Forewords‎ > ‎Reviews‎ > ‎

### Case Study: Structurally sound?

posted Jun 20, 2015, 9:18 AM by jeffery jim   [ updated Jan 14, 2018, 3:42 PM ]
 These photos were hot in a few open discussions at IEM and also my Class of 1995 Whatapps group (engineers with 15 years of experience) when earthquake with the magnitude of 6.0 hit Ranau, Sabah. So did the photo projected out about injustice or substandard built? As professional, we cannot simply summarized things that is not proven and therefore let us explore this issue one item at a time. Let us learn how to use visual judgement method. No scientific calculation needed.1. Size and DimensionThe Column size is estimated to be 250mmx250mm column which is almost the equivalent size of a commonly used 200mmx200mm reinforced concrete pile. Now, by layman reasoning, a single grade G45 250mmx250mm pile can hold up to 75 Tonne. So by parametric estimate, a grade G30 Structure should be able to carry up to 30 tonne (damn underload) of vertical load.2. Form and FunctionsThe area where the columns situated is at the middle of the building with intruded section. Besides that, the function of that area is not a heavy duty area, say with loading of slab at 2.5kN/m². From photo, we can give a rough estimate of 16M² of slab is supported by each column. The edge of the column is carrying 10kN or 1 tonne of loading for each floor. As per self weight and safety factor, say 2.5 tonnes.3. Design reduction factor.Now for column design, a reduction of 10% is allowed for each floor with maximum of 40% reduction. Three floors mean 30%. So now,Overall 3 floors of loading to a column is 2.5 tonne x 3 floorswhich is 7.5 tonne and the multiple with 70% (30% reduction)the column will take 5.25 tonne.So if the design is able to take an estimated 30 tonne and say add safety factor of 2, the design loading is 10.20 tonne against the column capacity of 30 tonne; then what is the problem with this design? Basically, there is no problem with this design, right. So this is a safe design.Whatapps and Facebook posts became viralBricked-up or boxed-up columns and the aftermathThe initial parametric estimate by visual (mentioned and elaborated above) was not accepted by layman, therefore a structural analysis was conducted. The bricked-up reinforced concrete column at Ranau was designed appropriately. Somehow, people are still talking about it. Now let me bury this issue to rest. Below are all the calculation from ESTEEM Structural Software based on BS8110.For your information, instead of using grade G30 as prescribed by JKR, i use G25 instead. Guess what buggers, the column is still okay. Read the design analysis below and if you can understand.FLOOR PATHNAME : T:\Design esteem\RANAU COLUMN\Ranau\rf\rf.ccdCOLUMN DETAILED DESIGN CALCULATION:CODE OF PRACTICE USED IS: BS8110:1985Floor D.L. L.L. fcu fy cover Load incre.rf 1.40 1.60 25 460 35 10Rebar maximum spacing = 250 mm, Minimum spacing = 40 mmRebar maximum size = 25 mm, Minimum bar size = 12 mmLink maximum size = 20 mm, Minimum link size = 6 mmMinimum rebar percentage used for Column Design = 1.00Design for Braced Column in X-directionDesign for Braced Column in Y-directionYield strain = Yield strength/Young Modulus =0.87*460/200000 =0.0020Location of Column: 1-AFloor No. = 5; Live load reduction = 0Column Fixity: Top X = Fixed; Top Y = Fixed; Bottom X = Fixed; Bottom Y = FixedColumn Effective Height Coefficient: X = 0.75; Y = 0.75Column X-Dimension,A = 250 mm; X-Effective Height = 2250 mmColumn Y-Dimension,B = 250 mm; Y-Effective Height = 2250 mmFactored Upper Moment,Mx = 17.7 kNm; My = 17.7 kNmFactored Lower Moment,Mx = 15.1 kNm; My = 15.1 kNmDL=1.40 & LL=1.60 Factored Moment,Mx = 17.7 kNm; My = 17.7 kNmDead Load,DL = 94.6 kN; Live Load,LL = 54.4 kNLoad Combination of DL = 94.6 kN & LL = 54.4 kNTotal Ultimate Load,UL = (1+Allowable increase)*(DLFac*DL+LLFac*LL) kN= (1+0.10)*(1.40* 94.6+1.60* 54.4) = 241.4 kNSo, design for Ultimate Load, N = 241 kN= 241401 NUltimate Mx = 17.7 kNm; My = 17.7 kNmDesign For X-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in X-Dimension = Hef/A =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentDesign For Y-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in Y-Dimension = Hef/B =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentLocation : 1-AX-Slenderness ratio = 0.0X-Slenderness ratio = 0.0 <= 15.0 --> Slender moment = 0.0Y-Slenderness ratio = 0.0 < 15.0 --> Slender moment = 0.0Notation: A = Rebar area in mm^2 ; TransY = Transformed Rebar Location in mm: fs = Rebar stress in N/mm^2 ; fsA = fs x A in kN ; Fs = Sum of fsA: fd = Rebar lever arm in mm ; fdA = fsA x fd in kNm ; Fsd = Sum of fdACalculate Moment Capacity in X directionDESIGN AXIAL LOAD = 241.4 kN ; NEUTRAL AXIS DEPTH, x = 97.5 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 391.3 78.7 78.7 82.0 6.45 6.45|| 82.0 -82.0 201 207.0 -400.2 -80.5 -1.8 -82.0 6.60 13.05|| 82.0 82.0 201 207.0 -400.2 -80.5 -82.3 -82.0 6.60 19.65|| -82.0 82.0 201 43.0 391.3 78.7 -3.6 82.0 6.45 26.10|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -3.6 kN ; Fsd = 26.10 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.5 N = 248.6 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 248.6*(125.0-88.9/2) kNmm = 20.03 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-3.6+248.6)*1.00 = 245.0 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.10+20.03)*1.00 = 46.13 kN-------------------------------------------------------------------------------------------Calculate Moment Capacity in Y directionDESIGN AXIAL LOAD = 241.4 kN ; NEUTRAL AXIS DEPTH, x = 97.5 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 391.3 78.7 78.7 82.0 6.45 6.45|| 82.0 -82.0 201 43.0 391.3 78.7 157.3 82.0 6.45 12.90|| 82.0 82.0 201 207.0 -400.2 -80.5 76.9 -82.0 6.60 19.50|| -82.0 82.0 201 207.0 -400.2 -80.5 -3.6 -82.0 6.60 26.10|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -3.6 kN ; Fsd = 26.10 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.5 N = 248.6 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 248.6*(125.0-88.9/2) kNmm = 20.03 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-3.6+248.6)*1.00 = 245.0 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.10+20.03)*1.00 = 46.13 kN-------------------------------------------------------------------------------------------Eccentricity 20 mm = 0.02*UL = 0.02*241.4 = 4.8 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*241.401 = 3.0 kNmX-Moment Eccentricity, Mxe = 3.0 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*241.401 = 3.0 kNmY-Moment Eccentricity, Mye = 3.0 kNmTotal steel area provided, As = 804 mm^2; i.e. 1.3%Pure Axial load