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2012 / 2013

FINAL YEAR PROJECT Submitted in fulfillment of the requirements for the

ENGINEERING DEGREE FROM THE LEBANESE UNIVERSITY FACULTY OF ENGINEERING- BRANCH III

Major : Civil Engineering

By:

Mortada Chamas ________________________________________________

Structural Design of Sky Tower Supervised by: Dr. JAMIL DAMAJ

Defended on Monday 23 septembre 2013 the jury:

Dr. JAMIL DAMAJ Dr. Hasan AL Haj Dr. Nayef Atrisi

President Member Member

SKY TOWERS PROJECT KHALDEH- LEBANON

STRUCTURAL REPORT Design criteria-Structural Analysis-R.C Design

1.

Definition of the Intervention

The aim of the present report is to conduct the structural study of the project parts and to assess the adequacy of the preliminary structural resisting systems for gravitational and lateral loads, as specified by the design criteria and according to the specifications. The assessment to the structural systems adequacy will be done considering the following factors: - The latest architectural drawings - The specified super imposed dead loads and live loads. - The structural response of the buildings to the lateral loads

In this Phase of study the basic design criteria (codes, loadings, materials…) and the analysis methods are presented. The basic assumptions of the numerical analysis are also stated. Based on the design criteria and assumptions data, a rigorous structural analysis is conducted with three dimensional models of the buildings using the ETABS software. The buildings response, obtained from the analysis results, led to the determination of: - the maximum lateral sway of buildings which allows the adjustment of the expansion joint gap. - the internal forces in the different structural elements, which allowed the checking / design of the vertical structural elements (columns, walls) - the transfer of data to other software (Safe, S-concrete…) which allowed the checking of the proposed foundations and slabs dimensions .

2. Preface

B

eing a civil engineer graduate, we are going to introduce the structural skills acquired through our learning process in the faculty of engineering-Lebanese University. Our project is one of the engineering articles concerning structural

detailing of a building. So we chose the SKY TOWER on KHALDEH-LEBANON to be our case of study. Designers obviously need the full data related to the building in order to be able to start his study, and he should determine the means that may help him creating his model. Architectural Details: the SKY TOWER in Lebanon is located in khaldeh, Beirut, on a rock type soil. The project consists of ten residential buildings of various heights and floor areas, summer club, and winter club. The current block A consists of two Basement floors, one Ground floor, 11 residential floors.

The project consists of ten residential buildings of various heights and floor areas, summer club, and winter club. The current block A (my project) consists of two Basement floors, one Ground floor, 11 residential floors.

BASEMENT PLAN

USUAL FLOOR PLAN

GF

3. Major Constraints The structural analysis and concrete design of the project was governed by the following constraints: - the architectural requirements of the buildings which induced irregularities in the buildings shapes and the distribution of the supporting elements. - the relatively large spacing between supports.

4. Design Criteria 4.1 Codes of Practice , standards The buildings straining forces (gravitational and lateral) and the capacity of the structural resisting elements were determined in accordance to the following code of practice: - the Uniform Building Code “UBC 97” for the determination of lateral forces intensity and distribution (Earthquake and Wind pressure). - “ACI 318-02” for the determination of loads combinations, the design and detailing of various concrete elements (slabs, beams, columns, walls and foundations). - “ASCE-05” code: for wind loads and analysis

4.2 software : In addition, the design is going to be done with the aid of the following software programs: - Autodesk AutoCAD Draw and plan and detail any needed figure, with 2D and 3D features.

- CSI- Etabs ETABS is a sophisticated special purpose analysis and design program developed specifically for building systems. It is mainly used for modeling, and mainly the design of vertical elements.

- CSI- Safe Design of slabs, beams and foundations, reinforced and post tensioned concrete.

- S-CONCRETE S-concrete is a stand-alone product that investigates, designs, and graphically details reinforced concrete beam, column, and wall sections.

- BEAMD Design and draw any given beam. Get the loads and gives the resulting forces and moments, and checks code capability with the results. - TALREN Design and draw the supporting system of any excavation, including piles, anchorages. And gives detailed report of the results. Used especially for sliding circles.

