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This document discusses different types and classifications of columns. It defines a column as a vertical structural member primarily designed to carry axial compression loads. Columns can be classified based on their shape, reinforcement, and type of loading. Common shapes include square, rectangular, circular, L-shaped, and T-shaped sections. Reinforcement types include tied columns with tie bars, spiral columns with helical reinforcement, and composite columns with encased steel. Columns are either concentrically loaded with forces through the centroid, or eccentrically loaded off-center. The document also covers column capacity calculations, resistance factors, and provides an example problem.

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Design of Reinforced Concrete Structure (IS 456:2000)

This is the 1st Lecture Series on Design Reinforced Cement Concrete (IS 456 -2000).
In this video, you will learn about the objective of structural designing and then basic properties of concrete and steel.
Concrete properties like...
1. Grade of Concrete
2. Modulus of Elasticity
3. Characteristic Strength
4. Tensile Strength
5. Creep and Shrinkage
6. Durability
Reinforced Steel Properties....
1. Grade and types of steel
2. Yield Strength of Mild Steel and HYSD Bars

Composite slab

This document discusses the behavior of composite slabs with profiled steel decking. It presents information on:
1) Composite slabs that use profiled steel sheets as permanent formwork and tensile reinforcement, allowing for 30% reduced concrete and lower structural weight.
2) The profiled steel decking used which is thin-walled, cold-formed sheets meeting ASTM and IS standards with a galvanized coating.
3) Three slabs - plain concrete, bar reinforced, and steel fiber reinforced - were tested for negative bending capacity, with the fiber reinforced slab showing over a 2.5x increase in load capacity compared to plain concrete.

Design of columns as per IS 456-2000

This document discusses reinforced concrete columns. It begins by defining columns and different column types, including based on shape, reinforcement, loading conditions, and slenderness ratio. Short columns fail due to material strength while slender columns are at risk of buckling. The document covers column design considerations like unsupported length and effective length. It provides examples of single storey building column design and discusses minimum longitudinal reinforcement requirements in columns.

Composite structure of concrete and steel.

This document discusses composite structures, which combine steel and concrete materials. The key elements of composite structures are composite deck slabs, beams, and columns, along with shear connectors. Composite structures take advantage of concrete's compressive strength and steel's tensile strength. They provide benefits like increased load capacity, stiffness, fire resistance, and cost savings compared to traditional steel or concrete construction alone. An example project, the Millennium Tower in Vienna, is described. The document analyzes costs and concludes that composite structures are best suited for high-rise buildings due to reduced weight, increased ductility, and savings of around 10% compared to reinforced concrete.

Ductile detailing

This document discusses ductile detailing of reinforced concrete (RC) frames according to Indian standards. It explains that detailing involves translating the structural design into the final structure through reinforcement drawings. Good detailing ensures reinforcement and concrete interact efficiently. Key aspects of ductile detailing covered include requirements for beams, columns, and beam-column joints to improve ductility and seismic performance. Specific provisions are presented for longitudinal and shear reinforcement in beams and columns, as well as confining reinforcement and lap splices. The importance of cover and stirrup spacing is also discussed.

Two way slab

This document discusses two-way slabs, which are supported on all four sides or at column centerlines. It describes two main types - edge supported slabs and column supported slabs. Edge supported slabs are suitable for spans of 20-30 feet and live loads of 60-120 psf. They have increased stiffness and low deflection. Column supported slabs include flat slabs and two-way ribbed/waffle slabs. Flat slabs have no beams or column capitals and are suitable for spans of 20-30 feet. Ribbed and waffle slabs have reduced dead load and architectural beauty, with spans of 30-48 feet and live loads of 60-120 psf. The document also discusses minimum

Hollow block and ribbed slabs

This report compares design codes for hollow block and ribbed slabs. It includes:
- A comparison of limitations between Egyptian, British, Euro and American codes on rib spacing, slab thickness, and other parameters.
- Solved examples for one-way and two-way slabs according to different codes, finding the Egyptian code most economical.
- Analysis of using one or two cross-ribs, determining one rib at midspan is sufficient.
- Different modeling methods for the slabs in structural analysis software, with minor differences in results.
- Case studies presented for one-way, cantilever, two-way hollow block slabs, and ribbed slabs using

DESIGN OF FLAT SLABS

This document summarizes the key aspects of flat slab construction and design according to Indian code IS 456-2000. It defines flat slabs as slabs that are directly supported by columns without beams, and describes four common types based on whether drops and column heads are used. The main topics covered include guidelines for proportioning slabs and drops, methods for determining bending moments and shear forces, requirements for slab reinforcement, and an example problem demonstrating the design of an interior flat slab panel.

Reinforced Concrete Design (2)

This slide is about the detailed designs of different frame structure buildings ,their cross sections etc.

Circular-Slabs.pptx

Circular slabs are commonly used as roofing elements or covers for circular structures. They experience bending stresses like a saucer with tension on the bottom and compression on top when loaded. Analysis of circular slabs is conducted using plate bending theory in polar coordinates, where bending moments are expressed as radial and tangential components. Common support conditions include simply supported, fixed, or partially fixed edges. Reinforcement is typically provided in a rectangular grid oriented for the maximum of the radial and tangential bending moments, with consideration for sign of moments at edges. An example problem demonstrates design and shear check of a circular slab.

Combined footing 1-1-18

This document discusses the design of combined footings. It defines a combined footing as one that supports two or more adjacent columns to provide uniform bearing pressure and minimize differential settlement. It describes the different types of combined footings based on connectivity (slab, slab-beam, strap-beam) and shape (rectangular, trapezoidal). The key steps of the design process are outlined, including determining the footing size based on load and soil capacity, performing structural analysis to calculate moments and shear, and designing the longitudinal, shear, and transverse reinforcement.

Raft foundations _design_and_analysis_with_a_practical_approach

This document discusses the need for raft foundations. Raft foundations are recommended when:
1) Building loads are heavy or soil capacity is low, so individual footings would cover too much area.
2) Soil contains weak lenses or cavities, making differential settlement hard to predict.
3) Structures are sensitive to differential settlement.
4) Structures like silos naturally suit raft foundations.
5) Floating foundations are needed over very weak soil.
6) Buildings require basements or underground pits.
7) Individual footings would experience large bending stresses.
Raft foundations increase capacity, decrease settlement, and equalize differential settlement compared to individual footings. However,

Composite column

A steel-concrete composite column consists of either a concrete encased steel section or a concrete filled steel tubular section used as a load-bearing member. There are three main types of concrete filled steel tube columns: circular, rectangular, and square. The advantages of composite columns include increased floor space for the same strength, good fire and corrosion resistance, and consistent dimensions between floors. Performance is measured using ductility index, strength index, and concrete contribution ratio.

