Full structural analysis and design of commercial building project (part  1)
Introduction
1.1 Project Description:
This project is a structural design of a Commercial Center shown in figure 11, with total area about 15,000 m2 distributed over fourteen floors, in which the first five floors are located underground and used as parking, the next four floors are used as commercial floors and the remaining floors are used as offices. Areas of each floor are shown in table 11.Elevation and section view is shown in figure 1.2
1.2 Location of Project:
This project is located in Basin number ( 19 ) district ( Masayef ) part number 72 in Jordan Street, Amman city, Jordan. Figure 1.4 shows the site plan of the project.
1.3 Architectural Drawings
Architectural plans of basement and typical floors are shown below in figures 1.5, 1.6 respectively.Elevation views of building are shown in figures 1.7 through 1.10 below.
1.4 Soil Description
Soil tests and site investigation were done and prepared by a certified Material Testing Center. We can summarize the results as follows:
Foundation ground is a layer of very pale brown to pale yellow moderately weak limestone.
Allowable bearing capacity (qall) is 4.5 Kg/cm²
Acceptable foundation settlement is 11.0 mm.
*Note that all this information is taken from the certified geotechnical material lab.
➧ Analysis of different structural elements.
➧ Structural design of different types of slabs using both systems (one way and two way) and other structural elements (beams, columns and footings) considering strength and serviceability requirements.
➧ Perform an economical study to choose the most economical type of slabs.
➧ Find center of mass and center of rigidity of one story to decide if the building is irregular so dynamic analysis must done or regular so static analysis will be enough and to determine the lateral load resisting system for the structure.
➧ Building irregularity which affects design of building to resist earthquake’s lateral loading.
➧ Large spans which affects slabs system, type and thicknesses, and beams thicknesses.
➧ Cantilever slabs in commercial and office floors.
➧ Openings in some commercial floors such as escalators.
Allowable bearing capacity (qall) is 4.5 Kg/cm²
Acceptable foundation settlement is 11.0 mm.
*Note that all this information is taken from the certified geotechnical material lab.
1.5 Objectives
➧ Determination of loads on different structural elements.➧ Analysis of different structural elements.
➧ Structural design of different types of slabs using both systems (one way and two way) and other structural elements (beams, columns and footings) considering strength and serviceability requirements.
➧ Perform an economical study to choose the most economical type of slabs.
➧ Find center of mass and center of rigidity of one story to decide if the building is irregular so dynamic analysis must done or regular so static analysis will be enough and to determine the lateral load resisting system for the structure.
1.6 Challenges
➧ Unsuitable distribution of columns which affects cars movement and parking in parking floors.➧ Building irregularity which affects design of building to resist earthquake’s lateral loading.
➧ Large spans which affects slabs system, type and thicknesses, and beams thicknesses.
➧ Cantilever slabs in commercial and office floors.
➧ Openings in some commercial floors such as escalators.
1.7 Openings
Many types of openings used in this project. Theses openings are:➧ Elevators opening: it is in the north edge of the building and it is surrounded by shear walls.
➧ Stairs openings: the main stairs are beside the elevators and surrounded by shear walls too.
➧ Electrical stairs: there are two electrical stairs used in first basement floor, three in ground floor and three in mezzanine, first and second floors.
➧ Three duct openings for mechanical and electrical pipes.
1.8 Modifications
Some of interior columns were eliminated from the basement floors to easy and offer more space for cars parking. This modification does not affect other floors but adjacent columns carry larger tributary area and so larger columns dimensions.Materials, Loads and Design Criteria
2.1 Materials
2.1.1 ConcreteConcrete specifications as follows:
Normal weight γc= 2500 kg/m3.
Compressive strength (fc’):
For slabs and beams fc’=25 MPa (N/mm2).
For columns and footings fc’=35 MPa.
Where: fc’ is the specified compressive strength of concrete after 28 days, using standard cylinders of with diameter of six inches and twelve inches height.
2.1.2 Structural Steel
Structural steel used as reinforcement steel which have the following properties:
Type: High Yield Strength steel.
Yield strength Fy=420 MPa.
Modulus of elasticity Es= 200000 MPa.
2.1.3 Hollow Block
Hollow block with dimensions of (30cmX40cmX20cm) and (25cmX40cmX20cm) used in ribbed slab.
2.1.4 Waffle templets
Waffle templets with dimensions of (52.5cmX52.5cmX30cm) used in waffle slab.
2.2 Loads
2.2.1 Gravity Loads
Gravity loads divided into two categories which are dead load and live load.
2.2.1.1 Dead Load (D.L)
Dead load of slabs are shown in table 2.1.2.2.1.1 Dead Load (D.L)
Table 2. 1: Dead Load Magnitudes
Floor

