ASSIGNMENT ON BEAM COUPLED STRUCTURAL WALLS

1. NINTRODUCTION

CHANNEL SECTIONS COUPLING BEAMSAPPLIED LATERAL LOADThe structural lay-out given above is that of a typical 20 storey building with a typical storey height of 3.8m. The channel sections forming the central core shall be connected monolithically by coupling beams at the floor height as shoen above. These coupling beams are expected to posses a depth far greater than their width. This very stiff flexural member provides a restrain to the walls causing them to deflect in a uniform manner rather than undergoing an individual free form of deflection. It is therefore expected that the bending stresses induced in the connected channel sections will be greatly reduced. 1.1ANALYSIS BY CONTINUUM MEDIUM TECHNIQUEThe continuum method of analysis shall be employed to carry out an approximate analysis of the above coupled channel sections in order to determine the depth of the coupling beam which would restrict the top drift to . In order to carry out this analysis, some assumptions are necessary:I. The properties of the channel sections and coupling beams remain constain throught the entire structural height.II. Coupling beams are considered to posses high degree of axial stiffness thereby cannot transmit in-plane forces. III. Point of zero moment in coupling beams lies at the mid span of the beamIV. Coupling beams shall be replaced by an equivalent connecting medium of flexural rigidity per unit height. V. Channel sections shall be replaced by their equivalent flexural cantilevers with moment of inertia and about the axis of bending in the loading direction. From the structural plan given above

1.1.1. DETERMINATION OF SECOND MOMENT OF AREA, AND AXIS OF BENDINGWith loading from the East-west direction on the structure, it is anticipated that the channel sections will undergo bending about their vertical axis. This is actually the weak axis of the section and as such the section will provide less stiffness to lateral load in the E-W direction than if the load orientation was in the N-S direction. From mechanics point of view the location of the vertical axis of bending from the left end of the C-section is given by : where A represents the area of each section that makes up the C-section and x represent the distance of their CG from the extreme left fiber. Using the above, the centroidal distance distance is obtained as 0.82m from the left extreme fibre end of each C-section. Therefore the distance between the centre of gravity of both C-section l is 8.36m. Also, by use of the parallel axis theorem, the moment of inertia of each C-section was obtained to be 5.29 i.e = 5.29; I = + = 10.58Due to symmetry the area of each C-section is the same. Which is = 5.01 and A = 10.02

1.1.2. DETERMINATION OF EFFECTIVENESS OF COUPLING BETWEEN CHANNEL SECTIONS AND COUPLING BEAMIn order to achieve a top drift of m, the parameter H shall be evaluated in the equation below: (1.0) Where . (1.1)Substituting the area, distance between centriodal axis of both walls and cumulative area into (1.1) the parameter is obtained as 0.943.With = 0.152m, a trial and error method approach was employed and an H value of 4.88 kept the top drift within the permissibly limit. With H = 76m; = 0.0642.

1.1.3. DETERMINATION OF DEPTH OF COUPLING BEAMIn order to determine the depth of the coupling beam required to limit the top drift to 0.152m, the equation relating the structural parameters and shall be employed as shown below: .. (1.2) & = (1.3)Where; h is the storey height is the second moment of area of the coupling beam.All other notations maintain their meanings as given in section 1.1.1 Using equation (1.2) is = Substituting the above value into (1.3) the required moment of inertia of the both beams is obtained connecting the C-sections together is obtained as: = = 5.03 The moment of inertia one connecting beam at the top floor is: 2.514 = ; d = 465mm. A depth of 480mm is adopted. 1.1.4. DETERMINATION OF TOP DRIFTHaving obtained the required depth of coupling, the top deflection shall be checked to make sure this is limited to 0.152m.Revised value of = = 5.53 Revised value of = 5.11 Revised value of = = 0.0673Revised value of H= 5.1148Comparing the value of the original H to the revised H, the increase in value was as a result of the deepening of the beam from an ideal value of 465mm to 480mm. Therefore the measure of the coupling effectiveness is expected to increase. Checking with (1.0) to make sure top deflection is still satisfied: 0.144m. Therefore to keep the top drift below the permissible limit of 0.152m, coupling beams of 300mm by 4800mm shall be provided at the top floor. Since the flexural rigidity of the coupling beams were represented in (1.3) in terms of storey height, the moment of inertia of beams to be provided at other floor levels shall be twice that at the top floor. = 5.53 for a single coupling beam at other levels Depth of beams required at other levels is therefore: 605mmTherefore coupling beams of 300mm by 6500mm shall be provided at other floor levels.