capacity, Nuz = fac*fcu*Ac+fyy*fy*As= 0.45*25*62500 + 0.87*460*804 = 1024985 N = 1025.0kNAlpha, x(>=1 && <=2) = 5*N/(3*Nuz) + 2/3 = 5*241.4/(3*1025.0) + 2/3 = 1.06(Mx/Mux)^x + (My/Muy)^x = (17.7/46.1)^1.06 + (17.7/46.1)^1.06 = (0.384)^1.06 + (0.384)^1.06 = 0.73Biaxial Iteration No. = 4 ; pfy_fcu = 0.24; Mux_bh2fcu = 0.12; Muy_bh2fcu = 0.12;nXYIt XIt YIt MLayer SLayer Nos As % Nuz Alpha Mx Mux RX My Muy RY Ratio3 2 2 1x 2T16 1x 2T16 4 804 1.3 1025 1.06 18 46 0.38 18 46 0.38 0.73Vu, Vu at 1-A = 0.0 kNVu Stress, v = V/bd = 0.0*1000/(250*207) = 0.000 N/mm^2Refer to BS8110:Part 1:1985 Table 3.9Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/207) = 1.932Concrete Grade ratio = min(40,fcu)/25 = min(40,25)/25 = 1.000Steel Percentage, 100As/(bd) = min(3,0.78) = 0.78vc = ( 0.79*(0.78)^1/3*(1.932)^1/4*(1.000)^1/3 )/1.25 = 0.685 N/mm^2Because of Tension force due to Transfer Wall --> Shear Capacity = 0.000 N/mm^2Vu Stress - Vu Capacity = v - vc = vd = 0.000 - 0.000 = 0.000 N/mm^2vd < 0.40 N/mm^2 --> Design for vd = 0.40 N/mm^2Steel area provided by Link size 6, Asv = 2*pie*dia*dia/4 = 2*3.1416*6*6/4 = 56.5 mm^2Link spacing required, Sv = 0.87*460*56.5/(250*0.400)= 226Vu Capacity provided by Link = 0.87*460*56.5/(226*250) = 0.400 N/mm^2Asv/Sv = 56.5/226= 0.250---------------------------------------------------------------------------------------Location of Column: 2-AFloor No. = 5; Live load reduction = 0Column Fixity: Top X = Fixed; Top Y = Fixed; Bottom X = Fixed; Bottom Y = FixedColumn Effective Height Coefficient: X = 0.75; Y = 0.75Column X-Dimension,A = 250 mm; X-Effective Height = 2250 mmColumn Y-Dimension,B = 250 mm; Y-Effective Height = 2250 mmFactored Upper Moment,Mx = 17.7 kNm; My = 17.7 kNmFactored Lower Moment,Mx = 15.1 kNm; My = 15.1 kNmDL=1.40 & LL=1.60 Factored Moment,Mx = 17.7 kNm; My = 17.7 kNmDead Load,DL = 94.0 kN; Live Load,LL = 54.2 kNLoad Combination of DL = 94.0 kN & LL = 54.2 kNTotal Ultimate Load,UL = (1+Allowable increase)*(DLFac*DL+LLFac*LL) kN= (1+0.10)*(1.40* 94.0+1.60* 54.2) = 240.2 kNSo, design for Ultimate Load, N = 240 kN= 240157 NUltimate Mx = 17.7 kNm; My = 17.7 kNmDesign For X-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in X-Dimension = Hef/A =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentDesign For Y-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in Y-Dimension = Hef/B =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentLocation : 2-AX-Slenderness ratio = 0.0X-Slenderness ratio = 0.0 <= 15.0 --> Slender moment = 0.0Y-Slenderness ratio = 0.0 < 15.0 --> Slender moment = 0.0Notation: A = Rebar area in mm^2 ; TransY = Transformed Rebar Location in mm: fs = Rebar stress in N/mm^2 ; fsA = fs x A in kN ; Fs = Sum of fsA: fd = Rebar lever arm in mm ; fdA = fsA x fd in kNm ; Fsd = Sum of fdACalculate Moment Capacity in X directionDESIGN AXIAL LOAD = 240.2 kN ; NEUTRAL AXIS DEPTH, x = 97.3 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 390.5 78.5 78.5 82.0 6.44 6.44|| 82.0 -82.0 201 207.0 -400.2 -80.5 -2.0 -82.0 6.60 13.04|| 82.0 82.0 201 207.0 -400.2 -80.5 -82.4 -82.0 6.60 19.63|| -82.0 82.0 201 43.0 390.5 78.5 -3.9 82.0 6.44 26.07|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -3.9 kN ; Fsd = 26.07 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.3 N = 248.0 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 