?
BEIRUT ARAB UNIVERSITY
FACULTY OF ENGINEERING
DEPARTEMENT OF CIVIL ENGINEERING

709 JAL EL DIB RESIDENTIAL BUILDING

Prepared by:
Kassem Al Hajjar
Ayman Mansour
Mohamad Banbouk
Mohammad Khawwam
Mostafa Jaffal

Supervised by:
Prof. Dr. Yehia Temsah
Dr. Zaher Abou Saleh

Spring 2017/2018
I- Acknowledgement:

We would like to thank Beirut Arab University and its honourable faculty who have always provided us with brightening information and gave us the opportunity to gain such a beneficial senior project.
We offer our deep thanks to the faculty of engineering in particular:
Prof. Yehya Temsah
Dr. Zaher Abou Saleh
Who were the supervisors of our project and were with us in every step of our work during this semester.
Thank you for being remarkable mentors and we are very grateful to have you as instructors.

II- Abstract:

This project is a structural analysis and design of a residential building located in JAL AL DIB, the building is consisted of 15 floors.

Technically speaking the project comprises the following floors:
1 basement floors
Ground floor
14 typical floors
Roof
Top roof

The final analysis and design of building is done using a three dimensional (3D) structural model by the structural analysis and design software ETABS.
Analysis and design of slabs is done using finite element software by SAFE software.

III- Table of Content:
I- Acknowledgement 3
II- Abstract 4
III- Table of Content 5
IV- List of Figures 8
V- List of Tables 10

? CHAPTER 1: INTRODUCTION 11
1.1 Description 11
1.2 Methodology of study 14
1.3 Design Criteria 15
1.4 Architectural Drawings 17
1.5 Major constraints 21
? CHAPTER 2: GRAVITY LOADS ON BUILDING 22
2.1 Material Self Weight 22
2.2 Superimposed Dead Load 22
2.3 Live Load 22
? CHAPTER 3: LATERAL LOADS ON BUILDING 24
3.1 Wind Load: 24
3.1.1 Wind Speed: 24
3.1.2 Wind exposure: 25
3.1.3 Wind directionality effect: 25
3.1.4 Important factor 26
3.1.5 Gust Factor 26
3.2 Earthquake Load: 27
3.2.1 Soil profile type 28
3.2.2 Importance Factor (I) 28
3.2.3 Redundancy factor (R) 29
3.2.4 Seismic coefficient of acceleration Ca 30
3.2.5 Seismic coefficient of velocity Cv 30
? CHAPTER 4: DESIGN FORCES AND COMBINATIONS 31
? CHAPTER 5: GRAVITY RESISTING SYSTEM 32
5.1 Examples of gravity load resisting floor systems 32
5.2 Factors effecting the selection of gravity resisting systems 34
5.3 Preliminary slab properties 34

? CHAPTER 6: LATERAL RESISTING SYSTEM 35
6.1 Braced Frames 35
6.2 Rigid Frames 35
6.3 Shear Wall System 36
? CHAPTER 7: MODELING 37
7.1 Modeling Using ETABS 37
7.2 Story Data 38
7.3 Stiffness Modifiers 38
? CHAPTER 8: STRUCTURAL ANALYSIS 40
8.1 Shear Walls Analysis 40
8.2 Seismic Analysis 41
8.3 Wind Analysis 45
8.4 Column Design 48
? CHAPTER 9: DESIGN OF COLUMNS 49
9.1 Types of Columns: 49
9.2 Reinforcement Limitation: 49
9.3 Design methodology 49
9.4 Design of column C9 (all floors) 50
9.5 Reinforcement detailing for columns 51
? CHAPTER 10: DESIGN OF SHEAR WALLS 52
10.1 Functions of a shear wall 52
10.2 Design of column C9 (all floors): 52
10.3 Walls Reinforcement detailing: 53
? CHAPTER 11: DESIGN OF CORE WALLS 54
11.1 Design of irregular shape core wall 54
11.2 Core wall Reinforcement detailing: 56
? CHAPTER 12: FLAT SLABS 57
12.1 Overview 57
12.2 Advantages and Disadvantages 57
12.3 Minimum Thickness 58
12.4 Deflection 58
12.5 Short term deflection 59
12.6 Long term deflection 59
12.7 Punching Shear 60
12.8 Slab Moments 61
12.9 Slab Reinforcement 62
12.10 Slab Reinforcement Detailing’s 64
? CHAPTER 13: RIBBED SLAB 67
13.1 Advantages 67
13.2 Minimum Thickness 67
13.3 Ribs Direction 68
13.4 Deflection 69
13.5 Design of Ribs 70
13.6 Slab full detailing 71
13.7 Design of Embedded Beams 72
? CHAPTER 14: FOUNDATION 74
14.1 Raft Thickness 74
14.2 Soil properties: 75
14.3 Concrete Properties 76
14.1 Check for Soil Pressure 76
14.4 Check Punching Shear 77
14.4 Slab Reinforcement 78
14.5 Raft Reinforcement Detailing’s 80
? CHAPTER 15: STAIRS 84
15.1 Dog Legged Stair Case 84
15.2 Step 1: General arrangement 85
15.3 Step 2: Design constants 87
15.4 Step 3: Determination of loading 87
15.5 Step 5: Reinforcement Calculation 89
15.6 Step 6: Detailing 90
? CHAPTER 16: BASEMENT WALL 91
16.1 Soil Properties 91
16.2 Lateral Earth Pressure (soil Load) 91
16.3 Uniform live load 92
? CHAPTER 17: BILL OF QUANTITIES 95
17.1 Flat Slab 96
17.2 Ribbed Slab 97
17.3 Conclusion 98
? APPENDIX 99
? REFERENCES 102

