design of reinforced concrete slabs by safe program

Al-Mansour University College Civil Engineering Department

DESIGN OF REINFORCED CONCRETE SLABS BY SAFE PROGRAM A Final Year Project Submitted to the Department Of Civil Engineering at Al-Mansour University College in Partial Fulfillment of the Requirements For the Degree Of BS.C in Civil Engineering. By 1-Ibrahem Thamer 2-Hairth Muthana 3-Assra Ali 4-Hawraa Alaaaldeen

Supervised by Dr. Ola Adel Qasim A.D 2016

A.H 1437

Abstract

Abstract

ABSTRACT Slabs are the flooring systems of most structures including office, commercial and residential buildings, bridges, sports stadiums and other facilities building. The main functions of slabs are generally to carry gravity forces, such as loads from human weight, goods and furniture, vehicles and so on. In modern structure design particularly for high rise buildings and basement structures, slabs as floor diaphragms help in resisting external lateral actions such as wind, earthquake and lateral earth load. The slab directly rests on beams or the column and load from the slab is directly transferred to the beams and columns and then to the foundation. To support heavy loads the thickness of slab near the support with the column is increased and these are called drops, or columns are generally provided with enlarged heads called column heads or capitals. Absence of beam gives a plain ceiling, thus giving better architectural appearance than in usual cases where beams are used. Designing of slabs depends upon whether it is a one-way or a two way slab, the end conditions and the loading. The design process of structural planning and design requires not only imagination and conceptual thinking but also sound knowledge of science of structural engineering besides the knowledge of practical aspects, such as recent design codes, bye laws, backed up by ample experience, intuition and judgment. The purpose of standards is to ensure and enhance the safety, keeping careful balance between economy and safety. Safe Program has a very interactive user interface which allows the user to draw the frame and input the load values dimensions and materials properties. Then according to the specified criteria assigned it analysis the structure and design the members with reinforcement details for reinforced concrete frames. The principle objective of this project is to analyze and design different slabs, beams, and columns using (Safe) program according to ACI Code. In order to design them, it is important to first obtain the plan of the particular building that is, positioning of the particular slab. There are many different methods for analysis of two-way reinforced concrete slabs. The most efficient methods depend on using certain factors given in different codes of reinforced concrete design which depend on coefficients taken from special Design of Reinforced Concrete Slabs by Safe Program

I

Abstract

tables available in codes. The other ways of analysis of two-way slabs are the direct design method and the equivalent frame method. But these methods usually need a long time for analysis of the slabs. These methods are approximate but practical and were formed in such a way that the moments are conservative because these methods neglected many important factors to obtain positive and negative bending moments by simple and fast way without complexity. The high accuracy in design calculations of structures is undesirable because there is no capability of estimating many factors affecting on design results such as live loads, material properties and methods of analysis and many other factors. In this research, a new program has been used to analyze the two-way slabs which is (safe), and the results of moments of final analysis of some examples have been compared with other different methods moments given in codes of practice. The comparison proof that this simple program gives good results and it can be used in analysis of two-way slabs instead of other methods. Different types of reinforced concrete slabs were choosing with different number of floors divisions, and analyzed by (Method II, direct design method and safe). A comparison between reinforcement depend on code methods and reinforcement details from safe program which shows that the safe program gives faster and a full map reinforcement details instead of losing time in the drawings. An excel programs were designed to calculate the moments in slabs with interpolations to factors.

This study is divided into Six chapters:  The first chapter presents the introduction and types of slabs.  The second chapter contains method of design of slabs.  The third chapter presents the drawing of slabs and the design and analysis of slabs by Method II with Safe Program.  The forth chapter presents the design and analysis of slabs by Direct Design Method.  The fifth chapter presents the Comparison of Method II with Direct design and program.  The Six chapters present the conclusions and recommendations of this study. Design of Reinforced Concrete Slabs by Safe Program

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Supervisor Certification

I certify that this project entitled (DESIGN OF REINFORCED CONCRETE SLABS BY SAFE PROGRAM) was prepared under my supervision in Al-Mansour University College as partial fulfillment of requirement for the degree of B.Sc in Civil Engineering.

Signature: Supervisor Name: Dr. Ola Adel Qasim Date:

/

/2016

Committe Certification

We certify that we have read this project entitled (DESIGN OF REINFORCED CONCRETE SLABS BY SAFE PROGRAM) and, we as the examming committee examined the students in its content and they did all the change we required and in our opinion it meets the standard of project for the degree of B.Sc in Civil Engineering.

Signature:

Signature:

Name:

Name:

Date:

/

/2016 (Chairman)

Signature: Name: Dr. Date:

/

/2016 (Supervisor)

Date:

/

/2016

(Member)

Contents

List of Contents SUBJECT Acknowledgment. Abstract. List of Contents. List of Symbols List of Tables. List of Figures.

PAGE NO. I III V VI VIII

Chapter One: Introduction 1-1Types of Slabs. 1-2 Choice Of Type Of Slab Floor. 1-3 Types of RCC Slabs. 1-3-1 Flat Plate System. 1-3-2 Ribbed and waffle slabs System. 1-3-3 Flat slabs. 1-3-4 One-way slabs. 1-3-5 Two-way slabs. 1-4 What is the basic difference between a slab and beam. 1-5 Openings in Slabs. 1-6 Types of Beam. 1-7 Column. 1-8 SAFE System. 1-8-1 The program deals in general with the following structural elements. 1-8-2 Safe used the following codes in design. 1-8-3 Input/Output Graphical Displays. 1-9 Design for ACI 318-08. 1-9-1 Design Load Combinations. 1-9-2 Limits on Material Strength. 1-9-3 Strength Reduction Factors. 1-9-4 Beam Design. 1-9-5 Design Flexural Reinforcement. 1-9-6 Determine Factored Moments. 1-9-7 Determine Required Flexural Reinforcement. 1-9-8 Slab Design. 1-9-9 Design for Flexure. 1-9-10 Determine Factored Moments for the Strip. 1-9-11 Design Flexural Reinforcement for the Strip. 1-9-12 Minimum and Maximum Slab Reinforcement. 1-9-13 Check for Punching Shear. 1-10 Scope of Work.

1 1 2 3 3 4 5 6 7 8 8 9 9 10 11 11 12 12 12 12 12 12 12 13 13 13 13 14 14 14 14

Chapter Two: Method of Design and analysis. 2-1 Analysis of Slabs. 2-2 ACI- Moment Coefficient for Two-Way Slab. Design of Reinforced Concrete Slabs by Safe Program

15 15 III

2-3 Direct design method (DDM). 2-4 Depth Limitations. 2-4-1 Slabs without Interior Beams. 2-4-2 Slabs with Interior Beams. 2-5 Distribution of Moments in Slabs.

16 18 18 20 20

Chapter Three: Design and Analysis of Slabs by Program and Method II. 3-1 Slab (work 1) CSI SAFE-Analysis and Design of Slab with interior Beams. 3-1-1 Prosperities and Descriptions of Slabs. 3-2 Slab (work 2) CSI SAFE-Analysis and Design of Slab with Beam. 3-2-1 Prosperities and Descriptions of Slabs.

24 24 36 36

Chapter Four: Design and Analysis of Slabs by Program and Direct Design Methods. 4-1 Types of Slabs and method of Calculations (direct design method). 4-1-1 Direct design Method (D.D.M). 4-1-2 Determination of two way slab thickness. 4-1-3 Estimating dimensions of Interior and Exterior Beams Sections. 4-1-4 Design Procedure. 4-1-5 Analysis of Slabs by Direct Design Method. 4-2 Slab (work 3) CSI SAFE-04-Analysis and Design of Slab without Interior Beam by Direct Design Method. 4-2-1 Prosperities and Descriptions of Slabs. 4-3 Slab (work 4) CSI SAFE-04-Analysis and Design of Slab without Interior Beam by Direct Design Method. 4-3-1 Prosperities and Descriptions of Slabs. 4-4 Slab (work 5) CSI SAFE-02-Analysis and Design of Slab with Beam. 4-4-1 Prosperities and Descriptions of Slabs. 4-5 Slab (work 6) CSI SAFE-04-Analysis and Design of Slab with Interior Beam by Direct Design Method. 4-6 Slab (work 7) CSI SAFE-04-Analysis and Design of Slab with Interior Beam by Direct Design Method.

41 42 42 43 43 46 46 46 52 52 56 56 63 69

Chapter Five: Comparison of Method II with Direct design & (SAFE) program. 5-1 Slab (work 8) CSI SAFE-Analysis and Design of Slab with Beam. 5-2 Prosperities and Descriptions of Slabs. 5-3 Analysis by using ACI 318M Method II. 5-4 Slab (work 9) CSI SAFE Analysis and Design of Slab.

73 73 75 78

Chapter Six: Conclusions and Recommendations. 6-1 Conclusions. 6-2 From compare the results between hands calculate and the program we find that. 6-3 Recommendations

85 86 86

References

Design of Reinforced Concrete Slabs by Safe Program

IV

List of Symbols Symbols A Ec Es L fc’ fy I hf (𝑦̅) Ib IS

∝𝑓

ln β 𝑀0 𝑙. 𝑙 D.l 𝑊𝑢 𝑉𝑢@𝑑 ∅𝑉𝑐 L 𝑙2 𝑙1 −𝑣𝑒 𝑀 𝑖𝑛𝑡 +𝑣𝑒 𝑀 −𝑣𝑒 𝑀 𝑐. 𝑠 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 b d

Definitions

Units

Cross Section area of reinforcement Modulus of elasticity of concrete, psi Modulus of elasticity of reinforcement Span length Ultimate compressive strength of concrete as Determined by cylinder at age of 28 days The yield stress of steel Moment of inertia Thickness of slab Distance from the top of the beam to it neutral axis The moment of inertia for the beams The moment of inertia of the gross section of the slab taken about the centroid axis and equal to h3/12 limes the slab width, where the width is the same as for α.

mm2 Mpa Mpa m, mm

Represent the ratio of the flexural stiffness (EcbIb) of a beam section to the flexural stiffness of the slab (EcsIs) whose width equals the distance between the centerlines of the panels on each side of the beam. The clear span in the long direction, measured face to face, of beams. The ratio of the long to the short clear span. Total moment applied on the frame Live load Dead load Ultimate factored load Shear force came from 𝑊𝑢 acting at distance=d on the slab from beam face Factored concert shear strength The largest distance carry the load 𝑊𝑢 to make maximum shear 𝑉𝑢@𝑑 Transfers length of span c/c Longitudinal length span c/c Negative moment Positive moment Negative moment of column stripe Positive moment of middle strip Width of section, in Distance from compression face to tension reinforcement, in


Mpa Mpa mm4 mm mm mm4 mm4

Unit less

mm dimension less kN.m kN.m kN.m kN.m kN kN m

m ,mm m, mm kN.m kN.m kN.m kN.m m, mm m, mm V

List of Tables Table No.

Subject

PAGE NO.

Chapter Two: Method of Design and analysis. (2-1) (2-2) (2-3) (2-4)

Coefficients of Method II. Table 9.5 (c): Minimum thickness of slabs without interior beams. Distribution factors applied to static moment Mo for positive and negative moments in end span. Column strip factored moments.

16 18 22 23

Chapter Three: Design and Analysis of Slabs by Program and Method II. (3-1) (3-2) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) (3-10)

Geometry and Descriptions of Slabs, Beam and Column. Concrete and steel Prosperities of slabs, beam and column. Loads Types and Calculations. Calculation of Moments for all slabs. Comparison of moment by method II and Safe. Geometry and descriptions of slabs, beam and column. Concrete Prosperities of slabs, beam and column. Loads Types and Calculations. Calculation of Moments for all slabs. Comparison of moment by method II and Safe.

24 24 24 25 36 36 37 37 39 40

Chapter Four: Design and Analysis of Slabs by Program and Direct Design Methods. (4-1) (4-2) (4-3) (4-4) (4-5) (4-6) (4-7) (4-8) (4-9) (4-10) (4-11) (4-12) (4-13) (4-14) (4-15) (4-16) (4-17)

minimum thickness of slabs without interior beams. distribution of total static moment in end spans. column strip factored moments. Geometry and descriptions of slabs, beam and column. Concrete and Steel Prosperities of slabs, beam and column. Loads Types and Calculations. Calculation of Moments for all slabs. Comparison of Moments for Strip (B). Comparison of Moments for Strip (C). Calculation of Moments for all slabs. Comparison of Moments for Strip (A). Calculation of Moments for all slabs. Comparison of Moments for Strip (A). Calculation of Moments for all slabs. Comparison of Moments for Strip (A). Calculation of Moments for all slabs. Comparison of Moments for Strip (A).

43 44 46 46 47 47 49 50 51 55 55 62 62 68 68 71 72

Chapter Five: Comparison of Method II with Direct design & (SAFE) program. (5-1) (5-2) (5-3) (5-4)

Geometry and descriptions of slabs, beam and column. Concrete and steel Prosperities of slabs, beam and column. Loads Types and Calculations. Interpolation Program for Solving Coefficients of Method II.


73 73 73 74 VI

(5-5) (5-6) (5-7) (5-8)

Calculation of Moments for all slabs. Calculation of Moments for all slabs. Calculation of Moments for Strip A by direct design method. Calculation of Moments by direct design method.


75 76 76 79

VII

List of Figures Figure No. Chapter One: Introduction (1-1) (1-2) (1-3) (1-4) (1-5) (1-6) (1-7) (1-8) (1-9) (1-10) (1-11)

Subject

Multi story building Flat plate system Ribbed and waffle system Flat slabs system One way slabs system Two way slabs system Slabs beam system Opening in slabs Common type of beams Exterior and interior column. Safe program

PAGE NO. 1 3 4 5 5 6 8 8 9 9 11

Chapter Two: Method of Design and analysis. (2-1) (2-2) (2-3) (2-4) (2-5)

Column strip for slab design by Direct design method. Examples of the portion of slab to be included with we beam under 13.2.4 Distribution of total static moment to critical section for positive and negative bending Final distribution of moments Torsional cross sectional dimensions for βt calculations.

18 19 21 22 23

Chapter Three: Design and Analysis of Slabs by Program and Method II. (3-1) (3-2) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) (3-10) (3-11) (3-12) (3-13)

3*3 span slab. Multi story (3*3 span slab). Program definition for design of slabs. Entry of slab shape and size. Entry of slab and beam and column properties. Entry of load types and factors. Deformation shape of slab. Results of program (slab forces, beam forces, axial force, stresses, moment, shear, reactions and punching shear). Results of program (slab moment, strip moment if short and long direction). Results of program (slab design and reinforcement). 3*3 span slab and strip position. Results of program (slab moment, strip moment if short and long direction). Deformation shape of slab.

25 26 27 28 29 30 31 33 34 35 37 38 39

Chapter Four: Design and Analysis of Slabs by Program and Direct Design Methods. (4-1) Type of two way slabs and method of design (4-2) Multi span slab (4-3) Effective beam section (a-interior beam, b-exterior beam). (4-4) Moment distribution. (4-5) Full map for building by safe program (4-6) Full map for building by Auto-cad program Design of Reinforced Concrete Slabs by Safe Program

41 41 43 44 47 48 VIII

(4-7) (4-8) (4-9) (4-10) (4-11) (4-12) (4-13) (4-14) (4-15) (4-16) (4-17) (4-18) (4-19) (4-20) (4-21) (4-22) (4-23)

Design strips for calculations of moments by safe program. Moment in negative and positive in slab. Column Strip Moment by Safe Program. Two way solid slab with beams Design strips and strip moment by safe program Beam sectional properties for relative stiffness calculations. Beam Sectional Properties for relative stiffness calculation. Design strips and strip moment by safe program. Moment in negative and positive in slab. Full map for building by safe program. Beam shape and position by safe program. Design strips for calculations of moments by direct design Method. Design strips and strip moment by safe program. Two way slabs dimensions. Column Strip Moment by Safe Program. Design strips for calculations of moments by safe program. Column Strip Moment by Safe Program.

