WATER RESEARCH COMMISSION. KSA 1: Water Resource Management. Thrust 2: Management of Natural and Human-induced Impacts on Water Resources

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1 WATER RESEARCH COMMISSION KSA 1: Water Resource Management Thrust 2: Management of Natural and Human-induced Impacts on Water Resources P3: Integrated flood and drought management REPORT ON DESIGN CODES : December 2009 The development and calibration of South Africa's National Standards for Water Retaining Structures Start date : 1 April 2007 End date : 30 March 2010 Lead Organisation : University of Stellenbosch, Department of Civil Engineering Prepared by : Prof J A Wium (30 November 2009)

2 THE DEVELOPMENT AND CALIBRATION OF SOUTH AFRICA'S NATIONAL STANDARDS FOR WATER RETAINING STRUCTURES REPORT ON DESIGN CODES : December 2009 TABLE OF CONTENTS EXECUTIVE SUMMARY Background Comparison of codes Introduction Design for the ultimate limit state : Design for the serviceability limit state Other considerations Discussion Design for the ultimate limit state Design for the serviceability limit state Proposal for design code Summary and conclusions References Annexure A : Bending in water-retaining structures Annexure B : Shear in water retaining structures Annexure C Detailing and anchorages Annexure D Crack width comparison Annexure E Crack control Annexure F Experimental measurements of crack width Annexure G Deflections of structures Annexure H L/d comparisons

3 THE DEVELOPMENT AND CALIBRATION OF SOUTH AFRICA'S NATIONAL STANDARDS FOR WATER RETAINING STRUCTURES REPORT ON DESIGN CODES : December 2009 EXECUTIVE SUMMARY In order to assist in design, construction, quality control and maintenance of water retaining infrastructure, it is important to use applicable South African National Standards. Considering the fact that no South African standard exists for the design of water retraining structures, a natural step is to develop such a standard for local application. Most frequently the British Standard BS 8007 is used as design code for water retaining structures in South Africa. However, consideration of local conditions, practice and materials is essential, calling for an in-depth study to ascertain appropriateness of design rules and guidelines, as well as harmonization of related codes. To achieve such rational and appropriate procedures and guidelines for the South African Industry, it is necessary that a South African National Standard for Water Retaining Structures is developed. In addition, the related standards for loading (SANS 10160) and relevant construction materials (SANS 10100) are to be revised to include appropriate provisions for water retaining structures. Furthermore, BS 8007 will soon be replaced by EN This report presents an evaluation of the concrete design code EN (Eurocode) which is the supporting design code for EN The aim of the report is to determine how EN compares with the South African standard (SANS ) and with BS The report considers the ultimate limit state, serviceability limit state, structural detailing and other considerations. It is shown that the Eurocode (EN ) is more comprehensive than SANS and that for some considerations, the Eurocode is less conservative. This specifically relates to the design of concrete in shear, and for deflections of structures with higher strength concrete. The criteria for evaluation of crack widths also differ between the codes and this subject needs careful consideration for a future code. The existing BS 8007 provides guidance to designers on testing of structures, details of joints and other consideration which are not part of the Eurocode (EN ). It is proposed that such items be included in a South African Standard for water retaining structures. It is therefore concluded that once a South African design code for water retaining structures is developed, it can be based on EN , but that it that will have to include aspects of BS 8007 as guidance for local designers. Furthermore, while the revision of SANS is currently in progress, eventually to be based on EN , it would be feasible to use the current SANS (2000) as supporting concrete design standard until a new revision, based on Eurocode (EN ), is issued. 2

4 THE DEVELOPMENT AND CALIBRATION OF SOUTH AFRICA'S NATIONAL STANDARDS FOR WATER RETAINING STRUCTURES 1. Background REPORT ON DESIGN CODES : December 2009 In order to assist in design, construction, quality control and maintenance of water retaining infrastructure, it is important to use applicable South African National Standards. Extensive research has and is being focused at deriving rational design rules for Civil Engineering Infrastructure and buildings internationally, and may be exploited for local application. However, careful translation to local conditions, construction materials and technologies is imperative. Considering the fact that no South African standard exists for the design of water retraining structures, a natural step is to develop such a standard for local application. Most frequently, reference is made to the British Standard BS 8007 for this purpose. However, consideration of local conditions, practice and materials is essential, calling for an in-depth study to ascertain appropriateness of design rules and guidelines, as well as harmonization of related codes. To achieve such rational and appropriate procedures and guidelines for the South African Industry, it is necessary that a South African National Standard for Water Retaining Structures is developed. In addition, the related standards for loading (SANS 10160) and relevant construction materials (SANS 10100) are to be revised to include appropriate provisions for water retaining structures. Furthermore, BS 8007, the design code most often used by local designers, will soon be replaced by EN (Eurocode for liquid retaining structures). EN was published in July 2006 and its National Annex on 31 October The creation of a code of practice for water retaining structures will form part of a basis from which the quality, durability and maintenance of water retaining infrastructure can be managed in South Africa. Although not an innovative creation on its own, it will provide local authorities and water authorities a basis from which systems can be set up in a co-ordinated manner for the management of durable infrastructure. The establishment of a code of practice for water retaining structures will thus provide one of the building blocks which is necessary to develop innovative water infrastructure management systems. This document reports on an investigation that was carried out to evaluate the following design codes: - EN in comparison with SANS and BS 8110 (1997); - EN in comparison with BS 8007 In this document, comparisons are made between the design codes for the following conditions : - Design for the ultimate limit state - Design for the serviceability limit state - Structural detailing - Other considerations The report is structured to first present a comparison of relevant items in the design codes. This is followed by a summary of items currently in BS 8007 but not in the Eurocode. A discussion of the comparison is then presented where the most important aspects are considered. The report is concluded with a summary of the major findings and conclusion are then drawn. 3

5 2. Comparison of codes 2.1 Introduction The current code for the design of concrete structures in South Africa is SANS (2000). A working group was created in 2007 for the revision of SANS Following a revision of the South African Loading Code for Building Structures (SABS ) which is based on the Eurocode (EN 1990 and EN 1991) it was decided by the working group to evaluate the Eurocode (EN ) as reference code for the revision of SANS It was decided by the working group responsible for the revisions of SANS that once the necessary comparisons have been carried out, the aim will be to adopt EN as South African design code for concrete structures. At present, the process of adoption entails a review of the contents of EN by a working group. The aim is to adopt the reference standard in a responsible manner. Individual committee members have been allocated sections of EN for which they are responsible. Each is tasked to determine by comparative calculations and by review, the effect which it would have on the local industry if EN is adopted for South Africa. It also entails identifying and motivating the choice of nationally determined parameters. Another matter which receives much attention is the characterizing of South African material properties for verification against those in the Eurocode. The process of verification and comparisons is scheduled to continue until June of A relevant issue which has been identified is the cross referencing between EN and other Eurocode standards or norms. An extensive effort is now required to identify the relevant national standards which would provide similar specifications. The impact of adopting EN also needs to be investigated on other South African standards. One such example is SABS , a materials standard currently being used in conjunction with the existing design standard. Much of this content (but not all!) is addressed in EN Early indications are that the matter of cross referencing, and the way in which accompanying standards are used, may become an onerous task. It is foreseen that ultimately a national standard would be issued with format and contents almost an exact copy of EN Differences would be the referencing of local standards and incorporation of nationally determined parameters into a single document. The information provided in this report is supported by several investigations at Stellenbosch University. Undergraduate final year research projects were used to investigate some of the aspects. Extracts from these research projects are included as annexures to this report. For the purpose of the development of a national standard for the design of concrete water retaining structures, a comparison of Eurocode (EN ) with SANS serves two purposes. These are : - To determine how compatible SANS would be with Eurocode (EN ) as design standard for concrete water retaining structures during an interim period in which SANS still remains to be the valid South African design standard for concrete structures. - To determine the implication of using Eurocode (EN ) as concrete design standard once it is adopted as South African Standard for the design of concrete structures. The following paragraphs present information obtained during investigations to compare EN and SANS The aspects considered are the following : - Design for the ultimate limit state : o Bending o Shear o Bond in reinforcement 4

6 o Other matters - Design for the serviceability limit state : o Crack width calculations o Deflections - Structural detailing 2.2 Design for the ultimate limit state : Although the design of water retaining structures is governed to a large extent by the conditions in the serviceability limit state, it is nevertheless necessary to perform a verification at the ultimate limit state. Selected topics were identified for verification and comparison in this study. The comparisons between EN and SANS are presented in this section. A comparison was made in 2008 between EN and SANS by G. Kretchmar (2008) as part of a final year undergraduate research project at Stellenbosch University. Extracts from the final year research project are enclosed as annexure to this report. Bending of reinforced concrete elements : An extract from the research project by G. Kretchmar (2008) is enclosed in Annexure A. The project made a comparison between EN and SANS for bending in reinforced concrete elements. A summary of the principle findings is presented in the following paragraphs. The custom in South Africa is to use concrete cubes as testing method for verification of the concrete characteristic strength. The cube strength is then used as parameter in the design of concrete members. The Eurocode (EN ) uses concrete cylinder strength as parameter in its formulations and equations. A table is provided in EN in which concrete cube strengths are shown for the corresponding cylinder strength. For this reason, some parameters are slightly different in the formulation of element resistance. The formulations for the bending resistance of concrete elements are provided in Annexure A for the case when only tension reinforcement is needed. A graphical comparison is also presented of the calculated resistance of members using the two design codes. The figure from Annexure A has been expanded to also include the case for when compression steel is also needed, and shown here as Figure 1. It can be seen that when reinforcement steel with the same yield strength is used, the formulations from the two design codes provide resistances which are virtually the same. The graphs presented here have been drawn based on a concrete characteristic cube strength of 30 MPa (SANS 10100) and a concrete characteristic cylinder strength of 25 MPa The compression steel requirement which should be read with the information in Figure 1 is shown in Figure 2. For both codes a characteristic steel yield strength of 450 MPa was used. It can be seen that EN allows sections to take more compression before compression steel is needed than in SANS This is basically because the compression block depth is limited to 0.5d in SANS , while the limit is 0.6d in EN Using EN for sections with high percentages of reinforcement (> 1.5%) will result in savings on compression steel as opposed to SANS This is however seldom a need in concrete water retaining structures. 5

7 AS2bd M/bd EN SANS As/bd Figure 1 : Comparison between SANS and EN for bending resistance of concrete elements (Moment resistance plotted against percentage of tensile steel) EN SANS As/bd Figure 2 : Comparison between SANS and EN for compression steel of concrete elements. Shear in reinforced concrete elements An extract of an evaluation on shear resistance from the research project by G. Kretchmar (2008) is enclosed in Annexure B. The project made a comparison between EN and SANS for the 6