IV- List of Figures:
Figure 1: Project Location 11
Figure 2: Perspective View 11
Figure 3: Elevation View 12
Figure 4: Boreholes’ Location Plan 15
Figure 5: Basement Plan 16
Figure 6: Ground Plan 17
Figure 7: First Floor Plan 18
Figure 8: Second to 13th Floor Plan 18
Figure 9: 14th Floor Plan 19
Figure 10: Roof Floor Plan 19
Figure 11: Section Elevation View 20
Figure 12: ETABS 3D Model 36
Figure 13: BMD and deflected shape of a wall 39
Figure 24 Interaction Diagram 47
Figure 14: Axial loads on vertical elements 47
Figure 16: S-concrete Load entry 49
Figure 15: Column Reinforcement schedule 50
Figure 16: Wall Reinforcement Schedule 52
Figure 17: Basement floor core wall detailing 55
Figure 19: Maximum permissible computed deflection 57
Figure 20: Short Term Deflection 58
Figure 21: Long Term Deflection 58
Figure 22: Punching Shear 59
Figure 23: X-Direction 60
Figure 24: Y-Direction 60
Figure 24: Additional Top Reinforcement X-direction 61
Figure 25: Additional Bottom Reinforcement X-direction 61
Figure 26: Additional Top Reinforcement Y-direction 62
Figure 27: Additional Bottom Reinforcement Y-direction 62
Figure 28: Top Reinforcement X-direction 63
Figure 29: Bottom Reinforcement X-direction 63
Figure 30: Top Reinforcement Y-direction 64
Figure 31: Bottom Reinforcement Y-direction 64
Figure 32: Additional Top Reinforcement X-direction 65
Figure 33: Additional Top Reinforcement Y-direction 65
Figure 34: Maximum Allowable Deflection Due to Long Term Deflection 68
Figure 35: BMD for Ribs 69
Figure 36: SFD for Ribs 69
Figure 37: Slab Distribution of Hollow Blocks 70
Figure 38: Embedded Beam Reinforcement 72
Figure 39: Embedded Beam Reinforcement 72
Figure 40: Soil Properties 74
Figure 42: Concrete Properties 75
Figure 43: Soil Pressure 75
Figure 44: Punching Shear 76
Figure 45: Additional Top Reinforcement X-direction 77
Figure 46: Additional Bottom Reinforcement X-direction 77
Figure 47: Additional Top Reinforcement Y-direction 78
Figure 48: Additional Bottom Reinforcement Y-direction 78
Figure 49: Top ; Bottom Reinforcement X-direction 79
Figure 50: Top ; Bottom Reinforcement Y-direction 80
Figure 51: Additional Top Reinforcement 81
Figure 52: Additional Bottom Reinforcement 82
Figure 53: Dog Leg Stairs 83
Figure 54: Stairs General Arrangement 84
Figure 55: Stairs Plan 85
Figure 56: BMD for Stairs 86
Figure 57: Detailing 89
Figure 58: Wall 90
Figure 59: Acting Loads 91
Figure 60: SFD ; BMD 91
Figure 61: Wall Design 92
Figure 62: Wall Detailing 93

V- List of Tables:
Table 1 : Wind directionality effect 24
Table 2 : Importance Factor 25
Table 3 : Gust Factor 25
Table 4 : Soil Profile 27
Table 5 : Importance factor for seismic analysis 27
Table 6 : Structural systems 28
Table 7: Siesmic Coefficient Ca 29
Table 8 : Siesmic Coefficient Cv 29
Table 9 : Minimum thickness for one way slab 33
Table 10 : Minimum thickness for two way slab 33
Table 21 : Story Data 37
Table 12: Stiffness modifiers 37
Table 33 : Story Drift 43
Table 45 : Building Sway 46
Table 56: Advantages ; Disadvantages 56
Table 67: Minimum Thickness 57
Table 18: Minimum Thickness for One Way Slabs. 66
Table 19:Maximum Allowable Deflection 68
Table 20:Weight of steel 94
Table 21:Unit Price 94
Table 22:Steel in flat slab 95
Table 23:Steel in ribs 96
Table 24:Steel in beams 96
Table 25:Steel for stirrups 96
Table 26:Steel for shrinkage 97
Table 27: ACI – 318 Appendix E 98

? CHAPTER 1: INTRODUCTION
1.1 Description
16 Story residential Building in Jal Al Dib

Figure 1: Project Location
This Project includes the following building components:
1 Basement
Ground Floor
15 Floor
Roof

Figure 2: Perspective View

Figure 3: Elevation View
Apartments:
2 apartments per floor in Block A
1 apartment per floor in block B.
The basement and ground floor are used as car parking.
Basement (parking) floor is connected to the Ground floor using ramp elements.
1st and typical floors till 14 are used as residential apartments over approximately half of basement area.

1.2 Methodology of study

Determination of which slab type to use after considering the different span lengths.
Determination of structural system used.
Story data.
Identification of loads and code of practice and standards.
Introducing the structural system to the software.
Check for story drift and sway.
Designing the structural elements.
Design of foundation.
Reinforcement detailing drawings.
Cost management

1.3 Design Criteria

Code Specifications:
The design code is referred to the American Institute of Civil Engineering (ACI 318-05) which covers the proper design and construction of buildings of structural concrete including: specifications, inspection, materials, durability requirements, concrete quality, reinforcement details, analysis and design, strength and serviceability, flexural and axial loads, shear and torsion, pre-stressed concrete, and provisions of seismic design.

Materials:
1- Concrete: The minimum 28 days’ compressive strength on cylinder are:
– Blinding concrete 25 MPa
– Columns, walls 40 MPa
– Ground slab, slabs & Beams 30 MPa
(40-30)/40×100 = 33% which is smaller than 40%

2- Steel: Yield steel, ASTM Grade 60, Fy = 4200 kg/cm² = 420 Mpa
Mild steel, ASTM Grade 40, Fy = 2800 kg/cm² = 280 Mpa
Bar size : ?8, T12, T14, T16, T20, T25

Codes of practice and standards:

The structure is to be designed to the requirements of the following standards:

– ACI 318 – 14
– UBC 1997
– ASCE 7-10

Software used:
– ETABS 16
– SAFE 16
– SAP2000
– AutoCAD
– Excel and Word

Soil Investigation:

5 Boreholes are drilled to depth 15 & 25 m
The recommended allowable bearing capacity is 3.0 kg/cm2
Subgrade modulus for soil K = 500 T/m3
Angle of internal friction ? = 30°
Soil profile type is SD

Figure 4: Boreholes’ Location Plan

1.4 Architectural Drawings

Figure 5: Basement Plan

Figure 6: Ground Plan

Figure 7: First Floor Plan

Figure 8: Second to 13th Floor Plan

Figure 9: 14th Floor Plan

Figure 10: Roof Floor Plan
1.5 Major constraints

There are no shear walls in X direction which may cause effect of lateral loads to be critical on that direction.

Slab Areas are large, so expansion joints may be used.

Differential settlement of foundation slab due to different load magnitude between north area (parking basement) and south area (rise of building) which may cause cracks. Settlement joint is needed.