Slab
Type

D.L
(ton/m^{2})

Basement floor

Solid Slab

1.027

Ribbed Slab

0.943


Waffle Slab

0.770


Flat Plate with edge
beams

1.152


Commercial floor

Solid Slab

0.902

Ribbed Slab

0.940


Waffle Slab

0.845


Flat Plate with edge
beams

1.127

2.2.1.2 Live Load (L.L)
Live loads can be determined from codes of practice. In this project life loads were taken from Jordanian Code. Table 2.1 shows live load magnitudes for different floors.
Floors

Usage

Load
(KN/m^{2})

Basement 1,2,3,4

Parking

4

Basement
5

Parking and storage

5

Ground floor, Mezzanine, floors 1,2

Commercial

4

Floors

Offices

4

*Note: These loads can be take from the local construction code of live loads, where every country has it's code for live loads for structural design purposes.
2.2.1.3 Lateral Loads
Lateral loads are loads which acts laterally on building such as wind load and earthquake load and earth pressure of the building.
These loads will be discussed in Part 2.
U = 1.2D + 1.6L
Where:
U: Ultimate Load.
D: Dead Load.
L: Live Load.
Table 2.3 shows ultimate load on slabs.
Lateral loads are loads which acts laterally on building such as wind load and earthquake load and earth pressure of the building.
These loads will be discussed in Part 2.
2.3 Load Combinations
One load combination used here since just dead load and live load (excluding snow) to be considered.U = 1.2D + 1.6L
Where:
U: Ultimate Load.
D: Dead Load.
L: Live Load.
Table 2.3 shows ultimate load on slabs.
Table 2. 3: Ultimate Load on Slabs.
Floor

Slab
Type

D.L
(ton/m^{2})

Basement floor

Solid Slab

2.245

Ribbed Slab

2.148


Waffle Slab

1.940


Flat Plate with edge
beams

2.400


Commercial floor

Solid Slab

2.100

Ribbed Slab

2.144


Waffle Slab

2.030


Flat Plate with edge
beams

2.370

2.4 Design Criteria
Two design criteria to be considered in this project which are: Strength criterion and Serviceability criterion.2.4.1 Strength Criterion
Ultimate strength method used in this project which indicates that structural member should be designed to avoid all potential modes of failure.
General Equation:
Where:
Ф: Strength reduction factor.
Rn: Nominal member strength
Ru: Ultimate strength (combination of factored different types of loads)
2.4.2 Serviceability Criterion
Structural members must designed so that they perform their purpose adequately in terms of deflections. So minimum thickness of slabs taken form ACI code to control deflections.
2.5 Construction Codes
ACI 318M11ACI 318M11 (American Concrete Institute) code used to design all types of structural members and methods of analysis based on it. Also reinforcement limitation and detailing taken from it.
ACI 315
This code used to simplify reinforcement detailing for structural members such as slabs and beams.
Jordanian Code
This code used to determine live load on different types of floors.
2.6 Computer Softwares
Analysis results of softwares compared to manual results and close result were determined so software used for analysis.Analysis programs used analysis are:
Sap2000 used to analyze beams.
Equivalent frame tool in SAFE2014 used to analyze flat plate.
AutoCad2015 used to draw structural drawings.
Slabs and Beams
3.1 SlabsTwo systems of slabs reinforcement will be considered which are oneway and twoway systems. Different types of slabs will be analyzed and designed to choose the most suitable one based on the cost of each type.
3.1.1 Oneway System
In this system we found the preliminary thicknesses of solid and ribbed slabs to control deflection based on ACI 318M11, table 9.5(a). The thicknesses are shown in table 3.1:
Floor

