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Chained lintels in a building – What are the implications?

A lintel is a horizontal structural member which spans across the supports of an opening such as a door or window in a building. Depending on the span of the opening, a lintel may be structurally significant or insignificant – considering whether it requires serious structural consideration or not. Lintels can be made of materials such as timber, concrete, or steel. Concrete lintels are usually provided with nominal reinforcement, due to the inherent low tensile strength of concrete. When a lintel is continuous in a building and connects all the structural members together, it is called a chained lintel.

In Nigeria, it is common to see residential buildings chained at the lintel level. What is meant by chaining is that all the structural members are joined monolithically at the lintel level with reinforced concrete. Chained lintels can also be called continuous lintels. This process is usually done when the blockwork is built alongside the columns of the building. It is rarely done in a purely framed building where the columns, beams, and slab are done before the blockwork panels are built.

Nicely done lintel in a building
Nicely done lintel in a building
Building with chained lintel
Building under construction with chained lintel

Eye brows can be raised over this ‘wasteful approach’ of using excessive concrete and reinforcement on elements that are not ‘structurally significant’. This can lead to questions such as;

(1) Is it possible that the amount of money spent on constructing blockwork simultaneously with the frame and adopting a chained lintel offsets the cost of constructing a purely framed building?
(2) Can chained lintels be entirely avoided irrespective of the approach used?
(3) Are there special advantages of doing chained lintel in a building?

This issue is pertinent because the structural frame of a building is usually designed to stand alone without considering the effect of such lintels. Also, such arrangement is not usually captured in the structural drawings of a building, but it is done on site for low scale residential buildings. Why the extra cost? The lintels are usually 230 x 230 mm in dimension.

Advantages of chained lintels

The perceived advantages of chained lintels are as follows;

(1) It can improves the rigidity of the building. This is a no-brainer since more redundants are being added to the frame of the building. As a result, the building can behave more as a unit due to the increased linking members.
(2) It improves the robustness of the building.
(3) It can improve the lateral stability of the building, even though it is rarely critical in simple residential buildings such as duplexes in a region of no seismic event.
(4) It can cover up the inherent dimensional inaccuracies associated with building the blockworks and the columns at the same time, even though strict quality control can improve that.
(5) Introducing chained lintels reduces the buckling length of columns.

Disadvantages of chained lintels
(1) All the advantages highlighted above are usually catered for when designing the building as a pure frame. What is then the need of the extra advantages in terms of cost?
(2) The reinforcements provided in the building are the same as when no consideration for chained lintels is made.
(3) The construction speed is reduced.

A Structural Perspective

To look at this issue from a structural perspective, let us investigate the effect of chained lintels on the structural response of a simple two storey building under the effect of normal actions. In order to achieve this, let us model a simple two storey residential building and investigate its structural behaviour with and without chained lintels. The building data is shown below;

General arrangement of the building
General layout of the building

Building Data
Dimension of all columns = 230 x 230 mm
Dimension of floor beams = 450 x 230 mm
Dimension of roof beams = 300 x 230 mm
Thickness of floor slab = 150 mm
Dimension of lintels (model 2) = 230 x 230 mm
ULS action on floor slabs = 12 kN/m2
ULS action on floor beams (blockwork + rendering + selfweight) = 15 kN/m
ULS action on roof beams = 5 kN/m
ULS action on lintels = 3.5 kN/m

(N/B): All loads were assumed.