Figure 11: Section Elevation View

? CHAPTER 2: GRAVITY LOADS ON BUILDING

The major gravity loads on building structures are dead and live loads.
Dead loads are fixed-position gravity loads (i.e. long-term stationary forces).
They consist of the weight of all materials of construction incorporated into the building
including architectural, structural, and MEP items. Dead load also includes the weight of any
fixed equipment.
2.1 Material Self Weight
Dead Loads have been calculated using the following assumed unit weights:
Concrete = 2.5 T/m3
Earth (saturated) = 2.48 T/m3
Water = 1.0 T/m3

2.2 Superimposed Dead Load
Hollow block (CMU) walls (including plaster):
100 mm thick 2.2 KN/m2 – 200 mm thick 3.2 KN/m2
150 mm thick 2.7 KN/m2 – 250 mm thick 3.7 KN/m2
Typical calculation of superimposed dead (without partition loads):
Finishes 2 KN/m2
Services 1 KN/m2 Total 3 KN/m2
SIDL = 2 KN/m2 (parking)
SIDL = 3 KN/m2 (residential floors)
SIDL = 2 KN/m2 (roof)

2.3 Live Load (IBC Code)
Live loads are short duration forces which change in location and magnitude during the life of the structure.
They include the weight of people, furniture and movable partitions.
They are based upon intended use or occupancy of the building (e.g. residential versus office).

Parking = 3.5 KN/m2
Basic floor area = 2 KN/m2
Balconies = 3 KN/m2
Stairs – Corridors = 4.8 KN/m2
Roof = 1 KN/m2
Top of Roof = 10 KN/m2 (Water Tank Load)
Live load has two components:
(1) Sustained, which is less uncertain and acts over a long period (e.g. furniture)
(2) Transient, which is more uncertain and acts over a short period (e.g. people)

? CHAPTER 3: LATERAL LOADS ON BUILDING
The major lateral loads on building structures are wind and earthquake loads.
3.1 Wind Load:
Wind load on structures is affected by:
Wind speed and gust effect
Height and stiffness of building
Cross-sectional shape of building
Surrounding topography and terrain
Presence of openings in the building envelope

P = Ce*Cq*qs*Iw
P = design wind pressure.
Ce = combined height, exposure and gust factor coefficient
Cq = pressure coefficient for the structure or portion of structure under consideration
Iw = Importance factor
qs = wind stagnation pressure

3.1.1 Wind Speed:
qs = 100 mph

3.1.2 Wind exposure:
We choose our category as exposure C

3.1.3 Wind directionality effect:
In our case, having a structure type is building Kd=0.85

Table 1 : Wind directionality effect

3.1.4 Important factor:
Our structure corresponds to category II

Table 2 : Importance Factor

3.1.5 Gust Factor:
Table 3 : Gust Factor

Our building height is 55.5m =182ft ? By interpolation using table Gust factor =1.84

3.2 Earthquake Load:
Earthquake load on structures is affected by several factors:
Earthquake intensity
Geotechnical data at building site
Mass of the building
Stiffness of the building
Cross-sectional shape of building
Height of the building

V = (C_v*I)/(R*T) W
Cv = Seismic coefficient of velocity
I = Importance factor
W = Total dead load plus sustained load
T = Period of vibration
R = Redundancy Factor

Lebanon Zone: Z = 0.25 m/s2

3.2.1 Soil profile type:
Our soil profile type is SD

Table 4 : Soil Profile
3.2.2 Importance Factor (I):
This factor is used to classify buildings according to use and importance

Table 5 : Importance factor for seismic analysis

3.2.3 Redundancy factor (R):
R is a factor in accordance to the over-strength or the extra or serve strength in the structure system. It comes from the practice of designing every member in a group according to the forces in the most critical member of that group
R = 5.5 for shear walls system

Table 6 : Structural systems

3.2.4 Seismic coefficient of acceleration Ca:
According to the table Ca = 0.29

Table 7: Siesmic Coefficient Ca

3.2.5 Seismic coefficient of velocity Cv:
According to the table Cv = 0.4

Table 8 : Siesmic Coefficient Cv

? CHAPTER 4: DESIGN FORCES AND COMBINATIONS

The design forces were obtained from the numerical analysis of the three-dimensional models due to the following straining forces:
Dead loads (DL): self-weight + super Imposed dead
Live Loads (LL): LL1 + LL2
Seismic forces(E) of both horizontal (X-Y) and vertical (Z) directions

The basic design load combinations as per ACI 318-14 code:
1.4DL
1.2DL + 1.6LL
1.2DL + 1LL + 1.0W
1.2DL + 1LL – 1.0W
0.9DL + 1.0W
0.9DL – 1.0W
1.2DL + 1.0LL + 1.0E
1.2DL + 1.0LL – 1.0E
0.9DL + 1.0E
0.9DL – 1.0E
“W” represents the Wind forces WX and WY
“E” represents the seismic quadratic combinations:
E = EQX + 0.3 EQY + EQZ
Or
E = 0.3 EQX + EQY + EQZ
EQX, EQY, and EQZ represent the seismic spectral response of the buildings due to earthquakes along X, Y, and Z directions respectively. These values are scaled with respect to the values obtained from the static analysis (equivalent seismic forces) as per the UBC97 specification (1631.5.4) with the condition of not being less than (1/R).

? CHAPTER 5: GRAVITY RESISTING SYSTEM
Structural behavior of gravity load resisting systems can be mainly classified as either 1-way or 2-way slab.

5.1 Examples of gravity load resisting floor systems:
1. Flat plate
2. Flat slab (with drop panels and/or column capitals)
3. Two-way slab
4. One-way slab on beams
5. One-way ribbed system
6. Two-way waffle system
7. PT Slab

Flat plate system. There are no beams between the columns. Instead, the floor is heavily reinforced in both directions. Edge beams may be used on the perimeter.

Flat slab with drop panels. This system consists of a flat plate with column capitals to provide shear resistance around the columns.

Two-way slabs are floor panels supported along all four sides by drop beams.

One-way slab on beams. The floor loads are transferred to parallel beams, which are then transferred to the columns.

One-way ribbed slab. The ribs act like small beams between a thin slab. They are created with removable forms or with permanent hollow concrete masonry units.

Two-way joist (or waffle) slab. This floor has joists in both directions. It is the strongest and will have the least deflection.