8 Shear resistance (Vc) shear resistance in reinforced concrete elements. A summary of the principle findings is presented in the following paragraphs. Shear resistance without shear reinforcement : The shear capacity of reinforced concrete sections without shear reinforcement is a function of dowel action from the tensile steel, aggregate interlock on the shear plane, and shear friction in the compressive zone in the case of bending or compressive axial forces. The approach to determine the resistance against shear failure is very similar between SANS and EN for the case where no shear reinforcement is required. The resistance is based on equations which are empirically based. The formulae do not differ substantially between the two codes and are presented in Annexure B. Figure 2 shows a comparison between the resistance provided by the formulae in the two codes. The results presented are shown for a concrete characteristic cube strength of 30 MPa (cylinder strength 25 MPa), and for member depths of 250 mm and 450 mm. It can be seen that there is only a small difference between the resistance values obtained with the two codes. The difference is 5.8% for the 450 mm deep member and 3.8% for the 250 mm deep member. The resistance provided by the formula in SANS is slightly more conservative than that of EN In other words, SANS provides a smaller shear resistance value than EN for the same percentage of tensile reinforcement SANS mm EN mm SANS mm EN mm Steel ratio (100As/bd) Figure 3 : Comparison between SANS and EN for concrete shear capacity without shear reinforcement 7

9 100A/bs (%) % of shear reinforcement EN SANS SANS Minimum % SANS Stress limit EN Minimum % Vu (MPa) Figure 4 : Comparison between SANS and EN for % shear reinforcement Shear resistance with shear reinforcement When the shear capacity of concrete is exceeded, both codes require that shear reinforcement be provided to enhance the strength of the section. There is quite a significant difference in the approach by the two codes. The method in SANS makes use of the traditional approach developed by Ritter in This approach is based on a planar truss analogy with a 45 planar truss model. The total sectional resistance is given my the summation of the concrete capacity and that of the shear reinforcement. EN considers a variable angle truss where the capacity of the concrete in compression is used to determine a strut angle, and the shear reinforcement is then obtained using this angle. The angle is defined to be > 21.8 degrees. This formulation does not add the resistance of the concrete to that of the shear reinforcement. A comparison between the shear resistance as calculated by the two codes is presented in Figure 4. The figure shows the required percentage of shear reinforcement as a function of the shear resistance on the section for concrete characteristic cube strength of 40 MPa and 1% tension reinforcement. The non linear shape of the graph showing the resistance by EN is a result of the variable angle truss analogy. It can be seen that there is a significant difference between the resistance provided by the two formulations as the applied shear stress (v u ) increases. For smaller values of v u (up to 1.2 MPa) there is very little difference between the two codes. SANS provides a much more conservative result for higher shear stresses., therefore requiring more shear reinforcement than EN

10 On the other hand, EN requires that the force in the tension reinforcement be increased to allow for the additional tensile force due to the truss analogy. The tensile reinforcement must be verified for the additional force, a verification not explicitly required in SANS Both codes allow for shear enhancement in the close proximity of supports. EN furthermore provides an alternative procedure for calculating the capacity of members with loads applied close to the support by referring to the section on strut and tie models. Bond in reinforced concrete elements Bond between steel and concrete is essential for the concept of reinforced concrete to function. Design codes give directions for the calculation and verification of bond stress in structural elements. Both EN and SANS assume the ultimate bond stress to be uniformly distributed along the length of the anchored bar. The ultimate allowable bond stress for normal conditions for the two codes is compared in Table 1. It can be seen that ultimate anchorage bond stress values are slightly higher in SANS than in EN Both codes allow for the bond stress to be reduced by 30% for top bars in sections. For EN it applies to sections deeper than 250 mm, while in SANS it applies to sections deeper than 300 mm. Both codes provide rules for adjusting the ultimate anchorage bond stress as a function of concrete cover, bar shape (end hooks) and bar spacing. These rules are very similar between the two codes. However, EN provides substantially more information for allowance of transverse bars, welded transverse bars and other conditions which could have an influence on bond between steel and concrete. Similarly, EN is more explicit in the provisions for laps length between bars. More information about the comparison between the codes can be found in the extract of an evaluation on bond in reinforced concrete from the research project by G. Kretchmar (2008) which is enclosed in Annexure C. Table 1 : Comparison of anchorage bond stress values between EN and SANS Concrete characteristic cube strength (Mpa) Ultimate anchorage bond stress EN (MPa) Ultimate anchorage bond stress SANS (MPa) Design for the serviceability limit state The considerations for the serviceability limit state which needs attention for concrete water retaining structures are crack width calculations and to a lesser extent, the calculations of deflections. 9

11 Crack width calculations Crack width calculation is very often the determining factor which governs the amount of reinforcement required in the section. For this reason a number of comparison have been made for this study. In 2007 a final year undergraduate research project was carried out by Le Roux (2007) in which crack width calculations were compared between the two codes EN and BS The results of the investigation were reported in a WRC Report (Wium, 2007). An extract from that report is presented here in Annexure D where this comparison can be seen. The final year research project by G Kretchmar (2008) investigated the differences in crack width calculation between BS 8007 and EN An extract from the research report is enclosed in this report as Annexure E. The formulations for crack width calculations by the two codes are given in this Annexure. From the results by Le Roux (2007) and Kretchmar (2008) it was apparent that crack widths are calculated to be similar between the two codes for a variety of parameters when a crack width of 0.2 mm is targeted. The influence of the amount of reinforcement on the crack width is for example shown in Figure 5. The figure shows the crack width for using BS 8007 and EN (EC2). Values are also presented from calculating crack width using the Prokon software suite. (2008). It can be seen that crack widths, as calculated using the two codes, are very similar for 2000 mm 2 and more, for the chosen section. Below 2000 mm 2 of reinforcement, the calculated crack width is larger when calculated with EN than for BS Based on these observations, a test series was conducted in 2009 as part of a final year undergraduate research project (Vosloo (2009)). The purpose of the tests was to measure crack widths on small specimens under short term loading, and to compare the results with calculations using the two codes (BS 8007 and EN ). The tests consisted of specimens with 3 different percentages of reinforcement. Figure 5 : Calculated crack width comparison between EN and BS 8007 (Kretchmar (2008)) 10

12 The results of the test series are shown in Figure 6. In these graphs, the crack width is presented against percentage of tensile reinforcement for three different levels of applied bending moment, ranging from 1.41 M a /M cr to 2.82 M a /M cr. In these ratios M a = the applied bending moment and M cr = bending moment at first cracking of the section. From the results it can be seen that EN may over estimate crack width at low levels of applied load for low levels of reinforcement, while the estimate is fairly accurate for higher levels of reinforcement. It can be concluded that EN gives a reasonable estimate of crack widths. An extract from the investigation report by Vosloo (2009) is enclosed in Annexure F. It also shows the test results presented in Figure 5 in another format. Allowable crack width The report by Kretchmar (2008) presents a comparison between BS 8007, EN and EN for the limits these codes place on concrete crack width. An extract from this report is presented in Annexure E. In short, the maximum design surface crack widths for direct tension and flexure or restrained temperature and moisture effects according to the BS 8007:1987 are: Severe or very severe exposure: Critical aesthetic appearance: 0.2 mm; 0.1 mm. EN recommends limits to which the maximum allowable surface crack width is determined. These values range from 0.2 mm to 0.4 mm depending on the type of exposure of the element. The British National Annex recommends values which differ only slightly, with the range being only between 0.2 mm and 0.3 mm. The superseding water retaining standard EN specifies different crack widths for different classes of water tightness. Sections for which water tightness Class 0 is considered need to comply with the requirements of EN The same crack width is considered acceptable for tightness Class 1 if the crack does not pass through the section. If through cracking is possible, then the allowable crack width is a function of the hydrostatic pressure and ranges from 0.2 mm to 0.05 mm. For water tightness Class 2 through cracks should be avoided, and for water tightness Class 3 special measures are required to ensure water tightness. These limits are potentially more restrictive than the current values in BS 8007 and will need special consideration if it is contemplated to adopt EN as design code for water retaining structures 11

13 Crcak Width [mm] Crcak Width [mm] Crcak Width [mm] 0.14 Crack Width vs. Reinforced Area at 1.41 Ma/Mcr Test result EN BS % Reinforcement 0.3 Crack Width vs. Reinforced Area at 2.12 Ma/Mcr Test result EN BS % Reinforcement 0.4 Crack Width vs. Reinforced Area at 2.82 Ma/Mcr Test result EN BS % Reinforcement Figure 6 : Crack width tests presented against design code values 12

14 Deflection (mm) Calculation of deflections Deflections are generally not a critical design consideration for concrete water retaining structures. In this report a brief overview is presented of comparisons performed in an undergraduate research project by J- L Maritz (2009). The investigation by Maritz considered the short term deflection of slab elements and is comparable to the deflection behaviour of cantilever walls. An extract from his research report is presented in Annexure G. Comparisons were made between the two design methods in SANS Annexure A and the method in EN The results of the comparison are shown in Figure 7. Also shown in Figure 7 are the results of the maximum deflections calculated at the service bending moment. It can be seen that the method in EN and in SANS Annexure A.2.3 predict the experimental results reasonable well Experiment SABS A.2.3 SABS A.2.4 Eurocode 2 Clause % 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.4% % Tension reinforcement Figure 7 : Comparison of deflection calculation methods from SANS and EN It is however custom to rather use the L/d ratios when verifying for deflections in normal design situations. SANS provides recommended L/d ratios for different structural conditions such as cantilever beams, single span beams and continuous beams. These values can also be used for slab (or wall) design, and may need an additional adjustment factor depending on the type of slab. Allowance can also be made to adjust these ratios as a function of the available tension reinforcement, compression reinforcement and span length. EN provides a similar approach by offering equations to calculate the L/d ratio as a function of the tension and compression reinforcement content. The information from the two codes was used to prepare Figures 8 and 9 which provide a comparison of the L/d rations. For the comparison a concrete characteristic cube strength of 30 MPa was assumed (cylinder characteristic strength is 25 MPa). Figure 8 shows the L/d ratios for cantilever beams (slabs) and 13

15 L/d Figure 9 shows L/d rations for the end span of a continuous beam (or slab). The L/d rations are presented as a function of the required tension reinforcement. The effect of providing additional reinforcement to increase the allowable L/d ratio is shown in Figures H.3 and H.4 in Annexure H. In these figures the percentage difference between the L/d ratios from EN and SANS can be seen. A positive percentage indicates that SANS has larger L/d ration than EN In a paper by Beal (2009) it is shown that for cases of higher concrete strength, the EN values can be significantly different from those in BS 8110 (BS 8110 is very similar to the values in SANS ). This can also be seen in Annexure H where the effect of concrete strength on L/d ratios is shown in Figures H.1 and H.2. While L/d ratios are relatively similar between the two codes for a concrete characteristic cube strength of 30 MPa, EN has significantly larger values for higher strength concrete (f cu 50 MPa) EN SANS As/bd Figure 8 : L/d ratios for cantilever elements as a function of the % tension reinforcement. 14