48 51 52 53 53 53 54 56 56 57 58 58 63 63 68 69 72

Chapter Five: Comparison of Method II with Direct design & (SAFE) program. (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (5-7) (5-8) (5-9) (5-10)

Slab span and dimensions. Slabs strip moment. Slab span and dimensions. bending moment diagram for column strip and the second for middle strip. reinforcement layout. program design preferences. program slabs design. entering of data. full bottom reinforcement of slabs from program. top bottom reinforcement of slabs from program.


74 77 78 79 80 81 82 82 83 84

IX

Chapter One

Introduction

Chapter one

Introduction

Chapter One INTRODUCTION 1-1Types of Slabs: A concrete slab is common structural element of modern buildings. Horizontal slabs of steel reinforced concrete, typically between (100 and 500 millimeters) thick are most often used to construct floors and ceilings. On the technical drawings, reinforced concrete slabs are often abbreviated to "R.C.C.slab" or simply "R.C.". A reinforced concrete slab is abroad flat plate usually with nearly parallel top and bottom surfaces and may supported by reinforced concrete beams or directly by columns or masonry brick wall or reinforced concrete walls (Shear walls).

Fig. (1-1) Multi-story Building.

1-2 Choice Of Type Of Slab Floor: The choice of type of slab for a particular floor depends on many factors. Economy of construction is obviously an important consideration, but this is a qualitative argument until specific cases are discussed, and is a geographical variable. The design loads, required spans, serviceability requirements, and strength requirements are all important. For beamless slabs, the choice between a flat slab and a flat plate is usually a matter of loading and span. Flat plate strength is often governed by shear strength at the Design of Reinforced Concrete Slabs by Safe Program

1

Chapter one

Introduction

columns, and for service live loads greater than (4.8 kN/m2) and spans greater than about (7 to 8 m) the flat slab is often the better choice. If architectural or other requirements rule out capitals or drop panels, the shear strength can be improved by using metal shear heads or some other form of shear reinforcement, but the costs may be high. Serviceability requirements must be considered, and deflections are sometimes difficult to control in reinforced concrete beamless slabs. Large live loads and small limits on permissible deflections may force the use of large column capitals. Negativemoment cracking around columns is sometimes a problem with flat plates, and again a column capital may be useful in its control. Deflections and shear stresses may also be controlled by adding beams instead of column capitals. If severe deflection limits are imposed, the two-way slab will be most suitable, as the introduction of even moderately stiff beams will reduce deflections more than the largest reasonable column capital is able to. Beams are also easily reinforced for shear forces. The choice between two-way and beamless slabs for more normal situations is complex. In terms of economy of material, especially of steel, the two-way slab is often best because of the large effective depths of the beams. There is a natural human tendency to want to repeat what one has previously done successfully, and resistance to change can affect costs. However, old habits should not be allowed to dominate sound engineering decisions. 1-3 Types of RCC Slabs: RCC slab can be various types depending on various criteria. Such as ribbed slab, flat slab, solid slab, continuous slab, simply supported slab etc. Today we are going to discuss the types of solid RCC slabs. For a suspended slab, there are a number of designs to improve the strength-to-weight ratio. In all cases the top surface remains flat, and the underside is modulated: 

Corrugated, usually where the concrete is poured into a corrugated steel tray. This improves strength and prevents the slab bending under its own weight. The corrugations run across the short dimension, from side to side.



A ribbed slab, giving considerable extra strength on one direction.


2

Chapter one 

A waffle slab, giving added strength in both directions.



A one way slab has structural strength in shortest direction.



A two way slab has structural strength in two directions.

Introduction

RCC solid slabs are three types depending on design criteria. 1-3-1 Flat Plate System: A flat plate is a one or two-way system usually supported directly on columns or load bearing walls. It is one of the most common forms of construction of floors in buildings. The principal feature of the flat plate floor is a uniform or near-uniform thickness with a flat soffit which requires only simple formwork and is easy to construct.

Fig. (1-2) Flat Plate System.

1-3-2 Ribbed and waffle slabs System: Ribbed and waffle slabs provide a lighter and stiffer slab than an equivalent flat slab, reducing the extended of foundations. They provide a very good form where slab vibration is an issue, such as laboratories and hospitals. Ribbed slabs are made up of wide band beams running between columns with equal depth narrow ribs spanning the orthogonal direction. A thick top slab completes the system. Waffle slabs tend to be deeper than the equivalent ribbed slab. Waffle slabs have a thin topping slab and narrow ribs spanning in both directions between column heads or band beams. The column heads or band beams are the same depth as the ribs. Ribbed floors consisting of equally spaced ribs are usually supported directly by columns. They are either one-way spanning systems known as ribbed slab or a two-way ribbed system known as a waffle slab. This form of construction is not very common because of the formwork costs and the low fire rating.


3

Chapter one

Introduction

Fig. (1-3) Ribbed and waffle slabs System.

1-3-3 Flat slabs: Flat slabs are highly versatile elements widely used in construction, providing minimum depth, fast construction and allowing flexible column grids. It is, also called as beamless slab, is a slab supported directly by columns without beams. A part of the slab bounded on each of the four sides by centre line of column is called panel. The flat slab is often thickened closed to supporting columns to provide adequate strength in shear and to reduce the amount of negative reinforcement in the support regions. The thickened portion i.e. the projection below the slab is called drop or drop panel. In some cases, the section of column at top, as it meets the floor slab or a drop panel, is enlarged so as to increase primarily the perimeter of the critical section, for shear and hence, increasing the capacity of the slab for resisting two-way shear and to reduce negative bending moment at the support. Such enlarged or flared portion of and a capital. Slabs of constant thickness which do not have drop panels or column capitals are referred to as flat plates. The strength of the flat plate structure is often limited due to punching shear action around columns, and consequently they are used for light loads and relatively small spans. The load from the slabs is directly transferred to the columns and then to the foundation.


4

Chapter one

Introduction

Fig. (1-4) Flat slabs System.

1-3-4 One-way slabs: A one-way slab needs moment resisting reinforcement only in its short-direction because the moment along long axes is so small that it can be neglected. When the ratio of the length of long direction to short direction of a slab is greater than 2 it can be considered as a one way slab. One way slab is supported on two opposite side only thus structural action is only at one direction. Total load is carried in the direction perpendicular to the supporting beam. If a slab is supported on all the four sides but the ratio of longer span (l) to shorten span (b) is greater than 2, then the slab will be considered as one way slab. Because due to the huge difference in lengths, load is not transferred to the shorter beams. Main reinforcement is provided in only one direction for one way slabs.


5

Chapter one

Introduction

Fig. (1-6) One-way slabs System.

1-3-5 Two-way slabs: Slabs categorized into two types, in general according to load transfer. When slabs supported on two opposite sides only which case the structural action of the slab is essentially one–way the loads being carried by the slab in the direction perpendicular to the supporting sides. There may be supports (Beams) on all four sides that two-way slab action is obtained. Intermediate beams may be provided. If the ratio of length to width of one slab panel is larger than about (2) most of the load is carried in the short direction to supporting beams and one-way action is obtained in effect even though supporting beams are provided on all sides. Two-way transfers the loaded and the slabs deflection two directions. When a Solid RCC slab rests on four beams but long-span of slab is less than or equal to two times of short-span then we can call that slab a “two-way slab”. In two-way slab, main reinforcement runs both in short and long direction and stay perpendicularly with one another.


6

Chapter one

Introduction

Fig. (1-5) Two-way slabs System.

Difference between One Way Slab and Two Way Slab: There are some basic differences between one way slabs and two way slabs. To clear the concept of one way and two way slabs a table is shown below. One Way Slab One way slab is supported by beams in only 2 sides. The ratio of longer span panel (L) to shorter span panel (B) is equal or greater than 2. Thus, L/B >= 2 Main reinforcement is provided in only one direction for one way slabs.

Two Way Slab Two way slab is supported by beams in all four sides. The ratio of longer span panel (L) to shorter span panel (B) is less than 2. Thus, L/B < 2. Main reinforcement is provided in both the direction for two way slabs.

1-4 What is the basic difference between a slab and beam?  Slab, more precisely concrete Slab is a common structural element of modern building. That is usually horizontal and has smaller thickness comparative of its span. Slabs are used to furnish a flat and useful surface in reinforced concrete construction.  Beam is a structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment. Beams are characterized by their profile (shape of cross-section), their length, and their material. Its a structural member constructed to transfer the loads from slab to the column. Slab on Beam can construct at all levels. It transfers load to beam and then on to the columns. This can ensure differential settlement up to one point. The initial


7

Chapter one

Introduction

construction cost is higher than slab on grade because formwork at the slab underside and the reinforcement to join beam and slab is needed.

Fig. (1-7) Slabs-Beam System.

1-5 Openings in Slabs: Almost invariably, flab systems must include openings. These may be of substantial size, as required by stairways and elevator shafts, or they may be of smaller dimensions, such as those needed to accommodate heating, plumbing, and ventilating risers; floor and roof drains; and access hatches. Relatively small openings usually are not detrimental in beam-supported slabs. As a general rule, the equivalent of the interrupted reinforcement should be added at the fides of the opening. Additional diagonal bars should be included at the corners to control the cracking that will almost inevitably occur there.

Fig. (1-8) Opening in Slab.

1-6 Types of Beam: Beams can be described as members that are mainly subjected to flexure and it is essential to focus on the analysis of bending moment, shear, and deflection. When the bending moment acts on the beam, bending strain is produced. The resisting moment is developed by internal stresses. Under positive moment, compressive strains are Design of Reinforced Concrete Slabs by Safe Program

8

Chapter one

Introduction

produced in the top of beam and tensile strains in the bottom. The most common shapes of concrete beams are single reinforced rectangular beams, doubly reinforced rectangular beams, T-shape beams, spandrel, the T-shape and L-shape beams are typical types of beam because the beams are built monolithically with the slab. When slab and beams are poured together, the slab on the beam serves as the flange of a T-beam and the supporting beam below slab is the stem or web.

Fig. (1-9) Common type of beams

1-7 Column: Columns support primarily axial load but usually also some bending moments. The combination of axial load and bending moment defines the characteristic of column and calculation method. To resist shear, ties or spirals are used as column reinforcement to confine vertical bars. Reinforced concrete columns are categorized into five main types; rectangular tied column, rectangular spiral column, round tied column, round spiral column, and columns of other geometry (Hexagonal, L-shaped, T-Shaped, etc).

Fig. (1-10) Exterior and interior column.

1-8 SAFE System: SAFE program for the analysis and design of concrete flat roofs and foundations with different formats and multiple thicknesses designed depending on the specific model by the investor. SAFE is special purpose software that automates the analysis and Design of Reinforced Concrete Slabs by Safe Program

9

Chapter one

Introduction

design process for the structural engineer with finite element method, lending greater sophistication to the engineering of slab systems. It is designed to minimize engineering man-hours and processing time associated with the design of concrete slab systems. It features a powerful graphical user interface unmatched in terms of ease-of-use and productivity. Creation and modification of the slab model, execution of the analysis, checking and optimization of the design and production of graphical displays of the results are all controlled through this single interface. The SAFE program will analyze and design slabs of arbitrary geometry including drop panels, openings, edge beams and embedded beams subjected to vertical point, line or surface loads. Column supports, wall supports, or soil supports for basemats can be modeled. Discontinuities in the slab system, due to slip joints or differences in slab elevations can be included. The slab is modeled with orthotropic plate elements. The design strip moments are obtained by integrating the finite element stresses using an algorithm that always satisfies equilibrium and accounts for the effects of twisting moments. The program was produced in the US construction Specifications Institute, which is symbolized by (CSI) after it was designed at the University of Berkeley in the state of California and is expressed for the program name (SAFE) (Slab analysis by the finite element method). 1-8-1 The program deals in general with the following structural elements: 1-two way slabs.

2-wafle slabs.

3-ripped slabs.

4-flat slab with drop panel and /or column capitals. The program calculates the following: Slabs reinforcing calculate based on user define design strip. Deflection calculates based on cracked section. Flexural and shear design of beams. Punching shear ratio.


10

Chapter one

Introduction

Fig. (1-11) Safe Program.

1-8-2 Safe used the following codes in design: 1-Design for ACI 318-08 2-Design for AS 3600-01 3-Design for BS 8110-97 4-Design for CSA A23.3-04 5-Design for Eurocode 2-2004 6-Design for Hong Kong CP-04 7-Design for IS 456-2000 8-Design for NZS 3101-06 9-Design for Singapore CP-65-99 10-Design for AS 3600-09 1-8-3 Input/Output Graphical Displays: • Undeformed structural geometry • Loading diagrams • Deformed shapes with animation • Slab displacement, moment, shear and bearing pressure contours • User controlled stress averaging for contours • Beam moment and shear diagrams • Reaction force diagrams • Integrated strip moment and shear diagrams • Numerical values of results shown as pointer moves over display analysis Options • Arbitrary geometry of slabs and basemats • Thickness variations, drop panels and openings • Edge beams and other beam support conditions • Slab shear and moment discontinuities due to slip joints or slab elevations • Column, wall or soil supports • Point loads, line loads, surface loads, self-weight • Orthotropic bending with thick and thin plate options • Beam element with flexural, shear and torsional deformations • Variations in soil modulus of subgrade reaction • Stiffness effect of walls • Automated cracked property calculations • Nonlinear no-tension soil model • Multiple load cases Design of Reinforced Concrete Slabs by Safe Program

11

Chapter one

Introduction

1-9 Design for ACI 318-08: Detail the various aspects of the concrete design procedure that is used by SAFE when the American code [ACI ] is selected. 1-9-1 Design Load Combinations: Various combinations of the load cases for which the structure needs to be designed. For ACI 318-08, a structure is subjected to dead (D), live (L), pattern live (PL), snow (S), wind (W), and earthquake (E) loads. 1-9-2 Limits on Material Strength: SAFE continues to design the members based on the input. 1-9-3 Strength Reduction Factors: The strength reduction factors are applied to the specified strength to obtain the design strength provided by a member as (ACI Code). 1-9-4 Beam Design: SAFE calculates and reports the required areas of reinforcement for flexure, shear, and torsion based on the beam moments, shear forces, torsion, load combination factors, and other criteria described in this section. The reinforcement requirements are calculated at each station along the length of the beam. 1-9-5 Design Flexural Reinforcement: The beam top and bottom flexural reinforcement is designed at each station along the beam. In designing the flexural reinforcement for the major moment of a particular beam, for a particular station, the following steps are involved:  Determine factored moments  Determine required flexural reinforcement 1-9-6 Determine Factored Moments: In the design of flexural reinforcement of concrete beams, the factored moments for each load combination at a particular beam station are obtained by factoring the corresponding moments for different load cases, with the corresponding load factors.


