STRUCTURAL DESIGN Lecture Notes - Reinforced Concrete Structures PDF

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Lecture Notes in Civil Engineering STRUCTURAL DESIGN PART I – REINFORCED CONCRETE STRUCTURES Chapters 1. Basic Properties of Materials 2. Limit State Method 3. Design for Flexure 4. Design for Shear 5. Design for Bond 6. Design of Slabs & Staircases KIRAN S. R. Lecturer Department of Civil Engin...

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Lecture Notes in Civil Engineering

STRUCTURAL DESIGN PART I – REINFORCED CONCRETE STRUCTURES

Chapters 1.

Basic Properties of Materials

2.

Limit State Method

3.

Design for Flexure

4.

Design for Shear

5.

Design for Bond

6.

Design of Slabs & Staircases

KIRAN S. R. Lecturer

Department of Civil Engineering

Central Polytechnic College Trivandrum

CHAPTER 1

BASIC PROPERTIES OF MATERIALS Concrete consists of the following ingredients: 1. 2. 3. 4. 5.

Cement – Binding material; Micro-void filler Fine Aggregate – Void filler (use Sand) Coarse Aggregate – Strength provider (use Hard blasted granite chips) Water – Hydrates cement; Controls workability and strength Admixture – modifies the property of concrete in fresh and hardened state

1. Cement [Cl. 5 of IS456] Manufactured by mixing Calcareous (limestone) & Argillaceous (clay) materials in definite proportions. It contains the following oxides: Constituent

Approximate Remarks % composition by volume CaO 62 Gives strength & soundness to cement. If excess, cause unsoundness. SiO2 22 Gives strength. If excess, delays setting Al2O3 5 Causes setting & lowers clinkering temperature Fe2O3 3 Gives color & hardness to cement MgO 2 Gives color & hardness to cement. If excess, cause unsoundness. SO3 2 If excess, cause unsoundness Alkalies (K2O, 1 If excess, cause alkali-aggregate reaction, Na2O) efflorescence & staining It is fed into a rotary kiln and blasted at 1500oC. Clinker (of nodular shape) is obtained, which is cooled and ground into fine powder. To this 3-5% Gypsum is added to prevent quick setting of cement. The cement, thus obtained, contains four major compounds known as Bogue’s Compounds:    

tricalcium silicate (C3S) dicalcium silicate (C2S) tricalcium aluminate (C3A) tetracalcium aluminoferrite (C4AF)

~ 50% by volume of cement ~ 25% ~ 15% ~ 10%

Page 1 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

 Hydration of cement: When Cement mixed with water, the Bogue’s compounds react with water and heat is liberated (Exothermic Reaction). This heat is called Heat of Hydration. Order of hydration is as follows: Bogue’s Compounds

Heat of Hydration

Remarks

C4AF C3A C3S C2S

100 cal/gm 200 cal/gm 120 cal/gm 60 cal/gm

Responsible for initial strength development of cement (33MPa, for 33grade cement. (P/4+3)% water to make cubes of 7cm size.

Types of cement – refer Cl. 5.1 of IS 456

2. Aggregates [Cl. 5.3 of IS456]  Fine Aggregates  particle size between 0.075mm and 4.75mm  generally used – river sand, manufactured sand     

Coarse Aggregates particle size > 4.75mm generally used – Hard blasted granite chips The nominal maximum size of aggregate should be < (1/4)th the minimum thickness of the member In case of heavily reinforced sections, nominal maximum size of aggregate should be  Clear distance between bars minus 5mm whichever is smaller  Minimum cover to reinforcements minus 5mm

 Grading of Aggregates  ‘Grading’ is the particle size distribution of aggregate; it is measured by sieve analysis, and is generally described by means of a grading curve, which depicts the ‘cumulative percentage passing’ against the standard IS sieve sizes.

Page 3 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

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In figure, standard grading curves 1, 2, 3 and 4 are shown (plotted per Indian Standards IS383). The particle size distribution of the given sample of aggregates shall conform to any of the zones A, B or C. Curve 1 represents the coarsest grading, while curve 4 represents the finest grading. The grading (as well as the type and size) of aggregate is a major factor which influences the workability of fresh concrete, and its consequent degree of compaction. This is of extreme importance with regard to the quality of hardened concrete, because incomplete compaction results in voids, thereby lowering the density of the concrete and preventing it from attaining its full compressive strength capability; furthermore, the impermeability and durability characteristics get adversely affected. It is seen from the figure given below that with 95% density (i.e., with 5 percent of voids), there is only 68% strength (i.e., 32% strength lost). This shows that the presence of just 5% voids can lower the strength by 32%.