16 L/d EN SANS As/bd Figure 9 : L/d ratios for end span of continuous beams as a function of the % tension reinforcement. Concrete detailing Kretchmar (2008) summarized the requirements of SANS and EN for reinforcement detailing. An extract from his report is enclosed in Annexure C. Both codes provide requirements for minimum and maximum percentages of reinforcement for different structural elements including walls, slabs, beams and columns (BD 2403 (2007)). The detailing requirements in SANS (2000) are very similar to those in BS 8110 (1997). Apart from the requirements in BS 8110 (1997), BS 8007 (1985) specify additional requirements for minimum percentage of reinforcement. BS 8007 (1985) has a tabulated requirement for a minimum of 0.35% of the gross area of the concrete section of high yield reinforcement (f y = 460 MPa). A figure defines the concrete section as surface zones presented for surface and suspended slabs. These requirements for minimum percentage of reinforcement from BS 8007 were plotted against the requirements of EN and SANS and are shown in Figure 10 as a function of the section height. Apart from the requirement by EN for minimum percentage of reinforcement, it is also required to verify concrete crack width during the design of a section. These requirements would normally exceed the minimum values presented in Figure 10. It can be seen that the minimum percentage reinforcement from EN is less than those of BS 8007 and SANS for section less than 0.65 mm in height. However, EN requires additional calculations to verify the reinforcement content to meet crack width requirements. 15

17 Area steel (% ) Minimum area steel (%) EN BS 8007 SANS bending SANS tension EN Walls Section height (m) Figure 10 : Minimum percentage reinforcement as specified in different codes 3. Other considerations Apart from design related matters, in order to provide a comprehensive overview of the implication of using EN as reference standard for a design code for water retaining structures in South Africa, the following items were identified as items addressed in BS 8007 but not directly in EN : - BS 8007 identifies the need for maintenance and inspection of the structure : Now addressed in SANS Draft (2009) - BS 8007 specifies certain operational safety considerations : Safety now addressed in SANS Draft (2009) - BS 8007 has a whole section on joints and jointing materials in water retaining structures - BS 8007 gives specifications for inspection and testing of structures : The broad concept of testing is addressed in SANS Draft (2009) 4. Discussion The following section provides a discussion of the comparisons presented in the previous section of this report. 16

18 4.1 Design for the ultimate limit state Bending of reinforced concrete elements : It is shown that the tension reinforcement requirement for EN is very similar to that of SANS The main difference is that SANS limits the depth of the compression block in the section to 0.5d, while EN has a maximum compression block depth of 0.6d. The result is that SANS requires more compression reinforcement for sections under high bending moments (> M/bd 2 = 4.6). When no compression reinforcement is required, the two codes provide almost the same requirement for tension reinforcement. Shear resistance without shear reinforcement : The approach to determine the resistance against shear failure is very similar between SANS and EN for the case where no shear reinforcement is required. The resistance is based on equations which are empirically based. The formulae do not differ substantially between the two codes and are presented in Annexure B. It can be seen that there is only a small difference between the resistance values obtained with the two codes. Shear resistance with shear reinforcement When the shear capacity of concrete is exceeded, both codes require that shear reinforcement be provided to enhance the strength of the section. There is quite a significant difference in the approach by the two codes which results in a significant difference between the resistance provided by the two formulations for higher applied shear stresses. SANS provides a much more conservative result at high shear stresses, therefore requiring more shear reinforcement than EN For low applied shear stress (< 1.2 MPa), the difference between the two codes is negligible. The difference increases as the applied shear stress increases. Bond in reinforced concrete elements The ultimate allowable bond stress for normal conditions for the two codes are very similar with the values in SANS BEING slightly higher (less conservative). Both codes allow for similar parameters which have an effect on the ultimate allowable bond stress. EN provides substantially more information for allowance of transverse bars, welded transverse bars and other conditions which could have an influence on bond between steel and concrete. Similarly, EN is more explicit in the provisions for laps length between bars. 4.2 Design for the serviceability limit state Crack width calculations Crack widths are calculated to be similar between the two codes for a variety of parameters when a crack width of 0.2 mm is targeted. 17

19 In a test series conducted in 2009 it was seen that EN may over estimate crack width at low levels of applied load for low levels of reinforcement, while the estimate is fairly accurate for higher levels of reinforcement. It was concluded that EN gives a reasonable estimate of crack widths. Allowable crack width The maximum design surface crack widths for direct tension and flexure or restrained temperature and moisture effects according to the BS 8007:1987 are: Severe or very severe exposure: Critical aesthetic appearance: 0.2 mm; 0.1 mm. EN the maximum allowable surface crack width ranges from 0.2 mm to 0.4 mm depending on the type of exposure the element is being subjected to. The British National Annex recommends values which differ only slightly, with the range being only between 0.2 mm and 0.3 mm. The superseding water retaining standard EN specifies different crack widths for different classes of water tightness. Sections for which water tightness Class 0 is considered need to comply with the requirements of EN The same crack width is considered acceptable for tightness Class 1 if the crack does not pass through the section. If through cracking is possible, then the allowable crack width is a function of the hydrostatic pressure and ranges from 0.2 mm to 0.05 mm. For water tightness Class 2 through cracks should be avoided, and for water tightness Class 3 special measures are required to ensure water tightness. The limits in EN are potentially more restrictive than the current values in BS 8007 and will need special consideration if it is contemplated to adopt EN as design code for water retaining structures It is suggested that the limiting crack width values currently used in South Africa, based on BS 8007, be retained until further investigations have demonstrated that it would be reasonable and advantageous to use values in EN Deflections A comparison of short term deflections for structural elements showed that the Eurocode (EN ) provides a reasonable estimate of expected deflections. The long term deflection calculations, which is of more relevance, was not investigated. Normally, deflection calculations is not a critical element in the design of water retaining structures. When deflections are calculated, the allowable L/d ratio is more often used during the design process than the direct calculation of deflections. It is shown in this report that for concrete with a characteristic cube strength of 30 MPa, the L/d ratios are very similar between SANS and EN for cantilever element. SANS is slightly less conservative for beam elements. When the concrete strength is increased, EN becomes increasingly un-conservative when compared with SANS It is recommended that the L/d ratios of SANS be used until further investigations have shows that the values in EN are reasonable for higher strengths concrete. 18

20 Concrete detailing The detailing requirements in SANS (2000) are very similar to those in BS 8110 (1997). Apart from the requirements in BS 8110, BS 8007 (1985) specify additional requirements for minimum percentage of reinforcement. BS 8007 has a tabulated requirement for a minimum of 0.35% of the gross area of the concrete section of high yield reinforcement (f y = 460 MPa). A figure defines the concrete section as surface zones presented for surface and suspended slabs. It is shown that the minimum percentage reinforcement from EN is less than those of BS 8007 and SANS for section S less than 0.65 mm in height. However, EN requires additional calculations to verify reinforcement content to verify compliance with crack width criteria. 5. Proposal for design code The South African Code SANS Basis of structural design and actions for buildings and industrial structures (2009) is currently in Draft format and has been circulated for public comment. This code is a revision of SABS 1060 (1989). EN 1990 and EN 1991 has been used extensively as reference codes in the development of this revision. The revision of SABS 0160 has set the example of how South African codes can be based on the Eurocode. South African concrete design codes have historically had very strong reference to British codes. The British codes are in the process of being withdrawn to make space for the Eurocode together with a British National Annex. In view of these developments, the development of a South African code for concrete water retaining structures can use the Eurocode (EN ) as a reference document. EN however uses EN as supporting concrete design code without which it can not exist. Any efforts to consider the development of a South African code for concrete water retaining structures therefore need to include an evaluation of EN as supporting document. The evaluation in this report shows the differences between SANS (and BS 8110) and EN It shows in general that although EN may at first glance be more difficult to use for the design engineer, it has more information available which allows for the treatment of special cases and situations. In general the following conclusions can be made after the evaluation between the two codes (SANS and EN ) : - Design for the ultimate limit state : o o o Design for bending is very similar, with EN slightly less conservative when compression steel is needed Design for shear : At low levels of applied shear, the two codes are very similar. For higher values of applied shear, EN is less conservative, increasingly so with increasing applied shear stress. Design of anchorage of reinforcement is very similar, except that EN provides significantly more guidance to allow for certain parameters and circumstances. - Design for the serviceability limit state : o o The calculation of crack widths provides very similar reinforcement requirements when a crack width of 0.2 mm is targeted. For larger cracks there is an increasing difference between the codes with decreasing reinforcement content. Comparison of short term crack width experimental results compare well with the EN calculation method. EN has a significantly more restrictive crack width requirement for cracks extending through the section. This may have a significant impact on the South African design environment if adopted. 19

21 o o The short term deflection calculations using EN gives similar results to one of the methods in SANS The deflections also compare well with limited tests performed at Stellenbosch University. Long term calculations are being investigated but have not been completed. Verification of deflections by L/d ratio is very similar for the two codes when concrete characteristic cube strength of 30 MPa is used. With increasing concrete characteristic cube strength, EN becomes increasingly less conservative. It is suggested that the values in EN first be evaluated before this formulation is accepted for higher characteristic concrete strengths. The process to revise SANS by using EN as reference code may still take a year or two. It is proposed that once the revision of SANS has been completed, the proposed code for concrete water retaining structures use the revised SANS as supporting concrete design code. In the interim, it will THUS be acceptable to continue to use SANS as supporting code for design of water retaining structures. In most cases this may result in slightly more conservative designs than when EN would be used, but similar to current practice. The proposed code for water retaining structures will have to include sections which are not included in EN These include : - maintenance and inspection of structures (verify the requirement against the contents of SANS Draft (2009) - operational safety considerations (verify the requirement against the contents of SANS Draft (2009) - joints and jointing materials in water retaining structures - specifications for inspection and testing of structures 6. Summary and conclusions In order to assist in design, construction, quality control and maintenance of water retaining infrastructure, it is important to use applicable South African National Standards. Considering the fact that no South African standard exists for the design of water retraining structures, a natural step is to develop such a standard for local application. Most frequently the British Standard BS 8007 is used as design code for water retaining structures in South Africa. However, consideration of local conditions, practice and materials is essential, calling for an in-depth study to ascertain appropriateness of design rules and guidelines, as well as harmonization of related codes. To achieve such rational and appropriate procedures and guidelines for the South African Industry, it is necessary that a South African National Standard for Water Retaining Structures is developed. In addition, the related standards for loading (SANS 10160) and relevant construction materials (SANS 10100) are to be revised to include appropriate provisions for water retaining structures. Furthermore, BS 8007 will soon be replaced by EN This report presents an evaluation of the concrete design code EN (Eurocode) which is the supporting design code for EN The aim of the report is to determine how EN compares with the South African standard (SANS ) and with BS The report considers the ultimate limit state, serviceability limit state, structural detailing and other considerations. It is shown that the Eurocode (EN ) is more comprehensive than SANS and that for some considerations, the Eurocode is less conservative. It is concluded that once a South African design code for water retaining structures is developed, it can be based on EN , but that it that will have to include aspects of BS 8007 as guidance for local 20

