REINFORCED CONCRETE DESIGN TO EC2
REINFORCEDCONCRETEDESIGN TO EC2FORMULAE AND DESIGN RULESFOR TEST AND FINAL EXAMINATION4th. Edition January 2014
CONTENTSPage1.0STRENGTH AND CHARACTERISTIC OF CONCRETE- Table 3.1: Strength and deformation characteristics for concrete(Ref. Section 3: MS EN 1992-1-1: 2010)- Table F.1: Recommended limiting values for composition and properties of concrete(Ref. Section 3: EN 206-1: 2000)12.0INDICATIVE DESIGN WORKING LIFE(Ref. Section 2.3: MS EN 1990: 2010)- Table 2.1: Indicative design working life33.0EFFECTIVE WIDTH OF FLANGES (ALL LIMIT STATES)(Ref. Section 5.3.2: MS EN 1992-1-1: 2010)- Figure 5.2: Definition of lo for calculation of effective flanged width- Figure 5.3: Effective flanged width parameters34.0DURABILITY, FIRE AND BOND REQUIREMENTS(Ref. Section 4: MS EN 1992-1-1: 2010)- Exposure Class- Table 4.1: Exposure class related to environmental conditions in accordance with EN 206-1(Ref. MS EN 1992-1-1: 2010)- Concrete Cover- Minimum Cover for Bond- Table 4.2: Minimum cover, cmin,b requirements regard to bond(Ref. MS EN 1992-1-1: 2010)- Minimum Cover for Durability- Table 4.4N: Minimum cover, cmin, dur requirements with regards to durability forreinforcement steel in accordance with EN 10080 (Ref. MS EN 1992-1-1: 2010)- Table 4.5N: Minimum cover, cmin, dur requirements with regards to durability forprestressing steel (Ref. MS EN 1992-1-1: 2010)- Table 4.3N: Recommended structural classification (Ref. MS EN 1992-1-1: 2010)- Minimum Cover for Fire (Ref. MS EN 1992-1-2: 2004)- Table 5.5: Minimum dimensions and axis distances for simply supported beamsmade with reinforced and prestressed concrete- Table 5.6: Minimum dimensions and axis distances for continuous beams madewith reinforced and prestressed concrete.- Table 5.8: Minimum dimensions and axis distances for simply supported one-wayand two-way solid slabs- Table 5.2a: Minimum column dimensions and axis distances for columns withrectangular or circular section45.0EFFECTIVE SPAN OF BEAMS AND SLABS IN BUILDING(Ref. Section 5.3.2.2: MS EN 1992-1-1: 2010)- Figure 5.4: Effective span, leff for different support conditions96.0DESIGN FOR FLEXURE(Ref. Section 6.1: MS EN 1992-1-1: 2010)- Design Procedure for Rectangular Section- Design Procedure for Flanged Section- Minimum and Maximum Area of Reinforcement (Ref. Section 9.2: MS EN 1992-1-1: 2010)107.0DESIGN FOR SHEAR(Ref. Section 6.2: MS EN 1992-1-1: 2010)- Members Requiring Design Shear Reinforcement- Procedure for Calculating Transverse Shear Reinforcement in Flanged Section- Minimum Area of Reinforcement in the Flange- Sections Not Requiring Design Shear Reinforcement12
8.0DEFLECTION14(Ref. Section 7.4: MS EN 1992-1-1: 2010)- Table 7.4N: Basic span/effective depth ratio(Typical values for rectangular section for steel grade fyk 500 N/mm2 and concrete class C30/35)9.0CRACKING(Ref. Section 7.3: MS EN 1992-1-1: 2010)- Table 7.1N: Recommended values of wmax (mm)- Minimum Reinforcement Area- Control of Cracking without Direct Calculation- Table 7.2N: Maximum bar spacing for crack control- Table 7.3N: Maximum bar diameters for crack control1510.0MOMENT AND SHEAR COEFFICIENT FOR CONTINUOUS BEAM- Table 3.5: Moments and shear coefficients of continuous beam (Ref. BS 8110: Part 1: 1997)1711.0SIMPLIFIED CURTAILMENT RULES FOR BEAM- Figure 1: Simplified detailing rules for beams1712.0MOMENT AND SHEAR COEFFICIENT FOR SOLID SLAB- Continuous One-way Slab- Table 3.12: Ultimate moment and shear coefficients in continuous one way slab(Ref. BS 8110: Part 1: 1997)- Two-way Simply Supported