Seismic Design of R.C and Steel

8/13/2019 Seismic Design of R.C and Steel

1/49


2/49


3/49


4/49


5/49


6/49

External Mom. 143.73 kNm Internal Mom. 227.33 kNm

" 232.25 kNm " 82.72 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. 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




7/49

External Mom. 160.65 kNm Internal Mom. -200.16 kNm 781.89

" -231.8 kNm " 83.45 kNm 699.69


" -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




Column Member

Axial Loads (kN)

Column Member

Combo 1 = 1.2D + 0.

Combo 2 = 0.9D

Column Member

Combo 3 = 1.2D


8/49

kN

KN

kN

KN

kN

3 - BE

3 - BE

5L 1.0E

1.0E

3 - BE

1.6L


9/49


10/49

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


11/49

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


12/49

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)


13/49

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


14/49

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


15/49


16/49

Step - 4-Asat external supports


phi, 0.9

fy(Mpa or Nmm-2); (ksi) 414 60.03

f'c(Mpa or Nmm-2); (ksi) 25 3.625


a 9073905.88

b -208656

c = Mu 232.25

As + (m ); (mm ) 0.02182227 21822.27

As - (m ); (mm ) 0.0011729 1172.902




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


17/49


18/49

Step 6 - Calc.+AsBottom Main Bars


phi, 0.9

fy(Mpa or Nmm-2); (ksi) 414 60.03

f'c(Mpa or Nmm-2); (ksi) 25 3.625


a 9073906

b -208656

c = Mu 160.65

As + (m ); (mm ) 0.022198 22197.58

As - (m ); (mm ) 0.000798 797.5922




45.88 mm


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



19/49

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


20/49

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.



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.


21/49


22/49

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


23/49


24/49

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


25/49

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)


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



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


26/49


27/49

Step 6 - Calc.+AsBottom Main Bars


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


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


71.74 mm 45.88 mm


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




28/49

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.


29/49

Top Steel

383.5 mm

200 mm OK

150 mm OK

Bottom Steel306.8 mm

160 mm OK

150 mm 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



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.


30/49


31/49

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


32/49


33/49

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


34/49

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

=


35/49

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


36/49

Column


37/49


38/49


39/49


" 56.22 kNm " 189.21 kNm


" 18.94 kNm " 191.42 kNm


" 230.15 kNm " 127.93 kNm




Combo 3 = 1.2D + 1.6LBeam Member #12 - AB






Linpro Analysis of Members to be designed

Moments (kNm)

Combo 1 = 1.2D + 0.5L 1.0E


40/49

External Mom. 90.96 kNm Internal Mom. 162.05 kNm 752.55

" 80.51 kNm " 165.85 kNm 704.6


" 51.55 kNm " 158.81 kNm

477.78

429.83


" 124.77 kNm " 228.4 kNm

1000.05

Column Member

Combo 3 = 1.2D

Beam Member #12 - AB Column Member


Combo 2 = 0.9D

Column Member


Axial Loads (kN)

Combo 2 = 0.9D 1.0E Combo 1 = 1.2D + 0.


41/49

kN

KN

kN

KN

kN

3 - BE

1.6L

3 - BE

1.0E

3 - BE

5L 1.0E


42/49


43/49

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


44/49

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


45/49

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


46/49


47/49

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


48/49


49/49

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

Seismic Design of R.C and Steel

Documents