22 designers. Furthermore, while the revision of SANS is currently in progress, eventually to be based on EN , it would be quite feasible to use the current SANS (2000) as supporting concrete design standard until a new revision is issued, based on Eurocode. 7. References 1. ACI /318R Building Code Requirements for Structural Concrete (ACI ) and Commentary (ACi 318R-02). Michigan: American Concrete Institute 2. Beal, A.N. Eurocode 2: Span/depth ratios for RC slabs and beams. The Structural Engineer. October BS EN Eurocode 2: Design of concrete structures. General rules and rules for building. BSI 4. NA to BS EN :2004. UK National Annex. National Annex to Eurocode 2: Design of concrete structures Part1. Brussels : British Standards Institution. 5. BS EN Eurocode Design of concrete structures Part 3: Liquid retaining and containment structures. BSI 6. BS 8007:1987. Design of concrete structures for retaining aqueous liquides. London: British Standards Institution 7. BS 8110:1985 Part The structural use of concrete. London : British Standards Institution. Companion Document. 8. Companion document on Eurocode Design of concrete structures Part1. London : Department for Communities and local Government. 9. Huber, UA. MscEng (civil) thesis report. Reliability of reinforced concrete and shear resistance. Stellenbosch : University of Stellenbosch, Kong, F. K., & Evans, R. H. (1987). Reinforced and Prestressed Concrete (Vol. Third Edition). London: Chapman & Hall. 11. Kretzschmar, G. (2008). Final year project. The differences between the South African SANS and the European (British) EN as they relate to the design in water retaining structures. Department of Civil Engineering, Stellenbosch University. 12. Maritz, J-L. (2009). Thesis nr. S-34. Deflections of reinforced concrete elements. Department of Civil Engineering, Stellenbosch University. 13. NA to BS EN :2004. UK National Annex. National Annex to Eurocode 2: Design of concrete structures Part1. Brussels : BSI 14. NA to BS EN :2006. UK National Annex to Eurocode 2: Design of concrete structures Part 3: Liquid retaining and containment structures. BSI. 15. Roux, W. L. (2007). Thesis nr. S-36. South-African Practice for the Design of Water Retaining Concrete Structures. Department of Civil Engineering, Stellenbosch University. 21

23 16. SANS The structural use of concrete. Part 1: Design. Edition 2.2. Pretoria: The South African Bureau of Standards 17. SABS : The general procedures and loadings to be adopted in the design of buildings. Pretoria: The South African Bureau of Standards 18. SANS WG Draft Basis of structural design and actions for building and industrial structures. Part 2: Self-weight and imposed loads. Pretoria: South African National Standard. 19. Vosloo, R.N. (2009). Thesis nr. S-33. South African Practice for the design of water retaining concrete structures. Department of Civil Engineering, Stellenbosch University. 20. Wium, J.A. (2007) The development and calibration of South Africa s National Standards for Water Retaining Structures. Department of Civil Engineering, Stellenbosch University 22

24 Annexure A : Bending in water-retaining structures (Extract from the final year undergraduate research report by G Kretchmar) This chapter aims to discuss the basic principles from which the bending resistance is derived. The basic principles i.e. the rectangular stress block will be used to illustrate the resisting bending moments of members. The basic theory is expected not to change between the two standards under discussion, since the equations being derived from the stress block rely on simple static equilibrium. Certain minor differences have indeed been identified. The resulting significance and implication of these is then again discussed and analyzed with the aid of a graphical presentation. Sections requiring tension reinforcement only are considered. 3.1 Stress distribution First, the older stress block lay-out is being assessed (SANS ). The size of the compression zone, its intensity and the lever arm to the tension steel is then compared to their respective parameters of the subsequent standard (EN ). SANS : Figure 3. 1: Stress distribution as in SANS Consider the square concrete cross-section being simply reinforced with steel bars as illustrated in Figure 3.1. The section is considered to be subjected to a simple bending moment about the neutral axis. The top half of the profile, in compression, is dealt with by the concrete compressive resistance of 0.67f cu /γm (where f cu is the characteristic compressive cube strength of concrete and γm is the partial material factor for concrete amounting to 1.5). 23

25 EN : Figure 3. 2: Stress distribution as in EN Consider the square concrete cross-section being simply reinforced with steel bars as illustrated in Figure 3.2. The section is considered to be subjected to a simple bending moment about the neutral axis. The top half of the profile, in compression, is dealt with by the concrete compressive resistance of 0.85f ck /γ m where f ck is the characteristic compressive cylinder strength of concrete and γ m is the partial material factor for concrete amounting to 1.5). 3.2 Resisting strength vs. Reinforcement quantity A characteristic strength for concrete (f cu in SABS and f ck in EN) was taken to be 30 MPa (both as cube tested strength), and for the yield stress in tension reinforcement steel (f y ) a standard 450 MPa was used. The Eurocode furthermore mostly specifies an ultimate yield at 500 MPa. The effect of this is also being observed. In the following, both the SANS and the EN stress blocks are being compared by means of a technique that allows quantifying their apparent divergence. It enables to prepare a curve that can clearly distinguish between the two codes. SANS : Firstly, taking the sum of moments about the tension reinforcement yields: M = ( ) (d - ) = f cu (b x) (d-0.45x) = f cu (bdx) ( [eq:3.1] 24

26 by taking γ m = 1.5 as the partial safety factor for concrete For: the lever arm between the compression and tension forces z = (d - ) EN : Again we take the sum of moments about the tension reinforcement: M = ( ) (d - ) = f ck (b x) (d-0.4x) = f ck (bdx) (1-0.4 [eq:3.2] by taking γ c = 1.5 as the partial safety factor for concrete. For: the lever arm between the compression and tension forces z = (d - ) Directly comparing equations eq:3.1 and eq:3.2 show a constant dissimilarity. The intention is to obtain two sets of equations of the same variables, namely the bending moment resistance and the reinforcing steel ratio (see Steps 1 and 2). Then, simultaneously solving and manipulating these equations (Steps 3 and 4) yields the final relationship to be plotted on a graph. SANS : Step 1: Taking the sum of moments about the compression block: M = A s (d - ) = 0.87 f s A s (d-0.45x) = 0.87 f s A s d [eq:3.3a] by taking γ m = 1.15 as the partial safety factor for reinforcement steel Step 2: Taking a static equilibrium of forces: F = 0.45 f cu (0.9bx) f s A s = 0 = f cu bx f s A s = f cu bx f s A s [eq:3.3b] Step 3: Manipulating e:3.3a by dividing both sides by (bd²) gives: = = 0.87f s [eq:3.4a] Step 4: Manipulating eq:3.3b by dividing both sides by (bd) gives: = = [eq:3.4b] Now, finally merging equation eq:3.4b into eq:3.4a gives us the planned relation of the computed bending resistance in terms of the steel ratio: =

27 = [eq:3.5] EN : Taking the sum of moments about the compression block yields roughly the same as for the South African, the only difference being the lever arm: Step 1: M = A s (d - ) = 0.87 f s A s (d-0.4x) = 0.87 f s A s d [eq:3.6a] by taking γ m = 1.15 as the partial safety factor for reinforcement steel Step 2: F = f ck (0.8bx) f s A s = 0 = f ck bx f s A s = f ck bx f s A s [eq:3.6b] Step 3: Manipulating e:3.6a by dividing both sides by (bd²) gives: = = 0.87f s [eq:3.7a] Step 4: Manipulating eq:3.6b dividing both sides by (bd) gives: = = [eq:3.7b] Again, merging eq:3.7b into 3.7a gives us (having f y = 450 MPa): = 0.87 (f y ) = [eq:3.8] When using f y = 500 MPa for the reinforcement, it generates: = = [eq:3.9] We now have three equations (eq:3.5, eq:3.8 and eq:3.9), all in terms of M/bd² and A s /bd. Where the variable factor A s /bd is, by observation, the percentage of reinforcement applied per sectional area (considering the square concrete section in Figure 3.1 and 3.2). A table was set containing values ranging from a bit less than minimum reinforcement per section to the maximum allowable reinforcement quantities in concrete section. The minimum and maximum reinforcement areas are discussed in chapter 5 (Annexure C of this report) By varying the steel content (As/bd), the resisting strengths have been computed by equations eq:3.5, eq:3.8 and eq:3.9 respectively and then plotted as shown in Figure 3.3 below. We can clearly observe a rise in strength as the steel content increases, of which both the standards experience similar behaviour. The EN 1992 curve seems marginally less conservative indicating a slight stronger theoretical resistance to the same reinforcement. 26

28 M/bd² As/bd SABS 0100 EN 1992 fyk=450 En 1992 fyk=500 Figure 3. 3: Bending moment resistance of a section as a function of steel area 3.3 Summary to bending The graph in Figure 3.3 clearly shows curves that are very similar in their behaviour, of which the differences are rather insignificant and negligible. The European stress block though, shows a tiny less conservative result to their approach by having a greater resistance to the same reinforcement. It shows that a longer lever arm has the upper hand in comparing it to the smaller compression area. Below the line, the difference of the computed resistance between the two standards can easily be neglected. And thus the new EN would do fine in collaboration with the present SABS standard. 27

29 Annexure B : Shear in water retaining structures (Extract from the final year undergraduate research report by G Kretchmar) Shear in beams still remains a matter being heavily debated concerning the predictability and safety. There are several different approaches which all are based on firm and well motivated assumptions. In general, members that are very vulnerable to shear are usually very short members, since once a member has a longer span in relation to the cross-section, members tend to fail in bending before shear failure becomes apparent. The designers usually try to omit the possibility of shear failure by ensuring that the beam fails due to bending first. This bypasses the fact that shear still is so unexplored, whereas bending is rather accurately predictable. In the following paragraphs sections without shear reinforcement are first considered before sections with shear reinforcement. 4.1 Sections without shear reinforcement To introduce the basic principles of shear a simple free body diagram is used. The forces and stresses applied are discussed and reviewed. The part is concluded by a graphical curve, having similar aims as in the previous chapter concerning the bending comparisons. This curve compares the equations used to calculate the shear resistance of the pure concrete section by the various standards, namely the SABS and the EN : The basic principles To understand the mechanisms of shear stresses in a beam, we first consider the basic concrete section containing no shear stirrups. Nominal longitudinal tension reinforcement is provided. There are a number of different approaches to model and simplify shear members, all the various different theories rely on the same principles though. Consider a beam with simple support and shear force V being resisted. The total shear force being resisted consists of the following components: V r = V cz + V ay + V d [eq:4.1] where V cz V ay V d the resistance offered by the uncracked concrete section in compression the resistance offered by interlocking aggregate (also referred to Interface Shear Transfer ) a resistance referred to as the Dowel action, is offered by the main longitudinal tension steel passing the cracked section. 28

30 Figure 4. 1: A shear failure crack displaying the resisting forces (Kong & Evans, 1987) Empirically, it was found that the total resisting force V r consists of the following approximate proportions with reference to eq:4.1 (Kong and Evans,1987): Shear compression zone V zc = 20-40% Dowel action V d = 15-25% Aggregate Interlock V a = 35-50% According to Kong and Evans, in the process of an increasing applied load, the shear stress increases. The dowel action reaches its maximum capacity first, after which the aggregate interlock provides resistance to provide the structural integrity. Once the frictional resistance is exceeded, all the stresses are delegated almost instantaneously to the only resistance left, being the concretes compressive zone. The sudden impairment causes an inevitable ultimate abrupt failure. This behaviour is to be prevented, as whole structures can simply fail with no indication prior to the collapse. In the following section the various codes similarity in calculating the concrete sections shear resistance is being assessed. SANS : The South African standard assumes and applies a theory firstly proposed by Mörsch in 1902 (Huber, 2006). Mörsch projected the shear stress to be: ν = [eq:4.2] where V is the applied shear force and b and d are the section s thickness and effective depth respectively. The shear resistance of a beam is given by two distinct components one of which is the shear resistance of the concrete and the other being the shear capabilities of the stirrups: ν r = ν c + ν s [eq:4.3] where the concretes shear resistance ν c is given by: 29