12

Chapter one

Introduction

The beam is then designed for the maximum positive and maximum negative factored moments obtained from all of the load combinations. 1-9-7 Determine Required Flexural Reinforcement: The program calculates both the tension and compression reinforcement. When the applied moment exceeds the moment capacity at this design condition, the area of compression reinforcement is calculated assuming that the additional moment will be carried by compression reinforcement and additional tension reinforcement. 1-9-8 Slab Design: SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The moments for a particular strip are recovered from the analysis, and a flexural design is carried out based on the ultimate strength design method (ACI 318-08). 1-9-9 Design for Flexure: SAFE designs the slab on a strip-by-strip basis. The moments used for the design of the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors. Those moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh. The design of the slab reinforcement for a particular strip is carried out at specific locations along the length of the strip. These locations correspond to the element boundaries. Controlling reinforcement is computed on either side of those element boundaries. The slab flexural design procedure for each load combination involves the following:  Determine factored moments for each slab strip.  Design flexural reinforcement for the strip. The maximum reinforcement calculated for the top and bottom of the slab within each design strip, along with the corresponding controlling load combination, is obtained and reported. 1-9-10 Determine Factored Moments for the Strip: Design of Reinforced Concrete Slabs by Safe Program

13

Chapter one

Introduction

For each element within the design strip, for each load combination, the program calculates the nodal reactive moments. The nodal moments are then added to get the strip moments. 1-9-11 Design Flexural Reinforcement for the Strip: The reinforcement computation for each slab design strip, given the bending moment, is identical to the design of rectangular beam sections described earlier. 1-9-12 Minimum and Maximum Slab Reinforcement: The minimum flexural tension reinforcement required for each direction of a slab is given by ACI Limit. 1-9-13 Check for Punching Shear: The punching shear is checked on a critical section at a distance of d/2 from the face of the support (ACI Limit for shear). For rectangular columns and concentrated loads, the critical area is taken as a rectangular area with the sides parallel to the sides of the columns or the point loads. The spacing between adjacent shear reinforcement shall not exceed 2d measured in a direction parallel to the column face. 1-10 Scope of Work: The project works is concerned with the analysis and design of different slabs with beams between interior supports and slabs with edge beam. Analysis of slab using software program (SAFE). A hand calculation used (method II and direct design method for analysis of slabs and compare it with computer program) to show that the safe program is faster and easier for solution than the others method. A computer program for the design of reinforced concrete two-way slabs made by excel worksheet used for design the slabs by method II and direct design method. 1. To use Autocad to sketch the floor plan and the details. 2. To use Microsoft EXCEL to facilitate the computations. 3. To use Safe package for the analysis of Multi story building. 4. To familiarize with ACI Code and other codes. 5. To use Reinforced concrete design Suite for the design of slabs, beams, column. Design of Reinforced Concrete Slabs by Safe Program

14

Chapter Two

Methods of Design and Analysis

Chapter Two

Design Method and Program

Chapter Two Methods of Design and Analysis 2-1 Analysis of Slabs: The slab provides a horizontal surface and is usually supported by columns, beams or walls. Slabs can be categorized into two main types: one-way slabs and two-way slabs. One-way slabs are supported by two opposite sides and bending occurs in one direction only. Two-way slabs are supported on four sides and bending occurs in two directions. One-way slabs are designed as rectangular beams placed side by side. However, slabs supported by four sides may be assumed as one-way slab when the ratio of lengths to width of two perpendicular sides exceeds 2. Although while such slabs transfer their loading in four directions, nearly all load is transferred in the short direction. Two-way slabs carry the load to two directions, and the bending moment in each direction is less than the bending moment of one-way slabs. Also two-way slabs have less deflection than one-way slabs. Compared to one-way slabs, Calculation of two-way slabs is more complex. Methods for two-way slab design and analysis include, Moment Coefficient Method, Direct Design Method (DDM), Equivalent frame method (EFM), Finite element approach, and Yield line theory. This project aims to use one of the most important programs in the analysis and design of concrete Slabs, which is the (SAFE) program for accuracy of the solution and the accuracy of the results provided by program. A slab may be designed by any procedure satisfying conditions for equilibrium and geometrical compatibility. In this chapter, the design method of a two-way reinforced concrete slab is presented. The design procedure adopted in this work is based on provisions of ACI Code (Moment Coefficient Method and direct design method). 2-2 ACI- Moment Coefficient for Two-Way Slab: The values of moment coefficient are calculated for various ratios of dimensions of two-way slabs from 0.55 to 1, and different conditions of the edges supports as shown in Design of Reinforced Concrete Slabs by Safe Program

15

Chapter Two


the Tables (2-1). This method applies to solid and ribbed slabs, isolated or continuous, supported on all four sides by walls or beams built monolithically with the slab. The bending moments shall be computed from the formula: 𝑴 = (𝑪𝒐𝒆𝒇𝒇. )𝒘𝒍𝟐𝒔 w = total load per unit area. Is = length of short span, [center to center distance between supports or the clear span plus twice the thickness of slab, whichever is smaller]. The panel may be divided to two column and one middle strips with the middle strip occupying half the width of the panel. The average moment per unit width of the column strip shall be two-thirds of the corresponding moments in the middle strip. Table (2-1) Coefficients of Method II. Slab Case

1 m=

2

3

4

5

Long Direction

Short Direction Position -ve con -ve dis

1 0.033 ---

0.9 0.04 ---

Modular Ratio (m) 0.8 0.7 0.6 0.048 0.055 0.063 -------

0.5 0.083 ---

All 0.033 ---

+ve

0.025

0.03

0.036

0.041

0.047

0.062

0.025

-ve con -ve dis +ve -ve con -ve dis

0.041 0.021 0.031 0.049 0.025

0.048 0.024 0.036 0.057 0.028

0.055 0.027 0.041 0.064 0.032

0.062 0.031 0.047 0.071 0.036

0.069 0.035 0.052 0.078 0.039

0.085 0.042 0.064 0.09 0.045

0.041 0.021 0.031 0.049 0.025

+ve

0.037

0.043

0.048

0.054

0.059

0.068

0.037

-ve con -ve dis +ve -ve con -ve dis

0.058 0.029 0.044 --0.033

0.066 0.033 0.05 --0.038

0.074 0.037 0.065 --0.043

0.082 0.041 0.062 --0.047

0.09 0.045 0.068 --0.053

0.098 0.049 0.074 --0.055

0.058 0.029 0.044 --0.033

+ve

0.05

0.057

0.064

0.072

0.08

0.083

0.05

2-3 Direct design method (DDM): It is an approximate semi-empirical procedure for analyzing two way slab systems. It applies to slab supported by beams or walls, flat slab, flat plates and waffle slabs. The code provides a procedure with which a set of moment coefficients can be determined. The method, in effect, involves a single-cycle moment distribution analysis of the structure based on (a) the estimated flexural stiffness's of the slabs, beams (if any), and columns and Design of Reinforced Concrete Slabs by Safe Program

16

Chapter Two


(b) the tensional stiffness's of the slabs and beams (if any) transverse to the direction in which flexural moments are being determined. Some types of moment coefficients have been used satisfactorily for many years for slab design. They do not, however, give very satisfactory results for slabs with unsymmetrical dimensions and loading patterns. Direct Design Method (DDM) for slab systems with or without beams loaded only by gravity loads and having a fairly regular layout meeting the following conditions: 1. There must be three or more continuous spans in each direction. 2. Panels should be rectangular and the long span is no more than twice the short span being measured c to c of supports. 3. Successive span lengths center-to-center of supports in each direction shall not differ by more than 1/3 of the longer span. 4. Columns must be near the corners of each panel with an offset from the general column line of no more 10% of the span in each direction. 5. The opening shout not be of large size in slabs. 6. The live load should not exceed 3 times the dead load in each direction. All loads shall be due gravity only and uniformly distributed over an entire panel. 7. 6-If a panel is supported on all sides by beams, the relative stiffness of those beams in the two perpendicular directions, as measured by the following expression: 8. 0,2 ≤

∝𝑓1 𝑙22 ∝𝑓2 𝑙12

≤ 5 where

Shall not be less than 0.2 or greater than 5.0.

The panels are divided into column and middle strips, as shown in Figure below, and positive and negative moments are estimated in each strip. The column strip is a slab with a width on each side of the column centerline equal to one-fourth the smaller of the panel dimensions l1 or l2. It includes beams if they are present. The middle strip is the pan of the slab between the two column strips. The part of the moments assigned to the column and middle strips may be assumed to be uniformly spread over the strips. The percentage of the moment assigned to a column strip depends on the effective stiffness of that strip and on its aspect ratio, (where l1 is the length of span, center to center, of supports in the direction in which moments are being determined and l2 is the span length, center to center, of Design of Reinforced Concrete Slabs by Safe Program

17

Chapter Two


supports in the direction transverse to l1). Note that the Figure below shows column and middle strips in only one direction. A similar analysis must be performed in the perpendicular direction. The resulting analysis will result in moments in both directions.

Fig. (2-1) Column Strip for slab design by direct design method.

2-4 Depth Limitations: 2-4-1 Slabs without Interior Beams: For a slab without interior beams spanning between its supports and with a ratio of its long span to short span not greater than 2.0, the minimum thickness can be taken from [Table 9.5(c) in the ACI code]. The values selected from the table, however, must not be less than the following values (ACI 9.5.3.2): - Slabs without drop panels 125 mm. - Thickness of those slabs with drop panels outside the panels 100 mm. Table (2-2) Table 9.5 (c): Minimum thickness of slabs without interior beams.

Without drop panels3 Yield Strength fy MPa2

Exterior panels Without edge beams

Interior panels

With edge beams

With drop panels1 Exterior panels Without edge beams

Interior panels

With edge beams

280 ℓn/33 ℓn/36 ℓn/36 ℓn/36 ℓn/40 ℓn/40 420 ℓn/30 ℓn/33 ℓn/33 ℓn/33 ℓn/36 ℓn/36 520 ℓn/28 ℓn/31 ℓn/31 ℓn/31 ℓn/34 ℓn/34 1-For two-way construction, (ℓn is the length of clear span in the long direction, measured face-to-face of supports in slabs. without beams and face-to face of beams or other supports in other cases. Design of Reinforced Concrete Slabs by Safe Program

18

Chapter Two


2-for fy between the values given in the table, minimum thickness shall be determined by linear Interpolation. 3-Slabs with beams between columns along exterior edges. The value of αf for the edge beam shall not be less than 0.8.

Very often slabs are built without interior beams between the columns but with edge beams running, around the perimeter of the building. These beams are very helpful in stiffening the slabs and reducing the deflections in the exterior slab panels. The stiffness of slabs with edge beams is expressed as a function of αf , which used to represent the ratio of the flexural stiffness (EcbIb) of a beam section to the flexural stiffness of the slab (EcsIs) whose width equals the distance between the centerlines of the panels on each side of the beam. If no beams are used, as in the case for the flat plate, αf will equal 0. For slabs with beams between columns along exterior edges, αf for the edge beams may not be < 0.8. 𝛼𝑓 =

𝐸𝑐𝑏 𝐼𝑏 𝐸𝑐𝑠 𝐼𝑠

Ecb = the modulus of elasticity of the beam concrete. Ecs= the modulus of elasticity of the column concrete. lb=the cross moment of inertia about the centroidal axis of a section made up of the beam and the slab on each side of the beam extending a distance equal to the projection of the beam above or below the slab (whichever is greater,) but not exceeding four times the slab thickness (ACI 13.2.41). ls = the moment of inertia of the gross section of the slab taken about the centroidal axis and equal to h 3/12 limes the slab width, where the width is the same as for α. For monolithic or fully composite construction, a beam includes that portion of slab on each side of the beam extending a distance equal to the projection of the beam above or below the slab, whichever is greater, but not greater than four times the slab thickness.

Fig (2-2). Examples of the portion of slab to be included with the beam under 13.2.4


19

Chapter Two


2-4-2 Slabs with Interior Beams: To determine the minimum thickness of slabs with beams spanning between their supports on all sides, Section 9.5.3.3 of the code must be followed. Involved in the expressions presented there are span lengths, panel shapes, flexural stiffness of beams, steel yield stresses, and so on. In these equations, the following terms are used: ℓn = the clear span in the long direction, measured face to face, of beams. β = the ratio of the long to the short clear span. αfm = the average value of the ratios of beam-to-slab stiffness on all sides of a panel. The minimum thickness of slabs or other two-way construction may be obtained by substituting into the equations to follow, which are given in Section 9.5.3.3 of the code. In the equations, the quantity p is used to take into account the effect of the shape of the panel on its deflection, while the effect of beams (if any) is represented by αfm. a) For αfm< 0.2, the minimum thicknesses are obtained as they were for slabs without interior beams spanning between their supports. b) For 0,2 2.0, the thickness shall not be less than 90 mm. 𝑙

ℎ=

𝑓𝑦 𝑛(0.8+ 1400)

36+5 𝛽

2-5 Distribution of Moments in Slabs: The basic design procedure of a two-way slab system has five steps. 1. Determine moments at critical sections in each direction, normally the negative moments at supports and positive moment near mid-span. 2. Distribute moment's transverse at critical sections to column and middle-strip and if beams are used in the column strip, distribute column strip moments between slab and beam. 3. Determine the area of steel required in the slab at critical sections for column and middle strips. Design of Reinforced Concrete Slabs by Safe Program

20

Chapter Two


4. Select reinforcing bars for the slab and concentrate bars near the column, if necessary. The critical section for negative bending moment is taken at the face of rectangular supports, or at the face of an equivalent square support. The total moment, Mo, which is resisted by a slab equals the sum of the maximum positive and negative moments in the span. It is the same as the total moment that occurs in a simply supported beam. For a uniform load per unit area, qu, it is as follows: 𝑀0 =

(𝑞𝑢 𝑙2 )(𝑙1 )2 8

In this expression, l1, is the span length, center to center, of supports in the direction in which moments are being taken and l2 is the length of the span transverse to l1, measured center to center of the supports. The moment that actually occurs in such a slab has been shown by experience and tests to be somewhat less than the value determined by the above Mo expression. For this reason, l1, is replaced with ln, the clear span measured face to face of the supports in the direction in which moments are taken. The code (13.6.2.5) states that ln may not be taken to be less than 65% of the span l1, measured center to center of supports. If l1, is replaced with ln, the expression for Mo, which is called the static moment, becomes: (𝑞 𝑙 )(𝑙 )2

𝑀0 = 𝑢 2 𝑛 8 When the static moment is being calculated in the long direction, it is convenient to write it as Mo1, and in the short direction as Mos. It is next necessary to know what proportions of these total moments are positive and what proportions are negative. If a slab was completely fixed at the end of each panel, the division would be as it is in a fixed-end beam, two-thirds negative and one-third positive.

Fig. (2-3) Distribution of total static moment Mo to critical sections for positive and negative bending. Design of Reinforced Concrete Slabs by Safe Program

21

Chapter Two


This division is reasonably accurate for interior panels where the slab is continuous for several spans in each direction with equal span lengths and loads. In effect, the rotation of the interior columns is assumed to be small, and moment values of 0.65 M0 for negative moment and 0.35 Mo for positive moment are specified by the code (13.6.3.2). For exterior spans, the code (13.6.3.3) provides a set of percentages for dividing the total factored static moment into its positive and negative. These divisions, which are shown in the Table below, include values for unrestrained edges (where the slab is simply supported on a masonry or concrete wall) and for restrained edges (where the slab is constructed integrally with a much reinforced concrete wall so that the little rotation occurs at the slab-to-wall connection). 13.6.3.3 In an end span, total factored static moment, Mo, shall be distributed as follows: Table (2-3) Distribution factors applied to static moment Mo for positive and negative moments in end span. 0) (2) (3) (4) (5) Exterior edge Slab with Slab without beams Exterior unrestrained beams between interior supports edge fully between all Without edge With edge restrained supports beam beam Interior negative factored moment 0.75 0.70 0.70 0.70 0.65 Positive factored moment 0.63 0.57 0.52 0.50 0.35 Exterior negative factored moment 0 0.16 0.26 0.30 0.65

Fig. (2-4) Final distribution of moments.


22

Chapter Two


The next problem is to estimate what proportion of these moments is taken by the column strips and what proportion is taken by the middle strips. Factored moments in column strips will be as the table below: Table (2-4) Column strip factored moments.

Fig. (2-5) Torsional cross sectional dimensions for βt calculations.

where βt is calculated in Eq. (13-5) and C is calculated in Eq. (13-6). 𝛽𝑡 =

𝐸𝑐𝑏 𝐶 2𝐸𝑐𝑠 𝑙𝑠

𝑥 𝑥 3𝑦 𝐶 = ∑ (1 − 0.63 ) 𝑦 3 The constant C for T- or L-sections shall be permitted to be evaluated by dividing the section into separate rectangular parts, as defined in 13.2.4, and summing the values of C for each part. In Section 13.6.5, the code requires that the beam be allotted 85% of the column strip moment if 𝛼𝑓1

𝑙2 𝑙1

≥ 1.0should𝛼𝑓1

𝑙2 𝑙1

be between 1.0 and 0, the moment allotted to the beam

is determined by linear interpolation from 85% to 0%.


23

Chapter Three

Design and Analysis of Slabs by Program and Method II

Chapter Three


Chapter Three Design and Analysis of Slabs by Program and Method II 3-1 Slab (work 1) CSI SAFE-Analysis and Design of Slab with interior Beams: 3-1-1 Prosperities and Descriptions of Slabs: Table (3-1) Geometry and Descriptions of Slabs, Beam and Column.

