DARGROUP

Project

Pearl ProjectJob Ref.

Q09077

Section

Medina CentraleSheet no./rev.

1 1

Calc. by

ENG.ICDate

09-Nov-07Chk'd by

DR.AEDate App'd by Date

RC RECTANGULAR COLUMN DESIGN (ACI 318-05)

600 m

m

542 m

m

350 mm

Geometry of column

Depth of column (larger dimension of column); h = 600 mm

W idth of column (smaller dimension of column); b = 350 mm

Clear cover to reinforcement (both sides); cc = 40 mm

Unsupported height of column; lu = 4500 mm

Effective height factor; k = 1.00

Check for overall column dimensions

h < 4b, column dimensions are OK

Reinforcement of column

Numbers of bars of longitudinal steel; N = 8

Longitudinal steel bar diameter number; Dbar_num = 6

Diameter of longitudinal bar; Dlong = 19 mm

Stirrup bar diameter number; Dstir_num = 3

Diameter of stirrup bar; Dstir = 9 mm

Specified yield strength of reinforcement; fy = 415 MPa

Specified compressive strength of concrete; f’c = 40 MPa

Modulus of elasticity of bar reinforcement; Es = 200000 MPa

Modulus of elasticity of concrete (cl. 8.5); Ec = 4700 (f’c 1 MPa) = 29725 MPa

Ultimate design strain; c = 0.003 mm/mm

Check for minimum area of steel (ACI 318-05, cl. 10.9)

Gross area of column; Ag = h b = 210000 mm2

Area of steel provided; Ast = N (/ 4) Dlong2 = 2268 mm2

Minimum required area of steel; Ast_min = 0.01 Ag = 2100 mm2

DARGROUP

Project

Pearl ProjectJob Ref.

Q09077

Section

Medina CentraleSheet no./rev.

2 1

Calc. by

ENG.ICDate

09-Nov-07Chk'd by

DR.AEDate App'd by Date

PASS - Ast > Ast_min, provided area of steel is greater than minimum required area of steel

Check for maximum area of steel (ACI 318-05, cl. 10.9)

Permissible maximum area of steel; Ast_max = 0.08 Ag = 16800 mm2

PASS - Ast < Ast_max, provided area of steel is less than permissible maximum area of steel

Braced column slenderness check (ACI 318-05, cl. 10.12)

Maximum slenderness ratio limit; sr_max = 100

Permissible slenderness ratio; sr_perm = 40

Slenderness check for braced column

Radius of gyration; rx = 0.3 h = 180 mm

ry = 0.3 b = 105 mm

rmin = min(rx, ry) = 105 mm

Actual slenderness ratio; sr_act = k lu / rmin = 42.86

Column slenderness limit OK, column is braced slender column

Design load and moments for biaxially loaded slender column

Ultimate axial force acting on column; Pu_act = 2750.00 kN

Ultimate moment about major (X) axis; Mux_act = 120.00 kNm

Ultimate moment about minor (Y) axis; Muy_act = 25.00 kNm

Contour beta factor; = 0.50

Ratio of DL moment to total moment; d = 0.65

Magnified moments for biaxial slender column (ACI 318-05, cl. 10.12)

Assuming strength reduction factor; = 0.65

Moment of inertia of section @ X axis; Igx = (b h3) / 12 = 6300000000 mm4

Moment of inertia of section @ Y axis; Igy = (h b3) / 12 = 2143750000 mm4

Euler’s buckling load @ X axis; Pcx = (2 0.4 Ec Igx) / ((1 + d) (k lu)2) = 22126.83 kN

Euler’s buckling load @ Yaxis; Pcy = (2 0.4 Ec Igy) / ((1 + d) (k lu)2) = 7529.27 kN