Slab- Table 3.13: Bending moment coefficient for simply supported two-way slab(Ref. BS 8110: Part 1: 1997)- Two-way Restrained Slab- Table 3.14: Bending moment coefficients for two-way restrained slab(Ref. BS 8110: Part 1: 1997)- Shear Force for Two-way Restrained Slab and Actions on Supporting Beams- Table 3.15: Shear force coefficients for restrained two-way slab (Ref. BS 8110: Part 1: 1997)1813.0CRACKING RULES FOR SLAB(Ref. Section 9.3: MS EN 1992-1-1: 2010)2114.0SIMPLIFIED CURTAILMENT RULES FOR SLAB(Ref. “How to design concrete structures using Eurocode 2”, The Concrete Centre, 2010)- Figure 2: Simplified detailing rules for slabs2115.0PRESTRESSED MEMBERS AND STRUCTURES- Limitation of Concrete Stress (Ref. Section 5.10.2.2: MS EN 1992-1-1: 2010)- Table 1: Limitation of Concrete Stress2216.0DESIGN OF COLUMNS- Slenderness ratio (Ref. Section 5.8.3.2 MS EN 1992:2010)- Slenderness Limit (Ref. Section 5.8.3.1 MS EN 1992:2010)- Longitudinal Reinforcement (Ref. Section 9.5.2 MS EN 1992:2010)- Transverse Reinforcement (Ref. Section 9.5.3 MS EN 1992:2010)- Design Moments (Ref. Section 5.8.7 MS EN 1992:2010)- Biaxial Bending (Ref. Section 5.8.9 MS EN 1992:2010)- Column design chart2317.0FRAME ANALYSIS- Method of Analysis (Ref. Section 5.1 MS EN 1992:2010)- Load Cases and Combination (Ref. Section 5.1.3 MS EN 1992:2010)- Analysis of Frame for Lateral Loads- Calculation of Wind Load29
18.0DESIGN OF FOUNDATIONS- Design of pad footing- Cracking and detailing requirements- Design of Pile Foundation3119.0DESIGN OF RETAINING WALLS- Table 1: Partial safety factor at the ultimate limit state- Stabililty analysis- Element design and detailing3620.0BAR AREAS- Table A: Sectional areas of groups of bars (mm )- Standard fabric382
15201.61.12.0271.8fck,cube(MPa)fcm (MPa)fctm (MPa)fctk,0.05(MPa)fctk,0.95(MPa)Ecm (GPa) c1 ( cu1 ( c2 ( cu2 (3.5 cu3 ()1.75)3.52.03.52.2333.82.02.9383730 2.1313.31.82.6333025 c3 2fck 64.92.73.85355452.45375.32.94.1586050Strength classes for 0( )( )See Figure 3.4for fck 50 MPaSee Figure 3.4for fck 50 MPafor fck 50 MPaSee Figure 3.2for fck 50 MPa( )See Figure 3.2for fck 50 MPa( )See Figure 3.2for fck 50 MPa( )( ))])See Figure 3.2[((2.8Analytical relation /Explanation1.0STRENGTH AND CHARACTERISTIC OF CONCRETETable 3.1: Strength and deformation characteristics for concrete (Ref. Section 3: MS EN 1992-1-1: 2010)
2Table F.1: Recommended limiting values for composition and properties of concrete(Ref. Section 3: EN 206-1: 2000)2
32.0INDICATIVE DESIGN WORKING LIFE(Ref. Section 2.3: MS EN 1990: 2010)Table 2.1: Indicative design working lifeDesign workinglife category12345(1)(1)3.0Indicative designworking life (years)1010 to 2515 to 3050100ExamplesTemporary structures (1)Replaceable structural parts, e.g. gantry girders, bearingsAgricultural and similar structuresBuilding structures and other common structuresMonumental building structures, bridges, and other civil engineeringstructuresStructures or parts of structure that can be dismantled with a view to being re-used should not beconsidered as temporaryEFFECTIVE WIDTH OF FLANGES (ALL LIMIT STATES)(Ref. Section 5.3.2: MS EN 1992-1-1: 2010)The effective flanged width, beff for a T-beam or L-beam may be derived as wherebeff, i 0.2bi 0.1lo 0.2loandbeff, i bilo is the distance between point of zero moment can be obtained from Figure 5.2. Other notations are given in Figure5.3.Figure 5.2: Definition of lo for calculation of effective flanged widthFigure 5.3: Effective flanged width parameters3