Reinforcement detailing

The document discusses proper detailing of reinforced concrete structures, which is essential for safety and structural performance. It provides guidelines and examples of good and bad detailing practices for common reinforced concrete elements like slabs, beams, columns, and foundations. Proper detailing is important to avoid construction errors and ensure the structural design works as intended under gravity and seismic loads.

Design of column according ACI codes

1) The document discusses design considerations for columns according to ACI code, including requirements for different types of columns like tied, spirally reinforced, and composite columns.
2) It provides details on failure modes of tied and spiral columns and code requirements for minimum reinforcement ratios, number of bars, clear spacing, cover, and cross sectional dimensions.
3) Lateral reinforcement requirements are discussed, noting ties help restrain longitudinal bars from buckling while spirals provide additional confinement at ultimate load.

Shear wall and its design guidelines

This document discusses shear wall analysis and design. It defines shear walls as structural elements used in buildings to resist lateral forces through cantilever action. The document classifies different types of shear walls and discusses their behavior under seismic loading. It outlines the steps for designing shear walls, including reviewing layout, analyzing structural systems, determining design forces, and detailing reinforcement. The document emphasizes the importance of properly locating shear walls in a building to resist seismic loads and minimize torsional effects.

Two way slab

1) Two-way slabs are slabs that require reinforcement in two directions because bending occurs in both the longitudinal and transverse directions when the ratio of longest span to shortest span is less than 2.
2) The document discusses various types of two-way slabs and design methods, focusing on the direct design method (DDM).
3) Using the DDM, the total factored load is first calculated, then the total factored moment is distributed to positive and negative moments. The moments are further distributed to column and middle strips using factors that consider the slab and beam properties.

Buckling types

In science, buckling is a mathematical instability, leading to a failure mode.
Buckling is characterized by a sudden sideways failure of a structural member subjected to high compressive stress, where the compressive stress at the point of failure is less than the ultimate compressive stress that the material is capable of withstanding

Columns

This presentation summarizes key aspects of columns for engineering. It defines a column as a structural member subjected to axial compression. It classifies columns as short, medium, or long based on their slenderness ratio. It describes the failure of columns by crushing (for short columns) or buckling (for long columns). Euler's theory of buckling is summarized, which models buckling based on a column's effective length, modulus of elasticity, and moment of inertia. Different effective lengths are defined for varying end conditions. Finally, Rankine's empirical formula is presented as applicable to both short and long columns.

Contents Reinforced Concrete LimitState-AKJ

This document provides information about a textbook on reinforced concrete limit state design published in 2012. It is the 7th edition of the first Indian book published on this subject in 1983. The book contains chapters covering topics such as materials for concrete, design of concrete mixes, design philosophies, definitions, design of beams, slabs, columns, foundations, retaining walls, multistorey buildings, prestressed concrete, and reinforced concrete bridges. It is authored by Ashok K. Jain, a professor and head of the civil engineering department at IIT Roorkee.

Design of Reinforced Concrete Structure (IS 456:2000)

Design of Reinforced Concrete Structure (IS 456:2000)

Composite slab

Composite slab

Design of columns as per IS 456-2000

Design of columns as per IS 456-2000

Composite structure of concrete and steel.

Composite structure of concrete and steel.

Ductile detailing

Ductile detailing

Two way slab

Two way slab

Hollow block and ribbed slabs

Hollow block and ribbed slabs

DESIGN OF FLAT SLABS

DESIGN OF FLAT SLABS

Reinforced Concrete Design (2)

Reinforced Concrete Design (2)

Circular-Slabs.pptx

Circular-Slabs.pptx

Combined footing 1-1-18

Combined footing 1-1-18

Raft foundations _design_and_analysis_with_a_practical_approach

Raft foundations _design_and_analysis_with_a_practical_approach

Composite column

Composite column

Reinforcement detailing

Reinforcement detailing

Design of column according ACI codes

Design of column according ACI codes

Shear wall and its design guidelines

Shear wall and its design guidelines

Two way slab

Two way slab

Buckling types

Buckling types

Columns

Columns

Contents Reinforced Concrete LimitState-AKJ

Contents Reinforced Concrete LimitState-AKJ

Presentation on Slab, Beam & Column

This is a Power Point Presentation discussing briefly about the Slab, Beam & Column of a building construction. It was presented on 6th March, 2014 as part of the Presentations of the subject: DETAILS OF CONSTRUCTION, at Ahsanullah University of Science & Technology (AUST)

Reinforced column design

The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is designed based on the column's expected loads and dimensions using methods specified in design codes like BS 8110.

Column detailing, Session 14-15 (DUET)

This document provides details on reinforcing concrete columns, including:
- Classification of columns as tied, spirally reinforced, or composite
- Minimum reinforcement requirements of 4 bars for tied columns and 6 bars for spiral columns
- Design considerations for tie ratio between 1-8% or 1-6% depending on code
- Clear cover and spacing requirements between bars
- Arrangement and sizing of ties and spirals
- Requirements for bundling, lapping, and hooking of reinforcement bars

Columns rajeevan sir

This document contains lecture notes on the design of concrete columns. It defines key terms like effective length, pedestal, column, and discusses the classification of columns based on type of reinforcement, loadings, and slenderness ratio. It describes the functions of bracing in columns and design requirements for longitudinal and transverse reinforcement. The document states assumptions in limit state design of columns and the need to consider minimum eccentricity in design. It concludes with sample exercises related to column design.

Lecture 1 what is rcc column and its importance

Columns are an important structural member that carry compressive loads and bending moments. They are composed of concrete reinforced with embedded steel. Columns make up 11% of a building's weight but must support 100% of the total weight. Reducing column size or number is not advisable. Column alignment and the moment of inertia 'I' value are also important, with a higher I providing more resistance to bending and deflection. Proper casting, curing, and avoiding honeycombing or voids are crucial for column strength.