Correction factor for actual to equiv. mmt.diagram; Cm = 1

Moment magnifier for M @ X axis; nsx1 = Cm / (1 - (Pu_act/ (0.75 Pcx))) = 1.199

Moment magnifier for M @ X axis; nsx = nsx1 = 1.199

Moment magnifier for M @ Y axis; nsy1 = Cm / (1 - (Pu_act / (0.75 Pcy))) = 1.949

Moment magnifier for M @ Y axis; nsy = nsy1 = 1.949

Ultimate magnified uniaxial M @ X axis; Mcx = nsx Mux_act = 143.84 kNm

Ultimate magnified uniaxial M @ Y axis; Mcy = nsy Muy_act = 48.73 kNm

Net magnified uniaxial M @ X axis; Mnx = Mcx = 221.28 kNm

Net magnified uniaxial M @ Y axis; Mny = Mcy = 74.97 kNm

Required eccentricities; ex = Mcx / Pu_act = 52 mm

ey = Mcy / Pu_act = 18 mm

Axial load capacity of biaxially loaded column assuming no Muy_act (ACI 318-05, cl 10.3.6)

c/dt ratio; rxb = 1.233

Effective cover to reinforcement; d’ = cc + Dstir + (Dlong / 2) = 59 mm

Depth of tension steel; dt = h - d’ = 542 mm

Depth of NA from extreme compression face; cx = rxb dt = 668 mm

Factor of depth of comp. stress block (cl.10.2.7.3); 1 = 0.764

Depth of equivalent rectangular stress block; ax = min((1 cx), h) = 510 mm

Stress in compression reinforcement; f’sx = Es c (1 - (d’ / cx)) = 547 MPa

DARGROUP

Project

Pearl ProjectJob Ref.

Q09077

Section

Medina CentraleSheet no./rev.

3 1

Calc. by

ENG.ICDate

09-Nov-07Chk'd by

DR.AEDate App'd by Date

Since abs(f'sx) > fy, hence f'csx = fy

f’csx = 415 MPa

Stress in tension reinforcement; fsx = Es c ((dt / cx) - 1) = -114 MPa

Since abs(fsx) < fy, fsx = ftsx

Capacity of concrete in compression; Ccx = 0.85 f’c b ax = 6074.92 kN

Strength of steel in compression; Csx = A’s f’csx = 470.72 kN

Strength of steel in tension; Tsx = As ftsx = 128.83 kN

Nominal axial load strength; Pnx = Ccx + Csx + Tsx = 6674.46 kN

Strength reduction factor; x = 0.65 = 0.650

Ultimate axial load carrying capacity of column; Pu1 = x Pnx = 4338.40 kN

PASS - column is safe in axial loading

Uniaxial moment capacity of column

Centroid of column along larger dimension; yx = h 0.5 = 300 mm

Nominal moment strength; Mox = = Ccx (yx - (0.5 ax)) + Csx (y - ccx) - Tsx (dt - yx) = 363.136

kNm

x = (Mnx / Mox) = 0.609

Ultimate moment strength; Mu1 = Mox x = 236.04 kNm

PASS - column is safe for bending

Eccentricity ratio

Actual eccentricity; ex = 52 mm

Allowable eccentricity; eall_x = Mu1 / Pu1 = 54 mm

Eccentricity ratio; erx = ex / eall_x = 0.961

Biaxially loaded column about minor axis

Details of column cross-section

c/dt ratio; ryb = 1.142

Effective cover to reinforcement; d’ = cc + Dstir + (Dlong / 2) = 59 mm

Area of each layer of steel; Ast_l = 2 (Dlong2) / 4 = 567 mm2

Spacing between bars; s = ((b - (2 d’))) / ((N / 2) -1) = 78 mm

Depth of tension steel; bt = b - d’ = 292 mm

Depth of NA from extreme compression face; cy = ryb bt = 333 mm

Depth of equivalent rectangular stress block; ay = min((1 cy), b) = 255 mm

Yield strain in steel; sy = fy / Es = 0.002

Strength reduction factor; y = 0.650

Details of concrete block

Force carried by concrete

Forces carried by concrete; Ccy = 0.85 f’c h ay = 5192.55 kN

Moment carried by concrete

Moment carried by concrete; Mccy = Ccy ((b / 2) - (ay / 2)) = 247.85 kNm

Details of steel layers

Details of first steel layer

Depth of first layer; x1 = d’ = 59 mm

Strain of first layer; 1 = 0.003 (1 - (x1 / cy)) = 0.00247

Stress in first layer; 1 = 415 MPa

DARGROUP

Project

Pearl ProjectJob Ref.