=max clear perimeter/180 =(4.7+3.7)*2000/180=93.333 mm Use h=130 mm From table (9.5 a0 ACI-318) =L/21=5000/21 =238.09 mm Use 500 mm =300 mm for beams. 300*300 mm

Thickness of slab

Depth of beam

Width of beam (b) column

Table (3-2) Concrete and steel Prosperities of slabs, beam and column.

24 kN/m3 30 MPa 400 MPa

Density of concrete Compressive strength (f'c) Yield stress (fy) Table (3-3) Loads Types and Calculations.

Live load (L.L) 4.79 kN/m2 Superimposed dead load (SDL) SDL=2.3 kN/m2 Dead load (D.L) =24*0.13=3.12 kN/m2 W.L=1.6*4.79=7.664 kN/m2 W.D=1.2*(3.12 +2.3)= 6.504 kN/m2 Wu=1.2*(3.12 +2.3)+1.6*4.79=14.168 kN/m2 Calculations of Moments by Method (II):

Ls=Sc/c for all panel. MUEW=WU*LS2*CEW

(C=factors from table of method II factors)

MU NS=WU*LS2*CNS


24

Chapter Three


Fig. (3-1) 3*3 span slab. Table (3-4) Calculation of Moments for all slabs. Slab

Slab 1 m=0.8 Case=3

Slab 2 m=0.8 Case=2

Slab 3 m=0.8 Case=3

Slab 4 m=0.8 Case=2

Slab 5 m=0.8 Case=1

Ls

Coef

-ve con -ve dis

Short Direction

0.064 0.032

Middle

Column

Mu kN.m/m 14.50803 7.254016

Mu kN.m/m 9.672021 4.836011

Long Direction

0.049 0.025

Middle

Column

Mu kN.m/m 11.10771 5.6672

Mu kN.m/m 7.405141 3.778133

Panel

5m 4m

4m +ve

0.048

10.88102

7.254016

0.037

8.387456

5.591637

-ve con -ve dis

0.055 0.027

12.46784 6.120576

8.311893 4.080384

0.041 0.041

9.294208 9.294208

6.196139 6.196139

+ve

0.041

9.294208

6.196139

0.031

7.027328

4.684885

-ve con -ve dis

0.064 0.032

14.50803 7.254016

9.672021 4.836011

0.049 0.025

11.10771 5.6672

7.405141 3.778133

+ve

0.048

10.88102

7.254016

0.037

8.387456

5.591637

-ve con -ve dis

0.055 0.055

12.46784 12.46784

8.311893 8.311893

0.041 0.021

9.294208 4.760448

6.196139 3.173632

+ve

0.041

9.294208

6.196139

0.031

7.027328

4.684885

-ve con -ve con

0.048 ---

10.88102 10.88102

7.254016 7.254016

0.033 ---

7.480704 7.480704

4.987136 4.987136

+ve

0.036

8.160768

5.440512

0.025

5.6672

3.778133

4m

5m 4m 5m 4m

4m

4m

4m


5m 4m 5m 4m

25

Chapter Three Slab 6 m=0.8

Slab 8 m=0.8 Case=2

Slab 9 m=0.8 Case=3

-ve con -ve dis

0.055 0.055

12.46784 12.46784

8.311893 8.311893

0.041 0.021

9.294208 4.760448

6.196139 3.173632

+ve

0.041

9.294208

6.196139

0.031

7.027328

4.684885

-ve con -ve dis

0.064 0.032

14.50803 7.254016

9.672021 4.836011

0.049 0.025

11.10771 5.6672

7.405141 3.778133

+ve

0.048

10.88102

7.254016

0.037

8.387456

5.591637

-ve con -ve dis

0.055 0.027

12.46784 6.120576

8.311893 4.080384

0.041 0.041

9.294208 9.294208

6.196139 6.196139

+ve

0.041

9.294208

6.196139

0.031

7.027328

4.684885

-ve con -ve dis

0.064 0.032

14.50803 7.254016

9.672021 4.836011

0.049 0.025

11.10771 5.6672

7.405141 3.778133

+ve

0.048

10.88102

7.254016

0.037

8.387456

5.591637

4m

Case2

Slab 7 m=0.8 Case=3


4m

4m

4m

5m 4m 5m 4m 5m 4m 5m 4m

Fig. (3-2) Multi story (3*3 span slab).


26

Chapter Three


Fig. (3-3) program definition for design of slabs.


27

Chapter Three


Fig. (3-4) Entry of slab shape and size.


28

Chapter Three


Fig. (3-5) Entry of slab and beam and column properties. Design of Reinforced Concrete Slabs by Safe Program

29

Chapter Three


Fig. (3-6) Entry of load types and factors. Design of Reinforced Concrete Slabs by Safe Program

30

Chapter Three


Fig. (3-7) Deformation shape of slab.


31

Chapter Three



32

Chapter Three


Fig. (3-8) results of program (slab forces, beam forces, axial force, stresses, moment, shear, reactions and punching shear). Design of Reinforced Concrete Slabs by Safe Program

33

Chapter Three


Fig. (3-9) results of program (slab moment, strip moment if short and long direction).


34

Chapter Three


Fig. (3-10) results of program (slab design and reinforcement). Design of Reinforced Concrete Slabs by Safe Program

35

Chapter Three


Table (3-5) Comparison of moment by method II and Safe. Long Direction Short Direction Slab Moment by Safe Ratio Moment by Safe Ratio Method (II) Program (Method Method (II) Program (Method kN.m Moment II/safe) *100 kN.m Moment II/safe) *100 (DDM) (DDM) kN.m kN.m Slab 1 Slab 2 Slab 3 Slab 4 Slab 5 Slab 6 Slab 7 Slab 8 Slab 9

14.50803 10.88102 7.254016 12.46784 9.294208 6.120576 14.50803 10.88102 7.254016 12.46784 9.294208 12.46784 10.88102 8.160768 10.88102 12.46784 9.294208 12.46784 7.254016 10.88102 14.50803 6.120576 9.294208 12.46784 7.254016 10.88102 14.50803

-8.9269 7.746533 -2.38197 -9.349 7.109733 -2.61887 -8.9269 7.746533 -2.38197 -9.00327 6.4746 -9.00327 -9.2598 5.836833 -9.2598 -9.00327 6.4746 -9.00327 -2.38197 7.746533 -8.9269 -2.61887 7.109733 -9.349 -2.38197 7.746533 -8.9269

-162.52 140.4631 -304.539 -133.36 130.7251 -233.711 -162.52 140.4631 -304.539 -138.481 143.5488 -138.481 -117.508 139.815 -117.508 -138.481 143.5488 -138.481 -304.539 140.4631 -162.52 -233.711 130.7251 -133.36 -304.539 140.4631 -162.52

5.6672 8.387456 11.10771 9.294208 7.027328 9.294208 11.10771 8.387456 5.6672 4.760448 7.027328 9.294208 7.480704 5.6672 7.480704 9.294208 7.027328 4.760448 5.6672 8.387456 11.10771 9.294208 7.027328 9.294208 11.10771 8.387456 5.6672

-3.33715 6.8919 -9.8323 -9.76475 5.8759 -9.76475 -9.8323 6.8919 -3.33715 -3.42085 6.3357 -9.4875 -9.3625 5.12185 -9.3625 -9.4875 6.3357 -3.42085 -3.33715 6.8919 -9.8323 -9.76475 5.8759 -9.76475 -9.8323 6.8919 -3.33715

-169.822 121.7002 -112.972 -95.1812 119.5958 -95.1812 -112.972 121.7002 -169.822 -139.16 110.9164 -97.9627 -79.9007 110.6475 -79.9007 -97.9627 110.9164 -139.16 -169.822 121.7002 -112.972 -95.1812 119.5958 -95.1812 -112.972 121.7002 -169.822

3-2 Slab (work 2) CSI SAFE-Analysis and Design of Slab with Beam: 3-2-1 Prosperities and Descriptions of Slabs: Design slab with beam system 3*3 panels with long direction 6.35 m c/c and short direction 5.6 c/c. The slab is to support a live load of 6 kN/m2 and a dead load of 5 kN/m2, including the slab weight. The columns are 350mm*350mm. the slab is supported by beams along the column line, (300*350 mm), f'c=21 MPa and fy=MPa. Table (3-6) Geometry and descriptions of slabs, beam and column.

Thickness of slab Depth of beam Width of beam (b) Column

=max clear perimeter/180=(5600+6530)*2/180≅150mm Use h=150 mm From table (9.5 a0 ACI-318)=L/21=6350/21 =302.38 mm…Use 350 mm =300 mm for beams. 350*350 mm


36

Chapter Three


Table (3-7) Concrete Prosperities of slabs, beam and column.

Density of concrete Compressive strength (f'c)

24 kN/m3 21 MPa

Table (3-8) Loads Types and Calculations.

Live load (L.L) Super Imposed Dead load (D.L) Dead load (D.L) Wu=1.2*5+1.6*6=15.6 kN/m2

6 kN/m2 1.4 kN/m2 =24*0.15=3.6

Fig. (3-11) 3*3 span slab and strip position.


37

Chapter Three


Fig. (3-12) results of program (slab moment, strip moment if short and long direction).


38

Chapter Three


Fig. (3-13) Deformation shape of slab. Table (3-9) Calculation of Moments for all slabs. Slab

Slab 1 m=0.8 8189 Case= 3 Slab 2 m=0.8 8189 Case= 2 Slab 3 m=0.8 8189 Case= 3 Slab 4 m=0.8 8189 Case= 2 Slab 5 m=0.8 8189 Case= 1 Slab 6 m=0.8 8189

Ls

5.6 m

Coef

-ve con -ve dis +ve

5.6 m

-ve con -ve dis +ve

5.6 m

-ve con -ve dis +ve

5.6 m

-ve con -ve dis +ve

5.6 m

-ve con -ve dis

Short Direction

0.058268 0.028724

Middle

Column

Mu kN.m/m

Mu kN.m/m

28.5055 14.05244

19.00367 9.368294

Long Direction

0.049 0.025

Middle

Column

Mu kN.m/m

Mu kN.m/m

23.97158 12.2304

15.98106 8.1536

Panel

6.35 m 5.6 m

0.043906

21.47928

14.31952

0.037

18.10099

12.06733

0.049268 0.024543

24.10256 12.00698

16.06837 8.004652

0.041 0.041

20.05786 20.05786

13.3719 13.3719

0.036906

18.05477

12.03651

0.031

15.1657

10.11046

0.058268 0.028724

28.5055 14.05244

19.00367 9.368294

0.049 0.025

23.97158 12.2304

15.98106 8.1536

0.043906

21.47928

14.31952

0.037

18.10099

12.06733

0.049268 0.049268

24.10256 24.10256

16.06837 16.06837

0.041 0.021

20.05786 10.27354

13.3719 6.849024

0.036906

18.05477

12.03651

0.031

15.1657

10.11046

0.041449 0

20.27743 0

13.51828 0

0.033 0

16.14413 0

10.76275 0

6.35 m 5.6 m 6.35 m 5.6 m

6.35 m 5.6 m 6.35 m 5.6 m

+ve 5.6 m

-ve con -ve dis

0.031087

15.20807

10.13871

0.025

12.2304

8.1536

0.049268 0.049268

24.10256 24.10256

16.06837 16.06837

0.041 0.021

20.05786 10.27354

13.3719 6.849024


6.35 m 5.6 m 39

Chapter Three Case2 Slab 7 m=0.8 8189 Case= 3 Slab 8 m=0.8 8189 Case= 2 Slab 9 m=0.8 8189 Case= 3

5.6 m

+ve -ve con -ve dis +ve

5.6 m

-ve con -ve dis

Design and Analysis of Slabs by Program and Method II 0.036906

18.05477

12.03651

0.031

15.1657

10.11046

0.058268 0.028724

28.5055 14.05244

19.00367 9.368294

0.049 0.025

23.97158 12.2304

15.98106 8.1536

0.043906

21.47928

14.31952

0.037

18.10099

12.06733

0.049268 0.024543

24.10256 12.00698

16.06837 8.004652

0.041 0.041

20.05786 20.05786

13.3719 13.3719

0.036906

18.05477

12.03651

0.031

15.1657

10.11046

0.058268 0.028724

28.5055 14.05244

19.00367 9.368294

0.049 0.025

23.97158 12.2304

15.98106 8.1536

0.043906

21.47928

14.31952

0.037

18.10099

12.06733

6.35 m 5.6 m 6.35 m 5.6 m

+ve

5.6 m

-ve con -ve dis

6.35 m 5.6 m

+ve

Table (3-10) comparison of moment by method II and Safe. Slab Moment by Method (II) kN.m

Slab 1 Slab 2 Slab 3 Slab 4 Slab 5 Slab 6 Slab 7 Slab 8 Slab 9

12.2304 18.10099 23.97158 20.05786 15.1657 20.05786 23.97158 18.10099 12.2304 10.27354 15.1657 20.05786 16.14413 12.2304 16.14413 20.05786 15.1657 10.27354 12.2304 18.10099 23.97158 20.05786 15.1657 20.05786 23.97158 18.10099 12.2304

Long Direction Safe Ratio Program (Method Moment II/safe) *100 (DDM) kN.m -4.52407 -270.341 21.89564 82.66937 -27.297 -87.8176 -26.5195 -75.6343 15.54786 97.54206 -26.5194 -75.6347 -27.2972 -87.8169 21.89586 82.66856 -4.52425 -270.33 -4.80132 -213.973 21.61257 70.17073 -30.3491 -66.0904 -29.3213 -55.0595 13.98061 87.48118 -29.3218 -55.0585 -30.3483 -66.0922 21.6115 70.17421 -4.80279 -213.908 -4.52407 -270.341 21.89564 82.66937 -27.297 -87.8176 -26.5195 -75.6343 15.54786 97.54206 -26.5194 -75.6347 -27.2972 -87.8169 21.89586 82.66856 -4.52425 -270.33


Moment by Method (II) kN.m 28.5055 21.47928 14.05244 -2.6947 16.83963 -19.7723 28.5055 21.47928 14.05244 24.10256 18.05477 24.10256 20.27743 15.20807 20.27743 24.10256 18.05477 24.10256 14.05244 21.47928 28.5055 12.00698 18.05477 24.10256 14.05244 21.47928 28.5055

Short Direction Safe Ratio Program (Method Moment II/safe) *100 (DDM) kN.m -17.1916 -165.811 18.54355 115.8315 -2.09696 -670.135 12.00698 -445.577 18.05477 107.2159 24.10256 -121.9 -17.1916 -165.811 18.54355 115.8315 -2.09696 -670.135 -16.9285 -142.379 11.78346 153.2212 -16.9285 -142.379 -19.2395 -105.395 8.962873 169.6785 -19.2395 -105.395 -16.928 -142.383 11.78366 153.2187 -16.928 -142.383 -2.09696 -670.135 18.54355 115.8315 -17.1916 -165.811 -2.6947 -445.577 16.83963 107.2159 -19.7723 -121.9 -2.096 -670.441 18.55797 115.7415 -17.1923 -165.804

40

Chapter Four

Design and Analysis of Slabs by Program and Direct Design Methods

Chapter Four

Calculation by Direct Design Method and Compare with Program

Chapter Four Design and Analysis of Slabs by Program and Direct Design Methods 4-1 Types of Slabs and method of Calculations (Direct Design Method): When the ratio of (L/S) is less than 2 the slab is called two way slab, bending will take place in the two directions, the main reinforcement is required in the two directions.

Fig. (4-1)Type of two-way slabs and method of design.

Fig. (4-2) Muli-span slab. Design of Reinforced Concrete Slabs by Safe Program

41

Chapter Four


4-1-1 Direct design Method (D.D.M):

4-1-2 Determination of two way slab thickness:


42

Chapter Four


Case 2: interior beam are not existing, thickness can be found according to table below: Table (4-1) minimum thickness of slabs without interior beams.