MODEL 1
Model 1 of the building (No lintel)
BENDING MOMENT ON EXTERNAL BEAM
Bending moment on external floor beam of model 1
BENDING MOMENT ON INTERNAL BEAM
Bending moment on internal floor beam of model 1

From the figures above, the maximum hogging moment on the internal and external beams are 45.5 kNm and 68.4 kNm respectively, while the sagging moments are 28 kNm and 41.3 kNm respectively.

corner column
Internal forces on corner column of building model 1
external intermediate column 1
Internal forces on middle external columns of building model 1

The results below show the building model with lintels and the internal forces acting on the building.

model 2
Model 2 of the building (with lintels)
BM EXTERNAL MODEL 2
Bending moment on external floor beam of model 2
bm internal model 2
Bending moment on internal floor beam of model 2
corner column model 2
Internal forces on corner column of building Model 2
external intermediate column model 2
Internal forces on middle external columns of building model 1

Comparison of results

Under the effect of gravity actions, the following results were observed in the structural members;

(1) Beams
In the building with chained lintel, the bending moment on the intermediate support of the external beam reduced by about 6.8%. However, the end support moment increased by about 43.8% (from 7.47 kNm to 13.3 kNm). A reduction in span moment was also observed for floor beams in buildings with chained lintel. This same behaviour was observed in the internals beams.

(2) Columns
The bending moment in the corner columns increased from 5.69 kNm to 12.338 kNm when chained lintels were introduced. This is due to the fact that lintels are subjected to the load from the blockwork courses that get to the sofit of the beams. Axial load in the columns also increased from 101 kN to 143 kN. This same increase in internal forces was observed for the intermediate columns.

Therefore, introducing chained lintels appears to worsen action effects on the columns, but favours the floor beams, except for end support moments.

Limitation of the study: The loadings on the lintels appeared to be exaggerated, and some considerations were not made to reduce the wall load on the floor beams since the chained lintel will carry some of the loads. The author therefore welcomes discussions and further investigations in the study.

Thank you for reading.

Download Top Civil Engineering Books for Free on Springer – COVID-19

Springer is a leading global scientific, technical and medical portfolio, providing researchers in academia, scientific institutions and corporate R&D departments with quality content through innovative information, products and services. With more than 2,900 journals and 300,000 books, Springer offers many opportunities for authors, customers and partners. Here is a list of top civil engineering related textbooks that you can download for free on Springer during this COVID-19 period.

(1) Fatigue of Structures and Materials (2nd Edition, 2009)
Author: J. Schijve

Fatigue of Structures and Materials

To download this textbook, click HERE

(2) Composite Materials (3rd Edition, 2012)
Author: Krishan K. Chawla

Composite materials

To download the text book, click HERE

(3) Introduction to Partial Differential Equations (1st Edition, 2016)
Author: David Borthwick

Introduction to partial differential equations

To download, click HERE

(4) Structural Analysis (2009)
Authors: O. A. Bauchau, J.I. Craig

structural analysis

Click HERE to download

(5) Irrigation and Drainage Engineering (1st Edition, 2016)
Authors: Peter Waller, Muluneh Yitayew

irrigation and drainage engineering

Click HERE to download

(6) Design and Analysis of Experiments (2nd Edition, 2017)
Authors: Angela Dean, Daniel Voss, Danel Draguljić

Design and Analysis of

To download the textbook, click HERE

(7) Engineering Mechanics 1 (2nd Edition, 2013)
Authors: Schröder, Wolfgang A. Wall, Nimal Rajapakse

Engineering Mechanics 1

To download the textbook, click HERE

(8) Fluid Dynamics (2015)
Author: Michel Rieutord

fluid dynamics

To download this textbook, click HERE

(9) Multivariate Calculus and Geometry (3rd Edition, 2014)
Author: Seán Dineen

Multivariate Calculus and Geometry

Click HERE to download

(10) Fundamentals of Structural Engineering (2nd Edition, 2016)
Authors: Jerome J. Connor, Susan Faraji

Fundamentals of Structural Engineering

Click HERE to download

(11) The Finite Element Method and Applications in Engineering Using ANSYS (2nd Edition, 2015)
Authors: Erdogan Madenci, Ibrahim Guven

fea ansys

Click HERE to download

(12) An Introduction to Soil Mechanics (1st Edition, 2020)
Author: Arnold Verruijt