Parking
floor

Commercial
floor

Solid slab thickness (cm)

44

40

Ribbed
slab thickness (cm)

56

54

Since thicknesses of one way slabs are high due to long spans, one way system was ignored.
3.1.2.1 Advantages and Disadvantages of each type of slabs
Advantages of Different Types of Slabs:
➧ Solid slab with beams: small thickness which leads to smaller amount of concrete and dead load which reduces steel quantities and hence smaller cost.
➧ Ribbed Slab with beams: small dead load and smaller amount of concrete and steel, also it is good for sound insulation which is required in office floors.
➧ Waffle slab with beams: it is useful for long spans, it requires small amount of steel due to reduction in dead load and hence smaller cost.
➧ Flat plate: no beams used and hence better appearance which is required especially in offices.
Disadvantages of Different Types of Slabs:
➧ Solid slab with beams: It is not effective for sound insulation and if beams drop is large, it will affect the appearance.
➧ Ribbed Slab with beams: Block cost increases the cost of slab.
➧ Waffle slab with beams: Requires special formwork and greater floor to floor height
➧ Flat plate: high thickness required to control deflection for long spans which increases load and hence steel quantity and maximum volume of concrete is used in this type.
3.1.2.2 Minimum Thickness to Control Deflections
Two floors (fifth basement and 3rd typical commercial floors) considered in analysis and design of three types of slabs: solid, ribbed and waffle. Flat plate only considered in basement floor. Table 3.21 shows the minimum thicknesses of two way slabs.
Floor

Parking
floor

Commercial
floor

TwoWay Solid Slab Thickness
(cm)

27

22

TwoWay
Ribbed Slab Thickness (cm)

35

33

TwoWay Waffle slab thickness
(cm)

35

33

Flat
Plate Thickness (cm)