Insert some activities into primavera p6

This document provides instructions for inserting activities into Primavera P6 to represent the construction schedule. It outlines the major work items for the foundation stage including pad footing and pedestal construction. Ten work items are listed to represent the pad footing and pedestal work. It then discusses the ground beam, slab, and steel column and beam work. Four work breakdown structure items are identified for these stages. The document instructs the user to add these work items and activities to the Primavera P6 project schedule.

Beams and columns

Reinforced concrete columns and beams are important structural elements that carry compressive and bending loads respectively. Columns can be categorized as short or long based on their height-width ratio and as spiral or tied columns based on their shape. Beams are classified based on their supports as simply supported, fixed, continuous, or cantilever beams. The construction of RCC columns and beams involves laying reinforcement, forming the structure, and pouring concrete to create these load-bearing elements.

Construction process''column,beam,slab''

The document describes the construction process for columns, slabs, and beams in reinforced concrete structures. It discusses the materials used and the typical steps involved, which include:
1) Layout and formwork installation
2) Placement of reinforcing steel based on structural designs
3) Pouring and finishing of concrete
4) Curing of concrete to gain full strength over 28 days
The columns transfer loads vertically through reinforced concrete that is mixed on site or delivered by ready-mix trucks. Slabs and beams are constructed through similar processes of steel reinforcement, formwork, concrete placement and curing.

Beam and slab design

The document summarizes the design of beam-and-slab systems. It describes how the one-way slab is designed as a continuous slab spanning the beam supports using moment distribution methods or a simplified coefficient method. Interior beams are designed as T-beams and edge beams as L-beams, which provide greater flexural strength than conventional beams. The beam and slab must be securely connected to transfer shear forces between them. The slab is reinforced as a one-way system and the beams are designed as simply supported beams spanning their supports.

Placing column layout

This document provides three thumb rules for column placement in building design:
1. The minimum column size should be 9"x9" for a single-story structure and 12"x9" for a 1.5-story structure, using appropriate concrete grades. Larger column sizes are needed for greater distances between columns or additional floors.
2. The distance between column centers should not exceed 4m for 9"x9" columns, and larger column sizes are needed to allow for greater distances.
3. Columns should be arranged in a rectangular grid or circular pattern, not zigzag, to avoid structural issues in load transfer, wall construction, and beam placement. Following these thumb rules can help prevent mistakes in structural

Columns lecture#4

The document discusses column behavior under different loading conditions. It presents the load and moment equations for columns under eccentric loading, and describes three failure cases: 1) pure axial load/crushing failure, 2) balanced failure, and 3) pure flexural failure. Equations are derived for the load-carrying capacity and moment capacity based on the stress-strain relationships of concrete and steel.

Moment Co-efficient Method

The document discusses the moment coefficient method for analyzing statically indeterminate structures. It provides definitions of statically indeterminate structures as those where there are more unknown reactions or internal forces than available equilibrium equations. The moment coefficient method uses coefficients provided in the ACI code that are based on elastic analysis but account for inelastic redistribution. The coefficients are multiplied by the total factored load and span length to determine bending moments. The method was first included in the 1963 ACI code and remains permissible for analyzing two-way slabs supported on all sides. Advantages include providing a more exact analysis and potential cost savings through more precise design.

Bar bending schedule(by akhil)

Bar Bending Schedule (BBS) is a chart which gives a clear picture of bar length, diameter of bar ,bar mark ,location of bar.
It allow workers to place steel properly.

Design of two way slab

This document discusses the design of two-way slabs. It defines a two-way slab as having a ratio of long to short spans of less than 2. The main types of two-way slabs described are flat slabs with drop panels, two-way slabs with beams, flat plates, and waffle slabs. The basic steps of two-way slab design are outlined, including choosing the slab type and thickness, the design method, calculating moments, determining reinforcement, and checking shear strength. Two common design methods are described: the direct design method which uses coefficients, and the equivalent frame method which analyzes frames cut between columns.

Engineering formula sheet

1. The document provides engineering formulas and equations for statistics, mechanics, electricity, fluid mechanics, thermodynamics, structural analysis, and simple machines.
2. Key formulas include those for mean, median, mode, standard deviation, and probability. Mechanics formulas include those for force, torque, energy, power, and kinematics.
3. Formulas are also provided for stress, strain, modulus of elasticity, beam deflection, truss analysis, and mechanical advantage of simple machines like levers, inclined planes, and gears.

ONE WAY SLAB DESIGN

This presentation summarizes the key aspects of one-way slab design. It defines one-way slabs as having an aspect ratio of 2:1 or greater, with bending primarily along the long axis. The presentation discusses the types of one-way slabs including solid, hollow, and ribbed. It also outlines the design considerations for one-way slabs according to the ACI code, including minimum thickness, reinforcement ratios, and bar spacing. An example problem demonstrates how to design a one-way slab for a given set of loading and dimensional conditions.

Design of R.C.C Beam

information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,

Presentation on Slab, Beam & Column

Presentation on Slab, Beam & Column

Reinforced column design

Reinforced column design

Column detailing, Session 14-15 (DUET)

Column detailing, Session 14-15 (DUET)

Columns rajeevan sir

Columns rajeevan sir

Lecture 1 what is rcc column and its importance

Lecture 1 what is rcc column and its importance

Insert some activities into primavera p6

Insert some activities into primavera p6

Beams and columns

Beams and columns

Construction process''column,beam,slab''

Construction process''column,beam,slab''

Beam and slab design

Beam and slab design

Placing column layout

Placing column layout

Columns lecture#4

Columns lecture#4

Moment Co-efficient Method

Moment Co-efficient Method

Bar bending schedule(by akhil)

Bar bending schedule(by akhil)

Design of two way slab

Design of two way slab

Engineering formula sheet

Engineering formula sheet

ONE WAY SLAB DESIGN

ONE WAY SLAB DESIGN

Design of R.C.C Beam

Design of R.C.C Beam

Intze PPT

The document compares the design of an Intze tank using membrane design and continuity analysis methods. Membrane design involves analyzing structural elements independently and designing for direct stresses only. Continuity analysis considers restraint at joints, resulting in secondary stresses from edge moments and varying hoop stresses. For a 9 lakh liter and 6 lakh liter tank, continuity analysis yields higher hoop forces, bending moments, and reinforcement areas compared to membrane design.