Presence of more “fines” (i.e., cement & sand) in a concrete mix would improve both workability and resists segregation (segregation means separation of grout from aggregates in a concrete mix due to addition of excess water to concrete)

3. Water [Cl. 5.4 of IS456]   

For mixing of fresh concrete For curing of concrete, while hardening Water used for concrete should be potable Parameters pH Organic Inorganic Sulphate Chlorides Suspended solids

Permissible limit ≥6 < 200 mg/L < 3000 mg/L < 400 mg/L < 500 mg/L for RCC < 2000 mg/L for PCC < 2000 mg/L

Page 4 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

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Excess water in concrete tends to rise up to the surface of the mix, as the solid constituents settle downwards. This is called Bleeding. Use of seawater for mixing or curing of concrete is not recommended due to the presence of harmful salts Generally, water content used in concrete is 180-200 L / m3 of concrete. Abrams’ Law: Compressive strength of hardened concrete is inversely proportional to the water-cement ratio (see figure below). A reduction in water-cement ratio generally results in an increased quality of concrete, in terms of density, strength, impermeability, reduced shrinkage and creep etc.

4. Admixtures [Cl. 5.5 of IS456]   

Added to concrete to modify its properties in fresh & hardened state Broadly, two types o Chemical Admixtures (liquid in form) o Mineral admixtures (fine granular in form) Types of Chemical Admixtures o Accelerators – accelerates the hardening process (early strength development) o Retarders – delays the setting of concrete, to reduce the heat generation o Superplasticizers – high range water reducers; increase flowability without increasing water content; produce high strength concrete o Air-entraining Agents – introduce microscopic air bubble cavities in concrete; minimize damage due to alternate freezing & thawing o Bonding admixtures – used to improve adherence of fresh concrete to old concrete

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Types of Mineral Admixtures (Puzzolonas) [Cl. 5.2 of IS456] – Mineral admixtures are generally used as partial replacement of cement in concrete. They react with Calcium hydroxide in the presence of water to form cementitious compounds. o Fly Ash o Ground Granulated BlastFurnace Slag (GGBS) o Silica Fume o Rice Husk Ash o Metakaoline

6. PROPERTIES OF FRESH CONCRETE  Workability  Workability is the ease with which the concrete can be mixed, placed, consolidated and finished.  Workable concrete is the one which exhibits very little internal friction between particle and particle or which overcomes the frictional resistance offered by the formwork surface or reinforcement contained in the concrete.  The factors affecting workability are given below:  Water Content  Mix Proportions  Size of Aggregates  Shape of Aggregates  Surface Texture of Aggregate  Grading of Aggregate  Use of Admixtures  The following tests are commonly employed to measure workability.  Slump Test  Compacting Factor Test  Flow Test  Kelly Ball Test  Vee Bee Consistometer Test  Segregation  Segregation can be defined as the separation of the constituent materials of concrete.  A good concrete has all its constituents properly distributed to form a homogenous mixture. To ensure this, optimum grading, size, shape and surface texture of aggregates with optimum quantity of cement & water makes a mix cohesive. Such a concrete does not exhibit the tendency for segregation.  Prime cause of segregation is the difference in specific gravity of constituents of concrete. Page 6 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

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Segregation may be one of the following types: o Coarse aggregate separating out of the rest o Cement paste or cement-fine aggregate matrix separating out from coarse aggregate o Water separating out of the rest The conditions that favour segregation are: o Bad mix proportion o Inadequate mixing o Excessive compaction by vibration of wet mix o Large height of dropping of concrete for placement o Long distance conveyance of mix

 Bleeding  Here, water from the concrete comes out to the top surface of the concrete after casting.

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The conditions that favour bleeding are: o Highly wet mix o Bad mix proportion o Inadequate mixing Sometimes, the bleeding water is accompanied to the surface by certain quantity of cement, which forms a cement paste (known as Laitance) at the surface.

7. PROPERTIES OF HARDENED CONCRETE  Grade of concrete  Designated in terms of letter ‘M’ followed by a number. ‘M’ refers to mix; the number represents the 28-day characteristic compressive strength of concrete cubes (150mm) expressed in MPa. Eg: M20 denotes the concrete mix with 28-day characteristic compressive strength of 20MPa. 

