed for the beam bottom
steel.
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Top Steel
383.5 mm
200 mm OK
150 mm OK
Bottom Steel306.8 mm
160 mm OK
150 mm OK
Note that the space referred to is the straight line from the inner column
face to the outer face of the hook = 400 > 306.80mm: OK
Rationale: Since I have 3 bars at the bottom external beam, I (multiply 3
bars by 20mm)+(306.80mm) and round it off by the nearest 50mm. This
gives me the distance I need for each of the 3 bars I designed for.
rebars to internal and external supports
Step 7 - Calc. and check anchorage lengths for
main rebars that end in the ext. column
Note that the space referred to is the straight line from the inner column
face to the outer face of the hook = 500 > 383.5mm: OK
Rationale: Since I have 3 bars on the top external beam, I (multiply 3 bars
by 25mm)+(383.50mm) and round it off by the nearest 50mm. This gives
me the ditance I need for each of the 3 bars I designed for.
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Step - 8 Calculate the Seismic Shear Rebar
1.0
1.25fy(Mpa or Nmm-
) 517.5
As1External Supports (mm ) 1473
As2Internal Supports (mm2) 1473
a External Supports (mm) 71.74
a Internal Supports (mm) 71.74
d (mm) 560
Mpr1 Ext. Supp. (kNm) 399.53
Mpr2 Int. Supp. (kNm) 399.53
wu= 1.2wD+ 1.6wL (kN/m)wD= Total Dead load from Frame Analysis 30.5 kN/m
wL= Total Live load from Frame Analysis 15 kN/m
Beam Span (m); (mm) 5.8 5800
wu 60.6 kN/m
Vu"+" 168.07 kN
Vu"-" -107.47 kN
Choose max. Vu 168.07 kN
Checks137.77 kN
84.03 kN
Pu(gravity load) taken from analysis 781.89 kN
300.00 kN
(lbs); (kN) use psi to calc. 43157.07 191.97
TRY ANOTHER CHECK
USE Calc. Vc in kN
24.1 kNVs 32.12 kN
Calc. stirrup spacing, s (mm)
Av= stirrup area for 2 legs (mm2) 157 (10 mm )
fyv= yield strength for stirrup (MPa) 275
753 mm
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Step - 9 Check stirrup spacing
d/4 (mm) 140 mm
160 mm
240 mm
possible smax 300 mm
Confinement zone = 2*600mm depth
s must be less than smax within the confinement zone
hence we choose the smallest = 140mm
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b D b h Beam
400 600 450 450
Occupancy Category 1 & 2 3 4
0.02hx 0.015hx 0.01hx
0.02 0.015 0.01
General Formula
1st floor 5 m (hx1)2nd floor 8.8 m (hx2)
roof 12.6 m (hx3)
1st floor max drift 0.1 m
2nd floor max drift 0.176 m
roof max drift 0.252 m
From our tabulated results, our nodes under earthquake load are node 4, 8 and 12
Beam Column
Max Drift Check
hxis the height of the floor at which the earthquake load is acting
Results Below are from LINPRO using the beam and column dimensions prescribed above
Floor Heights
=
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delta x 1 0.097669 OK
delta x 2 0.052173 OK
delta x 3 0.030685 OK
N.B. If the drifts exceed the max drift, change occupancy level or beam and column dimensions
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Column
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External Mom. 67.6 kNm Internal Mom. 186.33 kNm
" 56.22 kNm " 189.21 kNm
External Mom. 18.93 kNm Internal Mom. 191.41 kNm
" 18.94 kNm " 191.42 kNm
External Mom. 113.01 kNm Internal Mom. 223.46 kNm
" 230.15 kNm " 127.93 kNm
External Mom. -61.59 kNm Internal Mom. -98.92 kNm
External Mom. -115.65 kNm Internal Mom. -115.61 kNm
External Mom. 2.78 kNm Internal Mom. -5.38 kNm
Combo 3 = 1.2D + 1.6LBeam Member #12 - AB
Beam Member #13 - BC
Column Member #3 - BE
Beam Member #12 - AB
Beam Member #13 - BC
Column Member #3 - BE
Linpro Analysis of Members to be designed
Moments (kNm)
Combo 1 = 1.2D + 0.5L 1.0E
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External Mom. 90.96 kNm Internal Mom. 162.05 kNm 752.55
" 80.51 kNm " 165.85 kNm 704.6
External Mom. 51.54 kNm Internal Mom. 158.81 kNm
" 51.55 kNm " 158.81 kNm
477.78
429.83
External Mom. 116.17 kNm Internal Mom. 225.2 kNm
" 124.77 kNm " 228.4 kNm
1000.05
Column Member
Combo 3 = 1.2D
Beam Member #12 - AB Column Member
Beam Member #13 - BC
Combo 2 = 0.9D
Column Member
Column Member #3 - BE
Axial Loads (kN)
Combo 2 = 0.9D 1.0E Combo 1 = 1.2D + 0.