44.0DURABILITY, FIRE AND BOND REQUIREMENTS(Ref. Section 4: MS EN 1992-1-1: 2010)Exposure ClassTable 4.1: Exposure class related to environmental conditions in accordance with EN 206-1(Ref. MS EN 1992-1-1: 2010)ClassInformative examples where exposure classes mayDescription of the environmentdesignationoccur1No risk of corrosion attackXC0For concrete without reinforcement orConcrete inside buildings with very low air humidityembedded metal: all exposure except wherethere is freeze/thaw, abrasion or chemicalattackFor concrete with reinforcement orembedded metal: very dry2Corrosion induced by carbonationXC1Dry or permanently wetConcrete inside building with low air humidityConcrete permanently submerged in waterXC2Wet, rarely dryConcrete surfaces subject to long-term water contactMany foundationsXC3Moderate humidityConcrete inside buildings with moderate or high airhumidityExternal concrete sheltered from rainXC4Cyclic wet and dryConcrete surfaces subject to water contact, not withinthe exposure class XC23Corrosion induced by chloridesXD1Moderate humidityConcrete surfaces exposed to airborne chloridesXD2Wet, rarely drySwimming poolsConcrete components exposed to industrial waterscontaining chloridesXD3Cyclic wet and dryParts of bridges exposed to spray containingchloridesPavementsCar park slabs4Corrosion induced by chlorides from sea waterXS1Exposed to airborne salt but not in direct Structures near to or on the coastcontact to sea waterXS2Permanently submergedParts of marine structuresXS3Tidal, splash and spray zonesParts of marine structures5Freeze/Thaw attackXF1Moderate water saturation, without de-icingVertical concrete surfaces exposed to rain andagentfreezingXF2Moderate water saturation, with de-icingVertical concrete surfaces of road structures exposedagentto freezing and air-borne de-icing agentsXF3High water saturation, without de-icingHorizontal concrete surfaces exposed to rain andagentsfreezingXF4High water saturation, with de-icing agentsRoad and bridge decks exposed to de-icing agentsor sea waterConcrete surfaces exposed to direct spray containingde-icing agents and freezingSplash zone of marine structures exposed to freezing6Chemical attackXA1Slightly aggressive chemical environmentNatural soils and ground wateraccording to EN 206-1, Table 2XA2Moderately aggressive chemicalNatural soils and ground waterenvironment according to EN 206-1, Table 2XA3Highly aggressive chemical environmentNatural soils and ground wateraccording to EN 206-1, Table 24
5Concrete CoverThe nominal cover is given as:cnom cmin cdevwhere cdev is an allowance which should be made in the design for deviation from the minimum cover. It shouldbe taken as 10 mm. It is permitted to reduce to 5 mm if the fabrication subjected to a quality assurancesystemcmin is the minimum cover sets to satisfy the requirements for safe transmission of bond forces, durabilityand fire resistanceMinimum Cover for BondTable 4.2: Minimum cover, cmin, b requirements regard to bond (Ref. MS EN 1992-1-1: 2010)Arrangement of barsSeparatedBundledBond RequirementMinimum cover, cmin, b*Diameter of barEquivalent diameter 55 mmwhere nb is the number of bars in the bundle, which is limited tonb 4 for vertical bars in compressionnb 3 for all other cases* If the nominal maximum aggregate size is greater than 32 mm, cmin, b should be increased by 5 mmMinimum Cover for DurabilityTable 4.4N: Minimum cover, cmin, dur requirements with regards to durability for reinforcement steel in accordancewith EN 10080 (Ref. MS EN 1992-1-1: 01010152025Exposure Class according to Table 4.1 EC 53035403035404535404550XD3/XS3303540455055Table 4.5N: Minimum cover, cmin, dur requirements with regards to durability for prestressing steel(Ref. MS EN 1992-1-1: 51520253035Exposure Class according to Table 4.1 EC 54045504045505545505560XD3/XS34045505560655
