Design of Reinforced Concrete Structures

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This document does not claim any originality and cannot be used as a substitute for prescribed textbooks. I would like to acknowledge various sources like freely available materials from internet particularly NPTEL/ SWAYAM course material from which the lecture note was prepared. The ownership of the information lies with the respective authors or institutions. Further, this document is not intended to be used for commercial purpose and the BlogSpot owner is not accountable for any issues, legal or otherwise, arising out of use of this document.

This open resource is a collection of academic course of under graduation program for B. Tech (Civil Engineering) and M. Tech as per the syllabus of Dr. B.A.T University, Lonere, Raigad (m.s), India prepared by Dr. Mohd. Zameeruddin, Associate Professor, at MGM's College of Engineering, Nanded for use in the out-of-class activity. The content covers both theoretical and analytical studies. There are six lessons as part of this document, and each deals with an aspect related to Design of Concrete Structures.

Module 1: Basic Aspects of Structural Design

Module 2: Design of Beams and Slabs [WSM]

Module 3: Design of Columns, Footing and Stairs [WSM]

Module 4: Introduction to Limit State Approach

Module 5: Limit State of Collapse (Flexure)

Module 6: Limit States of Collapse (Shear and Bond)

What is a Structural Engineering?

Structural engineering is a sub-domain of civil engineering wherein the structural components are designed and configured in context to the structural action against design loads to achieve economy and safety for both structure and life (Refer Figure 1).

स्ट्रक्चरल इंजीनियरिंग सिविल इंजीनियरिंग का एक उप-डोमेन है जिसमें संरचना और जीवन दोनों के लिए मितव्ययिता और सुरक्षा प्राप्त करने के लिए डिज़ाइन लोड के विरुद्ध संरचनात्मक कार्रवाई के संदर्भ में संरचनात्मक घटकों को डिज़ाइन और कॉन्फ़िगर किया गया है (चित्र 1 देखें)।

Fig. 1: Glimpse of Modern Structural Engineering Practices

Objectives of Structural Engineering [S Unnikrishna Billai and Devdas Menon, 2003]

• Strength to resist safely the stresses induced by the loads in the various structural members
• Stability to prevent overturning, sliding or buckling of the structure, or parts of it, under the action of loads
• Serviceability to ensure satisfactory performance under service load conditions - which implies providing adequate stiffness and reinforcements to contain deflections, crack-widths and vibrations within acceptable limits, and also providing impermeability and durability (including corrosion-resistance), etc.

Purpose of Structural Analysis and Design

The work of structural designer can be separated in two heads; structural analysis and structural design. The purpose of structural analysis is to determine the resultant stresses and the quantification of displacements (or deformation) in the structural components or structure subjected to given combination of loading (Static or dynamic). The purpose of structural design is to estimate required cross-section of structural components, reinforcement requirements and connection design to withstand the applied loads with safely against serviceability and durability.

Different Types of Structures

The structures are classified as (as illustrated in Figure 2);

1. Based on material used for constructions

1. Mud made structures
2. Rock/ Stone structures
3. Brick masonry structures
4. Mortar structures
5. Plain concrete structures
6. Reinforced concrete structures
7. Pre-stressed concrete structures
8. Timber structures
9. Steel structures
10. Composite structures

Fig, 2(a): Based on material used for constructions

2. Based on geometry

     (a). 1-Dimensional structures
     (b)  2-Dimensional Structures
     (c)  3-Dimensional Structures
     (d)  Skeletal Structures

3. Based on the way they carries the loads

1. Beams
2. Trusses
3. Arches
4. Cables
5. Thin plates
6. Plane grids
7. Thin shells

3. Based on the load path

1. Load bearing structures (Slab-Wall-Foundation-Soil)
2. Framed structures (Slab-Beam-Column-Foundation-Soil)
3. Composite structures (LBS + Framed)
4. Retaining Structures (Water tank, Bunkers, Silos and Dams)
5. Gravity Structures (Retaining Walls and Dams)
6. Offshore Structures (Docks and Harbours)

Fig 2c: Based on the Load Path

4. Based on their Applications

1. Residential Structures 
2. Multi-Storied Structures
3. Industrial Structures
4. Transportation Structures
5. Monuments
6. Public and Recreational Structures
7. Military Structures

Fig 2(d): Based on their applications

What is a Concrete?