An Introduction to Soil Mechanics

Click HERE to download

(13) The Finite Volume Method in Computational Fluid Dynamics (1st Edition, 2016)
Authors: F. Moukalled, L. Mangani, M. Darwish

The Finite Volume Method in Computational Fluid Dynamics

Click HERE to download

(14) Statics and Mechanics of Structures (2013)
Authors: Steen Krenk, Jan Høgsberg

Statics and Mechanics of Structures

Click HERE to download

(15) Engineering Mechanics 2 (2nd Edition, 2018)
Authors: Schröder, Wolfgang A. Wall, Javier Bonet

Engineering Mechanics 2

Click HERE to download

(16) Structural Dynamics (6th Edition, 2019)
Authors: Mario Paz, Young Hoon Kim

Structural dynmcis

Click HERE to download

(17) Excel Data Analysis (2nd Edition, 2019)
Author: Hector Guerrero

Excel Data Analysis

Click HERE to download

(18) Statistical Mechanics for Engineers (1st Edition, 2015)
Author: Isamu Kusaka

Statistical Mechanics for Engineers

Click HERE to download

(19) An Introduction to Machine Learning (2nd Edition, 2017)
Author: Miroslav Kubat

An introduction to machine learning

Click HERE to download

(20) Elementary Mechanics Using Matlab (2015)
Author: Anders Malthe-Sørenssen

Elementary Mechanics Using Matlab

Click HERE to download

(21) Introduction to Artificial Intelligence (2nd Edition, 2017)
Author: Wolfgang Ertel

Introduction to Artificial Intelligence

Click HERE to download

(22) Computational Geometry (3rd Edition, 2008)
Authors: Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars

Computational Geometry

Click HERE to download

(23) Leadership Today (1st Edition, 2017)
Authors: Joan Marques, Satinder Dhiman

Leadership Today

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(24) Handbook of Marriage and the family (3rd Edition, 2013)
Authors: Gary W. PetersonKevin R. Bush

Handboo of marriage

Click HERE to download

(25) Neural Networks and Deep Learning (1st Edition, 2018)
Authors: Charu C. Aggarwal

Neural Networks and Deep Learning

Click HERE to download

IStructE to hold Webinar on Structural Uses of Stone

The Institution of Structural Engineers (IStructE) will be organising a webinar on the structural uses of stone. Stones are naturally occurring rocks of igneous, sedimentary or metamorphic origin, and has been used for thousands of years in construction.

Most rocks are sufficiently consolidated to enable them to be cut or made into various shapes and blocks to be used as walling, paving or roofing materials. Stones are categorised into building stones, ornamental stones and dimension stones.

As admitted in IStructE’s website,

“Dimension stone has been a structural material for thousands of years, yet its use has steadily declined. The perception is that it is too expensive to quarry, cut and transport. Many now see this as suitable only for cladding or flooring. Yet, with a modern approach to structural usage, stone can realise its potential as a material fit for the 21st century”

Therefore, the webinar seeks to explore the contemporary use of stone in a variety of structural applications. It will showcase the versatility of this often-overlooked material.

Date: 29th April, 2020
Time: 12:30 (BST)
Price: £45.5 + VAT (members)
£70 + VAT (Standard)

Key Learning Objectives of Webinar

  • Gain a basic understanding of the primary considerations when designing in stone
  • Knowledge of the design parameters required for un-reinforced and reinforced stone structures
  • Introduction to the basic principles of post-tensioned stone
  • Improved awareness of structural stone applications through a series of case studies
  • The live webinar includes an interactive Q&A session with the expert speakers. Booking will close 24 hours prior to the webinar.

To Register for this Webinar, click HERE to be directed to IStructE’s page.

Disclaimer:
Structville.com is not an agent and is in no way affiliated to the organisation of the above named event. We have presented this as news so that the civil engineering family in the world can be aware of reputable online events that can be of benefit to their careers. This is the commitment of Structville.

What is the cause of the failure of this staircase?