Minimum grade of concrete used is dictated by durability (the environment to which the structure is exposed to, expressed in terms of exposure conditions)

Page 7 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

Exposure Condition Mild Moderate Severe Very severe Extreme 

Minimum grade of concrete for RCC works M20 M25 M30 M35 M40

Classification o Ordinary concrete – M10 to M20 o Standard concrete – M25 to M55 o High Strength concrete – M60 and above

 Stress-strain curve of concrete  Stress-Strain curves of concrete for various grades obtained from uniaxial compression tests are shown in above figure  Maximum stress is attained by concrete at an approximate strain of 0.002  The strain at failure is in the range 0.003 to 0.005  The curves are linear within the initial portion of the curve. This is approximately true upto one-third of the maximum stress level, beyond which the non-linearity continues  For higher grades of concrete, the initial portion of the stress-strain curve is steeper, but the failure strain is low. For low strength concrete, the initial slope of curve is gentle but has high failure strain. (observe the above figure)

Page 8 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

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Poisson Effect: Failure of concrete subject to uniaxial compression is primarily initiated by longitudinal cracks (cracks developed parallel to direction of loading) formed due to lateral expansion (because lateral fibres experience tensile stress) and finally lateral strain exceeds limiting tensile strain of concrete of 0.0001 to 0.0002. These longitudinal cracks generally occur at coarse aggregate-mortar interface. The descending part of Stress-Strain curve is attributed to the extensive microcracking in mortar. This is called Strain-Softening of Concrete.

 Modulus of Elasticity of concrete  Young’s Modulus of Elasticity (equal to ratio of stress to strain, when the material is loaded within the linearly elastic limit) for concrete subjected to uniaxial compression, has validity only within the initial portion of the Stress-Strain curve. For concrete, there are 3 ways to determine the Modulus of Elasticity. This is shown in figure. o Initial Tangent Modulus – Slope of tangent at origin of curve; measure of Dynamic Modulus of Elasticity of concrete o Tangent Modulus – Slope of tangent at any point on the curve o Secant Modulus – slope of line joining origin & one-third of maximum stress level; measure of Static Modulus of Elasticity of concrete  Static Modulus of Elasticity of concrete – is applicable to static system of loads on structures  Dynamic Modulus of Elasticity of concrete – is applicable when structure is subject to dynamic loads (wind & earthquake loads)

Page 9 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

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Secant Modulus at one-third of maximum stress level represents the “Short-term Static Modulus of Elasticity of Concrete (Ec)”. “Short-term” means the long term effects of creep & shrinkage are not considered. According to IS456,

Ec = 5000 f where fck is the 28-day characteristic compressive strength of 150mm concrete cubes. Thus, it should be noted that Modulus of Elasticity of concrete is a function of its strength.

8. PROPERTIES OF STEEL 

Stress-strain curve of reinforcing steel  Reinforcing steel may be categorized broadly into: o Plain Mild steel bars  has well-defined yield point  Eg: Fe250 – Yield strength= 250MPa; Ultimate strength= 412MPa; Min % elongation= 22% o High Yield Strength Deformed bars  doesnot have well-defined yield point  these are cold-worked bars (involves stretching and twisting of mild steel bars)  Eg: Fe415 – Yield strength= 415MPa; Ultimate strength= 485MPa; Min % elongation= 14.5%  Eg: Fe500 – Yield strength= 500MPa; Ultimate strength= 545MPa; Min % elongation= 12%

Page 10 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

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Characteristic strength of reinforcing steel = o yield strength of steel– for those with well-defined yield point (Fe250) o 0.20% Proof Stress – for those without well-defined yield point (Fe415&Fe500) 0.2% Proof Stress is measured as shown below

9. PERMISSIBLE STRESSES IN CONCRETE AND STEEL [Refer Table21 & 22 in Annex B of IS456]  Permissible Stresses in Concrete Grade of Direct concrete Tension (N/mm2)

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Bending compression (N/mm2)

Direct compression (N/mm2)

Average bond for plain bars in tension (N/mm2) 5 0.8 6 0.9 8 1 9 1.1 10 1.2 in compression, increase the values of stress for

M20 2.8 7 M25 3.2 8.5 M30 3.6 10 M35 4 11.5 M40 4.4 13 For bond stress for plainbars bars in tension by 25% For bond stress for HYSD bars, increase the values of stress for bars in tension by 60%

 Permissible Stresses in Steel Reinforcement Type of stress in steel bars Tension (a) ≤ 20mm dia bar (b) > 20mm dia bar Compression in column bars

