ANALYSIS OF A HIGH RISE BUILDING

INTRODUCTIONThis assignment analyze behavior of a high-rise building for lateral loads, which is proposed in Colombo city limits. It is a reinforced concrete structure with a proposed deep foundation system. It is a 29-storey office building which includes two differently arranged floors at the bottom, which will be functioning as business complex. Building has a ground coverage of 50m x 38m and has height of 105.6m above ground level. Building consist of wall frame structure with moment resistant frame and shear walls. Shear walls are arranged around the service core and four corners of building to avoid lower torsional mode of frequency by having shear walls only at center. Main structural members are having dimensions as follows

Table1. Selected members dimensions

Beam650 mm x 450 mm

Column (above transfer plate)750 mm x 750 mm

Column (Below transfer plate)1500 mm x 1500 mm

Slab150 mm thickness

Shear wall250 mm thickness

Transfer plate1000 mm thickness

Fig.1.1 - Arrangement of Typical floors

LOADSThe loads are applied to beams directly as uniformly distributed loads by using table 3.16:BS8110:Part1:1985. Loads are considered as follows.

Table2. Loading of Building

Live load of office space2.5 kN/m2

Dead load of Slab3.6 kN/m2

Finishes and Partition 0.75 kN/m2

External Wall10 kN/m

Shear coefficient for slabs are calculated and by using the following equations, the loads are calculated and applied only on 75% of the mid span as mentioned in BS 8110: part1: 1985.

Vsx End shear on strips of unit width and span lx due to unit surface pressure on panel Vsy End shear on strips of unit width and span ly due to unit surface pressure on panel lx Shorter span of the slab panel3D model of the building is done with SAP2000 and the calculated unit loads are applied to building and factored with appropriate values in defining of the load cases. Modal is analyzed and end support loads are calculated to separately for dead and live loads, which is used to seismic load calculations later.

Fig.2.1 - Unit load distribution along the beams

DYNAMIC PARAMETERS Dynamic parameters such as frequency and oscillation time to each mode are derived from SAP2000 modal analysis. In modal analysis, 12 different modes are considered. Mass values are assigned by using predefined dead in SAP2000 and dead load of slab from the defined load cases.

Table 3. Modal Periods And Frequencies

Output CaseStep TypeStep NumberPeriodSecFrequencyCyc/secCircular Frequencyrad/secEigenvaluerad2/sec2

MODALMode1.0000003.0607443.2672E-012.0528E+004.2141E+00

MODALMode2.0000002.7411013.6482E-012.2922E+005.2542E+00

MODALMode3.0000002.7097593.6904E-012.3187E+005.3765E+00

MODALMode4.0000000.9414411.0622E+006.6740E+004.4542E+01

MODALMode5.0000000.8445791.1840E+007.4394E+005.5345E+01

MODALMode6.0000000.8100891.2344E+007.7562E+006.0158E+01

MODALMode7.0000000.5070491.9722E+001.2392E+011.5355E+02

MODALMode8.0000000.4623602.1628E+001.3589E+011.8467E+02

MODALMode9.0000000.4266652.3438E+001.4726E+012.1686E+02

MODALMode10.0000000.3414102.9290E+001.8404E+013.3869E+02

MODALMode11.0000000.3108903.2166E+002.0210E+014.0846E+02

MODALMode12.0000000.3040643.2888E+002.0664E+014.2700E+02

WIND LOADWind load calculations are done according to AS1170.2:1989, which is gust factor method.ReferenceDescriptionRemarks

Clause 4.2.2

Table 4.2.5.1Table 4.2.7Table 4.2.8Table 4.2.9

Clause 4.3

Clause 4.4.2

Table 4.4.2.1

Equation 4.4.2(4)

Table 4.4.2.2This sample calculation is done for ULS condition

V The basic wind speed (38m/s)M(z,cat) Terrain/ height multiplier (change with height z)Ms Shielding multiplier (Considered as no shielding buildings)Mt topography multiplier (1)Mi Structure importance factor is considered as 1 for normal structureThe free stream hourly mean dynamic wind pressure in kilopascals at height z is calculated by the following equation

Hourly mean net horizontal force acting on an area is calculated as follows

Cpe is external wall pressure coefficient, which is 0.8 for windward wall and 0.5 for leeward wallThe design peak wind force is calculated by multiplying mean net horizontal force by gust factor. Gust factor is calculated as follows.

where r is calculated as z = h by using the following equation,

Peak factor for the upwind velocity fluctuation gv is considered as 3.7. Effective turbulence length scale Lh is calculated by

