Commentary Eurocode
Copyright European Concrete Platform ASBL, June 2008 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the European Concrete Platform ASBL. Published by the European Concrete Platform ASBL Editor Jean-Pierre Jacobs All information in this document is deemed to be accurate by the European Concrete Platform...
Info Iba
0 0.5 10 IS 2.0 2.5 3.0 3.5 4 0 EcPUJ 0 0.5 10 IS 2.0 2.5 3.0 3.5 4 0 EcPUJ Figure 3.12. Comparison of basic and approximate design curves In clause 3.1.6 4 of EC2 as well the possibility is offered to work with a rectangular stress distribution, see fig. 12. This requires the introduction of a factor A for the depth of the compression zone and a factor n for the design strength, see Fig. 3.13. Figure 3.13. Rectangular stress distribution Figure 3.13. Rectangular stress distribution As a basis...
Info Imp
Fig.3.11. Design stress-strain curves with bilinear formation Fig. 3.12 shows the comparison for the basic design stress - strain relations derived from the mean curve by taking the characteristic value and dividing it by yc 1.5 and the simplified design curves, Nilson, A., High Strength Concrete- An Overview of Concrete Research, Proceedings of the Conference Utilisation of High Strength Concrete, Stavanger 1987. Walraven, J.C., High Performance Concrete Bridges, a European Perspective,...
Cc Gsh
Low consequence for loss of human life economic, social or environmental consequences small or negligible Agricultural buildings where people do not normally enter e.g. storage buildings , greenhouses Classes CC1 and CC2 correspond to importance classes I, II, whereas CC3 corresponds to classes III and IV, as from EN1998.1, Table 4.3. From this table it is apparent that it is the importance of the structure concerned which is the criterion for classification. Three reliability classes RC1, RC2,...
S Gxx
e02 the greater of the two first order eccentricities fo h slenderness corresponding to the limit for 10 moment increase at y 0 n relative normal force N Actcd nu0 load capacity for the current slenderness and y 0 yet effective creep ratio y- nL a here y 3 has been assumed nu1 load capacity including the effect of creep according to 1- step method nu2 load capacity including the effect of creep according to 2- step method The agreement between the 1-step and 2-steps methods is in most cases...
Info Url 1
Figure 6.36. Combination of truss and strut and tie Measurements on shear reinforcement showed that the stirrups just adjacent to the load- and support area do not reach the yield stress, Asin, 2000 . Therefore the shear reinforcement is considered to be effective only within the central 0,75 area between load and support. C6.4. Basic equation for symmetrical punching at interior columns 6.4.1. Punching shear capacity of non-prestressed slabs without punching reinforcement In ENV 1992-1-1 a...
Info Ltn
k same definition as for isolated members, see 3.2 L EI v ' 6 rotation for bending moment M compare figure 5.13 The factor S1 is an approximation, which has been derived by calibration against accurate numerical calculation for different numbers of storeys, see figure 5.18. The product S0S1 corresponds to S in expression H.2 in EN annex H. Figure 5.18. Effect of flexibility of end restraint for bracing units. Solid curves represent the exact solution, dashed curve the approximation according to...
Info Mkd
O beams without stirrups beams with stirrups Aiwfuw bs 0.58 MPa Figure 6.16. Results of tests on beams subjected to axial tension, bending and shear, and failing For similar arguments, reference is made to Bhide and Collins, 1989 In special cases, like for instance when pretensioned strands are used in members with reduced web widths, such as in prestressed hollow core slabs, shear tension failures can occur, Fig. 6.17. In this case failure occurs due to the fact that the principal tensile...
Info Seo
Fig 6.40. Verification of Eq. 6 with test results Fig 6.40. Verification of Eq. 6 with test results 6.4.2.3 Punching shear resistance of labs with punching shear reinforcement In ENV 1992-1-1, Eq. 6.34, it was assumed that the contribution of punching shear reinforcement to the total shear capacity can be accounted for by Adding this contribution to the punching shear capacity of a similar slab without shear capacity, according to Eq, 6.31, would gives the total punching shear resistance. A...