BEAM.pptx

This document provides specifications and information about beams and columns used in construction. It discusses reinforced concrete columns and different types of columns based on height-width ratios and shapes. It also describes the construction process for RCC columns. For beams, it defines reinforced concrete beams and classifies beams based on their supports. It discusses different types of beams and the construction process for beams.

Intze ppt

The document compares the design of an Intze water tank using membrane design and continuity analysis methods. Membrane design assumes members act independently and are only subjected to direct stresses, while continuity analysis considers restraint at edges causing secondary stresses. For a 9 lakh liter tank, continuity analysis results in higher hoop forces, moments, and steel reinforcement compared to membrane design. A similar trend is seen for a 6 lakh liter tank, with continuity analysis giving higher stresses and reinforcement.

DESIGN OF STEEL COLUMN.pptx

This document provides a summary of steel columns, including:
1. It defines steel columns and their key characteristics such as shape, load bearing capacity, and connections.
2. It classifies columns based on cross-sectional shape, loading type, reinforcement, and slenderness ratio.
3. It discusses effective length, slenderness ratio, column bases, and provides examples of calculating load capacity.

Building project rc column

This document provides information on the design of reinforced concrete columns, including:
- Columns transmit loads vertically to foundations and may resist both compression and bending. Common cross-sections are square, circular and rectangular.
- Columns are classified as braced or unbraced depending on lateral stability, and short or slender based on buckling resistance. Short column design considers axial load capacity while slender column design accounts for second-order effects.
- Reinforcement details include minimum longitudinal bar size and spacing and design of lateral ties. Slender column design determines loadings and calculates moments from stiffness, deflection and biaxial bending effects. Design charts are used to select reinforcement for columns under axial and uniaxial

RCC column_Shortly Axially Loaded column.pptx

The document discusses various types of compression members including columns, pedestals, walls, and struts. It describes design considerations for compression members including strength and buckling resistance. It defines effective length as the vertical distance between points of inflection when the member buckles. Various classifications of columns are discussed based on loadings, slenderness ratio, and reinforcement type. Code requirements for longitudinal and transverse reinforcement as well as detailing are provided. Two examples of column design are included, one with axial load only and one with spiral reinforcement.

Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...

Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Design I & Prof. Abdelhamid Charif)

Composite Design.pdf

This document discusses composite construction, specifically composite steel and concrete beams. It provides definitions and examples of composite construction, explaining that it aims to make each material perform the function it is best suited for. It then describes the differences between non-composite and composite beam behavior. The document goes on to discuss elements of composite construction like decking and shear studs. It also summarizes the design process for composite beams, covering moment capacity, shear capacity, shear connector capacity, and longitudinal shear capacity calculations.

Design of short columns using helical reinforcement

Helical reinforcement, also known as spiral reinforcement, is used in circular concrete columns. It consists of longitudinal bars enclosed within a continuously wound spiral reinforcement. Helical reinforcement is sometimes designed instead of normal links for columns because it provides increased strength and ductility. The spiral reinforcement acts compositely with the concrete core and allows the column to sustain higher loads than those with normal links. It also minimizes the risk of stirrups opening during seismic events. The document then provides details on the design of helical reinforcement for short concrete columns, including governing equations and an example problem.

Axially Loaded Column

The document discusses different types of columns based on bracing, length, and reinforcement. It describes braced and unbraced columns, long and short columns, and tied, spiral, and composite columns. Requirements for minimum reinforcement, lateral ties, and selection of column size are also summarized.

Compression member

The document discusses buckling of columns under axial compression. It describes:
1) Different buckling theories including elastic buckling, inelastic buckling using tangent modulus theory and reduced modulus theory. Shanley's theory accounts for the effect of transverse displacement.
2) Factors affecting buckling strength including end conditions, initial crookedness, and residual stresses. Effective length accounts for end restraint.
3) Local buckling of thin plate elements can reduce the column's strength before its calculated buckling strength is reached. Flange and web buckling must be prevented.

Prsesntation on Commercial building Project

The document describes the trainee's weekly activities during an industrial training at a construction company. Over 8 weeks, the trainee learned about:
1. Layout plans, column reinforcement, beams, and slab details.
2. Reinforcement techniques like lap joints, development lengths, and tie placement.
3. Radiant cooling pipes installed under slabs to provide cooling without AC units.
4. Construction of shear walls, columns, beams and slabs.
5. Block laying for boundary walls using aerated concrete blocks joined with special mortar.

PSC Design and construction.ppt

This document discusses prestressed concrete, including:
- The basic concepts of prestressing including using metal bands, pre-tensioned spokes, and introducing stresses to counteract external loads.
- Design concepts like losses in prestressing structures from elastic shortening, creep, shrinkage, relaxation, friction, and anchorage slip.
- Provisions for prestressing in the Indian Road Congress Bridge Code and Indian Standard Code.
- Construction aspects like casting of girders, post-tensioning work, and load testing of structures.

Lecture note on column design

This document discusses reinforced concrete columns. Columns act as vertical supports that transmit loads to foundations. Columns may fail due to compression failure, buckling, or a combination. Short columns are more prone to compression failure, while slender columns are more likely to buckle. Column sections can be square, circular, or rectangular. The dimensions and bracing affect whether a column is classified as short or slender. Longitudinal reinforcement and links are designed to resist axial loads and moments based on the column's effective height and end conditions. Design charts are used to determine reinforcement for columns with axial and uniaxial bending loads. Examples show how to design column reinforcement.

Conceps of RCC-PCC.pptx

This document discusses concepts related to the design of concrete beams including:
1. It introduces concepts like bending, shear, tension and compression as they relate to beam design.
2. It provides formulas for calculating reactions, shear forces, and bending moments in simply supported beams under different loading conditions.
3. It explains concepts like the neutral axis, stress blocks, and strain diagrams that are important to beam design.
4. It discusses factors that influence the strength of beams like the moment of inertia and reinforcement ratio.
5. It compares working stress and limit state methods of design.

rectangular and section analysis in bending and shear

The document discusses the design of reinforced concrete beams for bending and shear. It covers the analysis of singly and doubly reinforced rectangular beam sections. Key points covered include the concept of neutral axis, under-reinforced and over-reinforced sections, design of bending reinforcement, design of shear reinforcement including link spacing, and deflection criteria. Worked examples are provided to demonstrate the design of bending and shear reinforcement for rectangular beams.