Fe250 (N/mm2) 140 130 130

Fe415 Fe500 (N/mm2) (N/mm2) 230 230 190

275 275 190

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NOTE: When effects of temperature, shrinkage and wind (or earthquake) are considered, in addition to effects of dead, live & impact loads, then the above values of permissible stresses in concrete & steel may be exceeded upto a limit of 33.33%

10. DESIGN CODES, HANDBOOKS & OTHER REFERENCES Basic codes for Design

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1) IS 456 : 2000 — Plain and reinforced concrete – Code of practice Loading Standards : 1) IS 875 (Parts 1-5) : 1987 — Code of practice for design loads (other than earthquake) for buildings and structures (second revision) a. Part 1 : Dead loads b. Part 2 : Imposed (live) loads c. Part 3 : Wind loads d. Part 4 : Snow loads e. Part 5 : Special loads and load combinations 2) IS 1893 : 2002 — Criteria for earthquake resistant design of structures (fourth revision). Design Handbooks : 1) 2) 3) 4)

SP 16 : 1980 — Design Aids (for Reinforced Concrete) to IS 456-1978 SP 24 : 1983 — Explanatory Handbook on IS 456 : 1978 SP 34 : 1987 — Handbook on Concrete Reinforcement and Detailing SP 23 : 1982 — Design of Concrete Mixes

Other Relevant Codes

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1) IS 13920 : 1993 — Ductile detailing of reinforced concrete structures subjected to seismic forces. 2) IS 10262 : 2009 — Guidelines for Concrete Mix Proportioning Other Reference Books 1) Unnikrishna Pillai & Devdas Menon, “Reinforced Concrete Design”, 3rd Edition, Tata McGraw Hill Publishers, 2009 2) Ashok K. Jain, “Reinforced Concrete – Limit State Design”, 6th Edition, Nem Chand & Bros Publishers, 2002

. Page 12 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

CHAPTER 2

LIMIT STATE METHOD [Refer Section 5 – Page 67 of IS456]  

The acceptable limit for safety and serviceability requirements before failure occurs is known as Limit State. LSM involves underestimation of the material strength and overestimation of external loads. For this, the method uses partial safety factor format.

The design of any structure should satisfy the following 2 conditions: SAFETY SERVICEABILITY  With due consideration to strength,  Satisfactory performance of structure stability & structural integrity. under service loads. Ensures no discomfort to the user  If this condition is satisfied, the likelihood for “collapse” is acceptably  If this condition is satisfied, the low under service loads (usual or likelihood for “user discomfort” is expected loads) as well as probable acceptably low under service loads. overloads (extreme winds,  User discomfort may occur due to: earthquake etc.) o Deflection  Collapse may occur due to: o Cracking o Exceeding of strength of o Vibrations material or load bearing o Durability capacity of material. o Impermeability o Sliding o Thermal Insulation (or Fire o Overturning resistance) o Buckling  Limit states involved in user comfort o Fatigue are called “Limit state of o Fracture serviceability”, which are defined for, o Deflection  Limit states involved in collapse are called “Limit State of Collapse” or o Cracking “Ultimate Limit State”, which are o Durability defined for the following, o Fire Resistance o Flexure o Compression o Shear o Torsion

Page 13 of 95 Prepared by Kiran S. R., Lecturer, Department of Civil Engineering, Central Polytechnic College Trivandrum

IMPORTANT TERMINOLOGIES 1. Characteristic Strength  It is the strength of the material below which not more than 5% of the test results are expected to fall.  Characteristic strength of concrete = 28-day characteristic compressive strength of 150mm concrete cubes (fck). For the design of structures, only 67% of fck is considered.  Characteristic strength of reinforcing steel = yield strength of steel (fy) or 0.20% Proof Stress. 2. Characteristic Loads  Loads which have 95% probability of not being exceeded during the life of the structure.  Magnitudes of these loads are enlisted in: o IS 875 (Part 1) – Dead Loads o IS 875 (Part 2) – Live loads o IS 875 (Part 3) - Windloads o IS 875 (Part 4) - Snowloads o IS 875 (Part 5) – Load Combinations o IS 1893 – Seismic loads 3. Design strength 

Design strength =

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By this, the strength of material is underestimated Characteristic strength of material = 0.67 fck (for concrete) = fy (for reinforcing steel) Partial safety factor for material = 1.5 (for concrete) = 1.15 (for reinforcing steel) . Therefore, Design strength of concrete = = 0.447 fck ≈ 0.45 fck .

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and, Des...