Considering structural design and detailing standards, what do you think is the cause of the failure of this staircase?

Read also…
Comparative analysis of staircase using Staad Pro and manual calculation
Design of sawtooth (slabless staircase)
Structural analysis of free standing staircase
Design of reinforced concrete staircase

fw

Write your answer in the comment section. Thank you very much.

BIM can Assist Construction Robots in Object Recognition

The construction industry remains one of the least automated industries which depend on manual human labour for maximum productivity. The role of robots in construction operations is still very insignificant when compared other industries. However, robotic automation stands as a promising field for construction, as it offers a safer and efficient approach for handling building resources on site which extends the limits for more creative and customizable architecture.

Due to the complex and highly dynamic nature of the construction industry, robots cannot blindly execute predefined instructions as obtainable in other more deterministic industries. This makes it difficult for robots to adapt to the ever changing construction sites. It has therefore been found important that robots be equipped with advanced vision capabilities to enable them observe, cope, and adapt to busy construction sites.

construction robots
3d rendering robotic arms with building

Researchers from Barlett School of Architecture, UCL, London UK, investigated a flexible 3D object recognition approach to easily reference building components to a vision system and be able to deal with objects’ imprecision. This is due to the fact that dealing with unique, irregular structures require robust object estimation approaches to enable on-site autonomous robotic assembly applications. To achieve this, they used a virtual scanning process which takes the “ideal” representation model of all the objects found in the Building Information Modelling (BIM) model as the guide for finding all “best match objects” on site, without the need for physically scanning or labelling the objects to reference them. The study was published in Springer – Construction Robotics.

According to the authors,

Our overarching hypothesis is that using the available BIM data as the reference model will have the potential not only to locate highly matched known objects with a threshold to accommodate material deviations, but also flexibility to find the best match objects from an unknown pile… Our goal was to detect and manipulate the best-matched known objects in an unsorted pile on site according to a given design in the form of the BIM model. Therefore, we developed a holistic approach that includes our detection method, and an automated process to grasp, manipulate, and determine the assembly sequence based on the design scheme of the structure and awareness of the surrounding context.

In their methodology, 3D object recognition was adopted using global feature based approach due to its flexibility to work with noisy data. 3D CAD representation of the objects coming from the BIM model was used for training instead of using physical scan models of the objects. After the recognition stage, object to robot calibration was done.

Recognition framework
Recognition System Framework, which comprises two different phases: an online recognition phase and an offline virtual training stage [1]

The recognition system proposed in the study showed that the method of using the virtual representation coming from the BIM model instead of having to scan the actual model brings advantages regarding flexible setup and affordable recognition. The experiments also showed that the system able to detect and construct several structures with inherited imperfections within acceptable tolerances. However, it also showed several limitations related to the object’s geometrical characteristic and its implication on the successful detection of the whole process success.

Reference for the full research paper:
[1] Mohamed Dawod and Sean Hanna (2019): BIM‑assisted object recognition for the on‑site autonomous robotic assembly of discrete structures. Construction Robotics (2019) 3:69–81 https://doi.org/10.1007/s41693-019-00021-9

Disclaimer:
The findings of this research work has been shown on www.structville.com because it is an open access article which is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Non-linear Analysis of Cable Stayed Structures on Staad Pro

Non-linear analysis can be used when all of the members, elements and support springs are linear except for cables and/or preloaded truss members. This analysis is based on applying the load in steps with equilibrium iterations to converge at each step. In Staad Pro software, the iteration continues at each step until the change in deformations is small before proceeding to the next step. If not converged, then the solution is stopped. The user can then select more steps or modify the structure and rerun.

This method assumes small displacement theory for all members/trusses/elements other than cables and preloaded trusses. The cables and preloaded trusses can have large displacement and moderate/large strain. Pretension is the force necessary to stretch the cable/truss from its unstressed length to enable it to fit between the two end joints. Alternatively, you may enter the unstressed length for cables.