31 for which: γ m,c the material factor 1.4 f cu concrete cube compressive strength being the % longitudinal tension steel reinforcement supplied [eq:4.4] and f cu 40 MPa A s 0.03bd EN : The average shear distribution is also according to Mörschs predictions and follows the same behaviour as equation eq:4.3. The concrete shear resistance is given by the following equation: Where γ m,c the partial material factor for concrete = 1.5 f ck the concrete cylinder compressive strength [eq:4.5] Also, ν c is limited by the value: v c [eq:4.6] The concrete shear resistance equations differ significantly comparing the EN with SANS The exact magnitude of the observed difference is hard to determine without any numerical values Summary to sections without shear reinforcement In an attempt to illustrate the numerical difference between the European and South African standard concerning the above mentioned concrete shear resistance equations, the following constants were chosen: f cu = 30 MPa d = 450 mm = 25 MPa f ck when substituted into eq:4.4, eq:4.5 and eq:4.6, the following equations are obtained: SANS : ν c = EN : ν c = Now, gradually increasing the steel percentage ratio ranging from = 0.1 to the maximum allowable 3, we can generate the following graph: 30

32 Figure 4. 2: Relative shear resistance with increasing longitudinal tension steel ratio Considering the curves in Figure 4.2, it is observed that a higher resistance in shear is obtained using the Eurocode formulation. This is a slightly less conservative approach, since one would consequently be inserting less shear stirrups into the section. 4.2 Sections with shear reinforcement The same components that add to the beam shear resistance are still applicable. In the previous sections considered, the carrying capacity of the section was limited to the tensile strength of concrete. Now that shear reinforcement is introduced to enhance the sections capacity some tensile resistance is added to that of the concrete. Vertical stirrups are placed that allows the use of the following equation: V r = V cz + V ay + V d + V s [eq:4.7] for which V s is simply the contribution to shear resistance from the stirrups. The role of the shear reinforcement is made clear in Figure

33 Figure Figure 4. 3: 4. 3: Resistance Shear of stirrups the shear role reinforcement of resistance (Huber, 2006) When a simply supported beam under shear, as in Figure 4.3, is loaded extensively, the diagonal shear tension crack occurs as a result of the tensional failure of the concrete. The member experiences a tensile stress near the support of the structural member as indicated in Figure 4.3. Simultaneously, there is the compressive stress as indicated by the blue arrows in Figure 4.3. The orientation of the diagonal tension crack is to a maximum degree of about θ= 45 measured with respect to the direction of the shear stirrups. Now, the concrete resists compression stresses, whereas the tension is resisted by the shear stirrups. This system, similar to the bending stresses in ordinary bending-beam elements where steel takes care of tension and the concrete resists compressive stresses, ensures the integrity of the structures. In order to calculate the amount of steel reinforcement to be placed, in addition to the longitudinal tension steel, the two standards follow their respectable approaches. The approaches mainly differ in the angle θ. The older SABS standard assumes the angle to always be 45, whereas the subsequent Eurocode makes its distinction with a different model that allows θ to vary between a minimum of 21.8 and the maximum 45. These two approaches are discussed in the following paragraphs The 45 Planar Truss Model A historical approach to disintegrating shear reinforcement models, simplifying them, is referred to as the planar truss analogy. This methodology was first introduced by Swiss engineer Ritter in The following figure is used by Huber to explain the principles of Ritter s proposition. A shear members equilibrium is made up of diagonal compression struts encountered by the shear stirrups in tension reinforcement. 32

34 Figure 4. 4: 45 Planar Truss Analogy (Huber, 2006) The diagonal compression struts are seen to be forcing the top and bottom sections of the beam apart, where the shear stirrups are then accordingly inserted aiming to hold these very sections together. Ritter postulates the structural member to fail ultimately in shear once the stirrups loose their effect or alternatively the concrete compression struts fail. Stirrup yield at: ν s = [eq:4.8a] Compression struts: ν d = f d,max sinθcosθ [eq:4.8b] where A v f yv f d,max the area of shear reinforcement considering both legs of stirrups the steels yield strength concretes compressive capacity of diagonal struts 33

35 4.2.2 The Variable Angle Truss Model Huber furthermore considered the Variable Angle Model in his project. The main difference of the Variable Angle Model to the 45 Planar Model is that the Variable Angle Model allows the angle θ to deviate between 21.8 and 45. This is due to an assumption that not only the shear reinforcement but also the longitudinal tensional reinforcement in a beam can contribute to the shear capacity of the beam. The theory requires both the shear and longitudinal tension reinforcement to yield before ultimate failure. Now the effect of the longitudinal tension steel, depending on its quantity, causes the diagonal tension crack to occur at a steeper angle than previously assumed. There are two types of reinforced beams, the one being under-reinforced where both the shear and longitudinal steel yield before failure. The other scenario is when the beam is over-reinforced, here the members concrete compressive struts are being crushed before the steel yields in tension. The aim of design is to reach the absolute equilibrium ensuring optimum resistance to the loads. Stirrups yield: ν s = ρ v f yv cot θ [eq:4.9a] Concrete struts: ν d = f d sin θ cos θ [eq:4.9b] Longitudinal: ν sl = ρ l f yl tan θ [eq:4.9c] Where the factor ρ is the % steel provided in the respective sections, f is the prevailing steel yield strength and θ being the angle the diagonal tension crack makes with the vertical. Now, for tan θ =, cot θ = we can generate the following set of equations: ρ v f yv = f d cos² θ ρ l f yl = f d sin² θ ν = f d sin θ cos θ [eq:4.10a] [eq:4.10b] [eq:4.10c] Also, by using the trigonometric identity sin² θ + cos² θ = 1 (Remembering that: f d sin² θ + f d cos² θ = f d ) and the respective equations eq:4.10a and eq:4.10b we can deduce: ρ v f yv + ρ l f yl = f d [eq:4.11] We normalize the formula eq:4.11 by dividing the whole identity with the maximum possible compressive strength f d,max. + = Which gives: ω l + ω t = [eq:4.12] where, in the optimum balanced position, the longitudinal reinforcement index ω l is equal to 0.5, and the shear reinforcement index ω t equating to 0.5. This gives the optimum reinforcement for f d = f d,max. Therefore, for: Under-reinforced: ω l + ω t 1 Over-reinforced: ω l + ω t 1 and the balanced condition: ω l + ω t = 1 understanding that the shear reinforcement index ω can be regarded as the respectable normalized steel ratio inserted in the section s profile. 34

36 We can derive a formula to compute the angle Ѳ by dividing the equation eq:4.10b by eq:4.10a. This would then yield: = tan²ѳ = ω t /ω l and tan Ѳ = [eq:4.13] To be able to plot a relationship between the various relations, we want to be able to illustrate using a curve on a graph that can distinguish and differentiate between under-reinforced and over-reinforced sections. For a start we consider the balanced condition which is the apex of all the succeeding. Once we can establish the balanced curve, the rest should be directly visible. For the balanced condition we can substitute the three equations of eq:4.10 into each other. Note that: sin² θ = ρ l f yl / f d, cos² θ = ρ v f yv / f d, and ν = f d now cancelling the f d and dividing by f d,max we can say: ν/f d,max = [eq:4.14] The three cases for a balanced condition entail: ω l = ω t = 0.5 ω t 0.5 the both the longitudinal and shear reinforcement yield simultaneously here the shear reinforcement is expected to yield first due to a lower steel ratio in relation to the normalized steel quantity in the longitudinal direction. Also, the following holds: ω l = 1 - ω t. Note, that in this case Ѳ is always smaller than 45 for that: tan -1. ω l 0.5 the vice versa is about to happen. The angle Ѳ is expected to be more than 45. Now, finally, we consider the equation eq:4.14. We rearrange it as follows: (ν/f d,max )² =, squaring both sides and adding 0.5² to both sides raises: (ν/f d,max )² + 0.5² = ω t - ω t ² + 0.5² (ν/f d,max )² + (ω t ² - ω t + 0.5²) = 0.5² (ν/f d,max )² + (ω t - 0.5)² = 0.5² [eq:4.15] A little rearranging and simplification yields a better understanding. Notice: (ν/f d,max )² + (ω t - 0.5)² = 0.5² (y-a)² + (x-b)² = r² 35

37 For which the right hand side is the standard formula for a circular plot having its centroid at the coordinate (x,y) = (a,b) = (0.5,0.0) and a radius of r = 0.5. And hence, Figure 4.5 could be plotted. Figure 4. 5: Normalized comparison of Shear stress ratio vs. reinforcement ratios (Huber, 2006) Figure 4.5 illustrates a semi circle that demonstrates the balanced condition mentioned earlier. Once deviating off the curve depicted by eq:4.15, the section s shear strength is restricted to the capacity of the factor yielding first. For example, we say that: ω l = 0.3, and ω t = 0.7 remembering that ω is the normalized ratio of reinforcing steel inserted into the section. This gives us an angle Ѳ = tan -1 = Further, by eq:4.14 : ν/f d,max = = And by inspection : 2 x (ν/f d,max ) = = The optimum steel ratios are to be obtained by having striving to 1.0. This is obtained, by observation, at a diagonal crack angle Ѳ = 45. The Eurocode limits the allowable angle between 21.8 and 45 as mentioned previously. For Ѳ = 21.8, we can deduce that: 36

38 21.8 = tan -1 since ω l = 1 ω t. This implies that ω t = When ω t = 0.138, then: ω l = 1 ω t = Also : ν/f d,max = = and = The values just computed for when θ = 21.8 were shown on Figure 4.5. To follow is a comparing summary of all the above mentioned, we compare the graph in Figure 4.5 with added values used in the Former British-South African standards. 4.3 Direct comparison Both the 45 planar truss model and the Variable Angle Model are applied in the following paragraphs to present a comparison. SANS : The South African code, using the 45 planar model, adds an empirical constant concrete contribution term to the resisting strength in shear. This term corresponds to the offset of the line labelled SANS as shown in Figure 4.6. Notice the dashed line also being orientated at 45, and having an initial off-set of. Figure 4. 6: Shear stress ratio vs. reinforcement ratios added the concrete contribution (Huber, 2006) 37

39 EN : As previously mentioned, the Eurocode based on the Variable Angle Model, has the deviation of θ which ranges from 21.8 to 45. In contrast to the older standards, the European model neglects the tensile strength provided by the concrete in the diagonal shear crack zone. The values using the EN model are compared to that of SANS in Figure 4.7. Figure 4. 7: Close-up look at Shear stress vs. Reinforcement (Huber, 2006) Figure 4.7 provides a close-up view of the critical zone depicted in Figure 4.6. The axes were modified into usable units that result in the shear resistance being plotted against the shear reinforcement (both in MPa units). Huber uses a formula that provides the relationship between the shear index ω and the reinforcement ratio used in Figure 4.7. For ω t values of more than approximately 0.04, the Eurocode computes a higher section resistance than the former British standard. We can therefore deduce a more conservative behaviour from the older SANS standard. 38