5. Design Assumptions In order to be able to start our design, we must start from a definite point, where we determine the main materials that is going to be used. Also we should recognize the structural elements presented in the building, and give a predimension for each element to be checked then. Finally we have to load each member by the code’s recommended load related to its type.

5.1 Materials: Two main materials are to be used in the construction phase of the building: Concrete and Steel. In our project we will use concrete with f’c= 20MPa, and another type of f’c= 32MPa. And steel with tensile yield fy=420MPa for longitudinal reinforcement, and fy= 280 MPa for transversal reinforcement.

5.2 Structural elements and Predimnesioning As any alternative structure, our structure contains the following structural elements: slabs, columns, walls, beams, and footings. a) Slab: slabs assumptions are concerned about its type and thickness. Clearly the designer prefers less thickness that offers him less cost. These assumptions depend mainly on the spans found through the slab, and the type of support used. Due to long spans found between supports (columns), we decided to use a two way solid slab (flat plate). We will use a two way solid slab with 25cm thickness (refer to slab design section). As analysis results are derived, we are going to check the deflection and reinforcement. b) Columns: column sections will be taken as given by the architectural engineer. These sections will be checked to support its loads and will be reinforced by 1% steel of its gross section as a minimum reinforcement. If we have a slender column in the project then we are going to consider the PDelta effect, these checks will be done in the column design paragraph. c) Shear Walls: these sections are primarily determined by the architectural engineer. Walls sections and position will be checked against loads and mainly shear and torsion. d) Beams: beams are presented in the huge span found in the theatre, there sections will be detailed the frame design paragraph.

e) Footings: Thickness and dimensions are related to loads and bearing capacity of supporting soil. Thus whole design is found in footing design paragraph.

5.3 Dead Loads The dead loads of the buildings are: - self weight of the structural elements based on preliminary dimensioning of the structural sections and the materials specific unit weight - super imposed dead loads including finishing and partition: as indicated in the drawings Dead load is computed mainly for slabs: D.L. =

= 25 x 0.25 = 6.25 kPa

S.D.L. = 1.5 kPa for basement floors. = 4.0 kPa for GF and upper floors.

5.4 Live Loads Table 1.2 ACI-08: Type of use Apartment buildings Private units Public rooms Corridors Office buildings Offices Lobbies Corridors above first floor Garages (cars only) Stores First floor Upper floor Ware house Light storage Heavy storage

Minimum uniformly distributed life loads Lb/ft2 kPa=KN/m2 40 100 80

1.92 4.8 3.84

50 100 80 50

2.4 4.8 3.84 2.4

100 75

4.8 3.6

125 250

6.0 12.0

As our project is an residential building, in addition to car garages in the basement floors, we can assume live loads as follows:

Basement floors: L.L. = 2.5 kPa. Ground floor: L.L. =4.8 kPa. Upper floors: L.L. = 2.5 kPa.

5.5 Seismic load The UBC 97 recommends that the static lateral force procedure of Section 1630 may be used for the following structures: 1. All structures, regular or irregular, in Seismic Zone 1 and in Occupancy Categories 4 and 5 in Seismic Zone 2. 2. Regular structures under 240 feet (73 152 mm) in height with lateral force resistance provided by systems listed in Table 16-N, except where Section 1629.8.4, Item 4, applies. 3. Irregular structures not more than five stories or 65 feet (19 812 mm) in height. 4. Structures having a flexible upper portion supported on a rigid lower portion where both portions of the structure considered separately can be classified as being regular, the average story stiffness of the lower portion is at least 10 times the average story stiffness of the upper portion and the period of the entire structure is not greater than 1.1 times the period of the upper portion considered as a separate structure fixed at the base. [1--- 1629.8.3] The “sky tower is in zone 1 so the static analysis is required. Seismic load parameters are related to the zone of study, which is Beirut in our case. Beirut is said to be of zone 2B, referring to UBC97-TABLE 16-1, we find Seismic Zone Factor (Z) = 0.25 Soil investigations proved that the site is of dense sand type. Soil Profile Type = SC

Referring to UBC97-TABLE 16-J, TABLE 16-Q, TABLE 16-R, we find

Seismic Coefficient Seismic Coefficient

Referring to TABLE 16-N

Ca = 0.24 Cv = 0.32

UBC97

Over-strengthFactor, R = 4.5 (BWS)

Referring to UBC97-TABLE 16-K

Importance Factor = 1.5 Eccentricity Ratio = 0.05 Time Period, Ct (ft) = 0.02 for BWS Four load cases will be formed QX1 and QX2 with X direction and opposite y-eccentricity, and QY1 and QY2 with Y direction and opposite x-eccentricity. Also two dynamic loads are defined SPEC1 and SPEC2.