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Beam-column joints in reinforced concrete buildings must resist significant forces during earthquakes to avoid damage. These joints are vulnerable because the materials have limited strength. Closely spaced steel ties around the column bars in the joint region help control cracking and crushing of concrete by holding the joint together under forces. Sufficient column size and anchoring of beam bars into the column also improve the joint's ability to resist forces by providing better grip of the concrete on the steel reinforcement. Damage to beam-column joints during past earthquakes highlights their importance in earthquake-resistant design.

Design for Short Axially Loaded Columns ACI318

This document discusses the design of columns. It begins by defining columns and classifying them as short or long based on their slenderness ratio. Columns can be reinforced with ties or a spiral. Equations are provided for calculating the nominal axial capacity of columns based on the concrete compressive strength and steel reinforcement area. Minimum requirements are specified for reinforcement ratios, number of bars, concrete cover, and lateral tie or spiral spacing. Spirally reinforced columns can develop higher strength due to concrete confinement by the spiral. Design of the spiral pitch is discussed based on providing equivalent confining pressure.

Column

This document discusses different types of columns. It describes long columns as having an effective length to least lateral dimension ratio greater than 12, and short columns as having a ratio less than 12. It provides examples of column classifications based on shape, including square, rectangular, circular, L-section and T-section. Classifications are also given based on reinforcement, such as tied and spiral columns. The advantages and disadvantages of steel columns are outlined.

IRJET- Flexural Strength of Reinforced Concrete Beam with Hollow Core at Vari...

This document discusses a study on the flexural strength of reinforced concrete beams with hollow cores at various depths below the neutral axis. Four beams were cast - one control beam without a hollow core, and three beams with a hollow core created using a 25mm PVC pipe placed at depths of 46.5mm, 79mm, and 112.5mm below the neutral axis. The beams were tested after 28 days and the load carrying capacity, deflection behavior, crack patterns, and flexural strength were analyzed and compared. The results showed that the beam with a hollow core at 79mm depth had the highest load carrying capacity and flexural strength, indicating the optimal depth is below the neutral axis. Introducing a hollow core provided

Intze PPT

Intze PPT

BEAM.pptx

BEAM.pptx

Intze ppt

Intze ppt

DESIGN OF STEEL COLUMN.pptx

DESIGN OF STEEL COLUMN.pptx

Building project rc column

Building project rc column

RCC column_Shortly Axially Loaded column.pptx

RCC column_Shortly Axially Loaded column.pptx

Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...

Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...

Composite Design.pdf

Composite Design.pdf

Design of short columns using helical reinforcement

Design of short columns using helical reinforcement

Axially Loaded Column

Axially Loaded Column

Compression member

Compression member

Prsesntation on Commercial building Project

Prsesntation on Commercial building Project

PSC Design and construction.ppt

PSC Design and construction.ppt

Lecture note on column design

Lecture note on column design

Conceps of RCC-PCC.pptx

Conceps of RCC-PCC.pptx

rectangular and section analysis in bending and shear

rectangular and section analysis in bending and shear

20

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Design for Short Axially Loaded Columns ACI318

Design for Short Axially Loaded Columns ACI318

Column

Column

IRJET- Flexural Strength of Reinforced Concrete Beam with Hollow Core at Vari...

IRJET- Flexural Strength of Reinforced Concrete Beam with Hollow Core at Vari...

Columns lecture#6

The document discusses the analysis of reinforced concrete columns under various loading conditions. It presents 10 cases for analyzing columns, including when axial load is given and eccentricity is less than balanced, when moment is given and steel is yielding, and when depth of neutral axis is given. The key steps shown are setting up the load and moment equations, checking assumptions of steel stress, and iterating to find values of neutral axis depth and steel stresses that satisfy equilibrium. Design procedures are also outlined for short columns under uniaxial bending, with steps to calculate load capacity and check steel strain assumptions.

Columns lecture#5

1) This document discusses two cases for determining the failure mode of reinforced concrete columns: a dividing point between transition and tension failure, and when the nominal load exceeds the nominal bending capacity.
2) For the first case, equations are provided to calculate the unknown steel stress given other known values in order to then determine the nominal load and moment capacities.
3) For the second case, when the nominal load exceeds the nominal bending capacity, the document notes that the steel stress is not equal to the yield stress but the method to determine if the steel reaches its yield stress must be calculated.

Columns lecture#3

1. This document discusses trial sizing, design, and analysis of short columns under concentric axial loads.
2. The criteria for determining if a column is considered short is based on the slenderness ratio being less than a specified value depending on the column cross section shape.
3. A design example is provided for a 4m long square tied column and circular spiral column both carrying an axial load of 2000 kN. The design includes calculating reinforcement, checking reinforcement ratio, and detailing requirements.

Columns lecture#2

The document discusses the design of reinforced concrete columns. It provides formulas to calculate the nominal capacity of concentrically loaded columns based on steel ratio and material strengths. Minimum and maximum steel ratios of 1-8% are recommended, with a reasonable range of 1-3%. Clear cover requirements of 40-75mm are outlined depending on soil contact. Tie design considerations include bar diameter, shape, and longitudinal spacing. Spiral reinforcement provides increased ductility and the document discusses formulas for calculating confined concrete strength based on spiral ratio and properties. Minimum spiral ratios and pitch requirements are also provided.

Types of laods

This document discusses the different types of loads that structures must be designed to withstand. It identifies vertical loads like dead loads from structural elements and permanent fixtures, and live loads from temporary objects and occupancy. Horizontal loads include wind loads and seismic loads from earthquakes. Longitudinal loads also exist for some structures. Specific live loads are defined by building codes depending on a structure's use. Other load types addressed are wind loads, snow loads, hydrostatic pressure, soil pressure, and impact loads. Dead and live loads are explained in more detail.

Flexural design of Beam...PRC-I

Prepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

Flexural design of beam...PRC-I

Prepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

Types of cement

Gray Ordinary Portland Cement is the most commonly used type and is a high-quality, cost-effective building material composed mainly of clinker. White Portland Cement is produced with limestone, low iron kaolin clay, and gypsum for architectural works requiring brightness and artistic finishes. Masonry or mortar cement is mixed with finely ground limestone for uses like concrete blocks and brick work. Oil-well cement is a specially designed variety of hydraulic cement produced with gray Portland clinker for use in oil wells at high temperatures and pressures. Blended cements are produced by mixing Portland cement with materials like slag, fly ash, and lime to reduce CO2 emissions and offer more sustainable products.