40 Annexure C Detailing and anchorages (Extract from the final year undergraduate research report by G Kretchmar) This chapter consists of two distinctive parts. The first part discusses the differences in the minimum and maximum steel areas specified in the respectable standards. The second part presents the basic principles used to calculate the anchorage lengths of reinforcement. 5.1 Reinforcement areas Minimum area requirements The minimum requirements in steel areas are generally specified in terms of a percentage, where this is calculated in relation to the section effective area. The effective area of the section is referred to the area of the member cross-section that actively contributes to the structural integrity. For the reason that in water retaining structures there are rarely beams and columns forming part of the design, and even if this would be the case the design would be similar to standard calculations, the detailing specifications of beams and columns depicted in the codes where excluded in this presentation. SANS : Main: The minimum amount of vertical reinforcement in a wall should be no less than 0.4% of the gross cross-sectional area. (See section in (SABS Ed 2.2, 2000)) This reinforcement may be inserted in double or single layers. Secondary: In cases where the main vertical bars are inserted to resist a compressive load, the minimum secondary (horizontal) reinforcement shall be at least 0.25% of the crosssectional area. The bars shall be at least of 6 mm diameter or one quarter of the vertical main bar diameter. ( in (SABS Ed 2.2, 2000)) Shear: where the main vertical reinforcement in walls exceeds 2%, shear links should be added with diameter not less than 6 mm or one quarter of the diameter of the largest compression bar throughout the thickness of the wall section. ( in (SABS Ed 2.2, 2000)). The spacing of these links shall not exceed twice the wall thickness in both the vertical and horizontal spanning directions. Additionally, in the vertical direction the link spacing shall not be more than 16 times the bar diameter. Sections that are subjected to mainly tension, which would be the case for the horizontal reinforcement in a reservoir wall, the minimum area of reinforcement is specified as 0.45% of the cross-section. (Table 23 in (SABS Ed 2.2, 2000)). Rectangular sections subjected to bending have a specified minimum requirement of 0.13% of their cross-sectional area. In solid slabs, this reinforcement quantity is to be placed in both spanning directions. (Table 23 in (SABS Ed 2.2, 2000)). For other non-mentioned cases or any uncertainty, the SABS code provides a table (Table 23) providing all minimum reinforcement requirements. 39

41 EN : The Eurocode expresses all the minimum and maximum reinforcement areas in terms of the A s,vmin and the A s,vmax respectively. These are then defined as a ratio between a constant and A c. A c is the cross-sectional area of the member under consideration and the factor being a percentage. Vertical: A s,vmin = 0.002A c. (Meaning the vertical areas of reinforcement are to be no less than 0.2% of the cross-sectional area). Half of this value should be located on each face. This 0.2% is the recommended value, where the British National Annex uses the recommended value. Horizontal: A s,vmin = 25% of the vertical amounts or 0.001A c which ever is the greater is recommended. The British National Annex states to use the suggested values, it puts special emphasis on the thermal effects in the case of crack control though. Half of both the vertical and horizontal steel areas should be located at each face of the wall. Shear: In the case where the total vertical reinforcement area of the wall exceeds 0.02A c, shear links should be provided in accordance to the requirements of columns. This in turn details the link diameters to be either no less than 6 mm or one quarter of the maximum longitudinal bars. The spacing of shall not exceed the value given by s cl,tmax. This value is recommended to be the least of the following three distances: - 20 times the minimum longitudinal bar diameter - the lesser dimension of the column (wall thickness) mm The Eurocode furthermore gives additional specifications for shear link areas in cases where the main reinforcement is placed nearest to the external face of the wall. For other non-mentioned cases or any uncertainty, Section 9.6 in EN :2004 code depicts all detailed reinforcement requirements Maximum allowable reinforcement areas SANS : The area of reinforcement shall not exceed 4% of the cross-sectional area of the member. EN : Again, similar to the minimum steel area requirements, the max allowable areas are defined in terms of the A s,vmax. The A s,vmax = 0.04A c which is 4% of the cross-sectional area of the member. Additional rules are provided concerning laps as presented in EN :2004 section 9.6.2(1) Note Spacing of reinforcement Both standards describe a number of requirements for the minimum spacing of re-bars. These specifications mainly depend on the size of aggregate placed in the concrete. 40

42 SANS : Refer to the section in (SABS Ed 2.2, 2000) - When the diameter of the re-bars exceeds the maximum aggregate size plus 5 mm, a spacing of less that value should be avoided. - A pair of bars or a bundle of more than 2 bars should be regarded as a single bar having the diameter reaching an equivalent area. The spacing of bars should be made suitable for proper concrete compaction - The horizontal distance between bars should be no less than (h agg +5 mm) for which the h agg is the maximum coarse aggregate size. - In the case where there more than one row of reinforcement, the vertical distance between the bars should at least be 2/3h agg and the bars should be vertically in line. Additional rules and regulations are applicable in the case of pairs of bars and bundles of bars (Sections and of SABS ) Spacing of shear links is mentioned in section , as mentioned above under the minimum area requirements for shear reinforcements. EN : The clear spacing of bars relies on the same basic aggregate principles as described in the South African standard. Section 8.2 in EN :2004 describes: The reinforcement bars should be spaced such that the placing and compacting of concrete can be done adequately assuring optimum bond conditions. Any clear distance between the bars, horizontal or vertical, shall not be less than: - k 1 (bar diameter) - (d g + k 2 ) - 20 mm For which k 1 and k 2 are constants recommended to be 1 and 5 mm respectively. The British use the recommended values in their National Annex. Furthermore, the Eurocode specifies additional rules to be followed concerning the bar spacing. Assuring the minimum requirements of steel reinforcement areas, the vertical bar spacing (s) in a wall shall not exceed the lesser of 3 times the wall thickness or 400 mm. Whereas the horizontal bar spacing should be more than 400 mm. (Section 9.6). Further to the above regulations given in EN :2004, additional specifications are applicable to the detailing as specified in the superseding water retaining code EN :2005. In addition to Section in EN :2004, EN :2005 specifies that Sections and to be followed in cases of corner connections between walls and the provision for movement joints. 41

43 5.3 Anchorage Reinforcement bars subjected to direct tension must be firmly anchored if it is not to be pulled out of the concrete member. The anchorage depends on the bond condition between the re-bars and the concrete. SANS : The anchorage bond strength is assumed to be constant over the full length of the bars. The basic principles followed rely on the design bar force divided by the effective contact area of the bar. Table 24 details values for the ultimate anchorage bond stress f bu. Table 5. 1: Ultimate Anchorage bond strength according to SABS 0100 (SABS Ed 2.2, 2000) Bar type Ultimate anchorage bond stress f bu Mpa Concrete Grade Plain bar in tension Plain bar in compression Deformed bar in tension Deformed bar in compression The concrete grade of 35 MPa is not included in the original Table 24. Linear interpolation was done to obtain the f bu = 3.15 MPa. The required anchorage length can be calculated using: f b = f bu [eq:5.1] for: F s the force in the bar (or group of bars) F s = (f s /γ m )A s = 0.87f y A s bar diameter L being the anchorage length to solve for since the bond strength (f bu ) is known and can be read from Table 24. In elements where the member thickness exceeds 300 mm, a lower bond condition is assumed for elements in the top of horizontal sections and thus a 30% reduction of the f bu values in Table 24 is applicable. This has a direct 30% increasing effect on the eventual anchorage length (L) being calculated. 42

44 EN : Similar to the SANS , the length required relies mainly on the principle of the pull out force divided by the contact area : Tensile pull out force = (cross-sectional area of bar) x (direct stress) = f s [eq:5.2] Anchorage force = (contact area) x (anchorage bond stress) = (l b,rqd πø)xf bd [eq:5.3] And: Tensile pull out force = Anchorage force. Therefore equating the two and solving for the anchorage length (l b,rqd ) gives: l b,rqd = f s Ø/4f bd = (f yk Ø/4.6 f bd ) [eq:5.4] considering the partial safety factor for steel (γm) is 1.15 (f yk = f s /γ m ). For: l b,rqd anchorage length Ø bar diameter f bd ultimate anchorage bond stress direct tensile or compressive stress in the bar f s To calculate the ultimate anchorage bond stress f bd a simple equation is used. f bd = 2.25 η 1 η 2 f ctd [eq:5.5] For: f ctd the design concrete tensile strength f ctd = α ct f ctk,0,05 / γ m [eq:5.6] η 1 η 2 for: α ct a coefficient that takes account for the long term effects on the tensile strength and unfavourable effects. Can be taken as 1.0 as recommended f ctk,0,05 characteristic axial tensile strength of concrete obtainable from Table 3.1 in EN :2004. γ m being the partial safety factor for concrete (1.5) factor related to the quality of the bond condition, being 1.0 assuming good conditions and 0.7 for reasons where bad bond conditions can be deduced a factor related to the bar diameter η 2 = 1.0 for Ø 32 mm η 2 = (132- Ø)/100 for Ø 32 mm Lower bond conditions exist once the concrete member thickness exceeds 250 mm. Figure 5.1 provides information. 43

45 Figure 5. 1: Good bond conditions (EN , 2004) The design anchorage length l bd can now be calculated by: l bd = α 1 α 2 α 3 α 4 α 5 l b,rqd [eq:5.7] For: all constants are given in Table 8.2 in EN :2004 α 1 effect of the form of the bars α 2 effect of concrete minimum cover α 3 effect of confinement of transverse reinforcement α 4 the influence of one or more welded transverse bars along the design anchorage length α 5 effect of the pressure transverse to the plane of splitting along the design anchorage length Also: the product (α 2 α 3 α 5 ) 0.7; The Eurocode furthermore gives regulations for minimum requirements for the anchorage lengths. If no further limitation is provided, the minimum anchorage length in tension and compression is defined by two distinct equations 8.6 and 8.7 respectively. 5.4 Summary to detailing and anchorage Table 5.2 summarizes the findings and discussions used in chapter 5. 44