M Rqs
Figure 6.43. Approximate values for eccentricity factor in new draft Complementary to this simplified approach the more accurate method, given in MC'90 has been adopted in prENV 1992-1-1 2001. This method takes the effect of an unbalanced moment into account with the formulation where W1 is a function of the control perimeter u1 W J le The property W1 corresponds to a type of plastic distribution of the shear stresses as illustrated in Fig. 6.44. An analysis by Mast 34,35 on the basis of an...
L L 1
Mi, Mi restraining moments in members 1, 2 , see Figure 5.15 Ma restraining moment in the adjacent column, see Figure 5.15, calculated without taking into account the axial force Na a Na Nea Na axial force on the adjacent column Nea buckling load of the adjacent column can be estimated approximately, e.g. taking into account only the horizontal members adjacent to its nodes 5.8.3.3 Global second order effects in buildings Figure 5.15. Illustration of node with adjacent members. Figure 5.15....
Section Detailing Of Reinforcement And Prestressing Tendons General
8.2 Spacing of 8.3 Permissible mandrel diameters for bent 8.4 Anchorage of longitudinal 8.5 Anchorage of links and shear 8.6 Anchorage by welded 8.7 Laps and mechanical 8.8 Additional rules for large diameter 8.9 Bundled 8.10 Prestressing
Section Lightweight Concrete
11.1 11.3 SECTION 1 SYMBOLS SECTION 1. SYMBOLS For the purposes of this document, the following symbols apply. Note the notation used is based on ISO 3898 1987 Ac Cross sectional area of concrete Ap Area of a prestressing tendon or tendons As Cross sectional area of reinforcement As,min minimum cross sectional area of reinforcement Asw Cross sectional area of shear reinforcement Ec, Ec 28 Tangent modulus of elasticity of normal weight concrete at a stress of Oc 0 Ec,eff Effective modulus of...
A Ofp
0 0.5 1.0 1-5 2.0 2.5 3.0 C d o 0.5 1.0 1.5 Figure 6.47. Shear capacity of column bases 0 0.5 1.0 1-5 2.0 2.5 3.0 C d o 0.5 1.0 1.5 Figure 6.47. Shear capacity of column bases 6.5 Design with strut and tie models See example n. 6.15 No comments No comments Aparicio,A., Calavera, J., del Pozo, F.J., 2000 Testing strut compression shear failure in beams, Polytechnic University of Barcelona. Asin, M. 2000 , The behaviour of reinforced concrete deep beams, PhD-Thesis, Delft University of...
Info Xle 1
Figure 6.13. Shear strength of non-prestressed members without shear reinforcement, comparison of test results with Eq. Figure 6.13. Shear strength of non-prestressed members without shear reinforcement, comparison of test results with Eq. It was however argued, that the equation has two disadvantages the first is that it does not distinguish between persistent amp transient loading combinations and accidental loading combinations, for which different safety levels apply prEN 19921-1 2001...
V Fdb
Once determined x e as, the moment resistance results MRd - A'sfyd h-d' Asas -2-d P1xbfcd 2-P2x d In the fourth field NRd3 NEd NRd4 the moment resistance can be determined, with a good approximation, by the relation of proportionality indicated in fig. 6.8, which shows the final end of the interaction diagram M-N. Figure 6.8. Terminal end of the interaction diagram M-N The moment resistance reaches a maximum for x x2 where the analytic function that expresses it has an edge point due to the...
A
X Gk,j P VuQk,1 X V2,iQk,i Qfat where Qfat is the relevant fatigue load e.g. traffic load or other cyclic load . 2.6.1 Combinations of actions for the ultimate limit states verification of a building EN1990 Annex A1 gives rules for combinations of actions for buildings, on the basis of symbolic expressions and recommended values or of values given in the National Annex of partial factors to be applied to actions in the combinations. Eurocodes allow combinations of actions to contain two or more...