T-Beams...PRC_I

Prepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

Mechanism of load transfored...PRC-IPrepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

Types Of Cement...PRC-IPrepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

Doubly reinforced beams...PRC-I

Doubly reinforced beams have both tension and compression reinforcement, allowing for a shallower beam depth than a singly reinforced beam. There are two cases for the behavior of doubly reinforced beams at ultimate loading:
1) Case I occurs when both tension and compression steel yield. The neutral axis depth can be calculated and the moment capacities from compression steel, concrete, and tension steel determined.
2) Case II occurs when only the tension steel yields, and the compression steel does not yield. The strain in the compression steel must be calculated.
The document discusses the behavior of doubly reinforced beams under ultimate loading conditions for both cases when compression steel does and does not yield. It provides equations to calculate forces, strains, and moment

Hydration Of Cement...PRC-IPrepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

Geotech Engg. Ch#05 bearing capacity

This document provides information about bearing capacity of soil and different types of foundations. It discusses key topics like:
- Types of foundations including shallow foundations like spread footings, continuous footings, combined footings, strap footings, and mat/raft foundations. It also discusses deep foundations.
- Factors that determine the selection of a foundation type including the structure's function/loads, sub-surface soil conditions, and cost.
- Comparison of shallow and deep foundations in terms of depth, load distribution, construction, cost, structural design considerations, and settlement.
- Criteria for foundation design including safety against bearing capacity failure and limiting settlement, especially differential settlement.

Geotech. Engg. Ch#04 lateral earth pressure

This document provides an overview of lateral earth pressure and retaining wall design. It defines key terms like coefficient of lateral earth pressure (K), which is the ratio of horizontal to vertical stress. Retaining wall types are described including gravity, cantilever, counterfort and sheet piles. The theories of Rankine and Coulomb for calculating earth pressures are summarized. Equations are provided for determining the active (Ka) and passive (Kp) earth pressure coefficients based on the soil friction angle. Typical K values are listed for different soil types.

Goetech. engg. Ch# 03 settlement analysis signed

This document discusses settlement analysis and different types of settlement. It begins by defining settlement as the vertical downward deformation of soil under a load. There are two main types of settlement based on permanence - permanent and temporary. There are also different types based on mode of occurrence: primary consolidation, secondary consolidation, and immediate settlement. Differential settlement can cause structural damage, while uniform settlement has little consequence. The document outlines methods to estimate settlement, such as consolidation tests, and discusses remedial measures to reduce or accommodate settlement.

Goe tech. engg. Ch# 02 strss distribution

This document discusses stress distribution in soils. It defines stress as the internal forces per unit area within a body resisting external loads. Stress is calculated as force over cross-sectional area. Stresses in soil come from geostatic or self-weight stresses due to overburden pressure, or induced stresses from external loads like foundations or vehicles. Pore water pressure is stress transmitted by water in soil pores, while effective stress is that transmitted between soil grains, accounting for both normal and shear strength. Effective stress is calculated as total stress minus pore water pressure.

Bearing capacity ch#05(geotech)

This document provides information on bearing capacity of soil and foundations. It defines key foundation terms like contact pressure, foundation depth, shallow and deep foundations. It describes different types of shallow foundations like spread footing, continuous footing, combined footing, strap footing, and mat or raft footing. Factors for selecting a foundation type and comparing shallow vs deep foundations are also discussed. Design criteria of safety against bearing capacity failure and limiting settlement are covered.

Columns lecture#6

Columns lecture#6

Columns lecture#5

Columns lecture#5

Columns lecture#3

Columns lecture#3

Columns lecture#2

Columns lecture#2

Types of laods

Types of laods

Flexural design of Beam...PRC-I

Flexural design of Beam...PRC-I

Flexural design of beam...PRC-I

Flexural design of beam...PRC-I

Types of cement

Types of cement

T-Beams...PRC_I

T-Beams...PRC_I

Mechanism of load transfored...PRC-I

Mechanism of load transfored...PRC-I

Types Of Cement...PRC-I

Types Of Cement...PRC-I

Doubly reinforced beams...PRC-I

Doubly reinforced beams...PRC-I

Hydration Of Cement...PRC-I

Hydration Of Cement...PRC-I

Geotech Engg. Ch#05 bearing capacity

Geotech Engg. Ch#05 bearing capacity

Geotech. Engg. Ch#04 lateral earth pressure

Geotech. Engg. Ch#04 lateral earth pressure

Goetech. engg. Ch# 03 settlement analysis signed

Goetech. engg. Ch# 03 settlement analysis signed

Goe tech. engg. Ch# 02 strss distribution

Goe tech. engg. Ch# 02 strss distribution

Bearing capacity ch#05(geotech)

Bearing capacity ch#05(geotech)

Portfolio of Family Coat of Arms, devised by Kasyanenko Rostyslav, ENG

The Ukrainian and German journalist Rostyslav Kasyanenko has dedicated himself to genealogical research and heraldry. Originally Ukrainian, now living in Munich (Bavaria) he working in Ukrainian Free University (Est. 1921) as archivist. Curator of Heraldic Teams, Member of Ukrainian Heraldry Society (UHS) R.Kasyanenko is Deviser of the Family and Municipal Coat of Arms and Author of the exhibition concept project: “Maritime flags and arms of the Black Sea countries vs. Mediterranean: what has changed in 175 years?”
Author of scientific articles (2023-24):
Parallels between the meaning of Symbol and Myth according to Hryhorii Skovoroda and heraldic systems
Heraldry as a marker of evolution of national identity in Ukraine and Slovakia: from the Princely era to the "Spring of Nations" (XI-XIX centuries)
Historical parallels in the formation of national awareness in Ukraine and Slovakia in modern times (1848-1992)
Proto-heraldry of Kievan Rus': dynastic symbols of the Princely era, and how does the Palatine Lion relate to this?
Symbols of the House of Romanovyches: the Bavarian influence in Ukrainian heraldry
Participant of Scientific Conferences (2023-24):
- XXХІІІ Heraldic Conference of the Ukrainian Heraldry Society, October 13, 2023, Lviv
- International Conference “Slovak-Ukrainian Relations in the Field of Language, Literature, and Culture in Slovakia and the Central European Space”, University of Prešov, Institute of Ukrainian Studies, Faculty of Arts, 18-20.10.2023
- International Conference „The Past, Present, and Future of Heraldry: Universality and Interdisciplinarity“, Vilnius, 12-13.06.24
- International Conference "Coats of Arms as Weapons – Heraldic Symbols in Political, Dynastic, Military, and Legal Conflicts of the Middle Ages and Early Modern Period”, Alfried Krupp Wissenschaftskolleg Greifswald.
According to the heraldist, he has worked with many heraldic artists over
the years. However, he developed the ideas for all the coats of arms himself, except for his own. The case of the Kasyanenko (from the Shovkoplias clan) family coat of arms — featuring an audacious Cossack riding a rhinoceros — deserves special attention. "After all, one could talk about one's own crest, just like one's ancestors, for an eternity," he says.