46 Table 5. 2: Summary to detailing and anchorages Topic Former Subsequent 5.1 Reinforcement areas: Minimum required Main: A s 0.4% of A c Main: A s 0.2% of A c Horizontal: A s 0.25% of A c in the case where vertical bars to resist compression. For members in plain tension, A s 0.45% of A c Shear: applicable when main A s 2% of A c. Diameter provided to be 6mm or ¼ (main compression bar diameter). Spaced by twice the wall thickness and vertical direction additionally at 16 times bar diameter Maximum allowable A s 4% of A c A s 4% of A c Horizontal: A s 25% of amount placed vertically. Or A s 0.1% of A c whichever being the greater Shear: applicable when main As 2% of Ac. Diameter provided to be 6mm or ¼ (main vertical bar diameter). Spaced by either 20 times minimum vertical bar diameter, the wall thickness or 400 mm whichever the least. 5.2 Spacing of reinforcement: General Spacing to be such that the placing and compaction of concrete can be done adequately assuring proper reinforcement bond conditions Spacing to be such that the placing and compaction of concrete can be done adequately assuring proper reinforcement bond conditions Horizontal s (h agg + 5mm) s (bar diameter) Vertical s 2(h agg )/3, the bars should be vertically in line. (d g + 5mm) (20mm) whichever the biggest Vertical spacings to be the same as mentioned horizontal. 5.3 Anchorage L = F s /( πf bu ), for f bu (the ultimate bond strength) obtainable from Table 24 in SABS A 30% reduction in the ultimate bond strength is applicable for members having a depth exceeding 300mm f ctd = 0.87f ctk,0,05, further that ƒ bd = 2.25 η 1 η 2 f ctd, for ƒ bd the ultimate bond strength, and also l b,rqd = (ƒ yk Ø/4.6 ƒ bd ), leading finally to l bd = α 1 α 2 α 3 α 4 α 5 l b,rqd. The factor η 1 = 0.7 (decreasing the ultimate bond strength by 30%) in cases of good bond conditions. This relates to members whose thickness exceeds 250mm 45

47 5.4.1 Direct ultimate anchorage bond strength (f bu vs. f bd ) A comparison was made between the ultimate bond strength values presented by the two standards. The bond strength plays the determining factor in the calculation of anchorage lengths. SANS : Table 5. 3: Ultimate anchorage bond strength according to SABS 0100 (SABS Ed 2.2, 2000) Bar type Ultimate anchorage bond stress f bu Mpa Concrete Grade Plain bar in tension Plain bar in compression Deformed bar in tension Deformed bar in compression EN : Table 5. 4: Ultimate anchorage bond strength according to EN Bar type Ultimate anchorage bond stress f bu Mpa Concrete Grade Plain bar in tension Plain bar in compression Deformed bar in tension Deformed bar in compression These values were obtained by applying the equations as discussed in section 3.3 Anchorage of the research report. The following was assumed to apply: f ctd = α ct f ctk,0,05 /γ m where α ct = 1.0 and γ m = 1.5 Continuing the assumptions to calculate f bd = 2.25 η 1 η 2 f ctd : good bond conditions give: (η 1 = 1.0) re-bar diameter 32 mm gives: (η 2 = 1.0) We can deduce the values as shown in Table 5.5, 5.6 and in Figure

48 Table 5. 6: Calculation values of EN 1992 Table 5. 5: SABS 0100 vs. EN 1992 f ck,cube f ctk,0.05 f ctd SABS EN f ck,cube f bu f ck,cube f bd Figure 5. 2: Ultimate anchorage bond strength comparison The former standards (BS 8007, SANS ) do not specify any values for f bu that are applicable for concrete strengths beyond 40 MPa as shown in Table 5.3. The values for f bu are therefore assumed to stay constant for greater cube strengths. In the remaining parts of the figure (Fig. 5.2) is can be seen that there is a small difference between SANS and EN

49 Annexure D Crack width comparison (Extract WRC Report (Wium, 2007)) C.1.1 Crack width versus service moment Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure C.1 Crack width versus service moment 48

50 Figure C.1 presents an interesting comparison between the design codes and the manner in which the crack width increases with an increased service moment. It is clearly shown that the service moment is directly proportional to the predicted crack width which develops within the concrete. There is a slight difference between the BS 8007:1987 and the Eurocode 2 spreadsheet-values. The values obtained when using Prokon with BS 8007:1987 almost exactly match the values when using the BS 8007-spreadsheet. When using Eurocode 2 in Prokon, the values differ quite a lot from the spreadsheet values as can be seen with the bottom line which lies below the other three sets of values. 49

51 C.2.2 Crack width versus reinforcement area Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure C.2 Crack width versus reinforcement area Figure C.2 shows that the crack width increases dramatically when the reinforcement area dips below the value of 2000 mm 2 /m. There is however little change in the crack widths when increasing the reinforcement area above this value. This also shows that a minimum area of reinforcement of 2000 mm 2 is required to restrict the crack widths to 0.2 mm. 50

52 The values obtained from Prokon correspond almost exactly to the values from the spreadsheet calculations. C.2.3 Crack width versus section thickness Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure C.3 Crack width versus section thickness Figure C.3 shows a great variance in the crack widths calculated by the different design formulae. 51

53 These graphs differ a lot due to the different assumptions made regarding the surface zones of reinforcement. A. BS 8007 specifies the following surface zone depths : For h < 500 mm, assume each reinforcement face controls h/2 depth of concrete. Where h is the total depth of the slab. For h > 500 mm, assume each reinforcement face controls 250 mm depth of concrete, ignoring any central core beyond this surface depth. B. pren specifies : The effective tension area should be taken as having a depth equal to 2.5 times the distance from the tension face of the concrete to the centroid of the reinforcement, although for slabs the depth of this effective area should be limited to (h-x)/3 where x is the depth to the neutral axis. An overall upper limit of h/2 also applies. This means that the surface zone depth is the minimum value of: 2.5 x (h-d) (h-x)/3 h/2 52

54 C.2.4 Crack width versus steel ratio Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure C.4 Crack width versus steel ratio Figure C.4 shows that the values obtained from the two different codes vary considerably at higher steel ratios where the area of steel required exceeds the area of steel provided. 53

55 The Prokon values from the two codes however correspond to their respective values from the spreadsheet. This graph shows that a steel ratio of 0.5 is required to restrict the crack widths to a value of 0.2 mm. 54

56 C.2.5 Crack width versus moment ratio Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure C.1 Crack width versus moment ratio Figure C.5 shows that in the region where the crack width is in the range of mm, the value of all four data ranges corresponds. 55

57 Above the maximum allowable crack width of 0.2 mm the data values become scattered and the Eurocode 2 values moves away from the other three data sets. Following from Figure 11.5 we can see that for this specific section an ultimate moment (M u ) of almost half the moment of resistance (M r ) is required to restrict the crack width to 0.2 mm. 56

58 C.2.6 Crack width versus bar spacing Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure 02 Crack width versus bar spacing From Figure C.6 it is apparent that all four data sets exhibit an almost exponential trend at which the crack width changes relative to the spacing of the reinforcement bars. 57

59 Again, the Eurocode 2 values obtained from Prokon does not match the values of the other three data sets. At a crack width of 0.2 mm the other three data sets lie on the same line. This figure also shows that for this section a maximum bar spacing of 250 mm is allowed to restrict the crack widths to 0.2 mm. 58

60 C.2.7 Crack width versus bar diameter Graphs Variable Service Moment Variable Reinforceme nt Area Variable Section Thickness Variable Steel Ratio Variable Moment Ratio Variable Bar Spacing Variable Bar Diameter Figure C.3 Crack width versus bar diameter For smaller bar diameters Eurocode 2 predicts larger crack widths than calculated with BS The Prokon values almost exactly match the values from the spreadsheets. Following from Figure C.7 it seems that the maximum allowable bar diameter, to restrict crack widths to 0.2 mm, is a 25 mm bar for this specific concrete section. 59

61 Annexure E Crack control (Extract from the final year undergraduate research report by G Kretchmar) Both standards specify calculations for the crack spacing, calculations for the expected crack width, and both have prescribed minimum and maximum allowable limits to the parameters of a crack. The following content details formulas and equations to calculate the spacing of cracks, their maximum widths and also the maximum allowable crack widths. 2.1 Spacing of cracks The spacing of cracks refers to the expected clear distance between two or more cracks on the same element under consideration. SANS : When sufficient reinforcement is provided to distribute cracking, the likely maximum spacing of cracks is given by: s max [eq:2.1] for: s max the maximum spacing of cracks f ct the tensile strength of the concrete f b the average bond strength between concrete and steel the size of each reinforcing bar ρ the steel ratio based on the areas of surface zones The BS 8007:1987 provides additional specifications for square-mesh fabric reinforcement where the cross wires are not smaller than the main bars. EN : In situations where bonded reinforcement is fixed at reasonably close centres within the tension zone, the maximum final crack spacing can be calculated by: s r,max ck 3 + k 1 k 2 k 4 Ø / ρ p,eff [eq:2.2] for: s r,max the maximum spacing of cracks Ø the bar diameter c the concrete cover to the longitudinal reinforcement k 1 a coefficient that takes account of the bond properties of the reinforcement, being 0.8 for high bond bars, and 1.6 for bars with effectively plain surfaces k 2 accounting for the distribution of strain, being 0.5 for bending and 1.0 for pure tension. k 3 and k 4 may be found the in National Annex, recommended values are 3.4 and respectively, where the UK decided to use the recommended values. The Eurocode2 has the following additional special specifications: - For sections where more than one re-bar diameters are used, an Ø eq is calculated, to be used instead of Ø in equation eq2.2, with a given relation accounting for the relative weights that the bar contributes. 60

62 - For cases of eccentric tension in the re-bars k 2 may be calculated by using intermediate values. Additional formulas are given. - Provisions for when the calculated spacing exceeds a value calculated by 5(c+ Ø/2), or when there is no bonded reinforcement within the tension zone another rather simple calculation may be followed. Figure 2.1 (to be followed) might aid for a better understanding - A different formula takes account for where the angle between the axes of principle stresses and the direction of reinforcement, for members reinforced in two orthogonal directions, is significant (>15 ). - A simple factor may be applied for walls subjected to early thermal contraction where the horizontal steel area (A s ) doesn t fulfill earlier requirements and the bottom of the wall being restrained. The Eurocode furthermore provides a useful figure showing the relationship between the crack width w and the relative distance from a bar. (See Figure 2.1) Figure 2. 1: Crack width w at concrete surface relative to distance from a bar (EN , 2004) 2.2 Crack widths In both standards the approximate maximum crack spacing has to be calculated first before calculation of the estimated crack width. 61

63 SANS : For elements subjected to drying shrinkage and thermal contraction, the width of a fully developed crack can be acquired from: w max = s max є for: w max estimated maximum crack width s max maximum crack spacing є effective strain = [є cs + є te (100x10-6 )] where: є cs is the estimated shrinkage strain є te is the estimated total thermal contraction after peak temperature arising from thermal effects [eq:2.3] Provided that the strain in the tension reinforcement is limited to 0.8f y /E s and the stress in the concrete is limited to 0.45f cu, the design surface crack width w may be calculated using: w = [eq:2.4] for: a cr distance from the point being considered to the surface of the nearest longitudinal bar є m average strain at level being considered c min min cover to tension steel h overall depth of member x depth of neutral axis where: є m = є 1 є 2 (Strain at level considered strain due to stiffening effect) and: the stiffening effect may be assessed by a formula that depends on the limiting design surface crack. For w 0.2 mm: є 2 = [eq:2.5] and for w 0.1 mm: є 2 = [eq:2.6] and: Assessing the crack widths caused by direct tension, we use: w = 3a cr є m For a detailed interpretation of the equations, please refer to the respective standard with the aid of the list of Formulas and Equations under References. EN : Similar to the former standards, the Eurocode s calculations rely on the crack spacing initially to be computed. The crack width, w k, may be calculated from: w k = s r,max (ε sm - ε cm ) [eq:2.7] for: s r,max the maximum crack spacing ε sm the mean strain in the reinforcement under the relevant combination of loads, including the effect of imposed deformations and taking into account the effects of tension stiffening. Only the additional tensile strain beyond the state of zero strain of the concrete at the same level is considered is the mean strain in the concrete between cracks ε cm To calculate the factor (ε sm - ε cm ) the following equation is used in the EN :2004: 62