35



3.1.2.3 Thickness Check for Shear
For all types of slabs, factored shear force (Vu) is determined by analysis.
For all types of slabs excluding flat plate nominal shear strength of concrete Vc is given by formula:
For flat plate, check for shear strength done for twoway (punching) shear.
Where:
β: the ratio of the long side of column to the short side.
λ: modification factor reflecting the reduced mechanical properties of light weight concrete of the same compressive strength. λ=1 for normal weight concrete as in this project.
bw: web width but here it equals to design strip width.
d: the distance from extreme compression fiber to centroid of longitudinal tension reinforcement.
bo: perimeter of critical section for punching shear.
Shear transfer between slab and column ends included in calculations. The following equations from ‘Reinforced Concrete Design, Kia Wang, Salmon, Pincheira, 2007’used in calculations.
Where:
b1: critical
section dimension in the longitudinal direction.
b2: critical section dimension in the transverse direction.
Jc: polar moment of
inertia of the shear area.
vu: factored shear
stress .
Vu:
shear force.
Ac: shear area of
column.
x1,x2: neutral axis
distance as shown in figure 3.2
Where, Φ = 0.75.
Check on punching shear for flat plate done using SAFE2014 software. Results verified manually for one column sample.
Drop thicknesses used where punching problems occurred.
Drops of drop panels equals to 15cm and 25 cm used for most of first basement floor columns and drops of 15cm and 20cm used for most of 3rd typical commercial floor columns.
3.1.2.4 Shear Reinforcement for Slabs
When shear reinforcement is needed, shear strength provided by shear reinforcement (ΦVs) equals to VuΦVc.
The required area of shear reinforcement (Av) and Centertocenter spacing of stirrups (s) is given by:
Where:
f_{yt}: yield strength of transverse reinforcement.
f_{yt}: yield strength of transverse reinforcement.
Vu: ultimate shear force
ΦVc:
reduced shear capacity of concrete
In twoway ribbed
and waffle slabs, shear reinforcement is required since 1.1ΦVc ≥ Vu.
3.1.3 Analysis of slabs
3.1.3.1 Twoway System AnalysisSlabs were analyzed using different methods of analysis. Solid, ribbed and waffle slabs were analyzed using tabulated coefficients method. A check on limitations of direct design method (DDM) and equivalent frame method (EFM) to analyze flat plate showed that DDM can’t be used, so EFM used.
Tabulated Coefficients:
In this method for all the beams must be equal to or greater than 2 which means that all
Where:
E: Modulus of elasticity of
concrete =
according to ACI 318M11,
8.5.1
I:
Moment of inertia
It's found the preliminary dimensions of beams for both parking and commercial
floors so they are stiff, these dimensions will be mentioned in beams chapter.
This method of analysis was used to analyze twoway solid slab, ribbed slab and
waffle slab with beams.
Direct Design Method:
A check on direct design method conditions was made to know if we can use it in analysis or not. The conditions according to ACI 31808, 13.6 are:
There shall be a minimum of three continues spans in each direction: Applicable .
Panels shall be rectangular, with a ratio of longer to shorter span c/c of supports within a panel not greater than 2 : Applicable (for twoway panels only)
Successive span length in each direction shall not differ by more than one third the longer span: Not applicable (For the long direction).
➧ Offset of columns by a maximum of 10 percent of the span (in direction of offset) from either axis between center lines of successive columns shall be permitted
➧ All loads shall be due to gravity only and uniformly distributed over an either panel. The unfactored live load shall not exceed two times the factored live load.
➧ For a panel with beams between supports on all sides, Eq below shall be satisfied for beams in the two perpendicular directions
Because some conditions did not satisfied this method of analysis excluded.
Equivalent Frame Method:
To use this method the frames must be braced against lateral movement. And so stability index should calculated for every story but since the firstorder relative lateral deflection between the top and the bottom of the story considered depends on lateral loading resulted mainly from earthquakes and winds and lateral loading resisting system; it will be calculated in ENCE530. In order to use this method here we assumed that the frames are braced.
We used this method of analysis to analyze flat plate with edge beams in basement floor which are braced since it is surrounded by soil.
Analysis done using equivalent frame tool in SAFE2014 software. Results of this tool verified using moment distribution and SAP2000 program for one of the frames.
And analysis results are shown in table 3.2.
Table 3. 2: Analysis Results
Determined Manually and by Softwares
Moment

Moment distribution

SAP2000

SAFE2014

AB

9.9

11.4

15.9

BA

191.3

185.3

196

BC

191.4

193.4

208.7

CB

172.7

164

169

CD

149.2

151.8

156.8

DC

240.4

258.1

269.4

DE

303

283.5

303.8

ED

59.1

60.9

70.3

3.1.3.2 Oneway System Analysis
In solid, ribbed and waffle slabs using tabulated coefficients method; some panels (Five panels in parking floor and two in commercial floor) in two way system the ratio between larger dimension in the panel and the smaller dimension L2/L1 was greater than 2, so these panels considered as one way panels. Analysis of these panels were done using by hand using classical methods and by SAP2000 software.
3.1.4 Design of Slabs
3.1.4.1 Flexural ReinforcementAll types of slabs designed such that ΦMn ≥ Mu taking into consideration minimum and maximum reinforcement limits and shrinkage and temperature reinforcement
Where: Mu: ultimate moment based on load combinations determined from analysis.
Mn: nominal moment capacity of flexural element.
Φ=0.9.
3.1.4.2 Shear Reinforcement
Ribbed and waffle slabs reinforced such that ΦVc + ΦVs ≥ Vu taking into consideration minimum and maximum spacing limits.
3.1.4.3 Reinforcement Detailing
Details of reinforcement (lap splices, bars length and locations…etc.) can be fined in drawings in appendices.
3.2 Beams
In order to use tabulated coefficients, beams must be stiff as discussed before. Beams dimensions founded such that they are stiff, then they were analyzed and designed.Stiff beams dimensions for both basement and commercial floors are shown in table 3.3:
Table 3. 3: Dimensions of Stiff Beams
Slab type