The Stone (Slideshow by: Kal-el Marcus Renne Go)

This simple message illustrates that any object, circumstance or condition present in our pathway of life can be ignored, abused, or utilized.

How Can UI/UX Mastery Increase the Success of Your SaaS Pricing Page?

Integrating UI/UX design into your SaaS pricing page is increasingly popular among users. It transforms visitors into customers by reshaping how subscriptions are presented, enhancing user engagement. Discover the impact of UI/UX mastery on SaaS pricing page success and why it's essential.

Analysis-of-Finance-Bill-2024-13-May-2024_-002.pdf

Exam objectives for comptia a.Exam objectives for comptia a.

Pranay Mhatre Introduction cum Portfolio

Skilled User Experience Designer with 9.5+ years in UX/UI design, blending creative ingenuity with technical expertise. Specialized in user research, wireframing, prototyping, and creating intuitive user interfaces. Holder of a Bachelor of Science in Animation & Visual Effects [Assessed and Matched with Australian Qualifications Framework (AQF)] and a Post Graduate Diploma in IT Project Management (with specialization in Business Analysis). Proven ability to lead teams, manage stakeholders, build BRDs from scratch and deliver user-centric solutions for web and mobile applications.

A Green City is an urban area that prioritizes sustainability

A Green City is an urban area that prioritizes sustainability in its
development, operation, and maintenance.

This is Diva abaya look book portfolio .pdf

Diva abaya look book

Introduction of Stone Display Stand.pptx

We offer a comprehensive range of display equipment, including stone display stands, boxes, and booklets; ceramic tile display racks; countertop display racks; mosaic display stands; and wood floor display stands.

Surface Analysis Civil 3D using different tools

Civil 3D Surface

The Wise Way (Slideshow by: Kal-el Marcus)

Give the world the best you have, and it may never be enough; give the world the best you’ve got anyway.

S S Bhavikatti Civil Engineering Structural Designing

SS Bhavikatti Book

The Ultimate Logo Design Checklist for Entrepreneurs

Unlock the perfect logo for your brand with our logo design checklist. Essential tips and steps to create a standout logo for entrepreneurs. Start now! https://www.illuminz.com/blog/logo-design-checklist

Arch.Bob _ 005 _ Architectural Portfolio

Portfolio

Carleton University degree offer diploma Transcript

学历定制【微信号:95270640】《(CU毕业证书)卡尔顿大学毕业证》【微信号:95270640】《毕业证、成绩单、外壳、雅思、offer、真实留信官方学历认证（永久存档/真实可查）》采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【关于学历材料质量】
我们承诺采用的是学校原版纸张（原版纸质、底色、纹路）我们工厂拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有成品以及工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信号95270640】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信号95270640】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！

Fear and Faith (Slideshow by: Kal-el Go)

“Fear and Faith” contrasts the different effect of each of these, showing the quality of faith as opposed to the emotion of fear.

bedsores20-9-14-150627122143-lva1-app6892.pptx

Hhxincfivcxxjjfhvh

ITR Filing for the year of the 2023-24 .pdf

ITR Filing for the year of the 2023-24 .pdf

2024_summer_my_dream_from_users_gnjp_20240708

2024_summer_my_dream_from_users_gnjp_20240708

2024_summer_my_dream_gnjp_20240705_ks.pdf

2024_summer_my_dream_gnjp_20240705_ks.pdf

Portfolio of Family Coat of Arms, devised by Kasyanenko Rostyslav, ENG

Portfolio of Family Coat of Arms, devised by Kasyanenko Rostyslav, ENG

The Stone (Slideshow by: Kal-el Marcus Renne Go)

The Stone (Slideshow by: Kal-el Marcus Renne Go)

How Can UI/UX Mastery Increase the Success of Your SaaS Pricing Page?

How Can UI/UX Mastery Increase the Success of Your SaaS Pricing Page?

Analysis-of-Finance-Bill-2024-13-May-2024_-002.pdf

Analysis-of-Finance-Bill-2024-13-May-2024_-002.pdf

SMACNA - DUCT CONSTRUCTION STANDARDS-2005.pdf

SMACNA - DUCT CONSTRUCTION STANDARDS-2005.pdf

Pranay Mhatre Introduction cum Portfolio

Pranay Mhatre Introduction cum Portfolio

A Green City is an urban area that prioritizes sustainability

A Green City is an urban area that prioritizes sustainability

This is Diva abaya look book portfolio .pdf

This is Diva abaya look book portfolio .pdf

Introduction of Stone Display Stand.pptx

Introduction of Stone Display Stand.pptx

Surface Analysis Civil 3D using different tools

Surface Analysis Civil 3D using different tools

The Wise Way (Slideshow by: Kal-el Marcus)

The Wise Way (Slideshow by: Kal-el Marcus)

S S Bhavikatti Civil Engineering Structural Designing

S S Bhavikatti Civil Engineering Structural Designing

The Ultimate Logo Design Checklist for Entrepreneurs

The Ultimate Logo Design Checklist for Entrepreneurs

Arch.Bob _ 005 _ Architectural Portfolio

Arch.Bob _ 005 _ Architectural Portfolio

Carleton University degree offer diploma Transcript

Carleton University degree offer diploma Transcript

Fear and Faith (Slideshow by: Kal-el Go)