The analysis sequence is as follows:

(1) Compute the unstressed length of the nonlinear members based on joint coordinates, pretension, and temperature.

(2) Member/Element/Cable stiffness is formed. Cable stiffness is from EA/L and the sag formula plus a geometric stiffness based on current tension.

(3) Assemble and solve the global matrix with the percentage of the total applied load used for this load step.

(4) Perform equilibrium iterations to adjust the change in directions of the forces in the nonlinear cables, so that the structure is in static equilibrium in the deformed position. If force changes are too large or convergence criteria not met within 15 iterations then stop the analysis.

(5) Go to step 2 and repeat with a greater percentage of the applied load. The nonlinear members will have an updated orientation with new tension and sag effects.

(6) After 100% of the applied load has converged then proceed to compute member forces, reactions, and static check.

Note that the static check is not exactly in balance due to the displacements of the applied static equivalent joint loads.

Non-linear Cable Analysis Parameters

If you open the cable analysis command on Staad Pro, you will see cable analysis parameters which can be confusing at first sight. Staad Pro advanced training manual offers some insight on the definition of the parameters and the values to use.

NONLINERA CABLE ANALYSIS

Steps: The number of steps if entered should be in the range 5 to 145.

Eq-iterations: This is the maximum number of iterations permitted in each load step. The default value is 15 and should be in the range of 10 to 30.

Eq-tolerance: This is he convergence tolerance for the above iterations. Default value is 0.0005.

Sag minimum: Cables may sag when tension is low. This is accounted for by reducing the E value. Sag minimum may be between 1.0 (no sag E reduction) and 0.0 (full sag E reduction). Default is 1.0. If sag minimum is entered, it should be in the range 0.7 to 1.0 for a relatively simple process. As soon as SAGMIN becomes less than 0.95 the possibility exists that a converged solution will not be achieved without increasing the steps or the pretension loads. The Eq iterations may need to be 30 or more. The Eq tolerance may need to be greater or smaller.

Stability stiffness: A stiffness matrix value that is added to the global matrix at each translational direction for joints connected to cables and nonlinear trusses for the first Load Steps. The amount added linearly decreases with each of the Load Steps (Load Step is 1.0 if omitted). If stability stiffness is entered, use 0.0 to 2.0 but the default value is 0. For Load Steps use a maximum value of 145.

K small stiffness: This is a stiffness matrix value, that is added to the global matrix at each translational direction for joints connected to cables and nonlinear trusses for every load step. If entered, use values between 0.0 to 1.0 but the default value is 0.0. This parameter alters the stiffness of the structure.

Analysis Example
Let us analyse the cable stayed canopy loaded as shown below. The structure comprises of UB 254 x 102 x 22 stanchions supporting cantilevered trusses of UA 50 x 50 x 5 sections. Purlins on the trusses are made of channel sections CH 100 x 150 x 10. Cables are made of 30 mm diameter steel wires and UB 127 x 76 x 13 are used to brace the stanchions in the lateral directions. The loading applied on the structure is the self weight and UDL of 1.5 kN/m on the purlins.

cable structure model 1

In the analysis, an initial tension of 0.1 kN was applied in the cable members using the default parameters (leaving the cable analysis parameters blank). However, the load case refused to converge after iterations. The parameters that gave acceptable convergence are shown below.

parameters

Analysis Results

The displacement of the cable stayed canopy is shown below;

displacements 1

The maximum displacement in the truss was observed to be 17.155 mm.

BM 1

The bending moment in the intermediate column was observed to be 27.2 kNm. The shear force in the same column was observed to be 9.08 kN with an axial force of 45.5 kN.

The axial forces in the cables and trusses of the intermediate members are shown below;

AXIAL FORCE 1

The axial forces in the cables and trusses of the end members are shown below;

AXIAL FORCE 2

Thank you for visiting Structville today. God bless you.