Beams in long direction (bXh)

Beams in short direction (bXh)

Solid
slab

50cmX75cm

75cmX75cm

Ribbed slab

50cmX75cm

50cmX80cm

Waffle
slab

50cmX75cm

50cmX80cm

3.2.2 Analysis of Beams
Beams analysis were done manually by hand and by SAP2000 software taking into consideration load combinations and load cases and using Envelope to determine design values for both moment and shear.
3.2.3 Design of Beams
3.2.3.1 Flexural ReinforcementAll types of beams designed such that ΦMn ≥ Mu taking into consideration minimum and maximum reinforcement limits and shrinkage and temperature reinforcement since most of beams have a considerable depth.
Beams reinforced such that ΦVc + ΦVs ≥ Vu taking into consideration minimum and maximum spacing limits.
3.2.3.3 Reinforcement Detailing
Details of reinforcement (lap splices, bars length and locations…etc.) can be fined in drawings in part 2 and will be discussed.
Columns and Foundations
4.1 ColumnsOne interior column in analysis and design will be sturied to choose preliminary section and preliminary design so we can depend on it in part 2.
The column and its tributary area to be considered is shown in Figure 4.1.
4.1.1 Load Calculation and Dimensions of Column
Ultimate Axial Load on one interior column along the whole building calculated considering tributary area of slab, beams and walls weight. Solid slab considered in calculating load from slabs. Then column dimensions based on ultimate axial load were calculated and then designed for this load. Dimensions of column for each two Sequential floors were determined based on the higher load between them. Table 4.1 shows column ultimate axial load and cross sectional dimensions.
Table 4. 1: Column Ultimate Axial Load
and Dimensions.
Floor

Ultimate axial load
(ton)

Cross Section Dimensions
(cmxcm)

5^{th} basement

3439.416

130X130

4^{th}
basement

3220.834

130X130

3^{th} basement

3002.253

120X120

2^{th}
basement

2783.672

120X120

1^{th} basement

2565.091

115X115

Ground

2346.509

115X115

Mezzanine

2090.786

105X105

1^{st} floor

1825.063

105X105

2^{nd} floor

1564.34

90X90

3^{rd} floor

1303.616

90X90

4^{th} floor

1042.893

75X75

5^{th} floor

782.1698

75X75

6^{th} floor

521.4465

55X55

7^{th} floor

260.7233

55X55

4.1.2 Design of columns
Columns designed initially as axially loaded columns. Reinforcement ratio ρ taken to be between one and three percent to get stiff columns and for earthquake considerations. Table 4.2 shows the reinforcement of the selected columns.
Table 4. 2: Flexural and Shear Reinforcement.
Floors

Cross Section
Dimensions (cmxcm)

Longitudinal bars
number

Transverse ties
spacing (cm)