6The minimum cover values for reinforcement and prestressing tendons in normal weight concrete taking account ofthe exposure classes and the structural classes is given by cmin,dur.Note: Structural classification and values of cmin,dur for use in a Country may be found in its National Annex. The recommendedStructural Class (design working life of 50 years) is S4 for the indicative concrete strengths given in Annex E and therecommended modifications to the structural class is given in Table 4.3N. The recommended minimum Structural Class is S1.Table 4.3N: Recommended structural classification (Ref. MS EN 1992-1-1: 2010)X0Increaseclass by 2XC1Increaseclass by 2Structural ClassExposure Class according to Table reaseclass by 2class by 2class by 2class by 2 C30/37Reduceclass by 1Reduceclass by 1 C30/37Reduceclass by 1Reduceclass by 1 C35/45Reduceclass by 1Reduceclass by 1 C40/50Reduceclass by 1Reduceclass by 1 C40/50Reduceclass by 1Reduceclass by 1 C40/50Reduceclass by 1Reduceclass by 1 C45/55Reduce classby 1Reduce classby 1Reduceclass by 1Reduceclass by 1Reduceclass by 1Reduceclass by 1Reduceclass by 1Reduceclass by 1Reduce classby 1CriterionDesignWorkingLife of 100yearsStrengthClass (1) (2)Memberwith SlabGeometryXD3/XS2/XS3Increase classby 2(position ofreinforcementnot affected byconstructionprocess)SpecialQualityControl ofthe ConcreteProductionEnsuredNotes to Table 4.3N:1. The strength class and w/c ratio are considered to be related values. A special composition (type of cement,w/c value, fine fillers) with the intent to produce low permeability may be considered.2. The limit may be reduced by one strength class if air entrainment of more than 4% is applied.Minimum Cover for Fire (Ref. MS EN 1992-1-2: 2004)Rather than giving a minimum cover, the tubular method based on nominal axis distance is used. This is the distancefrom the centre of the main reinforcement bar to the top or bottom surface of the member. The designer shouldensure that:where the nominal axis distance, a is illustrated in Figure 5.2. The permissible combinations of member dimensionand axis distance are given in Table 5.5 and 5.6 for beams and Table 5.8 for slabs.Figure 5.2: Section through structural members, showing nominal axis distance a6
7Table 5.5: Minimum dimensions and axis distances for simply supported beams made with reinforced andprestressed concrete (Ref. Table 5.5 EN 1992-1-2)StandardFireResistanceMinimum Dimensions (mm)Possible combinations of a and bmin where aWeb thickness, bw (mm)is the average axis distance and bmin in theClass WA Class WB Class WCwidth of beam (mm)12345678R 30 bmin 80120160200808080a 252015*15*R 60 bmin 12016020030010080100a 40353025R 90 bmin 150200300400110100100a 55454035Rbmin 200240300500130120120120 a 65605550Rbmin 240300400600150150140180 a 80706560Rbmin 280350500700170170160240 a 90807570asd a 10 mm (see note below)For prestressed beams the increase of axis distance according to 5.2(5) should be noted.asd is the distance to the side of beam for the corner bars (or tendon or wire) of beams with only one layerof reinforcement. For values of bmin greater than that given in Column 4 no increase of asd is required* Normally the cover required by EN 1992-1-1 will controlTable 5.6: Minimum dimensions and axis distances for continuous beams made with reinforced and prestressedconcrete (Ref. Table 5.6 EN 1992-1-2)Standard