4-1-3 Estimating dimensions of Interior and Exterior Beams Sections:

Fig. (4-3) Effective beam section (a-interior beam, b-exterior beam).

4-1-4 Design Procedure:


43

Chapter Four


Table (4-2) distribution of total static moment in end spans.

Static moment Mo distributed as follows:

Fig. (4-4) Moment distribution.


44

Chapter Four



45

Chapter Four


Table (4-3) column strip factored moments.

4-1-5 Analysis of Slabs by Direct Design Method: This method depends on division of slabs to separated strip and every strip is divided to column strip and middle strip. This strip depends on dimension of each slab. Moment calculated in the end and the middle of each span by using factors depends on charts and tables. 4-2 Slab (work 3) CSI SAFE-04-Analysis and Design of Slab without Interior Beam by Direct Design Method: Building consist of 4 span with properties as shown in tables below. 4-2-1 Prosperities and Descriptions of Slabs: Multi story building (residence) consist of 4 story: Table (4-4) Geometry and descriptions of slabs, beam and column. Thickness of slab

=Ln=33=6.4*1000/33=193.94 mm Use h=200 mm =(7.7+6.7)*2000/180=160mm


46

Chapter Four


Use h=200 mm From table ACI-Code table 9.5c hs=Ln/33=6.4*1000/33=193.94 mm (fy=420MPa). ACI-Code table 9.5a hb=L/21=7000*1000/21=333.33 mm use Use hb=500 mm. =400 mm *500 for beams. Width of edge beam (b) 400*400 mm Column 600*600 mm Table (4-5) Concrete and Steel Prosperities of slabs, beam and column. Depth of beam

Density of concrete Compressive strength (f'c) fy

24 kN/m3 40 MPa 420 MPa


Live load (L.L) Superimposed dead load (SDL) Dead load (D.L) W.L=1.6*3=4.8 kN/m2 W.D=1.2*(4.8+2)=8.16 kN/m2 Wu=1.2*(4.8+2)+1.6*3=12.96kN/m2

3 kN/m2 SDL=24*0.07+0.025*1275*10/1000 =2 kN/m2 =24*0.2=4.8 kN/m2

Fig. (4-5) full map for building by safe program. Design of Reinforced Concrete Slabs by Safe Program

47

Chapter Four


Fig. (4-6) full map for building by Auto-Cad program.

Strip A

Strip A Strip C

Strip B

Strip D

Fig. (4-7) Design strips for calculations of moments by safe program. Design of Reinforced Concrete Slabs by Safe Program

48

Chapter Four


Calculation of constant βt:

Table (4-7) Calculation of Moments for all slabs. Design of Reinforced Concrete Slabs by Safe Program

49

31.2910

2.81348

8.3354

8.915962

50.5237

19.8132

28.729

3

5.6

1.5

152.4096

ve-

0.7

106.68672

0.75

80.01504

12.00226

68.0127

26.6716

38.673

3

6.6

1.5

211.7016

ve -

0.7

148.19112

0.75

111.1433

16.6715

94.4718

37.0477

53.719

3

6.6

1.5

211.7016

ve+

0.35

74.09556

0.7928

58.74296

8.811444

49.9315

15.3526

24.164

3 6. 5 6. 5 6. 5 6. 5 6. 5 6. 5

6.6

1.5

211.7016

ve-

0.65

137.60604

0.7928

109.0941

16.36411

92.7299

28.5119

44.876

5.5

3

318.5325

ve -

0.26

82.81845

0.9335

77.31102

77.31102

0

5.50742

5.5

3

318.5325

ve+

0.52

165.6369

0.6

99.38214

99.38214

0

66.2547

5.5

3

318.5325

ve-

0.7

222.97275

0.75

167.2296

167.2296

0

55.7431

6.4

3

431.3088

ve -

0.7

301.91616

0.75

226.4371

226.4371

0

75.4790

6.4

3

431.3088

ve+

0.35

150.95808

0.6

90.57485

90.57485

0

60.3832

6.4

3

431.3088

ve-

0.65

280.35072

0.75

210.263

210.263

0

70.0876

7

5.5

3

343.035

ve -

0.26

89.1891

7

5.5

3

343.035

ve+

0.52

7

5.5

3

343.035

ve-

7

6.4

3

464.4864

7

6.4

3

7

6.4

3

3

6.6

3

5.4994

107.0269

107.0269

0

71.3512

0.7

240.1245

0.75

180.0934

180.0934

0

60.0311

ve -

0.7

325.14048

0.75

243.8554

243.8554

0

81.2851

464.4864

ve+

0.35

162.57024

0.6

97.54214

97.54214

0

65.0281

464.4864

ve-

0.65

301.91616

0.75

226.4371

226.4371

0

75.4790

1.5

211.7016

ve -

0.65

137.60604

0.7928

109.0941

109.0941

0

28.5119

6.6

1.5

211.7016

ve+

0.35

74.09556

0.7928

58.74296

58.74296

0

15.3526

3

6.6

1.5

211.7016

ve-

0.7

148.19112

0.75

111.1433

111.1433

0

37.0477

3

5.6

1.5

152.4096

ve -

0.7

106.68672

0.75

80.01504

80.01504

0

26.6716

3

5.6

1.5

152.4096

ve+

0.52

79.252992

0.75

59.43974

59.43974

0

19.8132

3

5.6

1.5

152.4096

ve-

0.26

39.626496

0.929

36.81301

36.81301

0

2.81348

Interior Span End Span

0

Interior Span

83.6897

End Span

83.6897

178.3782

0.9383 4 0.6

End Span

For comparison we choose (Strip B and C as interior strip) which solved by direct design method and Program (Safe). Table (4-8) Comparison of Moments for Strip (B). Column Strip Moments Direct Design Position Positon Method Moment (Safe) (DDM) kN.m CSA7 Start 77.3 CSA7 Middle 99.38 CSA7 End 167.23 CSA9 Start 210.26 CSA9 Middle 90.57 CSA9 End 210.26 CSA10 Start 210.26 Design of Reinforced Concrete Slabs by Safe Program

Safe Program Moment (DDM) kN.m 70.185 83.3507 171.5038 183.8408 100.2148 191.3519 191.3519

Ratio (DDM/safe) *100 110.1375 119.2312 97.50804 114.3707 90.37587 109.8813 109.8813 50

End Span Interior Span

(kN.m)

CS.F

Total Slab Moment

5.521952

59.43974

MSM

36.81301

0.75

(kN.m)

0.929

79.252992

M Beam

39.626496

0.52

(kN.m)

0.26

ve+

MCS Slab

ve -

152.4096

MCS

152.4096

1.5

(kN.m)

1.5

5.6

positive and negative moments

5.6

3

L.F

3

Interior Span

Strip D

Mo= WuL2Ln/ 8(kN.m)

Strip C

CS width (m)

Strip B

LN (m)

Strip A


L2 (m)

Strip

Chapter Four

Chapter Four


CSA10 Middle 90.57 CSA10 End 210.26 CSA11 Start 167.23 CSA11 Middle 99.38 CSA11 End 77.3 Table (4-9) Comparison of Moments for Strip (C). Column Strip Moments Direct Design Position Positon Method Moment (Safe) (DDM) kN.m CSA7 Start 83.6897 CSA7 Middle 107.0269 CSA7 End 180.0934 CSA9 Start 243.8554 CSA9 Middle 97.54214 CSA9 End 226.4371 CSA10 Start 226.4371 CSA10 Middle 97.54214 CSA10 End 243.8554 CSA11 Start 180.0934 CSA11 Middle 107.0269 CSA11 End 83.6897

100.2148 183.8408 171.5038 83.3507 70.185

90.37587 114.3707 97.50804 119.2312 110.1375

Safe Program Moment (DDM) kN.m 73.1302 85.5006 179.5311 192.7916 102.1589 200.221 200.221 102.1589 192.7916 179.5311 85.5006 73.1302

Ratio (DDM/safe) *100 114.4 125.2 100.3 126.5 95.5 113.1 113.1 95.5 126.5 100.3 125.2 114.4

Fig.(4-8) moment in negative and positive in slab.


51

Chapter Four


Fig. (4-9) Column Strip Moment by Safe Program.

4-3 Slab (work 4) CSI SAFE-04-Analysis and Design of Slab without Interior Beam by Direct Design Method: 4-3-1 Prosperities and Descriptions of Slabs: For the two-way solid slab with beams on all column lines, shown in Figure, evaluate the moments, using the direct design method. All columns are 300× 300 mm in cross section, all beams are 300× 600 mm in cross section, slab thickness is equal to 140 mm. Use f'c= 28 MPa and fy 420 MPa. (L.L=4 kN/m2, D.L=1.83 kN/m2 and SD.L=3.36 kN/m2).


52

Chapter Four


Fig. (4-10) Two way Solid Slab with beams.

Strip A

Fig. (4-11) Design strips for calculations of moments by direct design Method.

Evaluate the constants α and βt: Beam sectional properties are shown in Figure. Calculation of relative beam stiffness α : Internal beams: relative stiffness of beam is calculated as follows:

Fig. (4-12) Beam sectional properties for relative stiffness calculations. Design of Reinforced Concrete Slabs by Safe Program

53

Chapter Four


Calculation of constant βt:

Fig. (4-13) Beam Sectional Properties for relative stiffness calculation.


54

Chapter Four


3- Evaluation of moments in one of the internal beams: For comparison we choose (Strip A as interior strip) which solved by direct design method and Program (Safe).

5.7

3

6

5.7

3

6

5.7

3

6

5.7

3

6

5.7

3

307.712 307.712 307.712 307.712 307.712

ve -

0.7

ve+

0.35

ve-

0.65

ve -

0.7

ve+

0.57

ve-

0.16

215.399 107.6995 200.0133 215.399 175.3963 49.23405

41.84894

6.277341

35.5716

7.3851

0.75

131.5472

19.73208

111.8151

43.849

0.75

161.5492

24.23238

137.3168

53.849

0.75

161.5492

24.23238

137.3168

53.849

0.75

80.77461

12.11619

68.65842

26.924

0.75

150.01

22.5015

127.5085

50.003

0.75

161.5492

24.23238

137.3168

53.849

0.75

131.5472

19.73208

111.8151

43.849

0.85

41.84894

6.277341

35.5716

7.3851

Table (4-11) Comparison of Moments for Strip (A). Column Strip Moments Direct Design Method Position (Safe) Positon Moment (DDM) kN.m CSA1 Start 13.63215 CSA1 Middle 63.44018 CSA1 End 77.90899 CSA2 Start 77.90899 CSA2 Middle 38.95449 CSA2 End 72.34406 CSA3 Start 77.90899 CSA3 Middle 63.44018 CSA3 End 13.63215


Safe Program Moment (DDM) kN.m 14.86 51.548 86.10 79.84 34.2034 79.84 86.10 51.548 14.86

13.63215 63.44018 77.90899 77.90899 38.95449 72.34406 77.90899 63.44018 13.63215

Ratio (DDM/safe) *100 91.73721 123.0701 90.48663 97.5814 113.8907 90.6113 90.48663 123.0701 91.73721

55

End Span

6

307.712

215.399

0.85

Interior Span

3

0.7

Total Slab Moment

5.7

ve-

(kN.m)

6

307.712

175.3963

MSM

3

0.57

(kN.m)

5.7

ve+

M Beam

6

307.712

49.23405

(kN.m)

3

0.16

MCS Slab

5.7

ve -

(kN.m)

6

307.712

MCS

3

CS.F

5.7


6

L.F

CS width (m) Mo= WuL2Ln/ 8(kN.m)

LN (m)

Strip A

L2 (m)

Strip

Table (4-10) Calculation of Moments for all slabs.

Chapter Four


Strip A

Fig. (4-14) Design strips and strip moment by safe program.

Fig.(4-15) moment in negative and positive in slab.

4-4 Slab (work 5) CSI SAFE-02-Analysis and Design of Slab with Beam: 4-4-1 Prosperities and Descriptions of Slabs: For the two-way solid slab with beams on all column lines, shown in Figure, evaluate the moments, using the direct design method. All columns are 300× 300 mm in cross section. Beams are (300× 500 mm) and (300× 400 mm) in cross section, slab thickness is equal to 160 mm. Use f'c= 28 MPa and fy 420 MPa. (L.L=4 kN/m2, D.L=24*0.16 kN/m2 and SD.L=3.84 kN/m2).


56

Chapter Four


Fig. (4-16) full map for building by safe program. Design of Reinforced Concrete Slabs by Safe Program

57

Chapter Four


Fig. (4-17)beam shape and position by safe program.

Strip A

Strip A

Fig. (4-18) Design strips for calculations of moments by direct design Method. Design of Reinforced Concrete Slabs by Safe Program

58

Chapter Four



59

Chapter Four



60

Chapter Four



61

Chapter Four


For comparison we choose (Strip A as exterior strip) which solved by direct design method and Program (Safe).

138.018

ve-

0.65

48.30661 89.71227

0.75 0.75

61.90146

9.28522

29.53562

4.430344

61.90146

9.28522

2.760377

5.6587

46.1404

24.38793

32.530

56.66365

29.9501

39.949

52.61624

27.8108

37.096

25.10528

18.77098

23.201

52.61624

27.8108

37.096

For comparison we choose (Strip A as interior strip) which solved by direct design method and Program (Safe). Table (4-13) Comparison of Moments for Strip (A). Column Strip Moments Direct Design Position Positon Method Moment (Safe) (DDM) kN.m CSA1 Start 5.6587 CSA1 Middle 32.530 CSA1 End 39.949 CSA2 Start 37.09 CSA2 Middle 23.20 CSA2 End 37.096 CSA3 Start 39.949 CSA3 Middle 32.530 CSA3 End 5.6587


Safe Program Moment (DDM) kN.m 6.655 39.8853 33.4648 33.2496 25.365 33.2516 33.4648 39.8853 6.655

Ratio (DDM/safe) *100 85.0 81.6 119.4 111.6 91.5 111.6 119.4 81.6 85.0

62

End Span

0.35

0.75

9.999467

16.42425

Interior Span

1.5

ve+

89.71227

66.66312

Total Slab Moment

4.7

138.018

0.65

0.75

8.142423

(kN.m)

3.15

1.5

ve -

96.61321

54.28282

MSM

4.7

138.018

0.7

0.75

2.898396

(kN.m)

3.15

1.5

ve-

78.67076

19.32264

M Beam

4.7

138.018

0.57

0.85

(kN.m)

3.15

1.5

ve+

22.08302

MCS Slab

4.7

138.018

0.16

MCS

3.15

1.5

ve -

(kN.m)

4.7

138.018

CS.F

3.15

1.5


4.7

L.F

3.15

CS width (m) Mo= WuL2Ln/ 8(kN.m)

LN (m)

Strip A

L2 (m)

Strip


Chapter Four


Fig. (4-19) Design strips and strip moment by safe program.

4-5 Slab (work 6) CSI SAFE-04-Analysis and Design of Slab with Interior Beam by Direct Design Method: Solving the same work (work2) but with direct design method.

Fig. (4-20) Two way slabs dimensions.