1.1.5. DETERMINATION OF AXIAL FORCES IN WALLSThe value of the axial force acting at the centroid of the Channel sections that form a couple and aid in resisting externally applied moment is given by the equation below: T = (1.4)Where x represents the variation of height along the structure; it should be noted that x varies from zero at the top of the structure to H at the bottom. All other notations maintain there already defined meaning. Using (1.4) the axial forces developed in the C-sections along the structural height are presented in the table below: STOREYAXIAL FORCE (KN)

200

19398.604

18819.2974

171279.139

161790.69

152362.844

143001.404

133709.474

124487.655

115334.089

106244.335

97211.077

88223.644

79267.307

610322.31

511362.58

412353.98

313252.13

213999.4

114521.21

BASE14721.04

Figure 1: AXIAL FORCE IN CHANNEL SECTION

1.1.6. DETERMINATION OF SHEAR OF COUPLING BEAMSThe shear force of the coupling beam shall be determined from the equation .. (1.5) where q is the laminar shear and h represents the storey height. q = .. (1.6)Using equation (1.6) above, the shear induced in the coupling beam along the structural height is presented in the table below:STOREYSHEAR (KN)

20394.5737

19406.3715

18437.8215

17483.9213

16540.6316

15604.6109

14672.9958

13743.2126

12812.8079

11879.2877

10939.9528

9991.722

81030.929

71053.081

61052.564

51022.273

4953.1456

3833.5655

2648.5982

1379.0093

1.1.7. DETERMINATION OF WALL MOMENTThe moment acting along the height of the C-sections that participate in resisting the external laterally induced moment are given by the equations: ..(1.7) .(1.8)Where and represent the moment along the structural height of the structure in the two C-sections that form the core. All other notations in (1.7) and (1.8) maintain their already defined meanings. Due to symmetry of the structure, the moment induced in both channel sections along the structural height shall be the same. Therefore moment in only one channel section was evaluated and is presented in the table below:

STOREYMOMENT (KNm)

200

19-1427.9

18-2471.62

17-3202.46

16-3672.93

15-3920.19

14-3968.51

13-3830.86

12-3509.76

11-2997.43

10-2275.32

9-1312.84

8-65.3927

71528.596

63551.698

56112.927

49354.906

313463.24

218678.74

125313.21

033770.04

Figure 2: MOMENT IN CHANNEL SECTIONS1.2. ANALYSIS BY DISCRETE METHOD (USING ETABS)The finite element analysis computer program ETABS was utilized to perform a computer analysis on the beam couple structural walls to obtain a more accurate structural behavior of the structure. 1.2.1. MODEL OF BEAM COUPLED CHANNEL WALL SECTIONSThe beam coupled shear wall structure was modeled in Etabs as a 3-dimensional model. Rigid diaphragms were used to connect both channel sections with the available rigid diaphragm function in Etabs. Below is a picture showing a plan view of coupled channel wall sections and coupling beams

1.2.2. APPLICATION OF LOADSSpecified lateral loads of 258.4KN were applied at all floor levels and 125.4KN at the roof slab in the direction of the weak axis in a 3-dimensional manner in real time. Unlike the continuum analogue where a uniformly distributed line load had to be determined and then applied to the 2-dimensional continuum model from base to top.

1.2.3. DETERMINATION OF LATERAL DEFLECTIONS The lateral deflections obtained by analysis of the beam coupled channel wall system are presented in the table below: STOREYLATERAL DEFLECTIONS (mm)

20150.8

19144.9

18138.7

17132.2

16125.3

15118.1

14110.4

13102.3

1293.7

1184.8

1075.6

966.2

856.6

746.9

637.5

528.4

419.9

312.4

26.2

11.9

00

1.2.4. MOMENTS IN COUPLED CHANNEL SECTIONS STOREYMOMENT (KNm)

200

19-1247.32

18-2176.6

17-2769.81

16-3090.96

15-3175.35

14-3048.48

13-2724.62

12-2208.2

11-1493.94

10-566.595

9599.9772

82044.311

73819.598

65996.793

58668.755

411955.67

316012.09

221035.84

127280.11

BASE 35068.59

1.2.5. AXIAL FORCE IN COUPLED CHANNEL SECTIONS

STOREYAXIAL FORCE (KN)

200

19355.5721

18749.0769

171176.198

161652.256

152185.702

142782.637

133446.477

124178.283

114976.791

105838.351

96756.707

87722.637

78723.407

69742.036

510756.3

411737.43

312648.43

213441.95

114057.41

BASE14417.3

1.2.6. SHEAR IN COUPLING BEAMS