I - Combinations:

Combinations used in our analysis are in accordance with UBC97-1612.2 for strength design, and UBC97-1612.3 for working stress design. Each load case will be placed at its appropriate position so we will have about

50 combos. II- Modifiers: 1- Slabs:

Membrane f11 modifier factor Membrane f22 modifier factor Membrane f12 modifier factor Bending moment M11 modifier factor Bending moment M22 modifier factor Bending moment M12 modifier factor Shear V1-3 modifier factor Shear V2-3 modifier factor Mass modifier factor Weight modifier factor

1 1 1 0.25 0.25 0.25 1 1 1 1

2- Shear Walls:

Membrane f11 modifier factor Membrane f22 modifier factor Membrane f12 modifier factor Bending moment M11 modifier factor Bending moment M22 modifier factor Bending moment M12 modifier factor Shear V1-3 modifier factor Shear V2-3 modifier factor Mass modifier factor Weight modifier factor

1 1 1 0.70 0.70 0.70 1 1 1 1

3- Columns:

Cross section (Axial Area) modifier factor Shear area in 2 direction

1 1

Shear area in 3 direction Torsional constant Moment of inertia about 2 axis Moment of inertia about 3 axis Mass modifier factor Weight modifier factor

1 1 0.70 0.70 1 1

4- Beams:

Cross section (Axial Area) modifier factor Shear area in 2 direction Shear area in 3 direction Torsional constant Moment of inertia about 2 axis Moment of inertia about 3 axis Mass modifier factor Weight modifier factor

1 1 1 1 0.35 0.35 1 1

III- Base Shear Calculation

Base shear (V) is the total lateral force or the shear at the base for which a building in a seismic zone is to be designed. The total design base shear in a given direction shall be determined from the following formula: V = Cv .I . The total design base shear need not exceed the following: Vmax = 2.5 Ca .I .W/R The total design base shear shall not be less than the following: Vmin = 0.11 Ca .I .W

Numerical Calculation under the effect of EQX1 for instance: V (Eqn 1) = 0.0215W V (Eqn 2) = 0.0302W V (Eqn 3) = 0.0060W V (Eqn 4) = 0.0097W V Used = 0.0474W = 1652.88

Then consider V = 0.0278W = 0.0278 x 177107.38 = 4923.6 T = 1652.88 (under EQx1) .

IV- Finding Period of the Building Structure The Value of the structure period T shall be determined from one of the following methods: Method A:

The value T may be approximated from the following formula: TA = Ct (hn)3/4 = 0.0488 x (65.7)3/4 = 2.16s. Where: Ct = 0.0488 for all other buildings except the steel moment-resisting frames and the reinforced concrete moment resisting-frames and eccentrically braced frames. H n: height in (m) above the base to the top level Method B: The fundamental period T may be calculated using the structural properties and deformational characteristics of the resisting elements in a properly substantiated analysis. The analysis shall be in accordance with the requirements of Section 1630.1.2. The value of T from Method B shall not exceed a value 40 percent greater than the value of T obtained from Method A in zone 1. (max TB adopted ≤1.4TA =2.04s).