3D Building Services Systems Integration in Design of Buildings

Building service systems (BSS) are important components that makes a building functional and habitable. BSS includes piping network of fresh water and wastewater, electrical installation network, air conditioning systems, fire prevention and protection systems, and communication systems. These are usually sumarised as MEP which stands for Mechanical, Electrical and Plumbing services design.

In the design process, BSS are improtant components which have great impacts on architectural and structural designs. It is generally accepted that integrating the service systems and their components into the architectural and structural designs, and coordinating between these systems help avoid major obstacles during the construction process. In some buildings in Nigeria, it is common to see incoherent arrangement of plumbing systems, chiselling/breaking down of structural members to accommodate mechanical systems and other construction setbacks due to uncoordinated MEP design at an early stage.

unsightly arrangement of MEP services
Unsightly and inefficient arrangement of plumbing system in a building

Usually, after completing the designs, the MEP coordination process begins by holding meetings between the representatives of the general contractor and specialty trades. The MEP systems coordination influences the productivity of all designers of multidisciplinary backgrounds involved in the design process. Any errors or mistakes during designing or constructing the project in the MEP systems would lead to time consuming tasks, budget waste, labour time increment, and project time extension.

clash of HVAC SERVICES IN A BUILDING
Service system, HVAC clashes with both fire system pipes and the suspended ceiling (Wael and Weldy, 2020)

In a research carried out by authors from Applied Science University, and University of Bahrain and published in Journal of Information Technology in Construction, the need to integrated BSS early into preliminary designs (architectural and structural) were reviewed and studied. According to the authors,

The integration BSS inside the building in the early phases of design will save cost and prevent time-consuming modifications. Due to the late integration of the building service systems BSS in the design, negative impact on both the exterior and the interior, may occur. Within the building industry, there has been increasing interest to the building service systems BSS integration, in order to enhance design outcomes, and to detect or even avoid the service systems’ clashes and conflicts.

Problems of 2D drawings

The coordination processes of overlaying two-dimensional drawings of different service systems, each of which is designed by different specialised designers has been identified by the authors as a major cause of clashes and conflicts. The accuracy of this process depends on the experiences of architects and structural engineers in order to avoid the possible conflicts and to include the systems’ components and spatial requirements into the design and its spaces.

Actually, errors may not be fully detected by these traditional processes till the construction stages. Identifying conflicts in the 2D-drawings of service systems is a challenging process, since it depends on designers’ experience. These possible errors or conflicts can negatively affect the projects in many aspects, particularly in the case of being undetected after the construction completion. This can consequentially impact the project’s spaces to accommodate the systems’ components and requirements.

3D to the rescue

Although 2D drawings are still extensively used in every aspect of a building project, there is a strong movement led by the architects to transform to 3D models.

Using 3D digital modelling in the processes of design and coordination not only improves the designers’ raw imagination by representing a 3D model including the components of the service systems, but also eliminates the errors generated from the lack of designers’ experiences by visually presenting all systems’ components. Employing digital modelling eases the processes of coordination and design, and makes them more accurate. Authorities, stakeholders and decision makers will gain many advantages, such as: creating a detailed model of both the design and the service systems which makes their decisions more reliable and accurate.

Building Information Modelling (BIM) is an approach and a process in which the design model potentially includes various building information of different components and spaces, in order for the users to visualise, manage, analyse and/or design in a better way. BIM approach offers an effective assistance represented in making a multidisciplinary model that has BSS in one detailed model, which helps discover and solve any obstacles of overlaps or/and conflicts. Unlike other digital tools that help the imagination capabilities of architects or architecture students, BIM proceeds beyond to unveil and expose possible problems that may appear in the later processes of designing and construction.

Conclusion

Citing previous research works, the authors concluded clash detection has been favoured over the clash avoidance due to cultural practices and lack of technologies to support clash avoidance. From empirical evidence of past research works, MEP-related clashes has been strongly linked to the cultural practices of isolated working among designers, and lack of specialised professional training among designers.