5.2 Factors effecting the selection of gravity resisting systems:
Several factors affect the selection of one structural floor system for gravity loads over another:
Economy of construction
Serviceability
Load carrying ability
Economy of material
Architectural considerations
5.3 Preliminary slab properties
Using ribbed slab(one way hollow block slab): from table of minimum thickness
Longest span: Ln= 5.6 m ? hmin = L/21 = 26.6 cm
Table 9 : Minimum thickness for one way slab

Using Flat plate (2 way slab): from table of minimum thickness
Longest span: Ln= 5.6 m ? hmin = Ln/33 = 16.9 cm

Table 10 : Minimum thickness for two way slab

we have two options: – 25 cm Ribbed Slab
– 23 cm Flat Slab
So Try flat plate slab of thickness 23 cm

? CHAPTER 6: LATERAL RESISTING SYSTEM
There are three main lateral load resisting structural systems for low and medium rise buildings.
1. Braced frames
2. Rigid frames
3. Shear walls
A combination of the above 3 systems may also be used in medium rise buildings.
6.1 Braced Frames
Such structures consist of a frame strengthened with diagonal bracing members. The columns and beams carry the gravity load, while the bracing carries the lateral load.
Braced frames are mostly used in steel buildings since the diagonal bracing has to resist tension.
Bracing generally takes the form of steel rolled sections, circular bar sections, or tubes.

6.2 Rigid Frames
Sometimes referred to as moment-resisting frames. They are composed of reinforced concrete portal frames, with the lateral load mainly resisted by flexure.
Rigid frames resist lateral loads through beams and columns.
They tend to have large drift (lateral deflection).
They are mainly used in low/medium-rise buildings (up to 20 stories).

6.3 Shear Wall System
They act like deep cantilevered beams supported at the ground. They can resist both gravity and lateral loads.
Shear wall buildings are very stiff structures against lateral loads.
They are often used on up to 30-40 stories.

For high-rise buildings, the lateral load resisting system is complex, and may consist of one of the followings:
1. Framed tube
2. Trussed tube
3. Tube-in-tube
4. Bundled tube

? CHAPTER 7: MODELING
7.1 Modeling Using ETABS

Figure 12: ETABS 3D Model

7.2 Story Data

Table 21 : Story Data

7.3 Stiffness Modifiers
The effects of concrete cracking can be considered with the ACI318 (6.6.3.1.1) reduced inertia for vertical and horizontal elements as follow:

Table 12: Stiffness modifiers

SLAB COLUMN

WALL

? CHAPTER 8: STRUCTURAL ANALYSIS

8.1 Shear Walls Analysis
Due to Earthquake
SFD BMD Deformed Shape Un-Deformed Shape

Figure 13: BMD and deflected shape of a wall

8.2 Seismic Analysis
Earthquake in x-direction
The Maximum Inelastic Response Displacement:
?M = Cd*?S
= 4.5*0.004915
= 0.0193 ; 0.02

TABLE: Story Drifts
Story Load Case/Combo Direction Drift 0.7*R*?S
Roof EX 1 X 0.004674 0.017995 OK
Roof EX 2 X 0.00457 0.017595 OK
Roof EX 3 X 0.004778 0.018395 OK
Roof EY 1 Y 0.00134 0.005159 OK
Roof EY 2 Y 0.001239 0.00477 OK
Roof EY 3 Y 0.001441 0.005548 OK
14th Floor EX 1 X 0.004759 0.018322 OK
14th Floor EX 2 X 0.004647 0.017891 OK
14th Floor EX 3 X 0.004872 0.018757 OK
14th Floor EY 1 Y 0.001551 0.005971 OK
14th Floor EY 2 Y 0.001404 0.005405 OK
14th Floor EY 3 Y 0.001698 0.006537 OK
13th Floor EX 1 X 0.004805 0.018499 OK
13th Floor EX 2 X 0.004691 0.01806 OK
13th Floor EX 3 X 0.004919 0.018938 OK
13th Floor EY 1 Y 0.001623 0.006249 OK
13th Floor EY 2 Y 0.001456 0.005606 OK
13th Floor EY 3 Y 0.00179 0.006892 OK
12th Floor EX 1 X 0.004883 0.0188 OK
12th Floor EX 2 X 0.004768 0.018357 OK
12th Floor EX 3 X 0.004997 0.019238 OK
12th Floor EY 1 Y 0.001634 0.006291 OK
12th Floor EY 2 Y 0.001465 0.00564 OK
12th Floor EY 3 Y 0.001803 0.006942 OK
11th Floor EX 1 X 0.004955 0.019077 OK
11th Floor EX 2 X 0.004841 0.018638 OK
11th Floor EX 3 X 0.005069 0.019516 OK
11th Floor EY 1 Y 0.00164 0.006314 OK
11th Floor EY 2 Y 0.001469 0.005656 OK
11th Floor EY 3 Y 0.001811 0.006972 OK
10th Floor EX 1 X 0.005008 0.019281 OK
10th Floor EX 2 X 0.004898 0.018857 OK
10th Floor EX 3 X 0.005121 0.019716 OK
10th Floor EY 1 Y 0.001638 0.006306 OK
10th Floor EY 2 Y 0.001465 0.00564 OK
10th Floor EY 3 Y 0.00181 0.006969 OK
9th Floor EX 1 X 0.005028 0.019358 OK
9th Floor EX 2 X 0.004951 0.019061 OK
9th Floor EX 3 X 0.00514 0.019789 OK
9th Floor EY 1 Y 0.001623 0.006249 OK
9th Floor EY 2 Y 0.001451 0.005586 OK
9th Floor EY 3 Y 0.001795 0.006911 OK
8th Floor EX 1 X 0.005003 0.019262 OK
8th Floor EX 2 X 0.004958 0.019088 OK
8th Floor EX 3 X 0.005112 0.019681 OK
8th Floor EY 1 Y 0.001593 0.006133 OK
8th Floor EY 2 Y 0.001423 0.005479 OK
8th Floor EY 3 Y 0.001763 0.006788 OK
7th Floor EX 1 X 0.004921 0.018946 OK
7th Floor EX 2 X 0.00491 0.018904 OK
7th Floor EX 3 X 0.005025 0.019346 OK
7th Floor EY 1 Y 0.001543 0.005941 OK
7th Floor EY 2 Y 0.001377 0.005301 OK
7th Floor EY 3 Y 0.001709 0.00658 OK
6th Floor EX 1 X 0.004771 0.018368 OK
6th Floor EX 2 X 0.004792 0.018449 OK
6th Floor EX 3 X 0.004869 0.018746 OK
6th Floor EY 1 Y 0.001471 0.005663 OK
6th Floor EY 2 Y 0.001312 0.005051 OK
6th Floor EY 3 Y 0.001631 0.006279 OK
5th Floor EX 1 X 0.00454 0.017479 OK
5th Floor EX 2 X 0.004592 0.017679 OK
5th Floor EX 3 X 0.004631 0.017829 OK
5th Floor EY 1 Y 0.001375 0.005294 OK
5th Floor EY 2 Y 0.001225 0.004716 OK
5th Floor EY 3 Y 0.001524 0.005867 OK
4th Floor EX 1 X 0.004217 0.016235 OK
4th Floor EX 2 X 0.004297 0.016543 OK
4th Floor EX 3 X 0.004299 0.016551 OK
4th Floor EY 1 Y 0.00125 0.004813 OK
4th Floor EY 2 Y 0.001113 0.004285 OK
4th Floor EY 3 Y 0.001387 0.00534 OK
3rd Floor EX 1 X 0.003806 0.014653 OK
3rd Floor EX 2 X 0.00389 0.014977 OK
3rd Floor EX 3 X 0.003858 0.014853 OK
3rd Floor EY 1 Y 0.001094 0.004212 OK
3rd Floor EY 2 X 0.000311 0.001197 OK
3rd Floor EY 2 Y 0.000973 0.003746 OK
3rd Floor EY 3 Y 0.001215 0.004678 OK
2nd Floor EX 1 X 0.00328 0.012628 OK
2nd Floor EX 2 X 0.003351 0.012901 OK
2nd Floor EX 3 X 0.003291 0.01267 OK
2nd Floor EY 1 X 0.000329 0.001267 OK
2nd Floor EY 1 Y 0.000905 0.003484 OK
2nd Floor EY 2 X 0.000264 0.001016 OK
2nd Floor EY 2 Y 0.000804 0.003095 OK
2nd Floor EY 3 Y 0.001006 0.003873 OK
1st Floor EX 1 X 0.002602 0.010018 OK
1st Floor EX 2 X 0.002658 0.010233 OK
1st Floor EX 3 X 0.002584 0.009948 OK
1st Floor EY 1 X 0.000252 0.00097 OK
1st Floor EY 1 Y 0.000681 0.002622 OK
1st Floor EY 2 X 0.000204 0.000785 OK
1st Floor EY 2 Y 0.000604 0.002325 OK
1st Floor EY 3 X 0.0003 0.001155 OK
1st Floor EY 3 Y 0.000757 0.002914 OK
Ground Floor EX 1 X 0.001651 0.006356 OK
Ground Floor EX 2 X 0.001682 0.006476 OK
Ground Floor EX 3 X 0.001621 0.006241 OK
Ground Floor EY 1 X 0.000143 0.000551 OK
Ground Floor EY 1 Y 0.000398 0.001532 OK
Ground Floor EY 2 X 0.000116 0.000447 OK
Ground Floor EY 2 Y 0.000353 0.001359 OK
Ground Floor EY 3 X 0.00017 0.000655 OK
Ground Floor EY 3 Y 0.000444 0.001709 OK
Basement 1 EX 1 X 0.000482 0.001856 OK
Basement 1 EX 2 X 0.000492 0.001894 OK
Basement 1 EX 3 X 0.000472 0.001817 OK
Basement 1 EY 1 X 0.000018 6.93E-05 OK
Basement 1 EY 1 Y 0.000085 0.000327 OK
Basement 1 EY 2 X 0.000029 0.000112 OK
Basement 1 EY 2 Y 0.000091 0.00035 OK
Basement 1 EY 3 X 0.000014 5.39E-05 OK
Basement 1 EY 3 Y 0.000087 0.000335 OK

