RC COLUMN DESIGN BS8110

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DESIGN OF UNBRACED RC COLUMN AND

DESIGN OF UNBRACED RC COLUMN AND PEDESTALPEDESTAL CoCode :de : SS CSS CP 65P 65 S

Sttrruuccttuurree :: CCoolluummnnMMaarrkk ::

1. Design Loads

1. Design Loads Units : kN, kN-mUnits : kN, kN-m

N

Noo.. CCoonnddiittiioonn LLC C ## BBeeaam m ## NN** MMxx MMyy VVxx VVyy Material Strength :Material Strength :

11 MMaax x NN 110022 2222 776655..55 2277..44 5500..44 2277..77 88..55 f f cucu = = 30 Mpa30 Mpa

22 MMiin n NN 224455 1166 --1144..22 113322..11 22..22 44..66 2277..44 f f yy = = 460 Mpa460 Mpa

33 Max MMax Mxx 229911 2222 665533..44 221111..44 00..33 88..66 6611..22 f f yvyv = = 460 Mpa460 Mpa

44 Min MMin Mxx 229922 1155 662211..22 221111..22 88..55 1122..99 6600..55 EEss = = 200000 Mpa200000 Mpa

55 Max MMax Myy 117744 551188 555522..00 1111..22 221155..66 5522..77 33..00

66 Min MMin Myy 116655 552211 553355..88 2277..99 220066..77 4488..44 77..99

* (-) negative signs indicates tension force * (-) negative signs indicates tension force 2. End Condition and Effective Length

2. End Condition and Effective Length (SS CP 65 Part 1 sec. 3.8.1.6)(SS CP 65 Part 1 sec. 3.8.1.6) ₁₂_{12 -- T2}_T200

Column Dimensions : Column Dimensions : Top Bottom Top Bottom b =b = 550 mm550 mm b bxx == 1.21.2 11 11 h =h = 550 mm550 mm b byy == 1.21.2 11 11 c.c. =c.c. = 50 mm50 mm llexex = = bbxx(L(Loxox)=)= 99990000 mmmm lloxox = = 8250 mm8250 mm lleyey== bbyy(L(Loyoy)=)= 99990000 mmmm lloyoy = = 8250 mm8250 mm LLexex/h =/h = 1188 >> 1100 TT1133 @@220000

LLeyey/b =/b = CC22 >> 1100 Design as slender column.Design as slender column.

3. Ultimate Design Moment

3. Ultimate Design Moment Units : kN-m, N/mmUnits : kN-m, N/mm22

No.

No. MMaddxaddx MMaddyaddy MMtxtx MMtyty MMtxtx//hh'' MMtyty//bb'' MMuu MMuu/bh/bh 22 M Muu/hb/hb 22 N/bh N/bh 11 6688..11 6688..11 9955..55 111188..55 220000..33 224488..55 220044..5 5 11..2233 22..5533 22 NNAA NNAA 113322..11 22..22 227766..99 44..66 113344..33 00..881 1 --00..0055 33 5588..11 5588..11 226699..55 5588..44 556655..11 112222..55 332233..33 11..995 5 22..1166 44 5555..33 5555..33 226666..55 6633..88 555588..77 113333..77 332255..22 11..996 6 22..0055 55 4499..11 4499..11 6600..33 226644..77 112266..55 555555..00 332200..8 8 11..9933 11..8822 66 4477..77 4477..77 7755..66 225544..44 115588..55 553333..33 332244..7 7 11..9966 11..7777

Formulas and Conditions for Ultimate Design Moment Calculation Formulas and Conditions for Ultimate Design Moment Calculation Addition

Additional Momenal Moment (SS CP t (SS CP 65 Part 65 Part 1 sec. 3.81 sec. 3.8.3).3) Addition

Additional and al and Maximum MoMaximum Moment abment about X-aout X-axisxis Additional and Additional and Maximum MoMaximum Moment abment about Y-aout Y-axisxis

kkxx== 1.01.0 eeminyminy = 20 mm = 20 mm kkyy== 1.01.0 eeminxminx = 20 mm = 20 mm

b baxax = = (l(lexex/b" )/b" ) 22 / 2000 / 2000 bbayay = = (l(leyey/b" )/b" ) 22 / 2000

/ 2000 where : h' =where : h' = effective depth along Yeffective depth along Y

== 00..116622 == 00..116622 == 44777 7 mmmm

aauxux = = b baxaxkkxxh =h = 0.0890.089 aauyuy = = b bayaykkyyb =b = 0.0890.089 b' = Xeffective b' =Xeffective depth depth along along YY