The paper based on the qualitative analysis of both the real projects of construction industry and the student projects of academia, concludes that integrating the MEP systems into the conceptual design phases eliminates the clashes and conflicts that may occur in later stages, and concurrently the possibility of not detecting these conflicts till the construction process.

Reference
Wael Abdelhameed, Weldy Saputra (2020): Integration of building service systems in architectural design. Journal of Information Technology in Construction (ITcon), Vol. 25, pg. 109-122, DOI: 10.36680/j.itcon.2020.007

Disclaimer
The findings of this research has been published on www.structville.com because it is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Restraint and Restraint Factors of Concrete

If movement (expansion and/or contraction) is restricted within a young concrete element, tensile stresses will develop which will lead to cracking. This restriction to movement is normally referred to as restraint. Restraints may be internal or external to the element. Internal restraint occurs due to differential temperature changes within a mass concrete element and can cause surface and/or internal cracking.  However, it is only significant in very thick sections (1000 mm or more). Internal restraints are not considered in this article.

External restraints are due to the support/casting condition of the concrete. However, external restraints take two basic forms;

(1) End restraints
(2) Edge restraints

End restraint

End restraints occurs when the edges of a young concrete are prevented from movement (see Figure below). This typically occurs in suspended slab cast between rigid cores, walls or columns, in infill bays, ground slab cast on piles, large area ground slabs restrained locally, e.g. by piles, columns or column foundations or by a build up of friction, walls cast against secant, contiguous concrete or steel sheet piled walls etc (CIRIA C660).

End restraint in concrete
Schematic model of end restraint in concrete

Edge restraint

This typically occurs where the young concrete section (say a wall) is cast on a hardened concrete base (see Figure below). This means that restriction is only in one direction, and there is interaction between the old and new concrete in terms of distribution of cracks. Edge restraint is different from end restraint because the crack width is a function of restrained strain rather than the tensile capacity of the concrete.

Edge restraint in concrete
Schematic model of edge restraint in concrete

In some cases also, there can be combination of end restraint and edge restraint.

Restraint Factors

The level of restraint in a young concrete imposed by adjoining element is commonly described using restraint factors. The degree of restraint, R, is generally defined as the ratio between the actual stress in a contracting body and the stress imposed under full restraint.

Degree of restraint R = Actual imposed stress / Imposed stress at full restraint

It is recognised that is difficult to determine the degree of restraint correctly, but it is important to obtain restraint factors that are as accurate as possible.  According to CIRIA C660, the restraint factors given by BS 8110-2 and HA BD 28/87 reflects true restraint values, while the restraint factors from BS 8007 and EN 1992-3 has a modification factor of 0.5 to account for creep under sustained loading.

ACI (1990) (cited by CIRIA C660) developed method for estimating edge restraint based on the relative geometry and stiffness of the old and new concrete. The equation is given by;

Restraint at the joint Rj = 1/(1 + AnEn/AoEo)

Where;

An is Cross-sectional area of the new (restrained) pour
Ao is the cross-sectional area of the old concrete
En is the modulus of elasticity of the new pour concrete
Eo is the modulus of elasticity of the old concrete              

However, CIRIA C660 identified that the relative areas of influence of Ao and An may be difficult to define. Therefore the following simple rules were recommended;

  1. For a wall cast at the edge of a slab (An/Ao) = (hn/ho) (thickness of new concrete/thickness of old concrete)
  2. For wall cast remote from the edge of the slab (An/Ao) = (hn/2ho)
  3. En/Eo ranges from 0.7 to 0.8 (but 0.8 is recommended)

Based on CIRIA C660, the values in Table 1 can be used for edge restraint based on An/Ao or An/2Ao ratio.

Table 1: Values of Edge Restraint Factors (According to CIRIA C660)

Edge restraint factors for concrete

The values of restraint factors for different conditions as given by different codes is summarised in the Table 2.