Concrete is the mechanized mixture of, cement, fine aggregates, coarse aggregates and water in certain proportions which results in  a matrix that hardens (cures) over time and gains a design strength.

[For basics of Concrete and Its Mixes Please refer the Post:  http://mzsengineeringtechnologies.blogspot.com/2015/08/element-of-civil-and-environmental.html]

Fig. 3: Preparation of Concrete Mix

What is Plain Cement Concrete?

Plain cement concrete is the mixture of the cement, fine aggregate (sand) and coarse aggregate, without the reinforcement steel bars.

What is Reinforced Concrete Structures?

Reinforced concrete (RC) is a composite material commonly used for buildings and civil infrastructures, in which reinforcing steel bars are embedded in the concrete to improve its tensile strength and ductility.

Reasons for Using Steel as Reinforcing Material

1. The bond between the steel and concrete is greater than other metals
2. Strength to weight ratio is greater for steel
3. Thermal coefficient of expansion of steel is approximately equal to the thermal coefficient of concrete

Advantages of Reinforced Concrete Structures

1. Strength

Concrete is a blended mixture of the cement, aggregates and water in certain proportions to achieve the targeted compressive strength. Concrete is weak in tension. Reinforcing steel, is a steel bar or mesh of steel wires used to develop tension strength. The compatibility of these two material results in a composite section which is capable to resist both compression and tension forces induced due to applied loading. Figure 4 describes composition of reinforced concrete section.

Fig. 4: Composition of reinforced concrete section

2.  Economical

The materials used for preparing the concrete are easily and locally available, thus reduces the construction cost. 

3. Versatility

Concrete possess more workability in its fresh state; hence can be placed into various shapes of formwork configurations to get the desired shape, surface texture, and sizes. This ability makes it more suitable materials for architectural requirements.

4. Durability

The raw materials used are durable in respect to exposure condition, thereby; increase its design life span. With improved permeability, concrete can resist dissolved chemicals in the water, such as sulphates, chloride and carbon dioxide. This improves its corrosion resistance of concrete making it suitable to use for underwater and submerged applications like pipelines, dams, canals, linings and waterfront structures.

5. Fire Resistance

The constituent materials of concrete do not allow it to catch fire or burn making it to act as fire resistance material. Compared to steel and wood structures reinforced concrete buildings are more fire resistant. This makes concrete suitable to be used in high temperature and blast applications.

6. Ductility

The combination of the steel reinforcement imparts ductility to the reinforced concrete structures. This ductility enables the concrete structure to show warning signs of cracking and deflection before complete failure. 

7. Ease of Construction

Compared to other construction materials, concrete does not need any special connection designs and skilled labour except in some critical situation. Thereby makes concrete economical.

Disadvantages of Reinforced Concrete Structures

1. Concrete is weak in tension, hence ignored in the design of reinforced concrete section. This has limited the use of concrete in tension dominated applications.

2. The concrete gains the strength in stages from the time of pouring to getting set (hardened). That demands to have a quality control checks at each stage of hardening of concrete. 

3. Special attention has to be given towards the provision of effective cover to the reinforcement and the concrete core to face the environmental exposure. 

4. In case of mass concreting there will be rise of the temperature of concrete due to the heat of hydration which will affect the strength. 

5. Utilization of concrete is not an environmentally friendly, as it releases the carbon dioxide.

Uses of Reinforced Concrete Structures

• Buildings
• Bridges, Flyovers and Culverts
• Arches and Retaining walls
• Chimneys and Towers
• Water Tanks
• Dams and Barrages
• Docks and Harbours

What is a characteristic strength of a concrete?

The compressive strength of concrete is given in terms of the characteristic compressive strength of 150 mm size cubes tested at 28 days (f_ck). As per IS 456-2000, the characteristic strength is defined as that strength of the concrete below which not more than 5% of the tests results are expected to fall. That is there is 5% probability or chance of actual strength being less than the characteristic strength.

There may exits considerable differ between the actual value of cube strength at the site compared to theoretical value or design value of cube strength. This difference may be attributed towards the preparation of concrete mix in the control condition in the laboratory compared to the uncontrolled state of mix preparation on site.