The fundamental period T may be computed by using the following formula:

The values of fi represent any lateral force distributed. The elastic deflections, δi, shall be calculated using the applied lateral forces, fi. Note: TB is calculated through the software: ETABS V - Finding the Distribution of Lateral Forces

In Accordance with section 1630.5 in UBC97, the total force shall be distributed over the height of the structure according to the general formula:

The concentrated force Ft at the top, which is in addition to Fn , shall be determined from the formula: Ft = 0.07 T.V = 4952 KN < 0.25V = 13061.6 KN. The remaining portion of the base shear shall be distributed over the height of the structure according to the following formula:

MODAL LOAD PARTICIPATION RATIOS (STATIC AND DYNAMIC RATIOS ARE IN PERCENT)

TYPE

NAME

STATIC

Load

DEAD

Load

SIDL

0.0374

0.0000

Load

LIVE

0.0146

0.0000

Load

EQX

99.9963

75.4668

Load

EQY

99.9994

91.8971

Load

WIND

Load

WIND-2

99.9999

98.7186

Load

WIND-3

99.9998

97.8448

Load

WIND-4

99.9998

97.8201

Load

WIND-5

99.9997

96.8875

Load

WIND-6

100.0000

99.0771

Load

WIND-7

99.9999

98.2314

0.0250

99.9998

DYNAMIC 0.0000

97.6071

Load

WIND-8

99.9999

98.1201

Load

WIND-9

99.9999

98.6219

Load

WIND-10

99.9998

97.2416

Load

WIND-11

99.9997

97.1819

Load

WIND-12

99.9999

98.5175

Accel

UX

99.9990

96.2777

Accel

UY

99.9999

99.5175

Accel

UZ

0.0000

0.0000

Accel

RX

100.0000

99.9991

Accel

RY

100.0000

99.9982

Accel

RZ

-802.9596

94.6961

5.6 Wind Pressure The project is studied for wind pressure corresponding to 100 mph wind speed and exposure type D, according to the ASCE7-02 specifications.. Wind speed

= 100 mph

Exposure type

=D

Importance Factor

=1.15 (occupancy IV, speed 0.7 s, then the limit will be: Story Drift < 0.02 x story height

The following table shows the drifts resulting from the Etabs analysis: Story STORY9 STORY9 STORY9 STORY9 STORY8 STORY8 STORY8 STORY8 STORY7 STORY7 STORY7 STORY7 STORY6 STORY6 STORY6 STORY6 STORY5 STORY5 STORY5 STORY5 STORY4 STORY4 STORY4 STORY4 STORY3

Item Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X

Load SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1

Point 1115 1151 1115 943 1115 1151 1115 943 1115 1151 1115 943 1115 1151 1115 943 1115 1151 1115 943 1115 1151 129 943 1115

DriftX 0.002385

DriftY 0.000942

0.000505 0.002048 0.00245 0.000961 0.000522 0.002052 0.002481 0.000966 0.000529 0.002026 0.002467 0.00095 0.000525 0.001959 0.002392 0.000914 0.000507 0.001839 0.002236 0.000851 0.000592 0.00165 0.001968

STORY3 STORY3 STORY3 STORY2 STORY2 STORY2 STORY2 STORY1 STORY1 STORY1 STORY1 GF GF GF GF BASE 1 BASE 1 BASE 1 BASE 1 BASE 2 BASE 2 BASE 2 BASE 2

Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Maximum drift

1151 163 943 1115 1151 1115 943 1115 1151 1115 1151 1438 1186 1438 200 1361 1186 15 200 1361 1186 15 200

0.000761 0.000436 0.001389 0.001511 0.000629 0.00034 0.000993 0.000738 0.00043 0.000244 0.000496 0.000128 0.000062 0.000042 0.000173 0.00001 0.000006 0.000007 0.000026 0.00001 0.000006 0.000007 0.002481

0.000026 0.002052

Now we will check Story Drift < 0.02 x story height We need to define: ΔS: elastic response displacement, etabs gives ΔS/h. ΔM: inelastic response displacement which should be checked, where ΔM= 0.7R ΔS The check then is going to be as ΔM < 0.02 (since ΔM is already divided by story height) ΔS/h = 0.002481 m, then ΔM/h = 0.7 x 4.5 x 0.002481 = 0.0078 0.0078 < 0.02 ok Then story drifts of our structure are allowed by UBC97 code.

iv-

Story Displacement

ASCE-code provide that story displacements due to wind load must not exceed the total height of the structure divided by 500. Getting story displacement tables from Etabs, gives us the maximum value of story displacement which is 0.0125 meters. The height if the building is 64 meters, divided by 500 it becomes 0.128. Note that 0.0125

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FINAL YEAR PROJECT Submitted in fulfillment of the requirements for the

ENGINEERING DEGREE FROM THE LEBANESE UNIVERSITY FACULTY OF ENGINEERING- BRANCH III

Major : Civil Engineering

By:

Mortada Chamas ________________________________________________

Structural Design of Sky Tower Supervised by: Dr. JAMIL DAMAJ

Defended on Monday 23 septembre 2013 the jury:

Dr. JAMIL DAMAJ Dr. Hasan AL Haj Dr. Nayef Atrisi

President Member Member

SKY TOWERS PROJECT KHALDEH- LEBANON

STRUCTURAL REPORT Design criteria-Structural Analysis-R.C Design

1.