Background factor B,

Then second order effects of turbulence intensity w is calculated as follows

A peak factor (gf), the ratio of the expected peak value, which occurs once per hour to the standard deviation of the resonant part of the fluctuating response is calculated,

Size factor S,

Effective reduced frequency (N) is calculated as follows,

Spectrum of turbulence in the approaching wind stream (E),

And finally gust factor G = 2.34The structural damping ratio ( )is considered as 0.05 for ultimate limit state and 0.01 for serviceability limit state 0.01.Table 4.2 shows the calculated wind pressure and force in both ULS and SLS conditions. Calculated load is applied through center of mass/center of rigidity of building is SAP 2000 model and appropriate deflection is derived.

Along wind acceleration () is calculated as follows,

Cross wind acceleration is calculated as follows,

G = 2.34

0.08 m/s2

0.04 m/s2

Table 4.1. Wind induced accelerations

ULS condition (m/s2)SLS condition (m/s2)

Along wind AccelerationDeflection (mm)Cross wind AccelerationAlong wind AccelerationDeflection (mm)Cross wind Acceleration

X direction0.0848 0.040.12410.05

Y direction0.075430.050.09370.058

Fig.4.1 Deformed shape of a typical frme for wind Fig.4.2. Bending moment for wind load

18

Table4.2 wind loads

H (m)ULS conditionSLS condition

Vz (m/s)qz (kPa)x - directionY - directionVz (m/s)qz (kPa)x - directionY - direction

Winward(kPa) Leeward (kPa)Force (kN)Winward (kPa) Leeward (kPa)Force (kN)Winward(kPa) Leeward (kPa)Force (kN)Winward(kPa) Leeward (kPa)Force (kN)