248.0*(125.0-88.6/2) kNmm = 20.01 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-3.9+248.0)*1.00 = 244.1 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.07+20.01)*1.00 = 46.08 kN-------------------------------------------------------------------------------------------Calculate Moment Capacity in Y directionDESIGN AXIAL LOAD = 240.2 kN ; NEUTRAL AXIS DEPTH, x = 97.3 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 390.5 78.5 78.5 82.0 6.44 6.44|| 82.0 -82.0 201 43.0 390.5 78.5 157.0 82.0 6.44 12.88|| 82.0 82.0 201 207.0 -400.2 -80.5 76.6 -82.0 6.60 19.47|| -82.0 82.0 201 207.0 -400.2 -80.5 -3.9 -82.0 6.60 26.07|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -3.9 kN ; Fsd = 26.07 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.3 N = 248.0 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 248.0*(125.0-88.6/2) kNmm = 20.01 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-3.9+248.0)*1.00 = 244.1 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.07+20.01)*1.00 = 46.08 kN-------------------------------------------------------------------------------------------Eccentricity 20 mm = 0.02*UL = 0.02*240.2 = 4.8 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*240.158 = 3.0 kNmX-Moment Eccentricity, Mxe = 3.0 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*240.158 = 3.0 kNmY-Moment Eccentricity, Mye = 3.0 kNmTotal steel area provided, As = 804 mm^2; i.e. 1.3%Pure Axial load capacity, Nuz = fac*fcu*Ac+fyy*fy*As= 0.45*25*62500 + 0.87*460*804 = 1024985 N = 1025.0kNAlpha, x(>=1 && <=2) = 5*N/(3*Nuz) + 2/3 = 5*240.2/(3*1025.0) + 2/3 = 1.06(Mx/Mux)^x + (My/Muy)^x = (17.7/46.1)^1.06 + (17.7/46.1)^1.06 = (0.385)^1.06 + (0.385)^1.06 = 0.73Biaxial Iteration No. = 4 ; pfy_fcu = 0.24; Mux_bh2fcu = 0.12; Muy_bh2fcu = 0.12;nXYIt XIt YIt MLayer SLayer Nos As % Nuz Alpha Mx Mux RX My Muy RY Ratio3 2 2 1x 2T16 1x 2T16 4 804 1.3 1025 1.06 18 46 0.38 18 46 0.38 0.73Vu, Vu at 2-A = 0.0 kNVu Stress, v = V/bd = 0.0*1000/(250*207) = 0.000 N/mm^2Refer to BS8110:Part 1:1985 Table 3.9Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/207) = 1.932Concrete Grade ratio = min(40,fcu)/25 = min(40,25)/25 = 1.000Steel Percentage, 100As/(bd) = min(3,0.78) = 0.78vc = ( 0.79*(0.78)^1/3*(1.932)^1/4*(1.000)^1/3 )/1.25 = 0.685 N/mm^2Because of Tension force due to Transfer Wall --> Shear Capacity = 0.000 N/mm^2Vu Stress - Vu Capacity = v - vc = vd = 0.000 - 0.000 = 0.000 N/mm^2vd < 0.40 N/mm^2 --> Design for vd = 0.40 N/mm^2Steel area provided by Link size 6, Asv = 2*pie*dia*dia/4 = 2*3.1416*6*6/4 = 56.5 mm^2Link spacing required, Sv = 0.87*460*56.5/(250*0.400)= 226Vu Capacity provided by Link = 0.87*460*56.5/(226*250) = 0.400 N/mm^2Asv/Sv = 56.5/226= 0.250---------------------------------------------------------------------------------------Location of Column: 1-BFloor No. = 5; Live load reduction = 0Column Fixity: Top X = Fixed; Top Y = Fixed; Bottom X = Fixed; Bottom Y = FixedColumn Effective Height Coefficient: X = 0.75; Y = 0.75Column X-Dimension,A = 250 mm; X-Effective Height = 2250 mmColumn Y-Dimension,B = 250 mm; Y-Effective Height = 2250 mmFactored Upper Moment,Mx = 17.7 kNm; My = 17.7 kNmFactored Lower Moment,Mx = 15.1 kNm; My = 15.1 kNmDL=1.40 & LL=1.60 Factored Moment,Mx = 17.7 kNm; My = 17.7 kNmDead Load,DL = 94.0 kN; Live Load,LL = 54.2 kNLoad Combination