M

Maddxaddx = Na= Nauxux MMaddyaddy == NaNauyuy == 44777 7 mmmm

M

Mminxminx = Ne= Neminxminx MMminyminy = = NeNeminyminy b"= b"= least least column column dimensiondimension

M

Mtxtx = = MMxx + M + Maddxaddx > M> Mminxminx MMtyty = = MMyy + M + Maddyaddy > M> Mminyminy == 55550 0 mmmm

Ultimate Design Moment for Biaxial Bending (Increase Moment about One Axis)

Ultimate Design Moment for Biaxial Bending (Increase Moment about One Axis) (SS CP 65 Part 1 (SS CP 65 Part 1 sec. 3.8.4.5)sec. 3.8.4.5) when M

when Mtxtx/h' > M/h' > Mtyty/b' ,/b' , MMuu= M= Mtxtx + ( + (bbh'Mh'Mtyty) / b') / b'

when M

when Mtxtx/h' < M/h' < Mtyty/b' ,/b' , MMuu = M = Mtyty + ( + (bbb'Mb'Mtxtx) / h') / h' where :where : ß = 1 - 7/6 N / bh f ß = 1 - 7/6 N / bh f cucu > 0.3 > 0.3

4. Arrangement of Reinforcement 4. Arrangement of Reinforcement Longitudinal Reinforcement

Longitudinal Reinforcement

number of bar bar parallel to

number of bar bar parallel to Y axis at one side Y axis at one side nnyy = = 44 , , ssppaacciinng g == 113344..77 mmm m <<== 115500..00

number of bar bar parallel to X at one side axis n

number of bar bar parallel to X at one side axis nxx = = 44 , , ssppaacciinng g == 113344..77 mmm m <<== 115500..00

P

Prroovviidde e :: 112 -2 - T20T20 A Asc,minsc,min== < < Asc Asc OK OK

A

Ascsc == 3,768.03,768.0 mmmm22 AAscsc/bh =/bh = 1.251.25 %%

Links Provided :

Links Provided : T13T13 @200 mm@200 mm no. of legs of links parallel to the Y axis =no. of legs of links parallel to the Y axis = 22

no. of legs of links parallel to the X axis =

no. of legs of links parallel to the X axis = 22

M

Miinniimmuum Dm Diiaammeetteer or of Lf Liinnkks :s : 6 m6 mmm ssaattiissffiieedd Area of links para Area of links parallel to Y llel to Y axis Aaxis Asvhsvh = = 265.5265.5 mmmm 22

Ma

Maxiximumum Sm Spapacicing ng of of LiLinknks :s : 24240 m0 mmm satitisfsa sfieiedd Area of Area of links paralinks parallel to X llel to X axis Aaxis Asvbsvb = = 265.5265.5 mmmm

Table 3.22 Table 3.22 1,210.0 mm² 1,210.0 mm² xx yy hh bb

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5. Capacity Analysis for N/bh - Mu /bh 2 h' / h= 0.87 Capacity Check No. N/bh Mu/bh 2 Remarks 1 0 0 2 0 0 3 2.16 1.95 OK 4 2.06 1.96 OK 5 0 0 6 0 0 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 N / b h ( M p a ) M_u/bh2_(Mpa)

INTERACTION CURVE N/bh - M

_u

bh

2 CURVE LOAD

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6. Capacity Analysis for N/bh - Mu /hb 2 b' / b= 0.87 Capacity Check No. N/bh Mu/hb2 Remarks 1 2.54 1.23 OK 2 0 0 3 0 0 4 0 0 5 1.83 1.93 OK 6 1.78 1.96 OK -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 N / b h ( M p a ) M_u/hb2_(Mpa)

INTERACTION CURVE N/bh - M

_u

hb

2 CURVE LOAD

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7. Check Of Shear Stress (sec. 3.8.4.6 SS CP65 Part 1)

Actual Concrete Shear Stress Units : m , N/mm

No. Mx/N Remarks My/N Remarks Vx / hb' Vy / bh'

1 0.036 > 0.06h 0.066 > 0.06b 0.11 0.03 2 9.290 > 0.06h 0.155 > 0.06b 0.02 0.10 3 0.324 > 0.06h 0.000 > 0.06b 0.03 0.23 4 0.340 > 0.06h 0.014 > 0.06b 0.05 0.23 5 0.020 < 0.06h 0.300 < 0.06b 0.20 0.01 6 0.052 > 0.06h 0.300 > 0.06b 0.18 0.03 where : 0.6h = 0.033 m 0.6b = 0.033 m