020.000.240.45-0.281000.44-0.2813017.000.170.33-0.21730.32-0.2095

4.220.000.240.45-0.281000.44-0.2813017.000.170.33-0.21730.32-0.2095

8.420.000.240.45-0.281000.44-0.2813017.000.170.33-0.21730.32-0.2095

1220.000.240.45-0.281000.44-0.2813017.480.180.35-0.22770.34-0.21100

15.620.000.240.45-0.281000.44-0.2813018.770.210.40-0.25890.39-0.25115

19.220.000.240.45-0.281000.44-0.2813019.570.230.44-0.27970.43-0.27125

22.820.290.250.46-0.291030.46-0.2913420.290.250.47-0.291040.46-0.29135

26.420.980.260.49-0.311100.49-0.3114320.980.260.50-0.311110.49-0.31144

3021.660.280.53-0.331170.52-0.3315221.660.280.53-0.331190.53-0.33154

33.622.080.290.55-0.341220.54-0.3415822.080.290.55-0.351230.55-0.34160

37.222.500.300.57-0.361260.56-0.3516422.500.300.58-0.361280.57-0.35166

40.822.880.310.59-0.371310.58-0.3617022.880.310.60-0.371320.59-0.37171

44.423.290.330.61-0.381360.60-0.3817623.290.330.62-0.391370.61-0.38178

4823.710.340.63-0.391400.62-0.3918223.710.340.64-0.401420.63-0.39184

51.624.050.350.65-0.411450.64-0.4018824.050.350.66-0.411460.65-0.40189

55.224.320.350.66-0.421480.66-0.4119224.320.350.67-0.421500.66-0.41194

58.824.620.360.68-0.431510.67-0.4219724.620.360.69-0.431530.68-0.42199

62.424.890.370.70-0.441550.69-0.4320124.890.370.71-0.441570.69-0.43203

69.625.420.390.73-0.451610.72-0.4521025.420.390.74-0.461640.72-0.45212

73.225.690.400.74-0.461650.73-0.4621425.690.400.75-0.471670.74-0.46216

76.825.950.400.76-0.471680.75-0.4721925.950.400.77-0.481700.75-0.47221

80.426.180.410.77-0.481710.76-0.4822226.180.410.78-0.491730.77-0.48224

8426.370.420.78-0.491740.77-0.4822626.370.420.79-0.491760.78-0.49228

87.626.600.420.80-0.501770.79-0.4923026.600.420.81-0.501790.79-0.50232

91.226.980.440.82-0.511820.81-0.5023626.980.440.83-0.521840.81-0.51238

94.827.060.440.82-0.511830.81-0.5123827.060.440.83-0.521850.82-0.51240

98.427.250.450.83-0.521850.82-0.5124127.250.450.84-0.531880.83-0.52243

10227.440.450.85-0.531880.84-0.5224427.440.450.86-0.541900.84-0.53246

105.627.610.460.86-0.541900.85-0.5324827.610.460.87-0.541930.85-0.53250

FOUNDATIONThe borehole test reveals that, bedrock is at 25m below from ground level and top soil layer has lower SPT (Standard Penetration Test) value. However, reactions at supports of foundations are in the range of 25000 kN. Soil capacity is not adequate to design a shallow foundation and therefore, it is decided to model a deep foundation system, which is pile foundation system. Due to the expected noise and disturbances, bored insitu cast piles are selected. Pile will be socketed in bedrock at 25m depth with appropriate amount of socketing. a. Pile Selected diameter of pile () = 1200 mm Assumed typical pile group has four piles in eachLoad on a pile (Pn)

Assumed there are no eccentricities,(Pn) = 25000/4 = 6250 kN End bearing capacity of bedrock at 25m depth is assumed as 5 N/mm2

Skin friction due to soil layers = 0.65 x SPT valueAssumed SPT values are shown belowTable 5.1 Assumed SPT values

DepthSPTSkin Friction (kN/m2)

0m 5m42.6

5m - 10m106.5

10m 15m127.8

15m 20m1811.7

20m 25m4026

= 1000 kN Skin friction due to socketingSkin friction of weathered and moderately weathered rock = 200 kN/m2 (ICTAD specification for)Depth of socketing is 2m,Therefore skin friction due to socketing = x 1.2 x 200 x 3 = 2260 kN Since, no filled material or clay layer are expected in soil profile, negative skin friction is neglected. Total allowable bearing capacity

Allowable bearing capacity = 6750 kN (FOS = 3) Load on single pile (6250 kN) < Allowable bearing capacity (6750 kN) Pile diameters and allowable bearing capacity 1200 mm 6750 kN1500 mm 10180 kN1800 mm 14340 kNb. Pile CapPile spacing = 2.5 = 3mDepth of pile cap = L/2 + 0.5m = 2mPile cap dimensions are shown below

Fig Sectional View of Pile capFig Plan view of pile cap

c. SAP2000 Modelling of Pile and Pile CapPile and pile caps are modelled in SAP 2000. Piles are modelled with frame element with appropriate diameter. The effect of soil in lateral direction of pile is simulated by using of spring elements in every 1m depth. Support condition of pile is considered as pinned. 1200mm and 1500mm piles are used to support columns and 1200 mm piles are used to support shear walls.Spring constant = 40 x FOS x Bearing capacity = 40 x 3 x 100 = 1200 kN/m

Fig. Axial load of column supporting piles, which is in the range of 6000 kN 10000kNFig. Axial load of Shear wall supporting piles which is in the range to 3000 kN 5000 kN

Pile cap is modelled with thick shell element to allow transverse directional shear deformation. The shell elements are meshed adequately and piles and columns are connected with nodes of those elements to ensure the connectivity.

Fig Bending moment of column pile capFig. Bending moment of shear wall pile cap

SEISMIC LOADEarthquake load calculations are done with UBC (Uniform Building Code) method.ReferenceDescriptionRemarks

The static base shear sample calculation is done for x direction: Total base shear is calculated by the following equation

Z seismic probability zone factor for SriLanka is taken as 0.125I occupancy importance factor is considered as 1.25 due to higher expected level of gathering of peopleK building type factor is selected as 0.8, because building is designed as wall frame structure with moment resistant joints and shear wallsC Seismic coefficient is calculated by using following equation

T = 3.06s for x directionC = 0.038 < 0.12S soil structure interaction factor is considered as 1.0. Because bedrock is at 25m at above a stiff soilCS = 0.038 < 0.14W is total dead load and 40% of live loadW = 1090000 kNV= 5178 kN (x-direction)Since fundamental period of vibration is > 0.7 s, a part of base shear (Ft) is applied as a concentrated load at top of building.