5^{th} & 4^{th} basements

130X130

60 Φ30

4 Φ14 @ 48

3^{rd} &
2^{nd} basements

120X120

56 Φ30

4
Φ14 @ 48

1^{st}
basement & ground floor

115X115

56 Φ25

4 Φ12 @ 40

Mezzanine & 1^{st}
floor

105X105

40 Φ25

3
Φ12 @ 40

2^{nd} & 3^{rd} floors

90X90

32 Φ25

2 Φ10 @ 40

4^{th} &
5^{th} floors

75X75

28 Φ20

2
Φ10 @ 32

6^{th} & 7^{th} floors

55X55

16 Φ16

2 Φ10 @ 25

4.2 Foundations
In order to choose
the best type of foundation, dimensions of each isolated footing and then total
area of all footings must be calculated. If the total area is greater than half
the total area of building then mat foundation will be more efficient. Here
isolated footing of one interior column (the same column mentioned in columns
section) will be considered since there is no exterior column because bearing
wall used and wall footing to be considered in ENCE530. All isolated footings
and wall footing will be considered in ENCE530 to decide if it’s necessary to
use mat foundation or isolated footing is enough.
All equations used based on ‘Foundation Analysis and Design, Bowels, 1997, chapter 8’.
To find area of footing (Af)
qall: allowable bearing capacity of soil.
Pult: ultimate factored load
To find effective depth of square footing
As : area of steel reinforcement
Ф = 0.90
Check on bearing of concrete
Ac: area of column
A1:
is the column contact area
A2: the base of the frustum that can be
placed entirely in the footing as shown in figure 4.2.
Minimum reinforcement for dowels (Asmin)
Asmin = 0.005*(Ac)
Number of dowels = number of column
longitudinal reinforcing bars
Development length (d) in tension zone:
Ab: bar area (mm^{2})
db: bar diameter (mm)
ld in mm
Development length in compression zone:
4.2.2 Dimensions and Reinforcement of footing
Economical Analysis
In order to select the best alternative of slab types, economical analysis done for basement floor. Quantities take off of each slab with its beams done and then the total price of each type calculated assuming the same labor cost for all slabs. Table 5.1 below shows bill of quantities (B.O.Q) and total price of each slab excluding labor cost.
Table 5. 1:
Bill of Quantities
Item

Quantity

Unit

Material cost/unit ($)

Total Cost ($)


Waffle slab

Concrete

224.9

m3

88

19,750

Reinforcement

31.3

ton

850

26,600


Waffle template

2447

unit

2.55

6,238


Total

52,589


Ribbed slab

concrete

286.9

m3

87.8

25,195

Reinforcement

36.8

ton

850

31,247


Hollow block

3824

unit

1.42

5,416


Total

61,886


Solid slab

Concrete

331.14

m3

87.8

29,080

Reinforcement

35.8

ton

850

30,424


Total

59,505


Flat plate

Concrete

422.3

m3

87.8

37,085

Reinforcement

41.38

ton

850

35,167


Total

72,253

From table above, Waffle slab is the most economical type of slabs so full design to be made in Part 2 of the article.
For Commercial and office floors another economical analysis is required to choose the best alternative excluding any type that is insufficient for floor usage. In part 2 of the article this will be done.
Seismic Analysis and Design
In this stage we will calculate only the center of mass and center of rigidity for 3rd floor (Typical commercial) to decide whether the building is regular or not which decides the method of analysis to be used (Dynamic Analysis or Static Analysis) and the best structural system for seismic load.Table 6.1 shows center of mass of typical commercial floor (CM) location and center of rigidity of shear walls (CR) location used in same floor.
Table 6. 1: Center of Mass and Center
of Rigidity Locations
X (m)

Y (m)


Center of mass (Cm)

24.87

13.43

Center
of Rigidity (Cr)

29.19

21.46

Figure 6.1 below shows CM and CR.
Figure 6. 1: CM and CR locations

It is obvious from figure 71 that Cr located far away from Cm and its location is between shear walls since they are the only lateral loading resisting system.
Difference between Cm and Cr in xdirection (Δx = 4.32m).
Difference between Cm and Cr in ydirection (Δy = 8.03m).
Lx = 52.75m
Ly = 26.11m
Conclusion
At the beginning, architectural drawings were studied, then two columns were eliminated from basement floors. Then minimum thicknesses to control deflections were taken from ACI318M11, and then full design of slabs and beams were done.
Sample column and footing were considered so a preliminary cross section and design were performed.
Economical Analysis were done for all basement floor slabs to select best alternative based on total cost. Waffle slab gave the minimum cost so it will be considered in part 2 of the article.
Finally, Center of mass and Center of rigidity were calculated to decide the best resisting lateral loads system and the method of analysis.
References
 Wang S, Salmon C and Pincheira J (2007) Reinforced Concrete Design. John Wiley, United States of America.
 Bowels J, (1997) Foundation Analysis and Design. McGrawHill, Singapore.
 Building Code Requirements for Structural Concrete (ACI318M11) and Commentary, American Concrete Institute.
 The Jordanian Code, 2nd Edition, 2006.
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