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kN
KN
kN
KN
kN
3 - BE
1.6L
3 - BE
1.0E
3 - BE
5L 1.0E
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Step 1 - Check Beam Strength
Mp (kip-ft); (kN-m)
Step 1 - Select Beam Sizes Mu (kNm)
W16x89 bMp (kN-m)
Beam AB Span (m); (ft) 5.2 17.06
Beam BC Span (m); (ft) 5.8 19.02
Area (in2) 26.2
Flange width (top) (mm); (in) 264.16 10.4
Flange width (bot) (mm); (in) 264.16 10.4
Flange thk (top) (mm); (in) 22.225 0.875
Flange thk (bot) (mm); (in) 22.225 0.875
Depth (mm); (in) 426.72 16.8
ryy(radius of gyration) (mm); (in) 63.246 2.49
tep - eam or oca
buckling stability
Web thickness 13.335 0.525 Flange check
E (Mpa or N/mm-2); (ksi) 200 29000 Max ps
fy(Mpa or N/mm2); (ksi) 0.345 50 bt/(2tf)
Le(Unbraced Length) (mm); (m)
- Assume one half length of
longest beam
2900 2.9
bt/(2tf) < Max ps
Zx (in3) 175
Web Check
Max ps
Select Column Size h/twor d/tw
W18x175 h/twor d/tw< Max ps
Column BE Span 5 16.4
Area (in2) 51.3
Flange width (top) (mm); (in) 289.56 11.4
Flange width (bot) (mm); (in) 289.56 11.4Step 3 - Chk Unbraced Lengthof Beam Compression Flanges
Flange thk (top) (mm); (in) 40.386 1.59 Max Length (m)
Flange thk (bot) (mm); (in) 40.386 1.59 Unbraced length check
Depth (mm); (in) 508 20
ryy(radius of gyration) (mm); (in) 70.104 2.76
Web thickness 22.606 0.89
E (Mpa or N/mm-2); (ksi) 200 29000
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fy(Mpa or N/mm2); (ksi) 0.345 50
Le(Unbraced Length) (mm); (m)
- Assume one half length of
longest beam 2.9
Zx (in3) 398
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Step 4 - Check the Strong-Column-
Weak-Beam Behaviour
729.17 988.62
Ry 1.1
191.42 Mp (kip-ft); (kN-m) 729.17 988.62
889.76 D.L. (kN/m) 30.5
OK L.L. (kN/m) 15
1.2D.L. + 1.6L.L. (kN/m); (kip/ft) 60.6 4.15
Left Beam
Vp (kip); (kN) 136.59 607.59
(kip-ft) 1091.73
Right Beam
Vp (kip); (kN) 127.82 568.58
Beam Strength M*
pb(kip-ft) 1078.28
Sum of beam strengths (kip-ft) 2170.02
7.22 M*pc col. strength (kip-ft)
5.94 (kip-ft) 1548.95
OK 3097.91 kip-ft
Adjustment for avg C.L to avg clearcolumn height 1.09
M*pc 3386.97
59.00 1.56
32 OK
OK
3.15
OK
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Step 5 - Check Column Local Stability
Flange check
Max ps 7.22
bt/(2tf) 3.58
bt/(2tf) < Max ps OK
Web Check
h/twor d/tw 22.47
h/twor d/tw< Max ps OK
Step 6 - Check Column Zone Strength
2
c= Y 0.90
Fcr (ksi) 34.32
c Pn (kips); (kN) 1496.49 6656.72
Pu/cPc Check 0.11 OK
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Step 7 - Check the beam-column panel
zone
For the 5.2m (17.07 ft) beam
Lc (m); (ft) 4.692 15.39
(kip-ft) 1874.36
For the 5.8m (19.02 ft) beam
Lc (m); (ft) 5.292 17.36
(kip-ft) 1853.33
Mf (kip-ft) 3727.69
Ru (kip) 2808.9
600 tp
154.39
formula 600tp + 154.39
tp (in) 4.4
in thick
This can be either one or two plates 1.767117 in thick
As the column web thickness is 0.89 in,
the doubler plate thicknes required3.5