0.07TV = 1109.1 kN0.25V = 1294.5 kNFt = 1109.1 kN (x-direction)V- Ft = 4068.9 kN

Table 6.1 Base shear and Top shear

x- direction (kN)Y direction (kN)

V51785450

Ft1109.11045.3

V-Ft4058.94404.7

V-Ft distributed over the height of the building

Distribution of V-Ft is shown below

Table 6.2 Distribution of Base shear

HiWiHiWiX direction (kN)Y direction (kN)

4.238680157862.110.6811.56

8.438680315724.121.3623.12

1242500.2451034.530.5133.03

15.637586.21586344.839.6742.94

19.237586.21721655.248.8252.85

22.837586.21856965.557.9762.76

26.437586.21992275.967.1372.67

3037586.21112758676.2882.58

33.637586.21126289785.4492.49

37.237586.21139820794.59102.40

40.837586.211533517103.74112.31

44.437586.211668828112.90122.22

4837586.211804138122.05132.12

51.637586.211939448131.21142.03

55.237586.212074759140.36151.94

58.837586.212210069149.51161.85

62.437586.212345379158.67171.76

6637586.212480690167.82181.67

69.637586.212616000176.98191.58

73.237586.212751310186.13201.49

76.837586.212886621195.28211.40

80.437586.213021931204.44221.31

8437586.213157241213.59231.22

87.637586.213292552222.74241.13

91.237586.213427862231.90251.04

94.837586.213563172241.05260.95

98.437586.213698483250.21270.86

10237586.213833793259.36280.76

105.637586.213969103268.51290.67

V= 5178 kN

TRANSFER PLATETransfer plate is located at the level two to change the column arrangement at level one. Transfer plates are modeled with thick shell element to account transverse direction shear deformation. Shell element is meshed enough to distribute load and columns are connected to the nodes. Obtained maximum bending moment at the point where top part of intermittent column punch the plate, which is around 7000 kNm.

Fig.7.1 Bending moment of transfer plate for ULS condtion

Fig.7.2 Deformed shape of transfer plate for ULS conditon

EARTHQUAKE DETAILINGColumns Since, moment resistance joints are used to resist lateral loads, the columns sizes are taken larger than 300 mm. The ratio of minimum to maximum column thickness of column is greater than 0.4 (1). The minimum diameter of column reinforcement should be greater than 12mm and minimum longitudinal reinforcement should be 1.0% of the cross sectional area. The confinement, restraint of longitudinal bars to prevent buckling and enhance shear resistance at the ends of columns are gained by provision of closed ties at end of the clear height of a column.

Fig 8.1 Column Detailing

Beams Beams of moment resistance frames should not have width to depth ratio lesser than 0.3 (provided 0.69) and minimum width should be greater than 250 mm (provided 450mm). The beams are not wider than that of columns. Minimum diameter of longitudinal steel is 12mm. There are no bent bars. To account reversals of bending moment, the top and bottom face of beam should be continuously reinforced with some amount of bars. The area of reinforcement provided in a span shall be, the positive moment strength at a support face is not less than one third of negative moment strength provided at support and neither negative nor positive moment strength at any section along the member is less than 20 % of maximum reinforcement provided at the face of either support.

Fig.8.2 Beam Detailing

Beam Column JunctionIn order to prevent the degradation of strength of beam column junction when subjected to cyclic loading, adequate confinement should be provided within the depth of junction. The transverse reinforcement may be half of that required in column and adequate links within the depth of the joint should be provided.Location of lapsLaps in reinforcement in frames must continue to function while the member or joint undergo larger deformation. Laps should be avoided in regions where high stress such as beam, column connections. Provision of Anchorage Sufficient anchorage can be achieved by straight length, 90 bends or 180 hooks. The links should have additional anchorage. When tensile reinforcement is anchored in regions of high tension, additional links should be provided to enhance confinement to concrete. When bends are used, it is necessary to limit bearing stress inside the bend to 1.5fcu / (1+2/ab).Foundation Detailing Columns are subjected to heavy earthquake forces thus requiring a high curvature ductility at foundation level. It is better to avoid laps provided with starter bars at foundation level. Therefore, using full bar lengths as starter bars for foundation will be a solution. Piles and caps should be tied together to ensure integral action in a lateral load situation. Sufficient reinforcement should be provided in non-tension piles to prevent separation of pile and cap due to ground movement. The tie beams should be properly detailed to resist both axial tension and compression. Detailing of WallsThe minimum diameter of vertical and horizontal steel should be 10 mm. The detailing of openings should be considered carefully. Minimum steel content would be 0.2% each faces in most cases. Opening detailing can be done as shown in fig.8.3.Detailing of SlabsSlab should behave as flexural member and diaphragm member to transfer lateral loads. The minimum bar diameter is 10mm. The minimum content of tension reinforcement in each direction should be 0.15% for high tensile steel. The minimum content of secondary reinforcement should be 0.15%. Cantilever part should be provided with bottom steel to account counter bending tension, which could occur in seismic event.

Fig.8.3 Slab Detailing