of DL = 94.0 kN & LL = 54.2 kNTotal Ultimate Load,UL = (1+Allowable increase)*(DLFac*DL+LLFac*LL) kN= (1+0.10)*(1.40* 94.0+1.60* 54.2) = 240.2 kNSo, design for Ultimate Load, N = 240 kN= 240157 NUltimate Mx = 17.7 kNm; My = 17.7 kNmDesign For X-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in X-Dimension = Hef/A =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentDesign For Y-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in Y-Dimension = Hef/B =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentLocation : 1-BX-Slenderness ratio = 0.0X-Slenderness ratio = 0.0 <= 15.0 --> Slender moment = 0.0Y-Slenderness ratio = 0.0 < 15.0 --> Slender moment = 0.0Notation: A = Rebar area in mm^2 ; TransY = Transformed Rebar Location in mm: fs = Rebar stress in N/mm^2 ; fsA = fs x A in kN ; Fs = Sum of fsA: fd = Rebar lever arm in mm ; fdA = fsA x fd in kNm ; Fsd = Sum of fdACalculate Moment Capacity in X directionDESIGN AXIAL LOAD = 240.2 kN ; NEUTRAL AXIS DEPTH, x = 97.3 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 390.5 78.5 78.5 82.0 6.44 6.44|| 82.0 -82.0 201 43.0 390.5 78.5 157.0 82.0 6.44 12.88|| 82.0 82.0 201 207.0 -400.2 -80.5 76.6 -82.0 6.60 19.47|| -82.0 82.0 201 207.0 -400.2 -80.5 -3.9 -82.0 6.60 26.07|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -3.9 kN ; Fsd = 26.07 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.3 N = 248.0 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 248.0*(125.0-88.6/2) kNmm = 20.01 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-3.9+248.0)*1.00 = 244.1 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.07+20.01)*1.00 = 46.08 kN-------------------------------------------------------------------------------------------Calculate Moment Capacity in Y directionDESIGN AXIAL LOAD = 240.2 kN ; NEUTRAL AXIS DEPTH, x = 97.3 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 390.5 78.5 78.5 82.0 6.44 6.44|| 82.0 -82.0 201 207.0 -400.2 -80.5 -2.0 -82.0 6.60 13.04|| 82.0 82.0 201 207.0 -400.2 -80.5 -82.4 -82.0 6.60 19.63|| -82.0 82.0 201 43.0 390.5 78.5 -3.9 82.0 6.44 26.07|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -3.9 kN ; Fsd = 26.07 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.3 N = 248.0 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 248.0*(125.0-88.6/2) kNmm = 20.01 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-3.9+248.0)*1.00 = 244.1 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.07+20.01)*1.00 = 46.08 kN-------------------------------------------------------------------------------------------Eccentricity 20 mm = 0.02*UL = 0.02*240.2 = 4.8 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*240.158 = 3.0 kNmX-Moment Eccentricity, Mxe = 3.0 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*240.158 = 3.0 kNmY-Moment Eccentricity, Mye = 3.0 kNmTotal steel area provided, As = 804 mm^2; i.e. 1.3%Pure Axial load capacity, Nuz = fac*fcu*Ac+fyy*fy*As= 0.45*25*62500 + 0.87*460*804 = 1024985 N = 1025.0kNAlpha, x(>=1 && <=2) = 5*N/(3*Nuz) + 2/3 = 5*240.2/(3*1025.0) + 2/3 = 1.06(Mx/Mux)^x + (My/Muy)^x = (17.7/46.1)^1.06 + (17.7/46.1)^1.06 = (0.385)^1.06 + (0.385)^1.06 = 0.73Biaxial Iteration No. = 4 ; pfy_fcu = 0.24; Mux_bh2fcu = 0.12; Muy_bh2fcu = 0.12;nXYIt XIt YIt MLayer SLayer Nos As % Nuz Alpha Mx Mux RX My Muy RY Ratio3 2 2 1x 2T16 1x 2T16 4 804 1.3 1025 