63

Chapter Four


 Assume a depth for the slab : ℎ=

𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑝𝑎𝑛𝑙𝑒

ℎ=

180

2∗(6530+5600) 180

≅ 150 𝑚𝑚

 Check depth limitations: Calculate beams and slab moment of inertia : 150 350

350 350 350

𝑁. 𝐴 𝑓𝑟𝑜𝑚 𝑡𝑜𝑝 (𝑦̅) =

All unit in mm 5002 1502 +350∗ 2 2

350∗

350

𝑦̅ = 209.6 𝑚𝑚

350∗500+350∗150

𝑏 ∗ ℎ3 + (𝐴 ∗ 𝑑2 ) 12 (350 + 350) ∗ 209.63 350 ∗ (500 − 209.6)3 350 ∗ (209.6 − 150)3 𝐼𝑏1 = + − = 4.98 ∗ 109 𝑚𝑚4 3 3 3 𝐼𝑏1 =

𝑁. 𝐴 𝑓𝑟𝑜𝑚 𝑡𝑜𝑝 (𝑦̅) =

2∗350∗

1502 5002 +350∗ 2 2

2∗350∗150+350∗500

𝑦̅ = 184.375 𝑚𝑚

184.3753 (500 − 184.375)3 2 ∗ 350 ∗ (184.375 − 150)3 + 350 ∗ − 3 3 3 9 4 = 5.85 ∗ 10 𝑚𝑚 Compute the value of Is in the edge strip, interior strip &∝ 𝒇 : (6350 + 350⁄2) ∗ 1503 𝐼𝑠 𝑒𝑑𝑔𝑒 𝑠𝑡𝑟𝑖𝑝 = = 0.94 ∗ 109 𝑚𝑚4 12 𝐼𝑏2 = (2 ∗ 350 + 350) ∗

∝ 𝑓1 =

4.98∗109

𝐸𝑐𝑏 ∗ 𝐼𝑏1

∝ 𝑓1 = 0.94∗109 = 5.3

𝐸𝑐𝑠 ∗ 𝐼𝑠

𝐼𝑠2 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 5.6 𝑙𝑜𝑛𝑔 𝑠𝑡𝑟𝑖𝑝 = ∝ 𝑓2 =

𝐸𝑐𝑏 ∗ 𝐼𝑏2 𝐸𝑐𝑠 ∗𝐼𝑠2

(6350 + 6350⁄2) ∗ 1503 = 1.79 ∗ 109 𝑚𝑚4 12 5.85∗109

∝ 𝑓2 = 1.79∗109 = 3.27


64

Chapter Four


𝐼𝑠3 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 6.35 𝑙𝑜𝑛𝑔 𝑠𝑡𝑟𝑖𝑝 =

5600 ∗ 1503 = 1.575 ∗ 109 𝑚𝑚4 12

∝ 𝑓3 =

5.85∗109

𝐸𝑐𝑏 ∗ 𝐼𝑏2 𝐸𝑐𝑠 ∗𝐼𝑠3

∝ 𝑓3 = 1.575∗109 = 3.7

*limitation in code: ∝𝑓1 ∗𝑙22 ∝𝑓2 ∗𝑙12

3.7∗5.62

= 3.27∗6.352 = 0.9

0.9 > 0.2

5.3 + 3.2 7 + 3.7 + 3.7 ≅4 4 6350−350 ∵∝ 𝑓𝑚 > 2.0 𝛽 = 5600−350 = 1.14 ∝ 𝑓𝑚 =

∴ ℎ𝑚𝑖𝑛, =

6000∗(0.8+

280 ) 1400

36+5∗(1.14)

= 143.9 < 150 𝑚𝑚

∴ ℎ𝑎𝑠𝑠𝑢𝑚𝑒𝑑,=150 𝑚𝑚 𝑖𝑠 𝑜𝑘

Find Moments:  Short direction /Exterior strip / Interior panel: 𝑀𝑜 =

15.6 ∗ (3.175 + 0.35⁄2) ∗ (5.6 − .35)2 8

= 180 𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 = 0.65 ∗ 180 = 117 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 0.15 ∗ 180 = 27 𝑘𝑁. 𝑚 𝑙2 6.35 𝑙2 ∝ 𝑓1 = 5.3 = = 1.13 ∝ 𝑓1 = 6 𝑙1 5.6 𝑙1 −𝑣𝑒 𝑀 = 117 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 27 𝑘𝑁. 𝑚 C.s % portion(table13.6.4.1)=0.72 C.s % portion(table13.6.4.4)=0.72 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 117 = 84.24 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 27 = 19.44 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 117 − 84.24 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 27 − 19.44 = 7.56 𝑘𝑁. 𝑚 = 32.76 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 84.24 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 19.44 = 12.63 𝑘𝑁. 𝑚 = 2.916 𝑘𝑁. 𝑚

 Short direction /Exterior strip / Exterior panel 350

𝑐 = ((1 − 0.63 ∗ 500) ∗ ( 𝐼𝑠 =

3350∗1503 12

500∗3503 3

= 0.94 ∗ 109 𝑚𝑚4 𝑀𝑜 =

150

)) +((1 − 0.63 ∗ 350) ∗ ( 4.28∗109

350∗1503 3

) =1.72*1010 mm4

using eq.

𝛽 = 2∗0.94∗109 = 2.27

15.6 ∗ (3.175 + 0.35⁄2) ∗ (5.6 − .35)2

8 From table 13.6.3.3 𝑀𝑜 shall be distributed as follows: −𝑣𝑒 𝑀 𝑖𝑛𝑡. = 0.7 ∗ 180 +𝑣𝑒 𝑀 = 0.57 ∗ 180 = 126 𝑘𝑁. 𝑚 = 102.6 𝑘𝑁. 𝑚 C.s % portion(table13.6.4.1)=0.72 C.s % portion(table13.6.4.4)=0.72 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 126 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 102.6 = 90.72 𝑘𝑁. 𝑚 = 73.87 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 126 − 90.72 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 102.6 = 35.28 𝑘𝑁. 𝑚 − 73.87 = 28.7 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 90.72 = 0.15 ∗ 73.87 = 9.72𝑘𝑁. 𝑚 = 11.8𝑘𝑁. 𝑚


= 180 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑒𝑥𝑡. = 0.16 ∗ 180 = 28.8 𝑘𝑁. 𝑚 C.s % portion(table13.6.4.2)=0.746 −𝑣𝑒 𝑀 𝑐. 𝑠 = 28.8 ∗ 0.711 = 20.47 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 28.8 − 20.47 = 7.32 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 21.48 = 3.07𝑘𝑁. 𝑚

65

Chapter Four


 Short direction /interior strip /interior panel:

15.6 ∗ 6.35 ∗ (5.6)2 = 342 𝑘𝑁. 𝑚 8 −𝑣𝑒 𝑀 = 0.65 ∗ 342 = 222.3 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 0.35 ∗ 342 = 119.7𝑁. 𝑚 𝑀𝑜 =

𝑙2 6.35 = = 1.13 𝑙1 5.6 −𝑣𝑒 𝑀 = 222.3 𝑘𝑁. 𝑚

𝑙2 = 3.695 𝑙1 +𝑣𝑒 𝑀 = 119.7 𝑘𝑁. 𝑚

∝ 𝑓1 = 3.27

C.s % portion(table13.6.4.1)=0.72 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 222.3 = 160.056𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 222.3 − 160.056 = 62.244 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 160.056 = 24 𝑘𝑁. 𝑚

∝ 𝑓1

C.s % portion(table13.6.4.4)=0.72 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 119.7 = 86.184 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 119.7 − 86.184 = 33.516 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 86.4 = 12.96 𝑘𝑁. 𝑚

 Short direction / interior strip / Exterior panel: 350

𝑐 = ((1 − 0.63 ∗ 500) ∗ (

500∗3503 3

150

)) +((1 − 0.63 ∗ 350) ∗ (

350∗1503

(6350 + 6350⁄2) ∗ 1503 = 1.79 ∗ 109 𝑚𝑚4 12 4.28 ∗ 109 𝛽= = 1.195 2 ∗ 1.79 ∗ 109

3

) =1.72*1010 mm4

𝐼𝑠 =

𝑀𝑜 =

15.6∗6.35∗(5.6)2 8

= 342 𝑘𝑁. 𝑚

From table 13.6.3.3 𝑀𝑜 shall be distributed as follows: −𝑣𝑒 𝑀 𝑖𝑛𝑡. = 0.7 ∗ 342 = 239.4 𝑘𝑁. 𝑚

+𝑣𝑒 𝑀 = 0.57 ∗ 342 = 194.94 𝑘𝑁. 𝑚

C.s % portion(table13.6.4.1)=0.72 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 239.4 = 172.368 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 239.4 − 172.368 = 67.032 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 172.368 = 21.06𝑘𝑁. 𝑚

C.s % portion(table13.6.4.4)=0.72 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.72 ∗ 194.94 = 140.4 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 194.94 − 140.4 = 54.54 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 140.4 = 21.06𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 𝑒𝑥𝑡. = 0.16 ∗ 342 = 54.72𝑘𝑁. 𝑚 C.s % portion(table13.6.4.2)=0.65 −𝑣𝑒 𝑀 𝑐. 𝑠 = 54.72 ∗ 0.65 = 35.568𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 54.72 − 35.568 = 19.152 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 35.568 = 5.335𝑘𝑁. 𝑚

 Long direction /Exterior strip / Interior panel: 𝑀𝑜 =

15.6 ∗ (5.6⁄2 + 0.35⁄2) ∗ (6.35 − 0.35)2

= 208.845 𝑘𝑁. 𝑚 8 −𝑣𝑒 𝑀 = 0.65 ∗ 208.845 = 135.74𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 0.35 ∗ 208.845 = 73.09 𝑘𝑁. 𝑚 𝑙2 5.6 𝑙2 ∝ 𝑓1 = 3.27 = = .88 ∝ 𝑓1 = 2.88 𝑙1 6.35 𝑙1 −𝑣𝑒 𝑀 = 135.74 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 73.09𝑘𝑁. 𝑚 C.s % portion(table13.6.4.1)=0.786 C.s % portion(table13.6.4.4)=0.786 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 135.74 = 106.69𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 73.09 = 57.45 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 29.05𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 15.636 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 106.69 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 57.45 = 8.6 𝑘𝑁. 𝑚 = 16 𝑘𝑁. 𝑚

 Long direction /Exterior strip / Exterior panel: 350

𝑐 = ((1 − 0.63 ∗ 500) ∗ (

500∗3503 3

))


66

Chapter Four


150

+((1 − 0.63 ∗ 350) ∗ ( 𝐼𝑠 =

350∗1503

3 (5600⁄2+350⁄2 )∗5600∗1503 12

𝑀𝑜 =

) =1.72*1010 mm4

= 0.836 ∗ 109 𝑚𝑚4

4.28∗109

𝛽 = 2∗0.836∗109 = 2.559

15.6 ∗ (5.6⁄2 + 0.35⁄2) ∗ (6.35 − 0.35)2

8 From table 13.6.3.3 𝑀𝑜 shall be distributed as follows: −𝑣𝑒 𝑀 𝑖𝑛𝑡. = 0.7 ∗ 208.845 +𝑣𝑒 𝑀 = 0.57 ∗ 208.845 = 146.19 𝑘𝑁. 𝑚 = 119.04 𝑘𝑁. 𝑚

= 208.845 𝑘𝑁. 𝑚

C.s % portion(table13.6.4.1)=0.786

C.s % portion(table13.6.4.4)=0.786

−𝑣𝑒 𝑀 𝑒𝑥𝑡. = 0.16 ∗ 208.845 … … . . = 33.4𝑘𝑁. 𝑚 C.s % portion(table13.6.4.2)= 0.786

−𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 146.19 = 114.9𝑘𝑁. 𝑚

+𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 119.04 = 93.56 𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 𝑐. 𝑠 = 33.4 ∗ 0.786 = 26.25𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 58884. 𝑚

+𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 47.953 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 93.56 = 14.034𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 7.14𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 114.9𝑘 = 17.235𝑘𝑁. 𝑚

−𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 26.25 = 3.93𝑘𝑁. 𝑚

 Long direction / Interior strip / Interior panel:

15.6 ∗ 5.6 ∗ (6.35 − 0.35)2 = 393.12 𝑘𝑁. 𝑚 8 −𝑣𝑒 𝑀 = 0.65 ∗ 393.12 = 255.528𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 0.35 ∗ 393.12 = 137.592 𝑘𝑁. 𝑚 𝑙2 5.6 𝑙2 ∝ 𝑓1 = 3.27 = = .88 ∝ 𝑓1 = 2.88 𝑙1 6.35 𝑙1 −𝑣𝑒 𝑀 = 255.528 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 = 137.592 𝑘𝑁. 𝑚 C.s % portion(table13.6.4.1)=0.786 C.s % portion(table13.6.4.4)=0.786 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 255.528 = 200.8𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 137.592 = 108.14 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 54.68𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 29.44 𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 200.8 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 108.14 = 30.12 𝑘𝑁. 𝑚 = 16.221𝑘𝑁. 𝑚 𝑀𝑜 =

 Long direction / Interior strip / Exterior panel: 350

𝑐 = ((1 − 0.63 ∗ 500) ∗ ( 𝐼𝑠 =

5600∗1503 12

500∗3503 3

150

)) +((1 − 0.63 ∗ 350) ∗ (

= 1.575 ∗ 109 𝑚𝑚4

350∗1503

4.28∗109

3

) =1.72*1010 mm4

𝛽 = 2∗1.575∗109 = 1.349

15.6 ∗ 5.6 ∗ (6.35 − 0.35)2 = 393.12 𝑘𝑁. 𝑚 8 From table 13.6.3.3 𝑀𝑜 shall be distributed as follows: −𝑣𝑒 𝑀 𝑖𝑛𝑡. = 0.7 ∗ 393.12 +𝑣𝑒 𝑀 = 0.57 ∗ 393.12 −𝑣𝑒 𝑀 𝑒𝑥𝑡. = 0.16 ∗ 393.12 = 275.184 𝑘𝑁. 𝑚 = 224.0784 𝑘𝑁. 𝑚 = 62.89𝑘𝑁. 𝑚 C.s % C.s % portion(table13.6.4.4)=0.786 C.s % portion(table13.6.4.2)= 0.786 portion(table13.6.4.1)=0.786 −𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 275.184 +𝑣𝑒 𝑀 𝑐. 𝑠 = 0.786 ∗ 119.04 −𝑣𝑒 𝑀 𝑐. 𝑠 = 33.4 ∗ 0.786 = 216.29𝑘𝑁. 𝑚 = 93.56 𝑘𝑁. 𝑚 = 26.25𝑘𝑁. 𝑚 𝑀𝑜 =

−𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 58884. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 114.9𝑘 = 17.235𝑘𝑁. 𝑚

+𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒. 𝑠 = 47.953 𝑘𝑁. 𝑚 +𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 93.56 = 14.034𝑘𝑁. 𝑚


−𝑣𝑒 𝑀 𝑚𝑖𝑑𝑑𝑙𝑒 . 𝑠 = 7.14𝑘𝑁. 𝑚 −𝑣𝑒 𝑀 𝑐. 𝑠 𝑓𝑜𝑟 𝑠𝑙𝑎𝑏 = 0.15 ∗ 26.25 = 3.93𝑘𝑁. 𝑚

67

Chapter Four


 Short direction /interior strip /interior panel:

5.6

3.175

342

119.7

ve+

86.184

12.9276

6.35

5.6

3.175

342

222.3

ve-

160.056

24.0084

MCS

Table (4-15) Comparison of Moments for Strip (A). Column Strip Moments Direct Design Position Positon Method Moment (Safe) (DDM) kN.m 86.2524 CSA1 Start 46.4436 CSA1 Middle 86.2524 CSA1 End

Safe Program Moment (DDM) kN.m 97.725 41.612 97.725

62.244 33.516 62.244

Total Slab Moment

6.35

136.04 76 73.256 4 136.04 76

MSM

24.0084

(kN.m)

160.056

(kN.m)

ve -

M Beam

222.3

(kN.m)

342

MCS Slab

3.175

(kN.m)

5.6

Moment factored

CS width (m)

6.35

Mo= WuL2Ln/ 8(kN.m)

LN (m)

Strip

L2 (m)

Strip


86.2524 46.4436 86.2524

Ratio (DDM/safe) *100 88.26032 111.6111 88.26032



68

Chapter Four


4-6 Slab (work 7) CSI SAFE-04-Analysis and Design of Slab with Interior Beam by Direct Design Method: Design slab with beam system 3*3 panels. The slab is to support a live load of 2.728 kN/m2 and a dead load of 4.82 kN/m2, including the slab weight. The columns are (250mm*250mm). The slab is supported by beams along the column line, (250*600 edge beam and 250*500mm internal beam).

Fig. (4-22) Design strips for calculations of moments by safe program.