FireResistanceMinimum Dimensions (mm)Possible combinations of a and bmin whereWeb thickness, bw (mm)a is the average axis distance and bmin inClass WA Class WB Class WCthe width of beam (mm)12345678R 30 bmin 80160808080a 15*12*R 60 bmin 12020010080100a 2512*R 90 bmin 150250110100100a 3525Rbmin 200300450500130120120120 a 45353530Rbmin 240400550600150150140180 a 60505040Rbmin 280500650700170170160240 a 75606050asd a 10 mm (see note below)For prestressed beams the increase of axis distance according to 5.2(5) should be noted.asd is the distance to the side of beam for the corner bars (or tendon or wire) of beams with only one layerof reinforcement. For values of bmin greater than that given in Column 3 no increase of asd is required* Normally the cover required by EN 1992-1-1 will control7
8Table 5.8: Minimum dimensions and axis distances for simply supported one-way and two-way solid slabs(Ref. Table 5.8 EN 1992-1-2)StandardFireResistanceMinimum Dimensions (mm)SlabOne-wayTwo-way spanningthickness, hsspanning(mm)12345REI 306010*10*10*REI 60802010*15*REI 901003015*20REI 120120402025REI 180150553040REI 240175654050lx and ly are shorter and longer span of the two-way slab For prestressed slabs the increase of axis distance according to 5.2(5) should be notedThe axis distance a in Column 4 and 5 for two-way slabs relate to slabs supported at all fouredges. Otherwise, they should be treated as one-way spanning slab.* Normally the cover required by EN 1992-1-1 will controlTable 5.5: Minimum dimension and axis distance of columns with rectangular or circular section(Ref. Table 5.2a EN 1992-1-2)Minimum dimensions (mm)Column width bmin/axis distance a of the main barsStandardfireresistanceColum exposed on more than one sideExposed on oneside fi 0.2 fi 0.5 fi 0.7 fi /35350/45450/40350/57450/51175/35 fi design axial load in the fire situation / design resistance at normal condition8
95.0EFFECTIVE SPAN OF BEAMS AND SLABS IN BUILDING(Ref. Section 5.3.2.2: MS EN 1992-1-1: 2010)The effective span of a member, leff should be calculated as follows:leff ln a1 a2whereln is the clear distance between the faces of the supporta1 and a2 is the min {0,5h; 0.5t}, where h is the overall depth of the member and t is the width of thesupporting elementFigure 5.4: Effective span, leff for different support conditions9
106.0DESIGN FOR FLEXURE(Ref. Section 6.1: MS EN 1992-1-1: 2010)Design Procedure for Rectangular SectionSupposed the bending moment is M, beam section is b b, concrete strength is fck and steel strength is fyk, todetermine the area of reinforcement, proceed as follows:The steps are only for valid for fck 50 MPa. For concrete compressive strength, 50 MPa fck 90 MPa,modification of the stress block should be in accordance to Section. 3.1.7: MS EN 1992-1-1: 2010.1.Calculate2.Calculatewhereand for 1.03. Kbal 0.167If K Kbal, compression reinforcement is not required, and[ ()]Calculate tension reinforcement:4.If K Kbal, compression reinforcement is required, and[ ()]Calculate compression reinforcement:Check d’/x:if d’/x 0.38orif d’/x 0.38wherefsc 700(1 – d’/x)Calculate tension reinforcement:()10
11Design Procedure for Flanged SectionSupposed the bending moment is M, beam section is bw b d hf, concrete strength is fck and steel strength isfyk, to determine the area of reinforcement, proceed as follows:()1.Calculate2.If M Mf , neutral axis lies in the flange[3. ()]If M Mf , neutral axis lies in the web(Calculate)()CalculateCompare M with Mbal4.IfM Mbal , compression reinforcement is not required(5.)If M Mbal , compression reinforcement is requiredMinimum and Maximum Area of Reinforcement(Ref. Section 9.2: MS EN 1992-1-1: 2010)The minimum area of reinforcement is given as:()and the maximum area of reinforcement is given as:11
