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 1-1, 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 1-1.

Figure 1. 1: The commercial center 3-D view

Table 1. 1: Areas of floors

Floor	Area (m2)
Basement 5,4,3,2	1236 (each floor)
Basement 1	1208
Ground floor	1019
Mezzanine floor	1036
Floor 1	926
Floors 2,3,4,5	959 (each floor)
Floor 6	910
Floor 7	785

Elevation and section view is shown in figure 1.2

Figure 1. 2: Elevation View of the commercial Center

Since the length of building equals to 57.22 meters, there is an expansion joint in the long direction of building as shown in figure 1.3 below, so the building is divided structurally into two parts.

Figure 1. 3: Plan View of Basement Floor shows the Location of Expansion Joint

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.

Figure 1. 4: Site plan.

1.3 Architectural Drawings

Architectural plans of basement and typical floors are shown below in figures 1.5, 1.6 respectively.

Figure 1. 5: Architectural Plan of Basement Floor

Figure 1. 6: Architectural Plan of Typical Floor

Elevation views of building are shown in figures 1.7 through 1.10 below.

Figure 1. 7: Eastern Elevation

Figure 1. 8: Western Elevation

Figure 1. 9: Northern Elevation

Figure 1. 10: Southern Elevation

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.

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 Concrete

Concrete 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.

Table 2. 1: Dead Load Magnitudes

Floor	Slab Type	D.L (ton/m2)
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.

Table 2. 2: Live Load Magnitudes.

Floors	Usage	Load (KN/m2)
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.

Snow load will be discussed in Part 2.

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.

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/m2)
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 318M-11
ACI 318M-11 (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 Soft-wares

Analysis results of soft-wares compared to manual results and close result were determined so soft-ware 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 Slabs
Two systems of slabs reinforcement will be considered which are one-way and two-way 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 One-way System
In this system we found the preliminary thicknesses of solid and ribbed slabs to control deflection based on ACI 318M-11, table 9.5(a). The thicknesses are shown in table 3.1:

Table 3. 1: Thicknesses of One-Way Slabs

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 Two-way System
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 3.2-1 shows the minimum thicknesses of two way slabs.

Table 2. 4: Minimum Thicknesses of Two-Way Slabs

Floor	Parking floor	Commercial floor
Two-Way Solid Slab Thickness (cm)	27	22
Two-Way Ribbed Slab Thickness (cm)	35	33
Two-Way 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 two-way (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.

αs is 40 for interior columns, 30 for edge columns, and 20 for corner columns.

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

If 1.1ΦVc ≤ Vu then thickness is adequate and no need for shear reinforcement but if 1.1ΦVc ≥ Vu then shear reinforcement is required.

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 Vu-ΦVc.

The required area of shear reinforcement (Av) and Center-to-center spacing of stirrups (s) is given by:

 

Where: 
f_yt: yield strength of transverse reinforcement.

Vu: ultimate shear force

ΦVc: reduced shear capacity of concrete

In two-way ribbed and waffle slabs, shear reinforcement is required since 1.1ΦVc ≥ Vu.

3.1.3 Analysis of slabs

3.1.3.1 Two-way System Analysis
Slabs 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 318M-11, 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 two-way 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 318-08, 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 two-way 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 un-factored 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 first-order 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 Soft-wares

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 One-way 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 soft-ware.

3.1.4 Design of Slabs

3.1.4.1 Flexural Reinforcement
All 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.

3.2.1 Beams Dimensions
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 soft-ware 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 Reinforcement
All 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.

3.2.3.2 Shear Reinforcement
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 Columns
One 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.

Figure 4. 1: Tributary Area of Column

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)
5th basement	3439.416	130X130
4th basement	3220.834	130X130
3th basement	3002.253	120X120
2th basement	2783.672	120X120
1th basement	2565.091	115X115
Ground	2346.509	115X115
Mezzanine	2090.786	105X105
1st floor	1825.063	105X105
2nd floor	1564.34	90X90
3rd floor	1303.616	90X90
4th floor	1042.893	75X75
5th floor	782.1698	75X75
6th floor	521.4465	55X55
7th 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)
5th & 4th basements	130X130	60 Φ30	4 Φ14 @ 48
3rd & 2nd  basements	120X120	56 Φ30	4 Φ14 @ 48
1st  basement & ground floor	115X115	56 Φ25	4 Φ12 @ 40
Mezzanine & 1st floor	105X105	40 Φ25	3 Φ12 @ 40
2nd & 3rd floors	90X90	32 Φ25	2 Φ10 @ 40
4th & 5th floors	75X75	28 Φ20	2 Φ10 @ 32
6th & 7th 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.

4.2.1 Equations used in design calculations of footing
All equations used based on ‘Foundation Analysis and Design, Bowels, 1997, chapter 8’.
To find area of footing (Af)

Pservice: service load
qall: allowable bearing capacity of soil.
Pult: ultimate factored load

qult: ultimate bearing capacity
Allowable values of punching shear (Vc)

Ф = 0.75
To find effective depth of square footing

B,l: dimensions of footing
x: dimension of square column
d: effective depth of footing
Vc: allowable punching shear

To find ultimate resisting moment (Mu)

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 (mm²)

db: bar diameter (mm)

ld in mm

Development length in compression zone:

4.2.2 Dimensions and Reinforcement of footing

Dimension of footing is (7.2mX7.2mX1.75m) and 58Φ30 bars in both ways are used as main reinforcement.

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 7-1 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 x-direction (Δx = 4.32m).
Difference between Cm and Cr in y-direction (Δy = 8.03m).

Lx = 52.75m
Ly = 26.11m

And hence building is irregular and dynamic analysis is required.

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 ACI318M-11, 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

1. Wang S, Salmon C and Pincheira J (2007) Reinforced Concrete Design. John Wiley, United States of America.
2. Bowels J, (1997) Foundation Analysis and Design. McGraw-Hill, Singapore.
3. Building Code Requirements for Structural Concrete (ACI318M-11) and Commentary, American Concrete Institute.
4. The Jordanian Code, 2nd Edition, 2006.