Exw

The design bending moment about the centroidal axis is expressed as MRd - Nc(h-P2x) + A's as'(-2-d) + Asas(-2-d) . In case both the reinforcing bars are yielded (as a's fyd ), NRd -b-pi-x-fcd - A's'fyd + As'fyd MRd -P1xbfCd( 2-p2x) + (As-A's)fyd(d-d') (6.3) pi and p2 are factors given in Tables 6.i or 6.2. 6.1.3. Design of reinforcing bars in case of bending without axial force and in case of bending with great eccentricity axial force Let's take a transversal section with axis of symmetry y...

En

A.Jx< p (14)(6 for circular rentiers 7 3 6) for 7-wire strands pi fytJdesign value of eel tensi le sir bod is design value of bond strength Not used as a separate parameter in S, 10.2 . bpd -Tpl > pi ctd(0 (6 9-12) where 1.4 for indented or crimped wires 1.2 for 7-wire strands rjpi 1.0 for good bond conditions 0.7 for other cases frjf(r) is design value of tensile strength at release r f 2.1 for indented wires 3.2 for 7-wire strands rfi 1.0 for good bond conditions acc. to 8.4.1 0.7...

Fat

Fatigue failure of the structure or structural members. Serviceability limit states correspond to conditions beyond which specified service requirements for a structure or structural member are no longer met. Exceeding these limits causes limited damage but means that the structures do not meet design requirements functional requirements (not only of the structure, but also of machines and services), comfort of users, appearance (where the term appearance is concerned with high deformation,...

I I I I I

Example of a structure where the magnification factor should be applied to horizontal forces rather than to bending moments. (No deformation is shown in this case, second order effects are instead assumed to be included in the fictitious, magnified horizontal force HEd.) Expressions (5.30) and (H.7) are useful if the global buckling load can be defined without difficulty, like in certain regular structures, see e.g. 5.8.3.3 and H.1. In other cases second order effects may be...

Krq

In chapter 5.8.5 an extended definition of the effective depth d has been introduced, in order to cover cases where there is no unambiguous definition of d see figure 5.34 where is is the radius of gyration of the total reinforcement area Figure 5.34.Effective depth in cross sections with reinforcement distributed in direction of bending In order to reduce the curvature in cases where yielding is not reached in the tensile reinforcement, a factor Kr is introduced (same as K2 in ENV 1992-1-1,...

Ii

Verification of Eg. 11.8 for the shear capacity of members without shear reinforcement with test results According to the level 2 method, a reliable design equation can be derived from test results with the general formulation BRd _ m-br(1 - Br p 5br) (11.9) BRd design value Pbr mean value of tests a,BR sensitivity factor for Br normally taken 0.8 in the case of one dominating parameter p target safety index, taken 3.8 5br coefficient of variation with pbr _ 0.162, aBR _ 0.8 and...

Info

Punching capacities related to resistance of the shear reinforcement (Regan 24 ) The increase of the punching shear capacity by shear reinforcement is limited to a bound. In the version of EC-2 of 1988 the upper bound was formulated as vRd,max 1.4 vRd1, where vRd1 follows from Eq. 6.31b. In a redraft in 1991 this value was increased to 1.6 vRd1. This upper limit will, however, hardly be reached in practical situations, where normal punching shear reinforcement is used. However,...

Dog

Remembering that MEsd As fyd z, with z (d- fc -x), finally As Fc must be equal and contrary to Ft , the resultant of traction of the reinforcement steel As , it can also be determined by - If MEsd is greater than MRd,lim , some reinforcement steel A's in compression is needed. To calculate it, AMEsd MEsd - MRd,lim. from which In such cases AMEsd must be sensibly smaller than MRd,lim , viz. it must not distort the problem. 6.1.4.2 Rectangular diagram of concrete stresses With reference to Fig....

J J

In the following figure the value of kc is plotted against o for a value of fctf of 2.9 Mpa according to both the above formulation and the equation of prEN. Figure 7.3. Value of kc as a function of the axial force Figure 7.3. Value of kc as a function of the axial force In the next figure the minimum reinforcement for a section subject to a compressive force (expressed in terms of a reduced axial force) is shown calculated according to 4 different methods - Compensation of tension block. This...

Sdr

Illustration of load history and deformations Figure 5.20. Illustration of load history and deformations The total deformation under long-term load can also be calculated directly using an equivalent E-modulus3 for the concrete, Ee E< (1+y). This corresponds to line AC in figure 5.20.4 The total deformation under design load can be calculated in a similar way if an effective creep ratio 9ef is used, line AD in figure 5.20. The effective equivalent concrete modulus would then be...