Table 33 : Story Drift

8.3 Wind Analysis
Wind in the x-direction
H = 52.5 m
H/500 = 105 mm ; 76.6 mm

TABLE: Joint Displacements
Story Label Unique Name Load Case/Combo UX (mm) UY (mm)
Roof 4 73 Wind 1 76.618 -0.515
Roof 4 73 Wind 2 -6.328 17.596
Roof 5 91 Wind 1 76.618 -0.524
Roof 5 91 Wind 2 -6.328 15.788
Roof 9 163 Wind 1 76.643 -0.535
Roof 9 163 Wind 2 -1.545 13.817
Roof 23 415 Wind 1 76.57 -0.444
Roof 23 415 Wind 2 5.197 9.997
Roof 24 433 Wind 1 76.57 -0.411
Roof 24 433 Wind 2 5.197 7.65
Roof 119 2453 Wind 1 76.625 -0.522
Roof 119 2453 Wind 2 -4.909 16.278
Roof 120 2452 Wind 1 76.625 -0.515
Roof 120 2452 Wind 2 -4.909 17.596
Roof 121 2485 Wind 1 76.642 -0.515
Roof 121 2485 Wind 2 -1.858 17.596
Roof 125 3063 Wind 1 76.623 -0.524
Roof 125 3063 Wind 2 -5.324 15.788
Roof 128 2381 Wind 1 76.645 -0.515
Roof 128 2381 Wind 2 -1.25 17.596
Roof 129 2380 Wind 1 76.651 -0.515
Roof 129 2380 Wind 2 -0.113 17.596
Roof 130 2413 Wind 1 76.651 -0.524
Roof 130 2413 Wind 2 -0.113 15.788
Roof 131 2431 Wind 1 76.645 -0.524
Roof 131 2431 Wind 2 -1.256 15.788
Roof 134 2615 Wind 1 76.659 -0.445
Roof 134 2615 Wind 2 -1.06 10.097
Roof 135 2614 Wind 1 76.615 -0.445
Roof 135 2614 Wind 2 2.081 10.097
Roof 136 2647 Wind 1 76.615 -0.414
Roof 136 2647 Wind 2 2.081 7.924
Roof 137 2669 Wind 1 76.634 -0.41
Roof 137 2669 Wind 2 0.749 7.599
Roof 138 2668 Wind 1 76.614 -0.41
Roof 138 2668 Wind 2 2.144 7.599
Roof 140 3085 Wind 1 76.634 -0.437
Roof 140 3085 Wind 2 0.749 9.532
Roof 142 2939 Wind 1 76.659 -0.431
Roof 142 2939 Wind 2 -1.06 9.105
Roof 146 3031 Wind 1 76.642 -0.524
Roof 146 3031 Wind 2 -1.858 15.788
Roof 149 2881 Wind 1 76.659 -0.44
Roof 149 2881 Wind 2 -1.06 9.708
Roof 151 2938 Wind 1 76.659 -0.416
Roof 151 2938 Wind 2 -1.06 8.012
Roof 160 2987 Wind 1 76.629 -0.535
Roof 160 2987 Wind 2 -4.219 13.779
Roof 162 3030 Wind 1 76.64 -0.524
Roof 162 3030 Wind 2 -2.221 15.788
Roof 164 3114 Wind 1 76.665 -0.415
Roof 164 3114 Wind 2 -1.424 7.949
Roof 165 3115 Wind 1 76.665 -0.451
Roof 165 3115 Wind 2 -1.424 10.461
Roof 166 3116 Wind 1 76.609 -0.451
Roof 166 3116 Wind 2 2.445 10.461
Roof 167 3117 Wind 1 76.609 -0.45
Roof 167 3117 Wind 2 2.445 10.411
Roof 168 3118 Wind 1 76.567 -0.45
Roof 168 3118 Wind 2 5.411 10.411
Roof 169 3119 Wind 1 76.567 -0.409
Roof 169 3119 Wind 2 5.411 7.537
Roof 170 3120 Wind 1 76.635 -0.409
Roof 170 3120 Wind 2 0.687 7.537
Roof 171 3121 Wind 1 76.635 -0.415
Roof 171 3121 Wind 2 0.687 7.949
Roof 172 3127 Wind 1 76.616 -0.513
Roof 172 3127 Wind 2 -6.579 17.96
Roof 173 3128 Wind 1 76.616 -0.526
Roof 173 3128 Wind 2 -6.579 15.424
Roof 175 3129 Wind 1 76.627 -0.526
Roof 175 3129 Wind 2 -4.52 15.424
Roof 176 3130 Wind 1 76.627 -0.537
Roof 176 3130 Wind 2 -4.52 13.415
Roof 177 3131 Wind 1 76.643 -0.537
Roof 177 3131 Wind 2 -1.607 13.415
Roof 178 3132 Wind 1 76.643 -0.535
Roof 178 3132 Wind 2 -1.607 13.716
Roof 179 3133 Wind 1 76.644 -0.535
Roof 179 3133 Wind 2 -1.371 13.716
Roof 774 6333 Wind 1 76.64 -0.518
Roof 774 6333 Wind 2 -2.221 17.03
Roof 88 526 Wind 1 76.634 -0.535
Roof 88 526 Wind 2 -3.315 13.779
MAX 76.665 17.96
MIN -6.579 -0.537

