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MEMBER NAME : C1 (Substructure)

1. Calculation Summary
(1) Check Design Parameter
Category Value Criteria Ratio Note
Rebar Ratio ( Min. ) 0.0155 0.0100 0.644 ρmin / ρ
Rebar Ratio ( Max. ) 0.0155 0.0600 0.259 ρ / ρmax

(2) Check Moment Capacity ( Neutral axis )

Category Value Criteria Ratio Note
Moment Capacity ( Dir. X ) ( kN·m ) 11.86 23.27 0.510 Mux / øMnx
Moment Capacity ( Dir. Y ) ( kN·m ) -128 247 0.515 Muy / øMny
Axial Capacity ( kN ) 90.28 176 0.514 Pu / øPn
Moment Capacity ( kN·m ) 128 249 0.515 Mu / øMn

(3) Check Shear Capacity

Category Value Criteria Ratio Note
Shear Strength ( Dir. X ) ( kN ) 131 512 0.256 Vux / øVnx
Spacing Limits for Reinforcement ( Dir. X ) ( mm )75.00 113 0.667 sx / sx,max
Shear Strength ( Dir. Y ) ( kN ) 171 512 0.335 Vux / øVnx
Spacing Limits for Reinforcement ( Dir. Y ) ( mm )75.00 113 0.667 sy / sy,max

(4) Check Dimension by Special Provision for Seismic Design

Category Value Criteria Ratio Note
Section Dimension Limit ( mm ) 450 300 0.667 Dimmin,limit / Dimmin
Section Dimension Ratio 1.000 0.400 0.400 Dimratio,min / Dimratio

(5) Check Rebar Limit by Special Provision for Seismic Design

Category Value Criteria Ratio Note
Amount of Transverse Rebar ( Dir. X ) ( mm² ) 226 184 0.811 Ashx,min / Ashx
Amount of Transverse Rebar ( Dir. Y ) ( mm² ) 226 184 0.811 Ashy,min / Ashy

2. Check slenderness ratio

(1) Calculate radii of gyration
rx = 0.3D = 135mm
ry = 0.3B = 135mm
(2) Calculate slenderness ratio
M1x
= 0.000
M2x
M1y
= 0.000
M2y
kx lux M1x
= 9.259 < min(34 + 12 , 40.0) = 34.00 → Not Slender
rx M2x
ky luy M1y
= 9.259 < min(34 + 12 , 40.0) = 34.00 → Not Slender
ry M2y
3. Check Magnified Moment
(1) Calculate moment magnification factor
δns.x = 1.000
δns.y = 1.000

4. Check Minimum Moment

(1) Calculate minimum eccentricity
emin.x = 15 + 0.03D = 28.50mm

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emin.y = 15 + 0.03B = 28.50mm

(2) Calculate minimum moment
Mmin.x = Pu emin.x = 2.573kN·m
Mmin.y = Pu emin.y = 2.573kN·m

5. Check design moment

(1) Calculate design moment
Mc.x = Mux = 11.86kN·m
Mc.y = Muy = -128kN·m
Mc = 128kN·m

6. Check Design Parameter

Calculation Summary ( Check Design Parameter )
Category Value Criteria Ratio Note
Rebar Ratio ( Min. ) 0.0155 0.0100 0.644 ρmin / ρ
Rebar Ratio ( Max. ) 0.0155 0.0600 0.259 ρ / ρmax

Rebar Ratio ( Min. ) 0.64

Rebar Ratio ( Max. ) 0.26

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
(1) Calculate rebar ratio
Ag = 202,500mm², Ast = 3,142mm²
ρmin = 0.0100, ρmax = 0.0600, ρ = 0.0155
ρmin < ρ < ρmax → O.K
(2) Calculate eccentricity
ex = Mc.y / Pu = 1,413mm
ey = Mc.x / Pu = 131mm
e = Mc / Pu = 1,419mm
Rotation angle of neutral axis = 86.02°
(3) Calculate concentric axial load capacity
P0 = 0.85f'c ( Ag - Ast ) + fy Ast = 6,046kN
P0.max = 0.80P0 = 4,836kN
Pt = fy Ast = -1,301kN

7. Check Moment Capacity ( Balanced axis )

(1) Calculate capacity of compression stress block
β1 = 0.850
c = 259mm, a = β1 ㆍ c = 220mm
Acom = 92,207mm²
ccx = 122mm, ccy = 5.737mm
Cc = 0.85 ㆍ f'c ㆍ Acom = 2,195kN
Mnx = Cc ㆍ ccy = 12.59kN·m
Mny = Cc ㆍ ccx = 268kN·m
(2) Calculate capacity of rebar
ds fs As Fs dy Mnx dx Mny
i εs
(mm) (MPa) (mm²) (kN) (mm) (kN) (mm) (kN)
1 438 -0.002070 -414 314 -130 -185 24.06 -185 24.06
2 425 -0.001921 -384 314 -121 0.000 0.000 -185 22.33
3 412 -0.001772 -354 314 -111 185 -20.60 -185 20.60
4 289 -0.000346 -69.25 314 -21.76 185 -4.025 -61.67 1.342
5 166 0.001080 216 314 67.84 185 12.55 61.67 4.183
6 42.68 0.002505 414 314 130 185 24.06 185 24.06
7 55.54 0.002356 414 314 130 0.000 0.000 185 24.06