Info Fzz
0 65 0 75 0.85 0.9s 1.05 1.15 125 135 1.45 Figure 6.39. Frequencies of relative punching shear carrying capacity Assuming a normal distribution, a mean value of 0.191 is obtained with a standard deviation of 5 0.0247, and a coefficient of variation v 0.13. Strictly speaking this would mean a characteristic lower bound value of 0.191 - 0.164 0.0247 0.15. assuming a safety factor of 1.5 this would result in a coefficient of 0.10 in stead of 0.12 in the equation of the design punching shear stress...
Cem I
However when using a CEM III B type of cement, see Figure 4.3b , the reliability index is reduced by 50 and is far below the reliability index proposed for this environmental class. An additional reduction of the concrete cover means a further reduction of the reliability index. The considerable difference in reliability index as a consequence of using two types of cements shows that the currently existing requirements for the determination of the concrete cover do not include all important...
Info Aqw
-A bd 0.5 total deflection -A bd 0.5 active deflection A bd 1.5 total deflection A bd 1.5 active deflection Figure 7.21. Influence of relative humidity on Slenderness Limits for Total and Active Deflections referred to 70 RH From Fig. 7.21 it can be seen that the influence of relative humidity on the slenderness ratio is important with a variation of 15 for the active deflection and 10 for total deflection from the reference value of 70 of relative humidity. The figure also shows that the...
Info Kgw
Figure 5.22. Effective creep ratio as a function of ratio Ml Md for a cracked rectangular cross section with tensile reinforcement only, based on d 0,9h and a 6. Basic creep coefficient 9 3 Figure 5.22. Effective creep ratio as a function of ratio Ml Md for a cracked rectangular cross section with tensile reinforcement only, based on d 0,9h and a 6. Basic creep coefficient 9 3 In this case the curves will approach the straight line according to expression 5.19 the higher the reinforcement ratio...
Z Ei
0 coefficient depending on number of storeys, distribution of vertical load etc. LEI total bending stiffness of bracing members to account for cracking in a simplified way LEI is based on 0,4-EcdIc and for uncracked section 0,8 may be used instead of 0,4 L total height Note Fv,bb is a nominal buckling load, calculated for a secant stiffness representing the relevant ULS conditions including lateral loading . It is not a load for which pure buckling without eccentricities or lateral loading...
Section Lightweight Concrete 1
SECTION 11 LIGHTWEIGHT CONCRETE C11.1 General A favourable circumstance for the preparation of Chapter 11 was that during the last years substantial work was conducted in updating the state-on-the-art on lightweight aggregate concrete to the most actual level. In this respect the joint CEB FIP now fib Task Group 8.1 published in 1999 fib Bulletin 4 Lightweight Aggregate Concrete Codes and Standards, a State-of-the-Art Report giving a good overview of common practice with regard to design...
Info Jmz
C7.4 Discussion of the general method followed for deflection calculation 7.4.2 Cases where calculations may be omitted 7.4.3 Checking deflections by calculation Instantaneous deflections are computed by applying the total load on a structure in which there is a reduction of the stiffness. The law to calculate the reduction of stiffness is deduced from equation 7.8 of prEN 1992-1 1 if 1- i M 1-o M- 7.61 From this equation, the following relationship is obtained
Foreward
The introduction of Eurocodes is a challenge and opportunity for the European cement and concrete industry. These design codes, considered to be the most advanced in the world, will lead to a common understanding of the design principles for concrete structures for owners, operators and users, design engineers, contractors and the manufacturers of concrete products. The advantages of unified codes include the preparation of common design aids and software and the establishment of a common...
Literature
Aitcin, P., Demystifying Autogenous Shrinkage, Concrete International, 1999, pp. 54-56. CEB-Bulletin 228, High Performance Concrete Recommended Extensions to Model Code 90, Report on the CEB-FIP Working Group on High Strength Concrete, July 1995. ENV 197-1 Cement - composition, specifications and conformity criteria - Part 1 Common cements, 1992 fib, Structural Concrete Text Book on Behaviour, Design and Performance, Upgraded Knowledge of the CEB FIP Model Code Han, N., Time dependant behaviour...