127.0DESIGN FOR SHEAR(Ref. Section 6.2: MS EN 1992-1-1: 2010)Members Requiring Design Shear ReinforcementThe following procedure can be use for determining vertical shear reinforcement.1.Determine design shear force VEd2.Determine the concrete strut capacity, VRd,respectively), where:(maxfor cot θ 1.0 and cot θ 2.5 (θ 45o and θ 22o,)3.If VEd VRd, max cot θ 1.0, redesign the section4.If VEd VRd, max cot θ 2.5, use cot θ 2.5, and calculate the shear reinforcement as follows5.If VRd, max cot θ 2.5 VEd VRd, max cot θ 1.0[])(Calculate shear link as6.Calculate the minimum links required 7.Calculate the additional longitudinal tensile force caused by the shearProcedure for Calculating Transverse Shear Reinforcement in Flanged Section1.Calculate the longitudinal design shear stress, vEd at the web-flange interface:()(where()and M is the change in moment over the distance x)2.If vEd is less than or equal to 0.4fctd 0.4(fctk/1.5) 0.27fctk, then no shear reinforcement is required.Proceed to Step 4.3.If vEd is more than 0.4fctd 0.4(fctk/1.5) 0.27fctk, check the shear stress
18.0 DESIGN OF FOUNDATIONS 31 - Design of pad footing - Cracking and detailing requirements - Design of Pile Foundation 19.0 DESIGN OF RETAINING WALLS 36 - Table 1: Partial safety factor at the ultimate limit state - Stabililty analysis - Element design and detailing
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vary the overall capacity of the reinforced concrete and as well as the type of interaction it experiences whether for it to be either over reinforced or under reinforced. 2.2.2.1 Under Reinforced Fig. 3. Under Reinforced Case Figure 3.2 shows the process in determining if the concrete beam is under reinforced. The
reinforced concrete for pavement applications. However, Merta et al., (2011) studied wheat straw reinforced concrete for building material applications. They concluded that there is an increase (i.e. 2%) in fracture energy of wheat straw reinforced concrete. Thus, wheat straw reinforced concrete needs to be investigated for rigid pavements.
Recommended Practice for Glass Fiber Reinforced Concrete Panels - Fourth Edition, 2001. Manual for Quality Control for Plants and Production of Glass Fiber Reinforced Concrete Products, 1991. ACI 549.2R-04 Thin Reinforced Cementitious Products. Report by ACI Committee 549 ACI 549.XR. Glass Fiber Reinforced Concrete premix. Report by ACI .
experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars" is done. D.Modeling . ANSYS Workbench 16.1 is used to model the concrete beams and 28 different models are considered. Concrete beams reinforced with reinforced with steel bars of circular cross
Concrete Beams 9 Lecture 21 Elements of Architectural Structures ARCH 614 S2007abn Reinforced Concrete - stress/strain Concrete Beams 10 Lecture 21 Elements of Architectural Structures ARCH 614 S2007abn Reinforced Concrete Analysis for stress calculations steel is transformed to concrete concrete is in compression above n.a. and
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lateral systems. The report focuses on 'Special Reinforced Concrete Moment Resisting Frames' and 'Special Reinforced Concrete Shear Walls'. The parent project aims to relate design and assessment for a broad spectrum of building layouts and heights, for both reinforced concrete and structural steel lateral resisting systems.