        There may exits considerable differ between the actual value of cube strength at the site compared to theoretical value or design value of cube strength. This difference may be attributed towards the preparation of concrete mix in the control condition in the laboratory compared to the uncontrolled state of mix preparation on site.

        These variations in strength are obtained from the frequency distribution curve by plotting the frequency ordinates at different intervals. If the obtained variation is normal, the curve is called normal (Gaussian) distribution curve. The value corresponding to peak of the curve is called as the mean value. The normal distribution curve is symmetrical along both the sides (see figure 5). The shaded region shows the probability of the fall in the characteristic strength.

Fig. 5: Normal (Gaussian) distribution curve for Concrete

The characteristic strength (f_ck) is obtained as;

f_ck = f_m – kS

Where;

f_ck is Characteristic strength

f_m is mean strength

S is standard deviation = √ (observed deviation) / (No. of samples -1)

k is probability constant (for 5% equals to 1.64)

Examples 1:

For a project M 20 grade concrete is decided to be used. The design mixes trails were tested in laboratory. The results obtained from the test are 21.5, 23.4, 26.2, 17.8, 25.7, 27.1, 22.8, 27.0, 26.4, 25.3, 26.8 and 26.90 (in MPa). Determine the acceptability of mix.

Solution:

Sr. No	Sample Data (f)	Mean Value (fm)	Delta (∆) (fm-f)	Delta (∆2)     (fm-f)2	Standard Deviation (S)
1	21.8	24.75	-3.15	9.92	2.85
2	23.4		-1.35	1.82
3	26.2		1.45	2.10
4	17.8		-6.95	48.30
5	25.7		0.95	0.90
6	27.1		2.35	5.52
7	22.8		-1.95	3.80
8	27.0		2.25	5.06
9	26.4		1.65	2.72
10	25.3		0.55	0.30
11	26.8		2.05	4.20
12	26.9		2.15	4.62
Total	297			89.29

Mean value (f_m) = 297/12 = 24.75 MPa

Standard deviation = √ ∆² / (n -1) = √ 89.29/ (12-1) = 2.85

 f_ck = f_m – 1.64S = 24.75 -1.64*2.85 = 20.076 MPa

Hence the strength is with the acceptable limits of the assign grade of concrete.

Examples 2:

What should be the average strength of samples of concrete if desired characteristic strength is 20 N/mm² and standard deviation is 4.1 N/mm².

Solution:

f_ck = f_m – 1.64S

f_m = f_ck + 1.64S = 20 + 1.64*4.1 = 26.724 N/mm²

Properties of Concrete

1. Compressive strength

It may be defined as the capacity of concrete to withstand the compressive load at failure either due to crushing or crippling. It is expressed as the compressive force per unit area of a concrete specimen (in N/mm² or MPa).

        To determine the compressive strength of concrete, cube moulds of size 150mm x 150 mm x 150 mm or cylindrical moulds of diameter 150 mm and height 300 mm are prepared and subjected to the gradual compressive loads. The strength of concrete in compression is  affected by the;

a) Specimen slenderness ratio

The experimental results conducted on the concrete specimens revealed that the compressive strength reduces as the slenderness ratio increase up to a certain value. When the slenderness ration (h/d) is equal to or more than 4 the strength remains constant and equals to 0.67 times the maximum strength.

b) Age effects

Seven day strength of concrete is less than 28 days strength, because of incomplete hydration of cement. This indicates that the gain of strength of concrete is dependent on age (measure from day of preparation of mix). Table 1 shows the compressive strength of concrete at various ages.

Table 1: Compressive strength of concrete at various ages (Approximate)

Age of concrete	Strength in percentage of 28 days compressive strength
1 day	16
3 day	40
7 day	65
14 day	90
28 day	99

The strength of concrete at 28 days is maximum and adopted for the design purpose.

c) Water- cement ratio 

To complete the hydration of cement 38% water of its weight is needed. If W/C ratio is greater than 38 % it will be of no use. The extra amount of water will get evaporated, thereby leaving pores or voids in concrete affecting the strength of concrete

2. Tensile Strength

Tensile strength of concrete in direct tension is obtained by testing the concrete cylindrical moulds in the split cylinder test. It is about 8 to 12 percent of maximum compressive strength of concrete. The other mode of obtaining the tensile strength is through flexural test where concrete beam moulds are subjected flexural loads.