 Frame A


69

Chapter Four



70

Chapter Four


 Frame B

6 6

Strip A

6 6 6

ve -

0.16

8.920898438

0.8

7.136719

1.070508

6.066211

1.78418

1.5

55.75562

ve+

0.57

31.78070068

0.6

19.06842

2.860263

16.20816

12.71228

1.5

55.75562

ve-

0.7

39.02893066

0.6

23.41736

3.512604

19.90475

15.61157

1.5

55.75562

ve -

0.65

36.2411499

0.6

21.74469

3.261703

18.48299

14.49646

1.5

55.75562

ve+

0.35

19.51446533

0.6

11.70868

1.756302

9.952377

7.805786

1.5

55.75562

ve-

0.65

36.2411499

0.6

21.74469

3.261703

18.48299

14.49646

3

107.0508

ve -

0.16

17.128125

0.8736

14.96313

2.24447

12.71866

2.164995

3

107.0508

ve+

0.57

61.01894531

0.6

36.61137

5.491705

31.11966

24.40758

3

107.0508

ve-

0.7

74.93554688

0.6

44.96133

6.744199

38.21713

29.97422

3

107.0508

ve -

0.65

69.58300781

0.6

41.7498

6.262471

35.48733

27.8332

3

107.0508

ve+

0.35

37.46777344

0.6

22.48066

3.3721

19.10856

14.98711

2.854688 15.57254

End Span

55.75562

19.12417 17.75816 9.562088

Interior Span

1.5


Total Slab Moment

MSM

(kN.m)

(kN.m)

M Beam

(kN.m)

MCS Slab

MCS

(kN.m)

CS.F


L.F

Mo= WuL2Ln/ 8(kN.m)

CS width (m)

LN (m) 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5 3.7 5

17.75816 4.409465 29.89929

End Span

3.1 25 3.1 25 3.1 25 3.1 25 3.1 25 3.1 25

36.71842 34.09567 18.35921

71

Interi or Span

Strip B

L2 (m)

Strip


Chapter Four 6

3.7 5

Calculation by Direct Design Method and Compare with Program 3

107.0508

ve-

0.65

69.58300781

0.6

Table (4-17) Comparison of Moments for Strip (A). Column Strip Moments Direct Design Position Positon Method Moment (Safe) (DDM) kN.m CSA1 Start 4.409465 CSA1 Middle 29.89929 CSA1 End 36.71842 CSA2 Start 34.09567 CSA2 Middle 18.35921 CSA2 End 34.09567

41.7498

6.262471

Safe Program Moment (DDM) kN.m -6.04 28.3617 -37.2311 -37.0584 18.6121 -37.0677

35.48733

27.8332

34.09567

Ratio (DDM/safe) *100 -73.0044 105.4214 -98.623 -92.0052 98.64126 -91.9822



72

Chapter Five

Comparison of Method II with Direct design & (SAFE) program

Chapter Five

Comparison of Method II with Direct design and program

Chapter Five Comparison of Method II with Direct design & (SAFE) program 5-1 Slab (work 8) CSI SAFE-Analysis and Design of Slab with Beam: 5-2 Prosperities and Descriptions of Slabs: Table (5-1) Geometry and descriptions of slabs, beam and column.

Thickness of slab

Depth of beam

Width of beam (b) column

=max clear perimeter/180 =(7.7+5.7)*2000/180=148 mm Use h=200 mm From table (9.5 a0 ACI-318) =L/21=8000/21 =380 mm Use 600 mm =300 mm for beams. 300*300 mm

Table (5-2) Concrete and steel Prosperities of slabs, beam and column.

Density of concrete Compressive strength (f'c) Yield stress (fy)

24 kN/m3 25 MPa 400 MPa


Live load (L.L) Superimposed dead load (SDL) Dead load (D.L) W.L=1.6*5= 8 kN/m2 W.D=1.2*(4.8 +3)= 9.36 kN/m2 Wu=1.2*(4.8 +3)+1.6*5=17.36 kN/m2

=5 kN/m2 =3 kN/m2 =24*0.2=4.8 kN/m2


73

Chapter Five


Fig. (5-1) slab span and dimensions. Table (5-4) Interpolation Program for Solving Coefficients of Method II.


74

Chapter Five


5-3 Analysis by using ACI 318M Method II:

Table (5-5) Calculation of Moments for all slabs. Slab

Slab 1 m=0.7 5 Case=3


Slab 3 m=1 Case=3


Ls

6m

6m

Coef

Short Direction

Middle

Column

Mu kN.m/m

Mu kN.m/m

Long Direction

Middle

Column

Mu kN.m/m

Mu kN.m/m

-ve con

0.0675

42.1848

28.1232

0.049

30.62304

20.41536

-ve dis

0.034

21.24864

14.16576

0.025

15.624

10.416

+ve

0.051

31.87296

21.24864

0.037

23.12352

15.41568

-ve con

0.0508

31.74797

21.16531

0.041

25.62336

17.08224

-ve dis

0.0252

15.74899

10.49933

0.041

25.62336

17.08224

+ve

0.038

23.74848

15.83232

0.031

19.37376

12.91584

-ve con -ve dis

0.049 0.025

30.62304 15.624

20.41536 10.416

0.049 0.025

30.62304 15.624

20.41536 10.416

+ve

0.037

23.12352

15.41568

0.037

23.12352

15.41568

-ve con -ve dis

0.06725 0.06725

29.1865 29.1865

19.45767 19.45767

0.041 0.021

17.794 9.114

11.86267 6.076

+ve

0.05075

22.0255

14.68367

0.031

13.454

8.969333

-ve con -ve con

0.05402 0.05402

23.44468 23.44468

15.62979 15.62979

0.033 0.033

14.322 14.322

9.548 9.548

6m

5m


Panel

8m 6m 7m 6m 6m 6m 8m 5m 7m 5m

5m +ve

0.0403

17.4902

11.66013


0.025

10.85

7.233333

75

Chapter Five Slab 6 m=0.8 33


-ve con -ve dis

0.05269 0.02601

22.86746 11.28834

15.24497 7.52556

0.041 0.021

17.794 9.114

11.86267 6.076

+ve

0.03935

17.0779

11.38527

0.031

13.454

8.969333

-ve con -ve dis

0.0675 0.034

18.7488 9.44384

12.4992 6.295893

0.049 0.025

13.61024 6.944

9.073493 4.629333

+ve

0.051

14.16576

9.44384

0.037

10.27712

6.851413

-ve con -ve dis

0.0738 0.0371

20.49869 10.3049

13.66579 6.869931

0.041 0.041

11.38816 11.38816

7.592107 7.592107

+ve

0.0556

15.44346

10.29564

0.031

8.61056

5.740373

-ve con -ve dis

0.0738 0.0372

20.49869 10.33267

13.66579 6.888448

0.049 0.025

13.61024 6.944

9.073493 4.629333

+ve

0.056

15.55456

10.36971

0.037

10.27712

6.851413

5m

Case2

Slab 7 m=0.5 Case=3

4m


4m


4m

6m 5m 8m 4m 7m 4m 6m 4m

For comparison we choose (Strip A which concluded of slab 1-2-3 in long direction as exterior strip with width of (L2=3.15m, Ln=7.7, 6.7 and 5.7 m) which solved by Method II and direct design method and Program (Safe). Table (5-6) Calculation of Moments for all slabs. Slab

Long Direction Moment in Moment in strip A by strip A by Method Direct design (II) kN.m Method kN.m -ve con

Slab 1

+ve -ve dis -ve con

Slab 2

+ve -ve con -ve con

Slab 3

+ve -ve dis

49.2156 72.83909 96.46258 80.71358 61.02734 80.71358 96.46258 72.83909 49.2156

14.521878 69.013572 84.753509 70.193998 57.157970 70.193998 56.354169 45.888394 9.1055012

Safe Program Moment (DDM) kN.m

14.0059 79.625 96.4349 93.4655 49.0565 69.4896 70.9413 58.9074 11.5358

Ratio (Method II/safe) *100

Ratio (DDM/safe) *100

Ratio (Method II/ DDM) *100

351.3919 91.47766 100.0287 86.35655 124.4021 116.152 135.9752 123.6502 426.6336

103.684 86.67325 87.88676 75.10151 116.5146 101.0137 79.43775 77.8992 78.93255

338.9066 105.5431 113.8154 114.9864 106.7696 114.9864 171.172 158.731 540.504

Table (5-7) Calculation of Moments for Strip A by direct design method. Strip Strip A Exteri or Strip A Middl

L2 3.1 5 3.1 5 3.1 5 3.1 5 3.1

Ln 7.7 7.7 7.7 6.7 6.7

L.F

(-ve and +ve moment)

CS. F

0.16

64.8442872

0.913

0.57

231.0077732

0.825

ve-

0.7

283.6937565

0.825

ve -

0.7

214.7919165

0.792

ve

0.57

174.9019892

0.792

Mo 405.276 8 405.276 8 405.276 8 306.845 6 306.845

ve ve +


MCS 59.2028 3 190.581 4 234.047 3 170.115 2 138.522

MCS Slab

M Beam

MSM

M Slabs total

8.880425

50.32241

5.641453

14.521878

28.58721

161.9942

40.42636

69.013572

35.1071

198.9402

49.64641

84.753509

25.51728

144.5979

44.67672

70.193998

20.77836

117.744

36.37961

57.157970

76

Chapter Five e

Strip A Exteri or

5 3.1 5 3.1 5 3.1 5 3.1 5

Comparison of Method II with Direct design and program 6

6.7 5.7 5.7 5.7

306.845 6 222.085 4 222.085 4 222.085 4

+ veve ve + ve-

4 0.7

214.7919165

0.792

0.7

155.4597765

0.75

0.57

126.5886752

0.75

0.16

35.5336632

0.875

170.115 2 116.594 8 94.9415 1 31.0919 6

25.51728

144.5979

44.67672

70.193998

17.48922

99.10561

38.86494

56.354169

14.24123

80.70028

31.64717

45.888394

4.663793

26.42816

4.441708

9.1055012

Fig. (5-2) Slabs strip moment. Design of Reinforced Concrete Slabs by Safe Program

77

Chapter Five


5-4 Slab (work 9) CSI SAFE Analysis and Design of Slab: Design of two way slab with no edge beam with interior column of 400*400 mm and exterior column of 300*300 mm and live load of 3 kN/m2, super imposed dead load =3 kN/m2 use f'c=28 MPa and fy 420 MPa.

Fig. (5-3) slab span and dimensions. Design of Reinforced Concrete Slabs by Safe Program

78

Chapter Five


 Calculate the slab thickness:

 Calculate the factored moment on the slab:

wu=1.2(5.28+3)+1.6*3=14.75 kN/m2  Calculate the strip moment in short direction: Width of intermediate strip =7000vmm and width of column strip is the smaller (l1/2) and (l2/2) taken ad (6000/2) mm  Total factored moment:

 Distribute the total factored moment into positive and negative moment.  Distribute the positive and negative moment to column and middle strip: Table (5-8) Calculation of Moments by direct design method.

Fig. (5-4) bending moment diagram for column strip and the second for middle strip. Design of Reinforced Concrete Slabs by Safe Program

79

Chapter Five


 Design of reinforcement:  (column strip reinforcement) Design of section at maximum positive and negative moments as rectangualr sections, where d=180 mm and b=300 mm f'c=28 MPa and fy=420 MPa

 and half middle strip reinforcement Design of section at maximum positive and negative moments as rectangualr sections, where d=180 mm and b=400 mm f'c=28 MPa and fy=420 MPa

Fig. (5-5) reinforcement layout. Design of Reinforced Concrete Slabs by Safe Program

80

Chapter Five


Example for calculations: ∅= 0.9

d short = t- cover – db/2

=220-20-12/2=194 mm

(cover =20 mm , db = 12mm)

……d long = d short – db = 194– 12 = 182mm

Short direction 𝑚

R=∅∗𝑏∗𝑑2 ∗𝑓𝑐 ′ =85.7*1000000/0.9*400*194*194*28= 0.2259

ω=

1−√1−2.36∗𝑅 1.18

ρ=ω*fc'/fy=0.0644073*28/400=0.01789363

= 0.2684045

As = ρ*b*d =0.00402546*1000*175=1388.546 mm2 As min= 0.0018 * b * t As > As min

=0.0018*1000*220=396 mm2

Number of bars = As req / Asbar=1388.546/113.04=12 As pro= n * Asbar=12*113.04=1356.48 mm2 S req = Asbar * 1000 / Aspro=113.04*1000/1388.546=81.4089 Smin=40 mm and Smax= minimum of [3*t], (600mm) or 500 mm; use 500mm. The program shows that the operation of calculation of moments and reinforcement very easy and simple and faster than the hand calculation which use many formulas and charts and table to calculate and need a programs to drawings the maps which program safe give full maps for moments, stresses, shear, axial forces, reinforcement maps, deformation shapes and gives drawings in (xy plan) and 3D).

Fig. (5-6) program design preferences. Design of Reinforced Concrete Slabs by Safe Program

81

Chapter Five


Fig. (5-7) program slabs design.

Fig. (5-8) entering of data.


82

Chapter Five


Fig. (5-9) full bottom reinforcement of slabs from program. Design of Reinforced Concrete Slabs by Safe Program

83

Chapter Five


Fig. (5-10) top bottom reinforcement of slabs from program. Design of Reinforced Concrete Slabs by Safe Program

84

Chapter Six

Conclusions & Recommendations

Chapter Fix

Conclusions and Recommendation

Chapter Six Conclusions & Recommendations 6-1 Conclusions: Slabs come in a wide amount of shapes, and have been adapted throughout history for a wide number of factors. RCC slab can be various types depending on various criteria. Such as ribbed slab, flat slab, solid slab, continuous slab, simply supported slab etc. There are many methods for design of two way slabs provided by ACI like (method II, The equivalent frame method, (EFM) and the direct design method (DDM). In this project we used Method II and the direct design method for calculation of Moment. The direct design method gives rules for the determination of the total static design moment and its distribution between negative and positive moment sections, then divide the moments found between the middle strip and column strips of the slab and the beams (if any), while method II uses factors to calculated the moments in the middle of strip and then multiplying it with 2/3 to calculated the column strip. A slab may be designed by any procedure satisfying conditions for equilibrium and geometrical compatibility if shown that the design strength at every section is at least equal to the required strength, and that all serviceability conditions, including specified limits on deflections, are met. The methods of elastic theory moment analysis such as the Finite Element satisfies. In this part we talk about the results that calculated from safe program and the results from method II and Direct design method for moment. From compare the results between hands calculate and the program we find that, the program very fast and accurate while the hand calculating is take long time. The degree of agreement of the results is good. Accuracy of the results depends upon the inputs accuracy. It's very easy for user while the hand calculate should be have more information for slab design and be more accrue in calculate . In the present study we take many two way slabs and analyzed by method II and Direct design method (Slabs with interior beam and without interior beam) by comparing moment in (middle strip and column strip), the program gives the design of Design of Reinforced Concrete Slabs by Safe Program

85

Chapter Fix

Conclusions and Recommendation

slabs with complete map instead of drawing it by AUTOCAD. We can choose ready shape slabs with different dimension or we can draw and entered our shape of building slabs. It gives complete shape in 2-D direction and 3 directions. From model button we can inter any model with different dimensions and column and beam shapes. The display bottom shows (unreformed shape, loads type, deformation shape, reaction forces, beam forces/stresses, slab forces/stresses, strip forces, slab design, beam design and punching shear design) depending of chosen code (ACI, BS Code, Euro code…etc). Safe deals with many codes and units (SI units and US). It gives detailing map for general notes, rebar shape, slabs (framing table, rebar table, bill of quantity….etc), reinforcement plan for top and bottom and middle and column strip, and beam framing and design and reinforcement. 6-2 From compare the results between hands calculate and the program we find that:  The programs very fast and time consuming so that the results show according a minute while the hand calculating take a long time.  In this project we design and analysis of slabs depending on equations chart and tables to design and analysis and solving which take along time.  The degree of agreement of the results is good and accuracy of the results depends upon the inputs accuracy.  It's very easy for user while the hand calculate should be have more information for slab design and be more accrue in calculate.  Method II gives very large value which is not accurate and takes only two way slabs with beams and direct design method is very difficult to calculate. 6-3 Recommendations: 1- Design and analysis of different type of slabs (ribbed slab and waffle slabs…etc). 2- Design and analysis of slabs with other codes not just ACI codes and compare the results. 3- Design and analysis of footings (single footing, combined footing ..etc).