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8 68.39 0.002207 414 314 130 -185 -24.06 185 24.06

9 191 0.000782 156 314 49.12 -185 -9.086 61.67 3.029
10 314 -0.000644 -129 314 -40.48 -185 7.489 -61.67 2.496

∑Fs = 82.80kN
∑Mnx = 10.39kN·m
∑Mny = 150kN·m
(3) Calculate nominal capacity for neutral axis
Pb = Cc + Ps = 2,277kN
Mnx = Mnx.conc + Mnx.bar = 22.98kN·m
Mny = Mny.conc + Mny.bar = 419kN·m
Mn = ( Mnx )2 + ( Mny )2 = 419kN·m

8. Check Moment Capacity ( Neutral axis )

Calculation Summary ( Check Moment Capacity ( Neutral axis ) )
Category Value Criteria Ratio Note
Moment Capacity ( Dir. X ) ( kN·m ) 11.86 23.27 0.510 Mux / øMnx
Moment Capacity ( Dir. Y ) ( kN·m ) -128 247 0.515 Muy / øMny
Axial Capacity ( kN ) 90.28 176 0.514 Pu / øPn
Moment Capacity ( kN·m ) 128 249 0.515 Mu / øMn

Moment Capacity ( Dir. X ) 0.51

Moment Capacity ( Dir. Y ) 0.52

Axial Capacity 0.51

Moment Capacity 0.52

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
(1) Calculate capacity of compression stress block
c = 107mm, a = β1 ㆍ c = 90.86mm
Acom = 33,935mm²
ccx = 187mm, ccy = 15.59mm
Cc = 0.85 ㆍ fck ㆍ Acom = 808kN
Mnx = Cc ㆍ ccy = 12.59kN·m
Mny = Cc ㆍ ccx = 151kN·m
(2) Calculate capacity of rebar
ds fs As Fs dy Mnx dx Mny
i εs
(mm) (MPa) (mm²) (kN) (mm) (kN) (mm) (kN)
1 438 -0.009278 -414 314 -130 -185 24.06 -185 24.06
2 425 -0.008917 -414 314 -130 0.000 0.000 -185 24.06
3 412 -0.008556 -414 314 -130 185 -24.06 -185 24.06
4 289 -0.005104 -414 314 -130 185 -24.06 -61.67 8.022
5 166 -0.001651 -330 314 -104 185 -19.19 61.67 -6.397
6 42.68 0.001802 360 314 113 185 20.95 185 20.95
7 55.54 0.001441 288 314 90.58 0.000 0.000 185 16.76
8 68.39 0.001081 216 314 67.90 -185 -12.56 185 12.56
9 191 -0.002372 -414 314 -130 -185 24.06 61.67 -8.022
10 314 -0.005825 -414 314 -130 -185 24.06 -61.67 8.022

∑Fs = -612kN
∑Mnx = 13.26kN·m
∑Mny = 124kN·m
(3) Calculate nominal capacity for neutral axis
Pn = Cc + Ps = 195kN

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Mnx = Mnx.conc + Mnx.bar = 25.85kN·m

Mny = Mny.conc + Mny.bar = 275kN·m
Mn = ( Mnx )2 + ( Mny )2 = 276kN·m
(4) Calculate strength reduction factor
εt.min = 0.0026, εt.max = 0.0050
εt = 0.009098
ø = 0.900
(5) Calculate axial load and moment capacities
øPn = 176kN
øMnx = 23.27kN·m
øMny = 247kN·m
øMn = 249kN·m
Mux / øMnx = 0.510 < 1.000 → O.K
Muy / øMny = 0.515 < 1.000 → O.K
Pu / øPn = 0.514 < 1.000 → O.K
Mc / øMn = 0.515 < 1.000 → O.K

P (kN)
6250
θ=84.63˚
N.A=86.02˚
5475

4700

3925

3144
3150

2375 eb=258.88mm

1600

825

(90,128) (176,249) M (kN·m)

050

-725

-1500
0
45

90

135

180

225

270

315

360

405

450

9. Calculate Shear Force by Special Provisions for Seismic Design (Direction Y).
(1) Calculate bending strength for design shear force.
ø = 1.000
Mprx,I.CW = 0.000kN·m
Mprx,J.CW = 429kN·m
Mprx,I.CCW = 0.000kN·m
Mprx,J.CCW = 429kN·m
(2) Calculate design shear force by special provision for seismic design
Vey1 = (Mprx,I.CW + Mprx,J.CW )/Lny = 171kN
Vey2 = (Mprx,I.CCW + Mprx,J.CCW )/Lny = 171kN
Vey = max(Vey1 , Vey2 ) = 171kN