Fear and Faith (Slideshow by: Kal-el Go)

bedsores20-9-14-150627122143-lva1-app6892.pptx

bedsores20-9-14-150627122143-lva1-app6892.pptx

- 1. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns LECTURE # 1 1. COLUMN: It is a vertical member which is primarily subjected to axial compression in which major deformation is shortening. 2. TYPES OF COLUMNS: i. Classification on the Basis of Shape: • Square section. • Rectangular section. • Circular section. • L-section. • T-section. Fig.1 Classification on the Basis of Shape 1
- 2. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns ii. Classification on the Basis of Reinforcement: • Tied Columns: These columns have the bars braced or tied at close intervals by close loops called ties. • Spiral Columns: These columns have the bars and the core concrete wrapped with a closely spaced helix. • Composite Columns: These columns consists of a structural steel or cast iron column encased in concrete reinforced with both longitudinal and transverse reinforcements. • Pipe Columns or Concrete Filled Steel Tubes: These columns are circular, rectangular or square hollow sections filled with concrete without any additional reinforcement. Fig.2(a) Classification on the Basis of Reinforcement 2
- 3. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns Fig.2(b) Classification on the Basis of Reinforcement iii. Classification on the Basis of Type of Loading: • Concentrically Loaded Columns: When the resultant of the load coincides with the centroid of the cross-section, the column is said to be concentrically loaded column. Fig. 3 shows a concentrically loaded column. • Eccentrically Loaded Columns: When the resultant of the load does Fig.3 Concentrically Loaded not coincide with the centroid of the Column cross-section, the column is said to be eccentrically loaded column. There are two types of eccentrically loaded columns; 1. Uni-axially eccentrically loaded columns. (Fig. 4(a)) 2. Bi-axially eccentrically loaded columns. (Fig. 4(b)) 3
- 4. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns Fig.4 Eccentrically Loaded Columns • Sources of Eccentricity in Columns: Eccentricity is due to following three reasons; 1. Eccentric loading. (Fig. 5(a)) 2. Initial crookedness. (Fig. 5(b)) 3. Out-of-plumbness. (Fig. 5(c)) Fig.5 Sources of Eccentricity in Columns 4
- 5. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns 3. CLASSIFICATION OF COLUMNS ACCORDING TO ACI CODE: • Short Column: In short columns there are no 2nd order effects and the failure is due to crushing of concrete without any instability. Moment magnification chances are very less in such columns because radius of gyration is more and length is small. 2 1 1234 M M r lK u −≤ Where, K = Effective length factor taken from alignment charts. M1 = Magnitude of smaller end moment with sign. M2 = Magnitude of larger end moment with sign. 2 1 M M = 0, for concentrically loaded columns. 2 1 M M = +ve, when member is bent in single curvature. 2 1 M M = −ve, when member is bent in reverse curvature. • Slender Columns: These columns fail due to buckling, instability or 2nd order effect. The failure load is less than that of a short column. As length of column increases, the probability of failure due to buckling increases. 4. TYPES OF REINFORCEMENT IN COLUMNS: • Longitudinal Steel: It is that steel which is present along the length of the column. Following are the various purposes of longitudinal reinforcement; 1. The main function of longitudinal reinforcement is to prevent creep and shrinkage in concrete. 5
- 6. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns 2. It provides resistance against lateral bending, cracking and reduction of moment of inertia value. 3. It reduces the size of the column. • Transverse Steel: 1. It provides confinement to the inner concrete or core concrete i.e. the concrete which is present inside the longitudinal reinforcement. Confinement provides ductility and it also increases the strength of the concrete. 2. Transverse steel reduces the chances of buckling of longitudinal steel. 3. It holds the longitudinal steel in position during casting 4. Transverse steel provides resistance against shear. 5. TYPES OF TRANSVERSE REINFORCEMENT: • Ties or Transverse Ties: Lateral ties are used in the columns because of lesser construction cost and ease of placement. • Spiral Reinforcement: Spiral columns are used where we need more ductility i.e., in earthquake zones. Spirals are mostly provided in circular columns. Spiral columns sustain maximum load at excessive deformation and thus prevent the complete collapse of the structure before the total redistribution of moments and stresses is complete. The disadvantage of spiral reinforcement is that it is very difficult to place in the field, so, due to this reason its use is practically limited. 6. CAPACITY OF CONCENTRICALLY LOADED SHORT COLUMNS: Steel always yields first because it is lesser in amount and due to pure compression it is yielded. εcu = 0.003 (Strain at which concrete crushes) εy = 0.0015 or 0.0021 (Strain at which steel yields) 6
- 7. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns After yielding of steel, load is taken by concrete alone and the resistance is provided by the concrete only. A stage comes when concrete crushes while steel is already yielded (final stage). If the bond between concrete and steel is perfect then they equally shorten. εc = c c E f and εs = s s E f εc = εs c c E f = s s E f Modular Ratio, c s E E n = fs = n fc Now, Ag = Ast + Ac Pn = Pc + Ps Pn = Ac fc + Ast fs Pn = fc ( Ag − Ast ) + Ast (n fc ) Pn = fc [Ag + ( n −1 )Ast ] (within elastic range, service loads) 7. PROBLEM: A R.C. concentrically loaded short column has a cross-sectional area 450 x 450 mm2 and is reinforced by Grade 420, 8 # 19 bars. If at any stage, concrete stress fc = 10 MPa ( fc’ = 20 MPa), what will be corresponding load carrying capacity of the column. Solution: fc << fc’ Therefore, material is within elastic range. Ec = 4700 'cf = 4700 20 = 21019 MPa n = 21019 200000 = c s E E ≈ 10 Now using, 7
- 8. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns Pn = fc [Ag + ( n −1 )Ast ] Ast = 8 # 19 = 8 x ( ) 4 19 2 π Pn = 10 [ (450 x 450) + ( 10 −1 )2268] Ast = 2268 mm2 Pn = 2229.12 kN 8. RESISTANCE FACTOR AT ULTIMATE STAGE: When we go to the ultimate stage then the first thing which we have to decide is the value of ‘φ’ and to do that we must know whether the section of column is tension controlled or compression controlled. Section of concentrically loaded column is always compression controlled. For tied columns, φ = 0.65 For spiral columns, φ = 0.70 As there is always some eccentricity in a column, some additional safety factor is applied to φ factor, Additional F.O.S. for tied columns = 0.80 Additional F.O.S. for spiral columns = 0.85 Therefore, total resistance factor for tied and spiral columns are; For tied columns = 0.80 x 0.65 For spiral columns = 0.85 x 0.70 8