1.06 18 46 0.38 18 46 0.38 0.73Vu, Vu at 1-B = 0.0 kNVu Stress, v = V/bd = 0.0*1000/(250*207) = 0.000 N/mm^2Refer to BS8110:Part 1:1985 Table 3.9Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/207) = 1.932Concrete Grade ratio = min(40,fcu)/25 = min(40,25)/25 = 1.000Steel Percentage, 100As/(bd) = min(3,0.78) = 0.78vc = ( 0.79*(0.78)^1/3*(1.932)^1/4*(1.000)^1/3 )/1.25 = 0.685 N/mm^2Because of Tension force due to Transfer Wall --> Shear Capacity = 0.000 N/mm^2Vu Stress - Vu Capacity = v - vc = vd = 0.000 - 0.000 = 0.000 N/mm^2vd < 0.40 N/mm^2 --> Design for vd = 0.40 N/mm^2Steel area provided by Link size 6, Asv = 2*pie*dia*dia/4 = 2*3.1416*6*6/4 = 56.5 mm^2Link spacing required, Sv = 0.87*460*56.5/(250*0.400)= 226Vu Capacity provided by Link = 0.87*460*56.5/(226*250) = 0.400 N/mm^2Asv/Sv = 56.5/226= 0.250---------------------------------------------------------------------------------------Location of Column: 2-BFloor No. = 5; Live load reduction = 0Column Fixity: Top X = Fixed; Top Y = Fixed; Bottom X = Fixed; Bottom Y = FixedColumn Effective Height Coefficient: X = 0.75; Y = 0.75Column X-Dimension,A = 250 mm; X-Effective Height = 2250 mmColumn Y-Dimension,B = 250 mm; Y-Effective Height = 2250 mmFactored Upper Moment,Mx = 17.7 kNm; My = 17.7 kNmFactored Lower Moment,Mx = 15.1 kNm; My = 15.1 kNmDL=1.40 & LL=1.60 Factored Moment,Mx = 17.7 kNm; My = 17.7 kNmDead Load,DL = 93.3 kN; Live Load,LL = 54.1 kNLoad Combination of DL = 93.3 kN & LL = 54.1 kNTotal Ultimate Load,UL = (1+Allowable increase)*(DLFac*DL+LLFac*LL) kN= (1+0.10)*(1.40* 93.3+1.60* 54.1) = 238.9 kNSo, design for Ultimate Load, N = 239 kN= 238914 NUltimate Mx = 17.7 kNm; My = 17.7 kNmDesign For X-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in X-Dimension = Hef/A =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentDesign For Y-Braced ColumnEffective height,Hef = 2250 mmSlenderness ratio,sr in Y-Dimension = Hef/B =2250/ 250 = 9.0Slenderness ratio = 9.0 < 15 ---> No additional momentLocation : 2-BX-Slenderness ratio = 0.0X-Slenderness ratio = 0.0 <= 15.0 --> Slender moment = 0.0Y-Slenderness ratio = 0.0 < 15.0 --> Slender moment = 0.0Notation: A = Rebar area in mm^2 ; TransY = Transformed Rebar Location in mm: fs = Rebar stress in N/mm^2 ; fsA = fs x A in kN ; Fs = Sum of fsA: fd = Rebar lever arm in mm ; fdA = fsA x fd in kNm ; Fsd = Sum of fdACalculate Moment Capacity in X directionDESIGN AXIAL LOAD = 238.9 kN ; NEUTRAL AXIS DEPTH, x = 97.0 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 389.7 78.4 78.4 82.0 6.42 6.42|| 82.0 -82.0 201 207.0 -400.2 -80.5 -2.1 -82.0 6.60 13.02|| 82.0 82.0 201 207.0 -400.2 -80.5 -82.6 -82.0 6.60 19.62|| -82.0 82.0 201 43.0 389.7 78.4 -4.2 82.0 6.42 26.05|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -4.2 kN ; Fsd = 26.05 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.0 N = 247.4 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 247.4*(125.0-88.4/2) kNmm = 19.98 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-4.2+247.4)*1.00 = 243.1 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.05+19.98)*1.00 = 46.03 kN-------------------------------------------------------------------------------------------Calculate Moment Capacity in Y directionDESIGN AXIAL LOAD = 238.9 kN ; NEUTRAL AXIS DEPTH, x = 97.0 