The flexural tensile strength (f_cr) equals to M/Z

Where; M is the applied moment and Z is elastic section modulus

IS 456:2000 provides empirical relation for calculating tensile strength of concrete as f_cr = 0.7√f_ck (Clause No. 6.2.2 IS 456:2000; IS 516; IS 5816)

3. Modulus of Elasticity

Basically, concrete is inelastic material, but for design purpose modulus of elasticity of concrete is estimated as E_c = 5000√fck. Actual measured values may differ by ± 20 percent from the values obtained from the above expression (Clause No. 6.2.3.1 IS 456:2000).

4. Unit weight

Concrete has ingredients like cement, sand, coarse aggregates, water and admixture (if needed) in different proportions. Thus, there is no exact estimation of density of concrete. The density varies in accordance with unit weight of ingredients. For plain cement concrete it varies between 20 to 22 KN/m³ and that for reinforced cement concrete is 23 to 26 kN/m³. IS 456:2000 recommends unit weight of plain cement concrete to be used as 24 kN/m³ and for reinforced cement concrete 25 kN/m³.

What is Reinforcement Steel?

Rebar, also known as reinforcement steel and reinforcing steel, is a steel bar or bundle of steel wires used in reinforced concrete to strengthen and hold the concrete in tension. To improve the quality of the bond with the concrete, the surface of reinforcing steel is often patterned.

 For the basics of reinforcement and their classification, please refer the Post:

http://mzsengineeringtechnologies.blogspot.com/2015/08/element-of-civil-and-environmental.html

Different uses of Rebar or Reinforcement 

• Main reinforcement: used to provide resistance to support the design loads.
• Distribution reinforcement: used for durability and aesthetic purposes by providing localized resistance to limit cracking and temperature-induced stresses.
• Anchoring steel: used to assist other steel bars in accommodating their loads by holding them in the correct position.
• Reinforced masonry tie bars to constrain and reinforce masonry structures.
• In the form reinforcing anchors for the grouting and lining.

Fig. 6: Types of Reinforcement Steel

Types of loads on reinforced Concrete Structures

• Dead loads – IS 875 Part 1
• Live Loads/ Super Imposed Loads– IS 875 Part 2
• Snow Loads– IS 875 Part 4
• Wind Loads– IS 875 Part 3
• Seismic Loads– IS 1893

Fig. 7: Types of loads [N. Subramanian]

For details about types of loading please refer

https://mzsengineeringtechnologies.blogspot.com/2015/08/element-of-civil-and-environmental.html

What do you mean by characteristic loads?

The characteristic load' means that value of load which has a 95 percent probability of not being exceeded during the design life of the structure.

The characteristic load (f_k) is obtained as;

f_k = f_m + kS

Where;

f_k is Characteristic load

f_m is mean value of load

S is standard deviation = √ (observed deviation (∆²)) / (No. of samples (n) -1)

k is probability constant (for 5% equals to 1.64)

Different component parts of reinforced concrete structures and predominate forces on them

Flexural Members – Beams, Slabs, Domes, Lintels, Arches, Chajjas, and Stairs

Compression Members – Columns, Footings, Shear Walls and Elevator Shafts

Write in Brief about the Design Philosophies used for Design of Reinforced Sections?

The various design philosophies used includes;

• Working Stress Method (WSM),
• Ultimate Load Method (ULM), and
• Limit State Method (LSM)

(a) Working Stress Method (WSM): 

The working stress method of design was proposed by Coignet and Tedesco in early 1900. In this method it is assumed that the structural material behaves in a linear elastic manner, and that adequate safety can be ensured by suitably limiting the stresses in the material induced by the expected 'working loads' (service loads) on the structure. This is achieved by keeping permissible ('allowable') stresses well below the elastic material strength (i.e., in the initial phase of the stress-strain curve).

        To extend this concept of a composite material like a reinforced concrete, strain compatibility (due to bond) is assumed, whereby the strain in the reinforcing steel is assumed to be equal to that in the adjoining concrete to which it is bonded. Furthermore, as the stresses in concrete and steel are assumed to be linearly related to their respective strains, it follows that the stress in the steel is linearly related to that in the adjoining concrete by a constant factor (called the modular ratio), defined as the ratio of the modulus of elasticity of steel to that of concrete. Mathematically, modular ratio (m) = E_s/ E_c. Where E_s, is modulus of elasticity of steel and E_c, is modulus of elasticity of concrete. The method is also called as “Elastic Method of Design”.