O I

Figure 7.8 Theoretical and actual values of Dmax. Comparison of the 3 models considered 7.3.4 Calculation of crack C7.3.4. Formula for crack width In the above expressions it has been assumed that h - d 0,1h and also that a problem of pure bending is being analysed and therefore, hcr 0.5h, kc 0.4 and k' 1. Furthermore, the tensile strength of concrete has been assumed to be 2.9 N mm2 (2.5 in case of EC2). If different values are assumed for these parameters, then the value obtained from the...

P

Figure 7.1 Minimum reinforcement concept For a rectangular cross section subject to combined bending and axial force, the cracking moment can be determined by After cracking this same bending moment, together with the axial force, must be taken by the cracked cross section 1 fh -- (f + hcr Asosz -NEd -(0,9h -z)) (7.2) The lever arm z, may be taken as a certain fraction a of h (around 0.8h for pure bending). Introducing the following notation

Rc

Measures of design and execution management and quality control are aimed at eliminating failures due to gross errors, and at ensuring that the design resistance is achieved. Design supervision and execution inspection levels are given at Tables 2.7 and 2.8, with reference to each reliability class. Table 2.T. Design supervision levels (DSL) Table (B4)-EN1990 Table 2.T. Design supervision levels (DSL) Table (B4)-EN1990 Minimum recommended requirements for checking of calculations, drawings and...

Section Basis Of Design Section Basis Of Design

Eurccode 2, Section 2, Part 1.1 states that corcrete structures should be designed in accordance with the general rules of EN1990 anc with actions defined in EN 1991. EN 1992 has some addnonal requirements. In particular. the basic requirements nf FN 1990 .Section 2 are deemed to he satisfied for fill concrete stiuctures if limit state design s carried out with the partial factor method in accordance with EN 1990. and If actions are defined In accordance with EN 1991. and If combinations of...

Section Durability And Section Durability And Concrete Cover Cover To Reinforcement

C4 The rules on design for durability in EC2 are substantially different than in the past. Previously the concrete cover was prescribed in dependence of the environmental class, but independent of the concrete quality. In the actual version of EC2 (EN 1992-1-1) the cover required depends not only on the environmental class, but as well on the concrete strength class, the required design working life and the quality control applied. In the following, background information is given with regard...

Section Materials

Section 3 of Eurocode 2, dedicated to materials, is structured in the following paragraphs 3.2 - Reinforcing steel. Annex C-EC2 is related to this paragraph This section deals with normal weight concrete, viz. according to EN 206-1 having density greater than 2000 but not exceeding 2600 kg m3. Light-weight concrete is dealt with in Sect.11-EC2. Compressive strength is defined in 3.1.2(1 )P-EC2 , in accordance with EN 206-1, by the characteristic value fck (5 fractile of distribution) obtained...

Section Structural Analysis

STRUCTURAL ANALYSIS C5.1 General Structural analysis is the process of determination of the effects of actions (forces, impressed strain) in terms of tensional states or strain on a geometrically and mechanically defined structure. The analysis implies a preliminary idealisation of the structure, based on more or less refined assumptions of behaviour. There are four types of idealisations - linear elastic behaviour that assumes, for analysis, uncracked cross sections and perfect...

Szn

Experimental results of shear tests on prestressed beams with shear reinforcement, in comparison with the calculated results according to the variable strut inclination method, with extension according to Eq. 6.29 6.2.3.3. Members reinforced in shear with loads near to supports Similar to members without shear reinforcement, in members with shear reinforcement the load bearing capacity is increased for loads near to supports. In the Standard Method, as formulated in ENV 1992-1-1...

Wk srm em scm

Asr is the stress calculated for the fully cracked cross section for the cracking moment. asr may be calculated by a _ fct,effActkck _ fct,effkck hcr (724) sr_ As ps,eff 2,5k'(h-d) 1 ' Introducing the expression of asr into equation (7.23), and rearranging In order to obtain numerical values from this expression, it is necessary to assume values for those coefficients which are not considered as variables in table 7.2. The following values have been assumed to derive table 7.2 k _ 1,0 h < 0,3...

S

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...

L L

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 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...

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...

Fdb

Pile Axial Force Bending Moment Diagram

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...

Euro Code Slenderness Moment Magnification

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...

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...

Creep Coefficient Eurocode

Stress Strain Relation For Concrete

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...

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...