mm-------------------------------------------------------------------------------------------| Rebar Coord/Area,A TransY fs fsA Fs fd fdA Fsd| -------------------------------------------------------------------------------------------| -82.0 -82.0 201 43.0 389.7 78.4 78.4 82.0 6.42 6.42|| 82.0 -82.0 201 43.0 389.7 78.4 156.7 82.0 6.42 12.85|| 82.0 82.0 201 207.0 -400.2 -80.5 76.2 -82.0 6.60 19.45|| -82.0 82.0 201 207.0 -400.2 -80.5 -4.2 -82.0 6.60 26.05|-------------------------------------------------------------------------------------------| Axial Load, fsA & Bending, Fsd: Fs = -4.2 kN ; Fsd = 26.05 kNm |-------------------------------------------------------------------------------------------Concrete Axial Load Capacity,Fcc = k1*bx*x = 10.20*250*97.0 N = 247.4 kNConcrete Bending Capacity, Fcd = Fcc*(by2- a/2) = 247.4*(125.0-88.4/2) kNmm = 19.98 kNmTotal Axial Load Capacity = (Fs + Fcc)*Fac = (-4.2+247.4)*1.00 = 243.1 kNTotal Bending Capacity = (Fsd + Fcd)*Fac = (26.05+19.98)*1.00 = 46.03 kN-------------------------------------------------------------------------------------------Eccentricity 20 mm = 0.02*UL = 0.02*238.9 = 4.8 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*238.914 = 3.0 kNmX-Moment Eccentricity, Mxe = 3.0 kNmEccentricity 5 percent = 0.05*h*UL = 0.05*250*238.914 = 3.0 kNmY-Moment Eccentricity, Mye = 3.0 kNmTotal steel area provided, As = 804 mm^2; i.e. 1.3%Pure Axial load capacity, Nuz = fac*fcu*Ac+fyy*fy*As= 0.45*25*62500 + 0.87*460*804 = 1024985 N = 1025.0kNAlpha, x(>=1 && <=2) = 5*N/(3*Nuz) + 2/3 = 5*238.9/(3*1025.0) + 2/3 = 1.06(Mx/Mux)^x + (My/Muy)^x = (17.7/46.0)^1.06 + (17.7/46.0)^1.06 = (0.385)^1.06 + (0.385)^1.06 = 0.73Biaxial Iteration No. = 4 ; pfy_fcu = 0.24; Mux_bh2fcu = 0.12; Muy_bh2fcu = 0.12;nXYIt XIt YIt MLayer SLayer Nos As % Nuz Alpha Mx Mux RX My Muy RY Ratio3 2 2 1x 2T16 1x 2T16 4 804 1.3 1025 1.06 18 46 0.39 18 46 0.39 0.73Vu, Vu at 2-B = 0.0 kNVu Stress, v = V/bd = 0.0*1000/(250*207) = 0.000 N/mm^2Refer to BS8110:Part 1:1985 Table 3.9Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/207) = 1.932Concrete Grade ratio = min(40,fcu)/25 = min(40,25)/25 = 1.000Steel Percentage, 100As/(bd) = min(3,0.78) = 0.78vc = ( 0.79*(0.78)^1/3*(1.932)^1/4*(1.000)^1/3 )/1.25 = 0.685 N/mm^2Because of Tension force due to Transfer Wall --> Shear Capacity = 0.000 N/mm^2Vu Stress - Vu Capacity = v - vc = vd = 0.000 - 0.000 = 0.000 N/mm^2vd < 0.40 N/mm^2 --> Design for vd = 0.40 N/mm^2Steel area provided by Link size 6, Asv = 2*pie*dia*dia/4 = 2*3.1416*6*6/4 = 56.5 mm^2Link spacing required, Sv = 0.87*460*56.5/(250*0.400)= 226Vu Capacity provided by Link = 0.87*460*56.5/(226*250) = 0.400 N/mm^2Asv/Sv = 56.5/226= 0.250----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------SUMMARY OF TOTAL LOADING WITHOUT LOAD ALLOWANCE OF 10 PERCENT:=================================================================================================Total number of Columnn Section for Analysis = 4Total number of Columnn Section being Analysed = 4Total Column Selfweight = 18 kNTotal Dead Load in key plan = 358 kNTotal Dead Load in the floor = 376 kNTotal Live Load in the floor = 217 kNTotal Dead Load in the floor & floors above = 376 kNTotal Live Load in the floor & floors above = 217 kN Tabulation of RC Columns designRest in Peace. Thanks to all Malim (mountain guides of Mount Kinabalu) for the prompt rescue