Definition of the Intervention

The aim of the present report is to conduct the structural study of the project parts and to assess the adequacy of the preliminary structural resisting systems for gravitational and lateral loads, as specified by the design criteria and according to the specifications. The assessment to the structural systems adequacy will be done considering the following factors: - The latest architectural drawings - The specified super imposed dead loads and live loads. - The structural response of the buildings to the lateral loads

In this Phase of study the basic design criteria (codes, loadings, materials…) and the analysis methods are presented. The basic assumptions of the numerical analysis are also stated. Based on the design criteria and assumptions data, a rigorous structural analysis is conducted with three dimensional models of the buildings using the ETABS software. The buildings response, obtained from the analysis results, led to the determination of: - the maximum lateral sway of buildings which allows the adjustment of the expansion joint gap. - the internal forces in the different structural elements, which allowed the checking / design of the vertical structural elements (columns, walls) - the transfer of data to other software (Safe, S-concrete…) which allowed the checking of the proposed foundations and slabs dimensions .

2. Preface

B

eing a civil engineer graduate, we are going to introduce the structural skills acquired through our learning process in the faculty of engineering-Lebanese University. Our project is one of the engineering articles concerning structural

detailing of a building. So we chose the SKY TOWER on KHALDEH-LEBANON to be our case of study. Designers obviously need the full data related to the building in order to be able to start his study, and he should determine the means that may help him creating his model. Architectural Details: the SKY TOWER in Lebanon is located in khaldeh, Beirut, on a rock type soil. The project consists of ten residential buildings of various heights and floor areas, summer club, and winter club. The current block A consists of two Basement floors, one Ground floor, 11 residential floors.

The project consists of ten residential buildings of various heights and floor areas, summer club, and winter club. The current block A (my project) consists of two Basement floors, one Ground floor, 11 residential floors.

BASEMENT PLAN

USUAL FLOOR PLAN

GF

3. Major Constraints The structural analysis and concrete design of the project was governed by the following constraints: - the architectural requirements of the buildings which induced irregularities in the buildings shapes and the distribution of the supporting elements. - the relatively large spacing between supports.

4. Design Criteria 4.1 Codes of Practice , standards The buildings straining forces (gravitational and lateral) and the capacity of the structural resisting elements were determined in accordance to the following code of practice: - the Uniform Building Code “UBC 97” for the determination of lateral forces intensity and distribution (Earthquake and Wind pressure). - “ACI 318-02” for the determination of loads combinations, the design and detailing of various concrete elements (slabs, beams, columns, walls and foundations). - “ASCE-05” code: for wind loads and analysis

4.2 software : In addition, the design is going to be done with the aid of the following software programs: - Autodesk AutoCAD Draw and plan and detail any needed figure, with 2D and 3D features.

- CSI- Etabs ETABS is a sophisticated special purpose analysis and design program developed specifically for building systems. It is mainly used for modeling, and mainly the design of vertical elements.

- CSI- Safe Design of slabs, beams and foundations, reinforced and post tensioned concrete.

- S-CONCRETE S-concrete is a stand-alone product that investigates, designs, and graphically details reinforced concrete beam, column, and wall sections.

- BEAMD Design and draw any given beam. Get the loads and gives the resulting forces and moments, and checks code capability with the results. - TALREN Design and draw the supporting system of any excavation, including piles, anchorages. And gives detailed report of the results. Used especially for sliding circles.

5. Design Assumptions In order to be able to start our design, we must start from a definite point, where we determine the main materials that is going to be used. Also we should recognize the structural elements presented in the building, and give a predimension for each element to be checked then. Finally we have to load each member by the code’s recommended load related to its type.