Table 45 : Building Sway

? CHAPTER 9: DESIGN OF COLUMNS

Columns are structural compressive elements subjected to transfer gravity loads and a part of lateral loads such as wind and earthquake from the upper levels to the lower ones and then the foundations.
The majority of reinforced concrete columns are subjected to primary stresses caused by flexure, axial force, and shear. Secondary stresses associated with deformations are usually very small in most columns used in practice.

9.1 Types of Columns:

There are three major types of reinforced concrete columns:

Tied columns: they are members having rectangular, square or circular cross section that is reinforced with longitudinal main steel to resist bending that might exist on the column, and its tie should be individual with a corresponding spacing varying between 250 and 500mm.

A spiral column: has a circular or square cross section, and in both cases, it has continuous spiral to hold the longitudinal bars in their position during concrete casting.

A composite column: is consisted of reinforced concrete and I-Beam steel shape that reduces the effect of creep and shrinkage. It may be used as square or spiral column with a structural steel or I-Beam shape.

9.2 Reinforcement Limitation:

The percentage of longitudinal reinforcement must be: 1%; ? ; 8% ACI code.
For cross-sections larger than required for loading, minimum reinforcement may be computed for the reduced effective area Ag; (ACI 10.8.4). Note that the provided strength from reduced area and resulting Ast must be adequate for loading. ? = As / Ag Where, As = total area of longitudinal reinforcement Ag= gross area of section

Figure 14: Axial loads on vertical elements

9.3 Design methodology

The design of the column will be held using S-concrete software
Step 1: Loads are taken from ETAB for each floor
Step 2: extract them to excel and modify the position of the forces and moments to be suitable for s concrete:
P: axial force
T: torsion
Vz: secondary shear
My: secondary moment
Vy: primary shear
Mz: primary moment
Step 3: Units and code should be modified for Metric and ACI 2008.

Figure 16: S-concrete Load entry

9.4 Design of column C165x40 (all floors)

Figure 17 Interaction Diagram
For column C165x40 (Basement Floor)

9.5 Reinforcement detailing for columns

Figure 15: Column Reinforcement schedule

? CHAPTER 10: DESIGN OF SHEAR WALLS

Shear walls are vertical elements of the horizontal force resisting system. They are typically wood frame stud walls covered with a structural sheathing material like plywood.
When the sheathing is properly fastened to the stud wall framing, the shear wall can resist forces directed along the length of the wall. When shear walls are designed and constructed properly, they will have the strength and stiffness to resist the horizontal forces.
Shear walls should be located on each level of the structure including the crawl space. To form an effective box structure, equal length shear walls should be placed symmetrically on all four exterior walls of the building. Shear walls should be added to the building interior when the exterior walls cannot provide sufficient strength and stiffness or when the allowable span-width ratio for the floor or roof diaphragm is exceeded.

10.1 Functions of a shear wall

Shear walls must provide the necessary lateral strength to resist horizontal earthquake forces. When shear walls are strong enough, they will transfer these horizontal forces to the next element in the load path below them. These other components in the load path may be other shear walls, floors, foundation walls, slabs or footings.

10.2 Design of Wall SW2 (all floors):

10.3 Walls Reinforcement detailing:

Figure 16: Wall Reinforcement Schedule

? CHAPTER 11: DESIGN OF CORE WALLS

Some designers use the core walls as shear walls, however the core walls not all the times work as shear walls, like the elevator walls, or decorative walls which carry only small loads, the shear walls are a structurally bearing walls and used to resist the bending moments resulted from wind pressures and any lateral loads.
A core wall is provided around staircases or lift wells. As core walls may be inside the building, they may not be as effective as shear walls provided at the edges. Moreover, core walls will have openings. However, core walls are 3-dimensional and may have more stability.
Both of walls are used to carry the lateral force exerted on the structure due to wind, earthquake or any other lateral load.
Core walls are created with combination of walls. They are arranged like a core and generally located at the geometric center of the building to void torsion. Also, core is used to install lifts and to accommodate services.
In addition, we can say that core walls are combination of shear walls.

11.1 Design of irregular shape core wall

11.2 Core wall Reinforcement detailing:

Figure 17: Basement floor core wall detailing

? CHAPTER 12: FLAT SLABS

12.1 Overview

A type of reinforced concrete slab where loads are transferred directly to the columns without the use of beams.

12.2 Advantages and Disadvantages
Advantages Disadvantages
Easier reinforcement placement Span length is medium, it is not possible to have large spans
Ease of framework installation Deflection may be critical
Less construction time

Table 56: Advantages ; Disadvantages

Figure 18: Typical Floor Plan
12.3 Minimum Thickness

Table 67: Minimum Thickness
The longest span in the slab is about 6 meters long. So according to the code the minimum thickness is Ln/33, which gives a minimum thickness of 19 cm. But in this case the deflection was very high and exceeded the allowable value so we chose a slab thickness of 23 cm

12.4 Deflection

Figure 19: Maximum permissible computed deflection

12.5 Short term deflection

Figure 20: Short Term Deflection
The allowable short-term deflection is Ln/360 which is 1.52 cm. So, the short-term deflection is safe.