Design Concrete Shear Stress (Table 3.9 of SS CP65 Part 1) vcy = 0.84(100Asy/bh') 1/3 (400/h')1/4/ γ_m (f cu/30) 1/2 = 0.53 N/mm2; <= vmax vcx = 0.84(100Asx/bh') 1/3 (400/b')1/4/ γm (f cu/30) 1/2 = 0.53 N/mm2; <= vmax vmax = 4.4 Mpa

Condition : if Mx/N < 0.06h, My/N < 0.06b, Vx/hb' < vcx, and Vy/bh' < vcY', Shear Check is not required

Modification of the design concrete shear stress: Sec 3.4.5.12 of SS CP65 Part 1) Units : N/mm2

No. vyh/Mx vxb/My v'cy v'cx 1 0.17 0.3 0.79 0.99 2 0.11 1 0.51 0.5 3 0.16 1 0.74 1.19 4 0.16 0.83 0.73 1.17 5 0.15 0.13 0.69 0.67 6 0.16 0.13 0.70 0.67

where : v'cy = vcy + 0.6NVyh' / (Mx Ac) <= vcy [1 + N/(Acvcy)] 0.5

v'cx = vcx + 0.6NVxb' / (My Ac) <= vcx [1 + N/(Acvcx)] 0.5

vcx = Vx/hb'

vcy = Vy/bh'

condition : if (vx/v'cx) + (vy/v'cy) < 1.0, provided minimum reinforcement

Design of shear reinforcement Unit : N/mm2, kN

No. v"cy V'cy Vsy Vy - V'cy Remarks v"cx V'cx Vsx Vx - V'cx Remarks

1 0.19 49.85 292.2 -41.35 OK 0.76 199.386 292.16 -171.69 OK 2 0.44 115.43 292.2 -88.03 OK 0.07 18.3645 292.16 -13.76 OK 3 0.65 170.53 292.2 -109.33 OK 0.15 39.3525 292.16 -30.75 OK 4 0.60 157.41 292.2 -96.91 OK 0.21 55.0935 292.16 -42.19 OK 5 0.04 10.49 292.2 -7.49 OK 0.63 165.2805 292.16 -112.58 OK 6 0.10 26.24 292.2 -18.34 OK 0.58 152.163 292.16 -103.76 OK Where : v''cx = v'cxvx / (vx + vy) v''cy = v'cyvy / (vx + vy) V'cx = v''cxbh' V'cy = v''cyhb' Vsx = 0.87f yv Asvbh / S Vsy = 0.87f yv Asvhb / S

Condition : if Vsy > Vy-V'cyand Vsx > Vx-V'cx, OK (shear reinforcement is adequate)

Condition : if Vsy < Vy-V'cyand Vsx < Vx-V'cx, NG (shear reinforcement is not adequate)

0.34 0.36 0.32 0.32 Remarks < 1.0 ,provide minimum. < 1.0 ,provide minimum. < 1.0 ,provide minimum. < 1.0 ,provide minimum. (vx/v'cx) + (vy/v'cy) 0.15 0.24 < 1.0 ,provide minimum. < 1.0 ,provide minimum. Remarks shear check is required shear check is required shear check is required shear check is required shear check is required shear check is required

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8. Biaxial Bending and Tension

Assuming that the lever arm to resist bending moment about each axis is the distance between the center of steel reinforcement on each face.

ax = 404 mm, distance of center of steel reinforcement parallel at X axis

ay = 404 mm, distance of center of steel reinforcement parallel at Y axis

Unit : mm2

No. Astx, required Astx, provided Remarks Asty, required Asty, provided Remarks Ast, required Ascor, required Ascor, provided Remarks

1 0 1256 OK 0 1256 OK 0 0 314 notension 2 817 1256 OK 14 1256 OK 36 217 314 OK 3 0 1256 OK 0 1256 OK 0 0 314 notension 4 0 1256 OK 0 1256 OK 0 0 314 notension 5 0 1256 OK 0 1256 OK 0 0 314 notension 6 0 1256 OK 0 1256 OK 0 0 314 notension where :

Area of bars required on each face parallel to the x-axis: Astx,required = Mx / [ (f yax / 1.15) ]

Area of bars required on each face parallel to the y-axis: Asty,required = My / [ (f yay / 1.15) ]

Area of steel required for tension: Ast,required = N / (f y / 1.15)

Area of bars provided on each face parallel to the x-axis: Astx,provided

Area of bars provided on each face parallel to the y-axis: Asty,provided

Required area for one corner bar : Ascor, required

= Astx,required / nx + Asty,required / ny + Ast,required / 4 Area of bar provided for one corner bar : Ascor, provided