86

References

References 1. Building Code Requirements for Structural Concrete (ACI318-14) and Commentary (ACI 318R-14), American Concrete Institute, P.O. Box 9094, Farmington Hills, Michigan. 2. Arthur H. Nilson, (Design of concrete structures), Tenth edition. 3. 2. D. Fanella, I. Alsamsam, “The Design of Concrete Floor Systems”, PCA Professional Development Series, 2005. 4. SAFETM (Design of Slabs, Beams and Foundations Reinforced and PostTensioned Concrete), Copyright © 1978-2009 Computers and Structures, Inc, SAFE is a trademark of Computers and Structures, Inc. Computers and Structures, Inc. 1995, University Avenue Berkeley, California 94704, USA, e-mail: [email protected], web: www.csiberkeley.com. 5. AUTO-CAD, Autodesk, 2013, http://www.autodesk.com. 6. Ali Ammar, et all., (A program to Design of two way slab by direct design method), A Report Submitted to the Department of Civil Engineer at AlMansour University College in Partial Fulfillment of the Requirements for the Degree of B.Sc. in Civil Engineering, May 2015.


Appendix

A-1 Slab (work 1) (Method II) Program results: Strip

Slab

Position

CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3

Span 7 Span 7 Span 7 Span 8 Span 8 Span 8 Span 9 Span 9 Span 9 Span 7-4 Span 7-4 Span 7-4 Span 8-5 Span 8-5 Span 8-5 Span 9-6 Span 9-6 Span 9-6 Span 4-1 Span 4-1 Span 4-1 Span 5-2 Span 5-2 Span 5-2 Span 6-3 Span 6-3 Span 6-3 Span 1 Span 1 Span 1 Span 2 Span 2 Span 2 Span 3 Span 3 Span 3 Span 7 Span 7 Span 7 Span 8 Span 8 Span 8 Span 9 Span 9 Span 9 Span 4 Span 4 Span 4 Span 5 Span 5 Span 5 Span 6 Span 6 Span 6 Span 1 Span 1 Span 1 Span 2 Span 2 Span 2 Span 3 Span 3 Span 3

Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End Start Middle End

Moment kN.m 2.4448 4.189 0.5346 0.4126 3.3245 0.4126 0.5346 4.189 2.4448 2.7271 5.9161 1.6031 0.1063 3.3288 0.1063 1.6031 5.9161 2.7271 2.7271 5.9161 1.6031 0.1063 3.3288 0.1063 1.6031 5.9161 2.7271 2.4448 4.189 0.5346 0.4126 3.3245 0.4126 0.5346 4.189 2.4448 8.6193 13.7838 0.0308 2.6927 11.7518 2.6927 0.0308 13.7838 8.6193 6.7552 12.6714 2.4885 1.1125 10.2437 1.1125 2.4885 12.6714 6.7552 8.6193 13.7838 0.0308 2.6927 11.7518 2.6927 0.0308 13.7838 8.6193

Moment kN.m -2.1898 3.9748 -6.3679 -6.2285 2.5533 -6.2285 -6.3679 3.9748 -2.1898 -4.8064 5.6784 -14.4186 -13.9507 1.5675 -13.9507 -14.4186 5.6784 -4.8064 -4.8064 5.6784 -14.4186 -13.9507 1.5675 -13.9507 -14.4186 5.6784 -4.8064 -2.1898 3.9748 -6.3679 -6.2285 2.5533 -6.2285 -6.3679 3.9748 -2.1898 -6.6743 13.7348 -19.6646 -19.5295 10.559 -19.5295 -19.6646 13.7348 -6.6743 -6.8417 11.4447 -18.975 -18.725 7.664 -18.725 -18.975 11.4447 -6.8417 -6.6743 13.7348 -19.6646 -19.5295 10.559 -19.5295 -19.6646 13.7348 -6.6743

Strip

Slab

Position

CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3




Moment kN.m 2.7536 3.9248 0.9893 0.5875 2.9596 0.5875 0.9893 3.9248 2.7536 2.9252 5.1213 2.2414 1.1174 2.7313 1.1174 2.2414 5.1213 2.9252 2.9252 5.1213 2.2414 1.1174 2.7313 1.1174 2.2414 5.1213 2.9252 2.7536 3.9248 0.9893 0.5875 2.9596 0.5875 0.9893 3.9248 2.7536 18.9927 23.2396 1.5367 0.249 19.4238 0.249 1.5367 23.2396 18.9927 16.5253 21.3292 2.6123 1.1144 17.5105 1.1144 2.6123 21.3292 16.5253 18.9927 23.2396 1.5367 0.249 19.4238 0.249 1.5367 23.2396 18.9927

Moment kN.m -1.4365 1.0135 -5.0394 -4.9497 1.2098 -4.9497 -5.0394 1.0135 -1.4365 -3.6447 2.2985 -11.9657 -11.5272 -0.9678 -11.5272 -11.9657 2.2985 -3.6447 -3.6447 2.2985 -11.9657 -11.5272 -0.9678 -11.5272 -11.9657 2.2985 -3.6447 -1.4365 1.0135 -5.0394 -4.9497 1.2098 -4.9497 -5.0394 1.0135 -1.4365 -7.1459 1.6504 -26.7807 -27.0098 10.4963 -27.0098 -26.7807 1.6504 -7.1459 -7.8566 2.7354 -28.047 -27.7794 7.9611 -27.7794 -28.047 2.7354 -7.8566 -7.1459 1.6504 -26.7807 -27.0098 10.4963 -27.0098 -26.7807 1.6504 -7.1459

Appendix A-2 Slab (work 2) (Method II) Program results: Strip

Slab

Position

CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA1 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA2 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA3 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 CSA4 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA1 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA2 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3 MSA3



Moment kN.m 9.0332 24.0708 -3.8037 -4.4988 16.6084 -4.498 -3.8012 24.0742 9.0387 17.575 54.7691 -18.6204 -21.4414 33.3228 -21.4404 -18.6234 54.7652 17.569 17.575 54.7691 -18.6204 -21.4414 33.3228 -21.4404 -18.6234 54.7652 17.569 9.0332 24.0708 -3.8037 -4.4988 16.6084 -4.498 -3.8012 24.0742 9.0387 32.445 61.3078 -6.8677 -7.8464 43.534 -7.846 -6.8671 61.3084 32.4454 31.3733 60.5152 -8.3677 -15.0862 39.1457 -15.0875 -8.3706 60.5122 31.3698 32.445 61.3078 -6.8677 -7.8464 43.534 -7.846 -6.8671 61.3084 32.4454

Moment kN.m -13.1194 16.979 -36.7389 -34.1912 10.9533 -34.1902 -36.741 16.9818 -13.1095 -34.556 31.483 -99.2951 -92.4441 19.1765 -92.4454 -99.2925 31.4797 -34.5662 -34.556 31.483 -99.2951 -92.4441 19.1765 -92.4454 -99.2925 31.4797 -34.5662 -13.1194 16.979 -36.7389 -34.1912 10.9533 -34.1902 -36.741 16.9818 -13.1095 -12.6674 39.754 -76.4316 -74.2547 29.345 -74.2543 -76.4322 39.7546 -12.6679 -13.4437 37.7343 -84.9775 -82.0995 25.3057 -82.101 -84.9752 37.7314 -13.4478 -12.6674 39.754 -76.4316 -74.2547 29.345 -74.2543 -76.4322 39.7546 -12.6679

Strip

Slab

Position

CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB1 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB2 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB3 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 CSB4 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB1 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB2 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3 MSB3




Moment kN.m 10.4412 17.6981 0.8263 1.2659 13.115 1.2659 0.8263 17.6981 10.4412 16.8706 36.9807 -5.9328 -11.2677 15.8816 -11.2677 -5.9328 36.9807 16.8706 16.8725 36.9874 -5.9308 -11.2681 15.8816 -11.2681 -5.9308 36.9874 16.8725 10.4402 17.7523 0.8258 1.2661 13.1156 1.2661 0.8258 17.7523 10.4402 44.5742 65.8296 10.3784 7.7586 41.8313 7.7586 10.3784 65.8296 44.5742 39.8714 59.7807 9.7975 0.7339 31.8182 0.7339 9.7975 59.7807 39.8714 44.5784 65.8808 10.3826 7.7596 41.832 7.7596 10.3826 65.8808 44.5784

Moment kN.m -8.3638 17.1778 -25.9299 -24.7701 10.5801 -24.7701 -25.9299 17.1778 -8.3638 -24.1381 28.3005 -73.9773 -70.3107 14.3943 -70.3107 -73.9773 28.3005 -24.1381 -24.1365 28.3029 -73.9791 -70.3102 14.3945 -70.3102 -73.9791 28.3029 -24.1365 -8.365 17.177 -25.9278 -24.77 10.5804 -24.77 -25.9278 17.177 -8.365 -7.4442 54.1911 -61.0302 -60.0961 39.4136 -60.0961 -61.0302 54.1911 -7.4442 -9.5662 49.605 -70.1918 -68.3001 30.822 -68.3001 -70.1918 49.605 -9.5662 -7.4408 54.1966 -61.0326 -60.0945 39.4141 -60.0945 -61.0326 54.1966 -7.4408

Appendix A-3 Slab (work 3) (Direct design)


Appendix A-4 Slab (4) (Direct design)






‫خالصة البحث‬ ‫ألبالطات الخرسانية هي جزء مهم من أنظمة الهياكل بما في ذلك المكاتب‪ ,‬المباني‬ ‫التجاريه والسكنية‪ ,‬الجسور‪,‬والمرافق االخرى‪ .‬المهام الرئيسية للبالطات حمل االوزان والقوى‬ ‫المسلطه على المنشأ التي تتمثل بالوزن البشري‪ ,‬البضائع‪ ,‬االثاث وغيرها من االحمال التي‬ ‫تسلط سواء كانت احمال حية او احمال ميتة‪ .‬كما تلعب دورا مهما في مقاومة االحمال الخارجيه‬ ‫التي تتثمل بالرياح‪ ,‬الزالزل وقوى التربة الجانبية‪.‬‬ ‫تصميم البالطات يعتمد في ما اذا كانت ذات أتجاه واحد (‪ )one way‬او اتجاهيين ( ‪two‬‬ ‫‪ )way‬وقابليتها على تحمل االوزان المسلطه عليها والتصمييم اليتطلب الخيال والحسابات فقط‬ ‫وانما التفكير الصحيح ومعرفة الجوانب العلمية المهمه التي تتمثل بالرموز‪ ,‬القوانيين‪ ,‬مدعومه‬ ‫بخبرة وافره والحكم وفق المعايير والغرض من ذلك هو ضمان وتعزيز السالمة اضافة الى ذلك‬ ‫الحفاظ على التوازن بين كلفة المشروع االكثر اقتصاديه وكفائته‪.‬‬ ‫برنامج )‪ (SAFE‬هو برنامج يحتوي على واجهة مستخدم تفاعليه جدا تسمح للمستخدم‬ ‫وبسهوله من رسم البالطات والبنايات وادخال كمية االحمال المسلطه واالبعاد اضافة الى‬ ‫خصائص المواد وفق معايير محدده تعتمد على تحليل الهيكل او المنشأ اوال ثم تصميمه مع‬ ‫تفاصيل التسليح ‪.‬‬ ‫الهدف الرئيسي من هذا المشروع هو تحليل وتصميم بالطات مختلفة االشكال واالبعاد‬ ‫والعتبات‪ ،‬واألعمدة باستخدام برنامج ( ‪ )safe‬باالعتماد على (‪. )ACI Code‬‬ ‫هناك العديد من الطرق المختلفة لتحليل البالطات الخرسانية المسلحة ذات االتجاهين‪.‬‬ ‫تعتمد األساليب األكثر الكفاءة في استخدام عوامل معينة بالنظر في رموز مختلفة من تصميم‬ ‫الخرسانة المسلحة التي تعتمد على معامالت مأخوذة من الجداول الخاصة المتاحة في المدونات‪.‬‬ ‫الطرق األخرى لتحليل البالطات ذات االتجاهين هي طريقة التصميم المباشر‪ .‬ولكن هذه‬ ‫األساليب عادة ما تحتاج وقتا طويال لتحليل البالطات‪ .‬وهذه األساليب هي تقريبية ولكن عملية‬

‫وتعتبر هذه الطرق طرق متحفظة ألن هذه األساليب أهملت العديد من العوامل الهامة للحصول‬ ‫على العزوم الموجبة والسالبة بطرق بسيطة وسريعة دون تعقيد‪.‬‬ ‫في هذا البحث‪ ،‬تم استخدام برنامج جديد لتحليل البالطات ذات االتجاهين وهو برنامج‬ ‫(‪ ،)safe‬حيث تم تحليل العديد من البالطات و نتائج التحليل النهائي للعزوم لبعض األمثلة تم‬ ‫مقارنتها مع عزوم الطرق المختلفة األخرى الواردة‪ .‬والمقارنة اثبتت أن هذا البرنامج بسيط‬ ‫وقادر على تحليل البالطات ويعطي نتائج جيدة ويمكن استخدامه في تحليل البالطات المختلفة‬ ‫بدال من الطرق اليدوية‪ .‬تم تحليل العديد من البالطات الخرسانية ذات تقسيمات عديدة‪ ،‬وتحليلها‬ ‫من قبل (الطريقة الثانية‪ ،‬وطريقة التصميم المباشر والبرنامج) ( ‪Method II, direct design‬‬ ‫‪ .)method and safe‬تمت المقارنة بين التسليح المعتمد على معادالت الكود و الخريطة‬ ‫الناتجة من البرنامج حيث أن هذا البرنامج له القدرة على اعاطاء نتائج سريعة وخرائط كاملة مع‬ ‫تفاصيلها بدال من إضاعة الوقت في الرسومات‪ .‬تم تصميم برنامج اكسل لحساب العزوم في‬ ‫البالطات مع الزيادات في العوامل‪.‬‬ ‫تنقسم هذه الدراسة إلى ستة فصول‪:‬‬ ‫‪ ‬يتضمن الفصل األول مقدمة وانواع البالطات‪.‬‬ ‫‪ ‬يتضمن الفصل الثاني طريقة تصميم البالطات‪.‬‬ ‫‪ ‬يتضمن الفصل الثالث رسم البالطات وتصميم وتحليل البالطات بطريقة المعامالت‬ ‫)‪ (Method II‬وتحليل البالطات ببرنامج )‪(SAFE‬‬ ‫‪ ‬يتضمن الفصل الرابع تصميم وتحليل البالطات بواسطة طريقة التصميم المباشر‬ ‫‪ (direct design).‬وتحليل البالطات ببرنامج )‪.(SAFE‬‬ ‫‪ ‬يتضمن الفصل الخامس مقارنة بين الطريقة الثانية مع تصميم المباشر والبرنامج‪.‬‬ ‫‪ ‬يتضمن الفصل السادس استنتاجات وتوصيات هذه الدراسة‪.‬‬

‫كلية المنصور الجامعة‬ ‫قسم الهندسة المدنية‬

‫تصميم السقوف الخرسانية باستخدام برنامج ‪Safe‬‬ ‫مشروع مقدم لقسم الهندسة المدنية في كلية المنصور الجامعة كجزء من متطلبات نيل‬ ‫شهادة بكلوريوس هندسة في الهندسة المدنية‪.‬‬

‫اعداد‬ ‫‪-1‬‬ ‫‪-2‬‬ ‫‪-3‬‬ ‫‪-4‬‬

‫ابراهيم ثامر‬ ‫حارث مثنى‬ ‫اسراء علي‬ ‫حوراء عالء الدين‬

‫اشراف‬ ‫د‪ .‬عال عادل قاسم‬ ‫‪2016‬‬

‫بغداد‬

‫‪1436‬هـ‬

design of reinforced concrete slabs by safe program

design of reinforced concrete slabs by safe program

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