Table 2: Values of Restraint Factors (BS 8110-2 and EN 1992-3)

Values of restraint factors

Thank you very much for reading.

Get this publication below for a cheap price by clicking on the image. It goes a long way in supporting what we do here at Structville. To read about the publication, click HERE. Thank you for your kind consideration.

TANK SUPPORT TEXTBOOK 1

Cracking in Concrete

Eurocode recognises that cracking is normal in concrete subjected to bending, shear, torsion, and restraint from movement (clause 7.3.1 EN 1992 1-1). Cracking is assumed to occur when the restrained strain exceeds the tensile strain capacity of the concrete. This means that for cracking to occur, some part or the whole of the concrete section must be in tension. Crack width is predicted by multiplying crack inducing strain, (the strain dissipated by the occurrence of cracking) εcr, by crack spacing, sr,max.

Cracking occurs due to the low tensile strength of concrete, and we normally use reinforcements to assist is controlling cracking. What happens in this case is that the tensile stress in the concrete must be transferred to the steel if cracking must be controlled.

To achieve this, a minimum amount of reinforcement must be provided in order to have small cracks occurring at intervals instead of having one single large crack. However, provision of this minimum reinforcement is not sufficient for controlling crack widths. As a matter of fact, direct crack width calculation must be carried out if the water tightness of the tank must be guaranteed.

Crack widths are normally calculated for;

(1) Restraint to movement (also called imposed deformations)
(2) Loadings

Cracking due to restraints are due to early thermal effects, autogenous shrinkage, and drying shrinkage. Cracking due to loading is usually from flexure or axial tension in the concrete.

Get this publication below for a cheap price by clicking on the image. It goes a long way in supporting what we do here at Structville. To read about the publication, click HERE. Thank you for your kind consideration.

TANK SUPPORT TEXTBOOK 1

Crack Width and Crack Spacing Calculation in Concrete

Cracking occurs in concrete when the restrained strain exceeds the tensile strain capacity of the concrete. In critical elements like water retaining structures, crack control is verified by carrying out direct calculation of the crack width. Crack width is calculated by multiplying the crack inducing strain and the crack spacing (i.e. the movement over a length equal to the crack spacing). This also involves limiting the bar size and/or spacing to recommended limits.

According to expression 7.8 of EN 1992-1-1, crack width wk in a concrete element is given by;

wk = sr,max εcr

where;
sr,max = Maximum crack spacing

sr,max= 3.4c + 0.425 (k1k2ϕ /ρp,eff)

Where;
c = nominal cover, cnom in mm in accordance with BS EN 1992-1

k1 = 0.8 for high-bond bars
(Note that for early age cracking calculations CIRIA C660 suggests a value of 1.14 to account for poor bond conditions, see EN 1992-1-1 for poor bond conditions)

k2 = 1.0 for tension (e.g. from restraint)
= 0.5 for bending
= (ε1 + ε2)/2ε1 for combinations of bending and tension where ε1 is the greater tensile strain at one surface of the section under consideration and ε2 is the lesser tensile strain (i.e. = 0 if strain at second surface is compressive).

ϕ = diameter of the bar in mm.

ρp,eff = As/Ac,eff

This is calculated for each face.

Ac,eff  = min[0.5h; 2.5(c + 0.5ϕ); (h x)/3]

Where;
h = thickness of section
x = depth to neutral axis.

εcr = Crack-inducing strain in concrete

εcr = (εsmεcm)

Crack-inducing strain is derived according to whether the element is subject to:

(1) edge restraint with

  • (a) early thermal effects or
  • (b) long term effects

(2) end restraint
(3) flexure and/or combinations of flexure and tension from load

Note: It is assumed that the reinforcement will be spaced at reasonably close centres. Where spacing exceeds 5(cnom + ϕ/2), BS EN 1992-1-1 Exp. (7.14) dictates that;

sr,max = 1.3 (h x)

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TANK SUPPORT TEXTBOOK 1