5.1 Materials: Two main materials are to be used in the construction phase of the building: Concrete and Steel. In our project we will use concrete with f’c= 20MPa, and another type of f’c= 32MPa. And steel with tensile yield fy=420MPa for longitudinal reinforcement, and fy= 280 MPa for transversal reinforcement.

5.2 Structural elements and Predimnesioning As any alternative structure, our structure contains the following structural elements: slabs, columns, walls, beams, and footings. a) Slab: slabs assumptions are concerned about its type and thickness. Clearly the designer prefers less thickness that offers him less cost. These assumptions depend mainly on the spans found through the slab, and the type of support used. Due to long spans found between supports (columns), we decided to use a two way solid slab (flat plate). We will use a two way solid slab with 25cm thickness (refer to slab design section). As analysis results are derived, we are going to check the deflection and reinforcement. b) Columns: column sections will be taken as given by the architectural engineer. These sections will be checked to support its loads and will be reinforced by 1% steel of its gross section as a minimum reinforcement. If we have a slender column in the project then we are going to consider the PDelta effect, these checks will be done in the column design paragraph. c) Shear Walls: these sections are primarily determined by the architectural engineer. Walls sections and position will be checked against loads and mainly shear and torsion. d) Beams: beams are presented in the huge span found in the theatre, there sections will be detailed the frame design paragraph.

e) Footings: Thickness and dimensions are related to loads and bearing capacity of supporting soil. Thus whole design is found in footing design paragraph.

5.3 Dead Loads The dead loads of the buildings are: - self weight of the structural elements based on preliminary dimensioning of the structural sections and the materials specific unit weight - super imposed dead loads including finishing and partition: as indicated in the drawings Dead load is computed mainly for slabs: D.L. =

= 25 x 0.25 = 6.25 kPa

S.D.L. = 1.5 kPa for basement floors. = 4.0 kPa for GF and upper floors.

5.4 Live Loads Table 1.2 ACI-08: Type of use Apartment buildings Private units Public rooms Corridors Office buildings Offices Lobbies Corridors above first floor Garages (cars only) Stores First floor Upper floor Ware house Light storage Heavy storage

Minimum uniformly distributed life loads Lb/ft2 kPa=KN/m2 40 100 80

1.92 4.8 3.84

50 100 80 50

2.4 4.8 3.84 2.4

100 75

4.8 3.6

125 250

6.0 12.0

As our project is an residential building, in addition to car garages in the basement floors, we can assume live loads as follows:

Basement floors: L.L. = 2.5 kPa. Ground floor: L.L. =4.8 kPa. Upper floors: L.L. = 2.5 kPa.

5.5 Seismic load The UBC 97 recommends that the static lateral force procedure of Section 1630 may be used for the following structures: 1. All structures, regular or irregular, in Seismic Zone 1 and in Occupancy Categories 4 and 5 in Seismic Zone 2. 2. Regular structures under 240 feet (73 152 mm) in height with lateral force resistance provided by systems listed in Table 16-N, except where Section 1629.8.4, Item 4, applies. 3. Irregular structures not more than five stories or 65 feet (19 812 mm) in height. 4. Structures having a flexible upper portion supported on a rigid lower portion where both portions of the structure considered separately can be classified as being regular, the average story stiffness of the lower portion is at least 10 times the average story stiffness of the upper portion and the period of the entire structure is not greater than 1.1 times the period of the upper portion considered as a separate structure fixed at the base. [1--- 1629.8.3] The “sky tower is in zone 1 so the static analysis is required. Seismic load parameters are related to the zone of study, which is Beirut in our case. Beirut is said to be of zone 2B, referring to UBC97-TABLE 16-1, we find Seismic Zone Factor (Z) = 0.25 Soil investigations proved that the site is of dense sand type. Soil Profile Type = SC

Referring to UBC97-TABLE 16-J, TABLE 16-Q, TABLE 16-R, we find

Seismic Coefficient Seismic Coefficient

Referring to TABLE 16-N

Ca = 0.24 Cv = 0.32

UBC97

Over-strengthFactor, R = 4.5 (BWS)

Referring to UBC97-TABLE 16-K

Importance Factor = 1.5 Eccentricity Ratio = 0.05 Time Period, Ct (ft) = 0.02 for BWS Four load cases will be formed QX1 and QX2 with X direction and opposite y-eccentricity, and QY1 and QY2 with Y direction and opposite x-eccentricity. Also two dynamic loads are defined SPEC1 and SPEC2.