             The working loads are fixed by limiting the stresses in the concrete and steel to a fraction of the value at which material fails. The ratio of the yield stress of the materials to working stress is called as a factor of safety. For concrete the factor of safety is taken as 3 and for steel factor of safety is taken as 1.80. Hence the modular ratio (m) = 280/3*σ_cbc. The loads are actual working loads [IS 456:1978].

(b) Ultimate Load Method (ULM)

The ultimate load method of design (ULM) was introduced in the 1950s and became an alternative to the WSM. This method is sometimes also referred to as the load factor method or the ultimate strength method. In this method, the stress condition in the state of impending collapse of the structure is analysed, and the non-linear stress-strain curves of concrete and steel make use of. The concept of 'modular ratio' and its associated problems are avoided entirely in this method. The safety measure in the design is introduced by an appropriate choice of the load factor, defined as the ratio of the ultimate load (design load) to the working load. ULM involves three stage procedure;

1. Assessment of suitable value of load factor so that the value of ultimate load may be determined corresponding to given working load.

2. Analysis of structure under the ultimate load so that the distribution of moments and loads may be determined at failure, and

3.The design of members to fall at moments or forces so determined. 

In ULM design the reserve strength in inelastic zone is used, which results in sections with very slender or thin cross-section. A possibility of failure due to cracking or excessive deformation arises, questioning the serviceability requirements.

(c) Limit State Method

Both the WSM and ULM describes the performance of structural members for working loads, which is unrealistic and irrational at an ultimate state of collapse. It is unwarranted in respect of serviceability requirements at service loads. Thus a new philosophy of combination of both ULM and WSM avoiding demerits has been emerging out, so called limit state method (LSM). 

    LSM may be defined as, “the acceptable limit of safety and serviceability requirements before failure occurs". Limit state is a stage where whole structure or part of it becomes unfit for use which may be because of a collapse or due to formation of collapse mechanism.

        This is taken care by using the resistance of member that it satisfactorily withstands against applied loads. In this method characteristic value of material strength and loads are used. Factor of safety applies to both material strength and loads known as a partial safety factor.

Three types of limit states are considered in the design; (1) Limit state of collapse (safety requirements), (2) Limit state of serviceability, and (3) Limit state of durability [Section 5, IS456:2000].

(1) Limit State of Collapse

Limit state of collapse is said to be reached, when the part or the whole structure becomes unfit for use due to rupture. This may be because of the failure due to the formation of the mechanism or the elastic/ inelastic failure of the structure. Collapse may be due to flexure, torsion, shear, compression or bond. 

(2) Limit State of Serviceability

This is related to the satisfactory behavior of structure at the working loads in the form of (i) limit state of deflection and (ii) limit state of crack. 

(i) Limit state of deflection: Excessive deformation in the structure may cause due to lack of safety, spoiling the appearance of the structure. This is taken care by restricting the actual deflection within the permissible limits.

(ii) Limit state of cracking: Cracking of any structural members due to entrance of moisture up to the reinforcement causing corrosion. This is taken care by specifying the maximum crack width for structure.

(3) Limit state of durability: 

This is related to the durability of structure withstanding with natural attacks like fire, chemical action, rain, etc. Depending upon such action the limit state can be of the following types. Limit state of fire resistance, Limit state of environmental or chemical action and Limit state of accidental collapse.

Advantages of Ultimate Load Method over Working Stress Method

Advantages of Limit State Method over Working Stress Method

References:

1. Dr. I. C. Syal and Dr. A. K. Goel. Reinforced Concrete Structures. S Chand and Company Ltd., New Delhi, India
2. S Unnikrishna Pillai and Devdas Menon. Reinforced Concrete Design. Tata McGraw-Hill Publishing Company Limited, New Delhi
3. N. Subramanian. Design of Reinforced Concrete Structures. Oxford University Press, New Delhi
4. IS 456 [1978 and 2000] Indian Standard Plain and Reinforced Concrete- Code of Practice. Bureau of Indian Standards, New Delhi, India