12.6 Long term deflection

Figure 21: Long Term Deflection
The allowable deflection for Long term deflection is Ln/240 which is 2.5 cm. So, the Long-Term Deflection is safe.
12.7 Punching Shear

Figure 22: Punching Shear

All results ; 1, punching shear does not exceed the capacity which is ok.

12.8 Slab Moments

Figure 23: X-Direction

Figure 24: Y-Direction

12.9 Slab Reinforcement

Figure 24: Additional Top Reinforcement X-direction

Figure 25: Additional Bottom Reinforcement X-direction

Figure 26: Additional Top Reinforcement Y-direction

Figure 27: Additional Bottom Reinforcement Y-direction

12.10 Slab Reinforcement Detailing’s

Figure 28: Top Reinforcement X-direction

Figure 29: Bottom Reinforcement X-direction

Figure 30: Top Reinforcement Y-direction

Figure 31: Bottom Reinforcement Y-direction

Figure 32: Additional Top Reinforcement X-direction

Figure 33: Additional Top Reinforcement Y-direction

? CHAPTER 13: RIBBED SLAB

13.1 Advantages

Hollow block slabs are good isolators for the sound and temperature because of the voids that are found in block. This why it is preferred to be used in residential building.
Good vibration resistance
Reduced self-dead load due to voids. Which lead to the reduction in the weight of the total structure.

13.2 Minimum Thickness

Table 18: Minimum Thickness for One Way Slabs.

For L = 5.2 m ? hmin = L/21 = 24.7 cm
Structural analysis was performed using finite element software and the concrete design was performed using SAFE software.
TRY ribbed slab of thickness 25 cm.

13.3 Ribs Direction

Zone 1

Zone 2

According to the geometry of slab: In zone 2 ribs are parallel to x-direction, while in zone 1 ribs are parallel to y direction

13.4 Deflection

Table 19:Maximum Allowable Deflection

Figure 34: Maximum Allowable Deflection Due to Long Term Deflection

Deflection check, the max value due to long term = 1.5 cm < allowable = L/240 = 2.3cm

13.5 Design of Ribs

Figure 35: BMD for Ribs

Figure 36: SFD for Ribs

13.6 Slab full detailing

Figure 37: Slab Distribution of Hollow Blocks

13.7 Design of Embedded Beams

Figure 38: Embedded Beam Reinforcement

Figure 39: Embedded Beam Reinforcement

? CHAPTER 14: FOUNDATION

Raft foundation is our choice for this project which is a single combined footing for the whole building and will support the high columns and walls loads.
In this case, piles where not necessary due to good soil bearing capacity.

Basic information:
Allowable net bearing capacity of soil is 300 KN/m2.
Concrete compressive strength f’c is 30 MPA.
Cover to reinforcement is 80 mm.
Loads on raft are exported from Etabs software and imported to Safe
Analysis of raft foundation using SAFE 2016

14.1 Raft Thickness

The thickness of the raft foundation is designed for punching shear capacity:
We tried thickness 800 mm but it wasn’t enough as seen for the intermediate columns:

So, we increased the thickness to 1300 mm and it was okay for punching shear:

14.2 Soil properties:
Bearing capacity 300 KN/m2
Subgrade modulus = 120*bearing capacity = 120*300 = 36000 KN/m3

Figure 40: Soil Properties
?
14.3 Concrete Properties
F’c = 30 MPa
weight per unit volume = 25 KN/m3
modulus of rupture = 0.625?f’c = 3.423

Figure 42: Concrete Properties
14.1 Check for Soil Pressure

Figure 43: Soil Pressure
Maximum value is -253.2 KN/m2 -300 (allowable bearing capacity of soil) ok So there is no need for piles
14.4 Check Punching Shear

All results ?V_u)?_R

O.K

15.6 Step 6: Detailing

The following points are to be remembered in detailing:
• The main reinforcement should be bent to follow the bottom profile of the stair.
• Near the landing the reinforcement should be taken straight up and then bent in the compression zone of landing.
• For tensile stress in the landing zone separate set of bars should be used as shown in the detailing.

• All the bars of the tensile reinforcement should be taken into the supports and anchorage and development length requirement must be fulfilled.
• Distribution bars should be used parallel to the width of the steps.

Figure 57: Detailing

? CHAPTER 16: BASEMENT WALL

Retaining wall is a structure that provides vertical or nearly vertical support to a differential level of masses of soil. They are used to bound soils between two different elevations often in areas of terrain possessing undesirable slopes or in areas where the landscape needs to be shaped severely and engineered for more specific purposes like hillside farming or roadway overpasses.
Retaining wall is a structure designed and constructed to resist the lateral pressure of soil when there is a desired change in ground elevation that exceeds the angle of repose of the soil.

A basement wall is thus one kind of retaining wall. The wall must resist the lateral pressures generated by loose soils or, in some cases, water pressures. In our project, there are 1 basement walls:

16.1 Soil Properties
??From H=0 to H=3m

?=?30?^o
? = 19KN/m³,
K? = 1-sin ? = 1-sin 30=0.5

16.2 Lateral Earth Pressure (soil Load)

??= K? ? H

??H=0 m ? ??=0 KN/m fig ##
H=3 m ? ??= 28.5 KN/m
Figure 58: Wall

16.3 Uniform live load
Ko x w = 5kN/m where w from highway and traffic load w= 10 KN/m
dealing with the retaining walls as continuous wall supported (pinned) at each slab and fixed down at the foundation level, the moments and reactions required for the design were calculated.