I - Combinations:

Combinations used in our analysis are in accordance with UBC97-1612.2 for strength design, and UBC97-1612.3 for working stress design. Each load case will be placed at its appropriate position so we will have about

50 combos. II- Modifiers: 1- Slabs:

Membrane f11 modifier factor Membrane f22 modifier factor Membrane f12 modifier factor Bending moment M11 modifier factor Bending moment M22 modifier factor Bending moment M12 modifier factor Shear V1-3 modifier factor Shear V2-3 modifier factor Mass modifier factor Weight modifier factor

1 1 1 0.25 0.25 0.25 1 1 1 1

2- Shear Walls:

Membrane f11 modifier factor Membrane f22 modifier factor Membrane f12 modifier factor Bending moment M11 modifier factor Bending moment M22 modifier factor Bending moment M12 modifier factor Shear V1-3 modifier factor Shear V2-3 modifier factor Mass modifier factor Weight modifier factor

1 1 1 0.70 0.70 0.70 1 1 1 1

3- Columns:

Cross section (Axial Area) modifier factor Shear area in 2 direction

1 1

Shear area in 3 direction Torsional constant Moment of inertia about 2 axis Moment of inertia about 3 axis Mass modifier factor Weight modifier factor

1 1 0.70 0.70 1 1

4- Beams:

Cross section (Axial Area) modifier factor Shear area in 2 direction Shear area in 3 direction Torsional constant Moment of inertia about 2 axis Moment of inertia about 3 axis Mass modifier factor Weight modifier factor

1 1 1 1 0.35 0.35 1 1

III- Base Shear Calculation

Base shear (V) is the total lateral force or the shear at the base for which a building in a seismic zone is to be designed. The total design base shear in a given direction shall be determined from the following formula: V = Cv .I . The total design base shear need not exceed the following: Vmax = 2.5 Ca .I .W/R The total design base shear shall not be less than the following: Vmin = 0.11 Ca .I .W

Numerical Calculation under the effect of EQX1 for instance: V (Eqn 1) = 0.0215W V (Eqn 2) = 0.0302W V (Eqn 3) = 0.0060W V (Eqn 4) = 0.0097W V Used = 0.0474W = 1652.88

Then consider V = 0.0278W = 0.0278 x 177107.38 = 4923.6 T = 1652.88 (under EQx1) .

IV- Finding Period of the Building Structure The Value of the structure period T shall be determined from one of the following methods: Method A:

The value T may be approximated from the following formula: TA = Ct (hn)3/4 = 0.0488 x (65.7)3/4 = 2.16s. Where: Ct = 0.0488 for all other buildings except the steel moment-resisting frames and the reinforced concrete moment resisting-frames and eccentrically braced frames. H n: height in (m) above the base to the top level Method B: The fundamental period T may be calculated using the structural properties and deformational characteristics of the resisting elements in a properly substantiated analysis. The analysis shall be in accordance with the requirements of Section 1630.1.2. The value of T from Method B shall not exceed a value 40 percent greater than the value of T obtained from Method A in zone 1. (max TB adopted ≤1.4TA =2.04s).

The fundamental period T may be computed by using the following formula:

The values of fi represent any lateral force distributed. The elastic deflections, δi, shall be calculated using the applied lateral forces, fi. Note: TB is calculated through the software: ETABS V - Finding the Distribution of Lateral Forces

In Accordance with section 1630.5 in UBC97, the total force shall be distributed over the height of the structure according to the general formula:

The concentrated force Ft at the top, which is in addition to Fn , shall be determined from the formula: Ft = 0.07 T.V = 4952 KN < 0.25V = 13061.6 KN. The remaining portion of the base shear shall be distributed over the height of the structure according to the following formula:

MODAL LOAD PARTICIPATION RATIOS (STATIC AND DYNAMIC RATIOS ARE IN PERCENT)