Info Hke
Figure 3.5. Stress-strain relations for several time durations of axial compressive loads Rusch, 1960 As can be seen, the longer the loading time, the more the ultimate strength approaches the long-term value 80 . The tests carried out by Rusch were limited to concrete's with a maximum cube strength of about 60Mpa. Tests by Walraven and Han on concrete's with cube strength's up to 100 Mpa showed that the sustained loading behaviour for high strength concrete is similar to that of conventional...
Info Ifc
strength at time of loading N mm2 Figure 11.2. Final specific creep as a function of strength at the age of loading 7 For normal strength concrete the shrinkage is formulated as where Scs final shrinkage strain Scd drying shrinkage strain Sca autogenous shrinkage The component Scd, representing the drying shrinkage strain, is known to be higher for lightweight concrete. In 8 it is reported that the final shrinkage of LWAC is about 1-1.5 times the final shrinkage of NDC of the same strength....
t t y
where t0 is the creep coefficient related to Ec , the tangent modulus, which may be taken as 1,05 Ecm as from Table 3.1-EC2 . Annex B of the Eurocode gives detailed information on the development of creep with time. Where great accuracy is not required, the value found from Figure 3.1 may be considered as the creep coefficient, provided that the concrete is not subjected to a compressive stress greater than 0,45fck tc at an age to. The values given in Figure 3.1 are valid for ambient...
Info Qku
Clause 3.1.4-EC2 is about creep and shrinkage. These two phenomena are typical of concrete. The first relates to the increase in the deformation with time in presence of permanent actions, the second is a spontaneous variation of volume. The development of both phenomena depends on the ambient humidity, the dimensions of the element and the composition of the concrete. Creep is also influenced by the maturity of the concrete when the load is first applied and depends on the duration and...
Info Eea
Figure A2-2. Example of interaction curves. fck 40, co 0,2, ef 2. general method - stiffness method, expressions 5.22 - 5.24 curvature method, expressions 5.31 - 5,36 upper curve, Ky 1 --------- curvature method, expressions 5.31 - 5.37 lower curve, according to 5.43 For 105 and 140, 5.43 gi gt es K0 1, therefore there is only one curve in these cases. 1 Westerberg, B Design Methods for Slender Concrete Columns. Tyrens Technical Report 1997 1. Stockholm, September 1997. 2 FIP Recommendations,...
N
where see figure 5.28 M total moment Mo first order moment M2 second order moment N axial force y deflection corresponding to 1 r 1 r curvature corresponding to y l length c factor for curvature distribution Figure 5.28. Illustration of deformations and moments in a pin-ended column. In the figure, first order moment is exemplified as the effect of a transverse load. First order moment could also be given by eccentricity of the axial load. The difference between the two methods lies in the...
Prof J.hellesland Slenderness
9ef effective creep ratio see 5.8.4 if ef is not known, A 0,7 may be used ro As yd Acfcd mechanical reinforcement ratio if ro is not known, B 1,2 n may be used As total area of longitudinal reinforcement n A Ed Acfcd relative normal force M01, M02 first order end moments, M02 gt M01 2 If the end moments M01 and M02 give tension on the same side, rm should be taken positive i.e. C lt 1,7 , otherwise negative i.e. C gt 1,7 . In the following cases, rm should be taken as 1,0 i.e. C 0,7 - for...
Info Vol
Figure 3.17. Calculated values for and A for a rectangular and triangular cross-section, in comparison with the design The flexural tensile strength is larger than the concentric tensile strength. This is caused by strain softening at cracking concrete. The size effect of concrete in bending is therefore the same as for concrete subjected to shear or punching see f.i. Walraven, 1995 , so that the size factor k 1 may be expected to apply for the relation between flexural tensile strength and...