Figure 59: Acting Loads

Figure 60: SFD & BMD

This results in 2 moments, 1 positive and 1 negative providing that negative reinforcement in the direction of soil and positive reinforcement in the direction of building. For the ease of design, we used s-concrete

Figure 61: Wall Design

Figure 62: Wall Detailing

? CHAPTER 17: BILL OF QUANTITIES

Bar Weight (kg/m)
T8 0.395
T10 0.617
T12 0.888
T14 1.21
T16 1.58
T20 2.47
Table 20:Weight of steel

Item Price
Steel 800 $/ton
Concrete 80 $/ m3
Table 21:Unit Price

?
17.1 Flat Slab

Steel:
Mesh T12 @ 200mm ? In 1 m2, L = 5*1m*4 = 20 m/m2
Total Mesh Weight = 465 m2 * 20 m/m2 * 0.888 kg/m = 8258.4 kg = 8.25 tons
Additional Steel:
Bar Length (m) Weight (kg)
T12 1351 1203.3
Table 22:Steel in flat slab

Total Weight = 8.25 + 1.2 = 9.5 tons
Steel Price = 9.5 * 800$ = 7600 $
Concrete:
Total Area = 527 m2
Area of Voids = 62 m2
Net Area = 465 m2
Thickness = 23 cm
Volume = 465 * 0.23 = 107 m3
Concrete Price = 107*80$ = 8560 $
Total Price of Flat Slab = 16160 $
?
17.2 Ribbed Slab

Steel:
Ribs:
Bar Length (m) Weight (kg)
T12 1061 942
T16 1061 1676
Table 23:Steel in ribs

Weight of Steel in Ribs = 2618 kg = 2.618 tons
Beams Area:
Bar Length (m) Weight (kg)
T12 855 753
T14 879 1064
T16 850 1342
T20 445 1099
Table 24:Steel in beams

Weight of Steel in Beams = 4258 kg = 4.258 tons
Stirrups:
Spacing of Stirrups: each 150 mm
Number of Stirrups = 1840/ 0.15 = 12270 Stirrups
Length of Stirrup = 2 * (15+25) = 0.8 m
Bar Length (m) Weight (kg)
T8 2833 1119
Table 25:Steel for stirrups

Weight of Steel for Stirrups = 1119 kg = 1.119 tons

Shrinkage Mesh:
Bar Length (m) Weight (kg)
T8 2521 996
Table 26:Steel for shrinkage

Weight of Steel for Shrinkage = 996 kg = 0.996 tons
Total Weight of Steel = 2.6 + 4.258 + 1.119 + 0.996 = 9 tons
Steel Price = 9 * 800$ = 7200 $
Concrete:
Ribbed Area:
Volume = 292*(0.18*0.15+0.55*0.07)/0.55 = 35 m3
Beams Area:
Net Area = 172 m2
Volume = 172 * 0.25 = 43 m3
Total Volume of Concrete = 43 m3 + 35 m3 = 78 m3
Concrete Price = 78*80$ = 6240 $
Hollow Blocks:
# of Hollow Blocks = 2639 block
Block Price = 2639*1$ = 2639 $
Total Price of Ribbed Slab = 16079 $

Conclusion

In conclusion, 23 cm flat slab system cost 16160$ while 25 cm ribbed slab costs 16079$ which is approximately the same. Our choice is for ribbed slab because ribbed slabs are good isolators for the sound and temperature because of the voids that are found in block. This why it is preferred to be used in residential building.

? APPENDIX

Table 27: ACI – 318 Appendix E
List of Abbreviations/Acronyms

A
A = name for area
A_g = gross area, equal to the total area ignoring any reinforcement
A_s = area of steel reinforcement in concrete beam design
?A ‘?_s = area of steel compression reinforcement in concrete beam design
A_st = area of steel reinforcement in concrete column design
A_v = area of concrete shear stirrup reinforcement
ACI = American Concrete Institute
ASTM American Society for Testing and Material.
B
b = width, often cross-sectional
b_e = effective width of the flange of a concrete T beam cross section
b_f = width of the flange
b_w = width of the stem (web) of a concrete T beam cross section
C
Cover = shorthand for clear cover
C.C = center to center
D
d = effective depth from the top of a reinforced concrete beam to the centroid of the tensile steel
d´ = effective depth from the top of a reinforced concrete beam to the centroid of the compression steel
d_b = bar diameter of a reinforcing bar
DL = shorthand for dead load
DRG = drawing
E
E = modulus of elasticity or Young’s modulus
EQ or E = shorthand for earthquake load
E_c = modulus of elasticity of concrete
E_s = modulus of elasticity of steel
F
f = symbol for stress

fc = compressive stress
f’c = concrete design compressive stress
f_pu = tensile strength of the prestressing reinforcement
fs = stress in the steel reinforcement for concrete design
?f’?_s = compressive stress in the compression reinforcement for concrete beam design
f_y = yield stress or strength
H
h = cross-section depth
H = shorthand for lateral pressure load
h_nf = depth of a flange in a T section
I
I = moment of inertia
I_transformed = moment of inertia of a multilateral section transformed to one
P
P_o = maximum axial force with no concurrent bending moment in a reinforced concrete column
P_n = nominal column load capacity in concrete design
P_u = factored column load calculated from load factors in concrete design
R_n = concrete beam design ratio
S
s = spacing of stirrups in reinforced concrete
S = spacing of Rebar in reinforced concrete
T
t = name for thickness
T = name for a tension force
K
k = effective length factor for columns
L
l_d = development length for reinforcing steel
l_dh = development length for hooks
l_n = clear span from face of support to face of support in concrete design
L = name for length or span length, as is l
LL = shorthand for live load
M
Mn = nominal flexure strength with the steel reinforcement at the yield stress and concrete at the concrete design strength for reinforced concrete beam design
Mu = maximum moment from factored loads for LRFD beam design
U
U = factored design value
V
V_c = shear force capacity in concrete
?_c = shear strength in concrete design

Vs = shear force capacity in steel shear stirrups
Vu = shear at a distance of d away from the face of support for reinforced concrete beam design
W
wDL = load per unit length on a beam from dead load
w_ll = load per unit length on a beam from live load
w_Dl = load per unit length on a beam from died load

w_f = load per unit length on a flight- stair
w_L = load per unit length on a loading – stair
W = shorthand for wind load
X
x = horizontal distance
Y
y = vertical distance

?_1 = coefficient for determining stress block height, a, based on concrete strength, fc?
? = elastic beam deflection
? = strain
? = resistance factor
?_c = resistance factor for compression
? = density or unit weight
? = radius of curvature in beam deflection relationships
= reinforcement ratio in concrete beam design = As/bd
?_balanced = balanced reinforcement ratio in concrete beam design
? DIAMETER
?? ?_c = unit weight of concrete
UNIT
kN kilonewton
N newton
cm centimeter
m meter
mm millimeter

? REFERENCES

Building Code Requirements for Structural Concrete (ACI 318-2014)

American Society of Civil Engineering (ASCE 7-16)

Reinforced Concrete Design of Tall Buildings (Bungale S. Taranath)

Principles of Foundation Engineering (7th Ed – Braja M. Das)

Reinforced Concrete Mechanics & Design (6th Edition – James Mcgregor)

Structural Modeling of Buildings (Dr. Yehia Temsah)