10. Calculate Shear Force by Special Provisions for Seismic Design (Direction X).
(1) Calculate bending strength for design shear force.
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ø = 1.000
Mpry,I.CW = 0.000kN·m
Mpry,J.CW = 328kN·m
Mpry,I.CCW = 0.000kN·m
Mpry,J.CCW = 328kN·m
(2) Calculate design shear force by special provision for seismic design
Vex1 = (Mpry,I.CW + Mpry,J.CW )/Lnx = 131kN
Vex2 = (Mpry,I.CCW + Mpry,J.CCW )/Lnx = 131kN
Vex = max(Vex1 , Vex2 ) = 131kN

11. Check Shear Capacity

Calculation Summary ( Check Shear Capacity )
Category Value Criteria Ratio Note
Shear Strength ( Dir. X ) ( kN ) 131 512 0.256 Vux / øVnx
Spacing Limits for Reinforcement ( Dir. X ) ( mm )75.00 113 0.667 sx / sx,max
Shear Strength ( Dir. Y ) ( kN ) 171 512 0.335 Vux / øVnx
Spacing Limits for Reinforcement ( Dir. Y ) ( mm )75.00 113 0.667 sy / sy,max

Shear Strength ( Dir. X ) 0.26

Spacing Limits for Reinforcement ( Dir. X ) 0.67

Shear Strength ( Dir. Y ) 0.33

Spacing Limits for Reinforcement ( Dir. Y ) 0.67

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
(1) Calculate maximum space
ø = 0.750
hx = 207mm
Smax1 = min[6DMainBar , 0.25B, 0.25D, 150] = 113mm
Smax2 = 100 + (350-hx )/3 = 148mm
Smax = min(Smax1 , Smax2 ) = 113mm
(2) Calculate Shear Strength (Direction X)
s = 75.00mm < smax = 113mm → O.K
Nu
øVc = ø0.17 (1+ ) f'c bw d = 128kN
14Ag
Av fyt d
øVs = ø = 384kN
s
øVn = øVc + øVs = 512kN
Vu / øVn = 0.256 → O.K
(3) Calculate Shear Strength (Direction Y)
s = 75.00mm < smax = 113mm → O.K
Nu
øVc = ø0.17 (1+ ) f'c bw d = 128kN
14Ag
Av fyt d
øVs = ø = 384kN
s
øVn = øVc + øVs = 512kN
Vu / øVn = 0.335 → O.K

12. Check Dimension by Special Provision for Seismic Design

Calculation Summary ( Check Dimension by Special Provision for Seismic Design )
Category Value Criteria Ratio Note
Section Dimension Limit ( mm ) 450 300 0.667 Dimmin,limit / Dimmin
Section Dimension Ratio 1.000 0.400 0.400 Dimratio,min / Dimratio

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Section Dimension Limit 0.67

Section Dimension Ratio 0.40

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
(1) Calculate section dimension limit
Dimmin,limit = 300mm
Dimmin = 450mm
Dmin > Dmin,limit → O.K
(2) Calculate section dimension ratio
Dimratio,min = 0.400
Dimratio = 1.000
Dimratio > Dimratio,min → O.K

13. Check Rebar Limit by Special Provision for Seismic Design

Calculation Summary ( Check Rebar Limit by Special Provision for Seismic Design )
Category Value Criteria Ratio Note
Amount of Transverse Rebar ( Dir. X ) ( mm² ) 226 184 0.811 Ashx,min / Ashx
Amount of Transverse Rebar ( Dir. Y ) ( mm² ) 226 184 0.811 Ashy,min / Ashy

Amount of Transverse Rebar ( Dir. X ) 0.81

Amount of Transverse Rebar ( Dir. Y ) 0.81

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
(1) Calculate amount of transverse rebar (Direction X)
sbc f'c Ag
Ash,min1 = 0.3 (( )-1 ) = 111mm²
fyt Ach
sbc f'c
Ash,min2 = 0.09 = 184mm²
fyt
Ash,min = max (Ash,min1 Ash,min2 ) = 184mm²
Ashx = 226mm² > Ashx,min = 184mm² → O.K
(2) Calculate amount of transverse rebar (Direction Y)
sbc f'c Ag
Ash,min1 = 0.3 (( )-1 ) = 111mm²
fyt Ach
sbc f'c
Ash,min2 = 0.09 = 184mm²
fyt
Ash,min = max (Ash,min1 Ash,min2 ) = 184mm²
Ashy = 226mm² > Ashy,min = 184mm² → O.K

2024-01-19 14:42 6