Q09077

Section

Medina CentraleSheet no./rev.

4 1

Calc. by

ENG.ICDate

09-Nov-07Chk'd by

DR.AEDate App'd by Date

Force carried by first layer; F1 = 1 Ast_l = 235.33 kN

Moment carried by first steel layer; M1 = F1 ((b / 2) - x1) = 27.42 kNm

Details of second steel layer

Depth of second layer; x2 = x1+s = 136 mm

Strain of second layer; 2 = 0.003 (1 - (x2 / cy)) = 0.00177

Stress in second layer; 2 = 355 MPa

Force carried by second layer; F2 = 2 Ast_l = 201.13 kN

Moment carried by second steel layer; M2 = F2 ((b / 2) - x2) = 7.81 kNm

Details of third steel layer

Depth of third layer; x3 = 214 mm

Strain of third layer; 3 = 0.00107

Stress in third layer; 3 = 215 MPa

Force carried by third layer; F3 = 3 Ast_l = 121.78 kN

Moment carried by third steel layer; M3 = F3 ((b / 2) - x3) = -4.73 kNm

Details of fourth steel layer

Depth of fourth layer; x4 = 292 mm

Strain of fourth layer; 4 = 0.00037

Stress in fourth layer; 4 = 75 MPa

Force carried by fourth layer; F4 = 4 Ast_l = 42.44 kN

Moment carried by fourth steel layer; M4 = F4 ((b / 2) - x4) = -4.94 kNm

Tensile force carried by steel

Sum of tensile forces by steel; Tsy = 0.00 kN

Compressive force carried by steel

Sum of compressive forces by steel; Csy = 600.67 kN

Total force carried by column

Nominal axial load strength; Pny = 5793.22 kN

Strength reduction factor; y = 0.65 = 0.650

Ultimate axial Load carrying capacity of column; Pu2 = y Pny = 3765.59 kN

PASS - column is safe in axial loading

Moment carried by biaxial column minor axis

Nominal moment strength; Moy = 273.40 kNm

Contour beta factor

Contour beta factor; = 0.500

Mnx_upon_Mox = x = 0.609

From Contour beta factor chart for rectangular columns in biaxial bending

Mny_upon_Moy = 0.391

Net moment along minor axis resisted by column; Mny1 = Moy (Mny_upon_Moy) = 106.90 kNm

Ultimate moment along minor axis; Mu2 = Mny1 y = 69.49 kNm

Check for moment capacity about minor axis

PASS - column is safe for bending

Eccentricity ratio

Actual eccentricity; ey = 18 mm

Allowable eccentricity; eall_y = Mu2 / Pu2 = 18 mm

DARGROUP

Project

Pearl ProjectJob Ref.

Q09077

Section

Medina CentraleSheet no./rev.

5 1

Calc. by

ENG.ICDate

09-Nov-07Chk'd by

DR.AEDate App'd by Date

Eccentricity ratio; ery = ey / eall_y= 0.960

Design of column ties (ACI 318-05, cl. 7.10)

16 times longitudinal bar diameter; sv1 = 16 Dlong = 304 mm

48 times stirrup bar diameter; sv2 = 48 Dstir = 432 mm

Least column dimension; sv3 = min(h, b) = 350 mm

Maximum allowable stirrup spacing; s = min(sv1, sv2, sv3) = 304 mm

Design summary

Column is 350 mm wide and 600 mm deep with 40 MPa concrete and 415 MPa steel.

Longitudinal reinforcement is 8 No.6 and lateral reinforcement for shear is 2 legs No.3 stirrup @ 304 mm center to center

Design status

PASS - column is safe