TYPE

NAME

STATIC

Load

DEAD

Load

SIDL

0.0374

0.0000

Load

LIVE

0.0146

0.0000

Load

EQX

99.9963

75.4668

Load

EQY

99.9994

91.8971

Load

WIND

Load

WIND-2

99.9999

98.7186

Load

WIND-3

99.9998

97.8448

Load

WIND-4

99.9998

97.8201

Load

WIND-5

99.9997

96.8875

Load

WIND-6

100.0000

99.0771

Load

WIND-7

99.9999

98.2314

0.0250

99.9998

DYNAMIC 0.0000

97.6071

Load

WIND-8

99.9999

98.1201

Load

WIND-9

99.9999

98.6219

Load

WIND-10

99.9998

97.2416

Load

WIND-11

99.9997

97.1819

Load

WIND-12

99.9999

98.5175

Accel

UX

99.9990

96.2777

Accel

UY

99.9999

99.5175

Accel

UZ

0.0000

0.0000

Accel

RX

100.0000

99.9991

Accel

RY

100.0000

99.9982

Accel

RZ

-802.9596

94.6961

5.6 Wind Pressure The project is studied for wind pressure corresponding to 100 mph wind speed and exposure type D, according to the ASCE7-02 specifications.. Wind speed

= 100 mph

Exposure type

=D

Importance Factor

=1.15 (occupancy IV, speed 0.7 s, then the limit will be: Story Drift < 0.02 x story height

The following table shows the drifts resulting from the Etabs analysis: Story STORY9 STORY9 STORY9 STORY9 STORY8 STORY8 STORY8 STORY8 STORY7 STORY7 STORY7 STORY7 STORY6 STORY6 STORY6 STORY6 STORY5 STORY5 STORY5 STORY5 STORY4 STORY4 STORY4 STORY4 STORY3

Item Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X Max Drift Y Max Drift X

Load SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1 SPEC1 SPEC2 SPEC2 SPEC1

Point 1115 1151 1115 943 1115 1151 1115 943 1115 1151 1115 943 1115 1151 1115 943 1115 1151 1115 943 1115 1151 129 943 1115

DriftX 0.002385

DriftY 0.000942

0.000505 0.002048 0.00245 0.000961 0.000522 0.002052 0.002481 0.000966 0.000529 0.002026 0.002467 0.00095 0.000525 0.001959 0.002392 0.000914 0.000507 0.001839 0.002236 0.000851 0.000592 0.00165 0.001968

STORY3 STORY3 STORY3 STORY2 STORY2 STORY2 STORY2 STORY1 STORY1 STORY1 STORY1 GF GF GF GF BASE 1 BASE 1 BASE 1 BASE 1 BASE 2 BASE 2 BASE 2 BASE 2

Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Max Drift X SPEC1 Max Drift Y SPEC1 Max Drift X SPEC2 Max Drift Y SPEC2 Maximum drift

1151 163 943 1115 1151 1115 943 1115 1151 1115 1151 1438 1186 1438 200 1361 1186 15 200 1361 1186 15 200

0.000761 0.000436 0.001389 0.001511 0.000629 0.00034 0.000993 0.000738 0.00043 0.000244 0.000496 0.000128 0.000062 0.000042 0.000173 0.00001 0.000006 0.000007 0.000026 0.00001 0.000006 0.000007 0.002481

0.000026 0.002052

Now we will check Story Drift < 0.02 x story height We need to define: ΔS: elastic response displacement, etabs gives ΔS/h. ΔM: inelastic response displacement which should be checked, where ΔM= 0.7R ΔS The check then is going to be as ΔM < 0.02 (since ΔM is already divided by story height) ΔS/h = 0.002481 m, then ΔM/h = 0.7 x 4.5 x 0.002481 = 0.0078 0.0078 < 0.02 ok Then story drifts of our structure are allowed by UBC97 code.

iv-

Story Displacement

ASCE-code provide that story displacements due to wind load must not exceed the total height of the structure divided by 500. Getting story displacement tables from Etabs, gives us the maximum value of story displacement which is 0.0125 meters. The height if the building is 64 meters, divided by 500 it becomes 0.128. Note that 0.0125

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