64 [eq:2.8] of which some of the variables are easily obtainable, by either simple constants depending only on the long term or short term loading, whereas others rely on further equations to be followed. The superseding water retaining standard (EN :2005) specifies a number of other overruling equations to be followed in order to calculate the (ε sm - ε cm ) factor. The formulas mainly depend on the type of restraint the member is subjected to. Figure 2. 2: Restraint factors for crack widths (EN , 2005) For the case in (a) in Figure 2.2, (ε sm - ε cm ) = 0.5 α e k c kƒ ct,eff (1+1/(α e ρ))e s [eq:2.9] and for (b), (ε sm - ε cm ) = R ax ε free [eq:2.10] for: R ax the restraint factor (as depicted in Figure L.1 (Annex L in EN :2005)) The EN :2004 has additional specifications to determine the control of cracking without direct calculations (Section in (1)). It provides tables of the maximum bar diameters for crack control and the maximum bar spacing. Modifications to certain exceptions are also possible by applying a formula that accounts for bending and cases in direct tension. 2.2 Crack width limits Both standards specify the maximum allowable surface crack widths in reinforced concrete members. If not complying with the following margins, a different concrete strength or other detailing specifications might have to be considered. SANS : The permissible crack widths should be controlled considering the required tightness and/or aesthetic appearance. The maximum design surface crack widths for direct tension and flexure or restrained temperature and moisture effects according to the BS 8007:1987 are: Severe or very severe exposure: Critical aesthetic appearance: 0.2 mm; 0.1 mm. 63

65 According to SABS , the general allowable width of 0.3 mm should not be exceeded. Where, however, the concrete is exposed to particularly aggressive conditions (see SABS ), the surface width of cracks at points nearest to the main reinforcement are to be limited to times the nominal cover to the main reinforcement. EN : The Eurocode EN :2004 details a number of rather simple general considerations that have to be taken care of. An example might be cracking shall be limited to an extent that will not impair the proper functioning or durability of the structure. The standard recommends using Table 7.1N to obtain values of w max which describes the limits to which the maximum allowable surface crack width is determined. These values range from 0.2 mm to 0.4 mm depending on the type of exposure the element is being subjected to. The British National Annex recommends using a different table (Table NA.4), which differs only slightly, where the range is only between 0.2 mm and 0.3 mm. The superseding water retaining standard EN :2005 classifies the constraints to which surface cracks are limited by the degree of protection against leakage that is prescribed or required by the user. Table 2. 1: Tightness class for crack control (EN , 2005) Tightness Class 0. the provisions in of EN :2004 may be adopted. Tightness Class 1. cracks which can be expected to pass through the full thickness of the section should be limited to w k1 (see equation eq:2.7). The given provisions in of EN :2004 apply in cases where the full thickness of the section is not cracked. Two further conditions that require a more detailed observation are also to be fulfilled. Tightness Class 2. cracks which may be expected to pass through the full thickness of the section should generally be avoided unless appropriate measures have been incorporated. Tightness Class 3. special measures will be required to ensure water tightness. The value w k1 (see equation eq:2.7) depends on a ratio between the hydrostatic pressure (h D ) and the wall thickness (h) of the containing structure. If h D /h 5, w k1 =0.2 mm; h D /h 35, w k1 =0.05 mm; 64

66 For intermediate values between the 5 and 35 ratios, linear interpolation may be used between 0.05 mm and 0.2 mm. 2.3 Summary to cracks The following table provides a summary of the topics and details discussed before. Table 2. 2: Summary to cracks Topic Former Subsequent 2.1 Spacing of cracks: s max = f ct /f b x Ø/2ρ; additional specs s r,max = k 3 c + k 1 k 2 k 4 Ø/ρ p,eff ; where on square mesh fabric reinforcement the k constants account for bond properties, bending/tension strain distributions etc. A number of various additional specs are detailed. 2.2 Crack widths: Thermal & Moisture effects: w max = s max є ; for which є being the effective strain [є cs + є te (100x10-6 )] Flexural effects: Comment: The formulas used in the calculation of crack widths arising from flexure, are rather too complex to be described in this "summary format". It is recommended to see either the standards or the detailed description in the report. w k = s r,max (ε sm - ε cm ) ; of which the (ε sm - ε cm ) part is being calculated using further complicated formulas The formulas used in the calculation of crack widths arising from flexure, are rather too complex to be described in this "summary format". It is recommended to see either the standards or the detailed description in the report. 2.3 Crack width limits Comment: (1) Severe exposure: 0.2mm; (2) Aesthetic appearance: 0.1mm; (3) In general 0.3mm Depends on: (1) the degree of exposure, and (2) the quantity of leakage allowed (prescribed by the user). Values range from 0.05mm to 0.2mm determined by simple applicable ratios. Values depend on many variables. It is advised to see the detailed report section and/or the applicable standards. 65

67 2.4.1 Graphical comparison By observation, the formulas and equations represented in Table 2.2 are relatively dissimilar. The following figure was prepared W le Roux in Figure 2. 3: Relationship of crack width vs. Reinforcement area (le Roux, 2007) Figure 2.3 was prepared comparing BS 8007:1987 and the Eurocode2 to the commercial software package Prokon. Ignoring the Prokon curves it can be seen that there is a good similarity in the curves between the codes. 66

68 Annexure F Experimental measurements of crack width APPARATUS AND PLANNING I(Extract from the final year undergraduate research report by R Vosloo) This chapter presented the planning that took place for the practical experiments, the apparatus used and the setup of the experiments. The following items are addressed Concrete mix Framework design Reinforcement design Apparatus used Apparatus design Experimental setup Experimental arrangement : 9 beam specimens were prepared. Three specimens were cast for each of three reinforcement arrangements : 2-Y10 2-Y12 3-Y12 All the specimens had the same dimensions. Length = 2400 mm Width = 200 mm Height = 150 mm Figure 1 shows the experimental set-up. 67

69 667 mm 2000 mm Figure 4: Experimental arrangement RESULTS AND DISCUSSION The results of the two codes (BS 8007 and EN ) are compared by means of graphs. First, to verify that the spreadsheet calculations are accurate, they are compared with Prokon crack width simulation by means of graphs. SPREADSHEET RESULTS VS. PROKON The previously discussed parameters are incremented into the spreadsheet calculations and Prokon. Different service moments are then inserted into the spreadsheet and Prokon to tabulate the crack results. The tabulated values are then plotted onto specific graphs to compare the results graphically. The parameter that stayed constant during the specific analysis is shown on the top right hand corner of each graph. Both design codes are simulated in Prokon and compared to both spreadsheet design codes. The following four data sets are presented in each of the following figures: BS8007 Data from the spreadsheets when using BS 8007:1987. EC 2 Data from the spreadsheets when using pren Prokon_BS Data from Prokon when using BS 8007:1987. Prokon_EC Data from Prokon when using pren (Eurocode 2). The following three graphs are shown to compare the Prokon crack widths with the spreadsheet crack widths: Figure 5: Crack Width vs. Service Moment Figure 6: Crack Width vs. Moment Ratio Figure 7: Crack Width vs. Reinforcement Area 68

70 Figure 5: Crack Width vs. Service Moment Figure 5 presents the comparison between the crack width and the service moment. The crack width increases linear as the service moment increases. It can be seen that Eurocode 2 predicts a slightly wider crack width under the same service moment than BS 8007:1987 for higher service moments. However, at a very low service moment the BS 8007:1987 predicts a wider crack width than the Eurocode 2. In the design region of 0.2 mm the two codes provide very similar results when performing the hand calculations. 69

71 Figure 6: Crack Width vs. Moment Ratio Figure 6 presents the crack width against the moment ratio. It can be seen that where the crack width is between mm, the results corresponds favourably between the codes. However, for larger moment ratios the values differ increasingly. The Eurocode 2 spreadsheet calculations are very similar to the Prokon simulation. 70

72 Figure 7: Crack Width vs. Reinforcement Area Figure 7 shows that the crack width increases significantly as the reinforcement area decreases from below the value of 600 mm 2. The BS 8007:1987 crack width decreases slower than the Eurocode 2 as the reinforcement area increases. The BS 8007:1987 overlaps at 0.75 mm crack width. The values from the spreadsheet calculations correspond almost exactly with the Prokon values. From these graphs it is reasonable to believe that the spreadsheet calculations are sufficiently accurate to be used in this study. SHREADSHEET RESULTS VS. PRACTICAL RESULTS In this section the practical experiment result are compared with the spreadsheet calculation results to determine which code is more reliable. The example used in this section is the beam with 2-Y10 reinforcement. The practical results are analyzed on Spreadsheet Appendix D (of the Vosloo report). The crack width over the effective area was measured and tabularized as shown on Table 1. The average crack width values are to be compared with the BS 8007:1987 and the Eurocode 2. 71

73 Table 1: Practical Experiment Results (2-Y10) 2-Y10 Crack Number Avarage Appleid Load [KN] Crack Width The experimental results are compared with the Spreadsheet results with the same applied loads. The comparison is shown in Figure 8. As = 2-Y10 Figure 8: Crack Width vs. Applied Moment Figure 8 shows that the practical results mature towards the Eurocode 2 results as the applied force increases. At low loads the crack width is smaller than both design codes, possibly because the crack depth has not fully developed all the way to the reinforcement. This implies that crack width is not fully dependent on the strain in the reinforced steel bars and that the strain of the concrete on the crack position still plays a role on the crack width. The applied force is determined at the instant the crack originates. This is done with the Instron results of applies force vs. vertical displacement as shown on Figure 9. All the beams gave similar results because 72

74 at the instant the crack occurs only the concrete strain has an effect on the crack width. The tabularized results are shown in Appendix A (of the Vosloo report). Figure 9: Applied Force vs. Vertical Displacement The applied force at which the crack would originate was determined by calculating the position where the two linear lines overlap. The average original applied cracking force is 7.08 KN for all 9 specimens. The horizontal sections on the graph illustrate the crack width still being developed after the applied force is paused. Figure 10 presents a three dimensional graph that allows an improved overview of the comparison between the two codes and the practical results. The tabularized form of this graph is in Appendix B (of the Vosloo report). 73

75 Figure 10: Crack Width vs. Area Ratio vs. Moment Ratio The three dimensions shown in Figure 7 are : Ratio of Service Moment/Crack Moment The service moment is calculated with an applied force of 10kN, 15kN and 20kN. The average crack moment is calculated with the crack force that was recorded. Ratio of Area reinforcement/area concrete This dimension is the ratio of the percentage area reinforcement in the concrete area. 74