CONCEPTUAL DESIGN OF BUILDINGS
CONCEPTUAL DESIGN OF BUILDINGSProjectConception, analysis and design of a 3D steel buildingPerformed by:Project group 10Maksym PodgayskyyMD Refat AhmedEuropean Erasmus Mundus Master CourseSustainable Constructionsunder Natural Hazards and Catastrophic Events520121-1-2011-1-CZ-ERA MUNDUS-EMMC
List of contents1. Introduction.2. General safety criteria, actions and combinations of actions.2.1 Loads evaluation.2.2 Load combinations.3. Pre-design3.1 Preliminary evaluation of cross sections.3.2 Consideration of horizontal and vertical deformations.4. Structural analysis.5. Checking of elements.5.1 Verification of beams.5.1.1 Secondary beams (IPE 360).5.1.2 Main beam (IPE 450).5.2 Verification of columns5.2.1 Central column (HEA 450).5.2.2 Perimeter column (HEA 300).5.3 Verification of bracing.6. Verification of joints6.1 Column base.6.2 Beam-Beam connection.6.3 Beam-to column connection.6.4 Bracing joint (gusset plate connection).7. References.Annex 1. Calculation of column base joint in software ROBOT.Annex 2. Calculation of beam-beam joint in software ROBOT.Annex 3. Calculation of column (flange) to beam joint in software ROBOT.Annex 4. Calculation of column (web)to beam joint in software ROBOT.Annex 5. Drawn part (3D view, plan view, elevations, execution drawing for a column,execution drawing for a beam, joint details).2
1. IntroductionThe building analyzed in this project is based in steel-framed structure and has got followingcharacterisitics:1) Type of use – residential building;2) Location – Guarda, Portugal;3) Span – L 6m;4) Bay – B1 6m, B2 6m;5) Number of floors – 3;6) Floor height – 4 m.Scheme of the building is given on the following visualization:3
2. General safety criteria, actions and combinations of actionsThe quantification of the actions and their combinations was made according to EN 1990, EN 19911-1, 1991-1-3, considering the permanent actions that correspond to the self-weight of the structureand non-structural members, the variable actions corresponding to imposed loads, snow and windloads.2.1 Loads evaluation.1. Permanent actions:According to EN 1991-1-1 permanent actions include the self-weight of the structural elements andnon-structural elements.Self-weight of structural elements includes the weight of steel structure (weight is obtained duringthe calculations in software ROBOT).Self-weight of non-structural elements includes following positions:a) Roof slab:LayerThickness, mmSpecific weight, kN/m3Weight, kN/m2Hydro insulation0.003Thermal insulation801.40.112Slope concrete50241.2Vapors foil0.30.20.00006RC slab115252.87Steel sheeting1780.078Gypsum plaster board12150.18Total4.48b) Current floorLayerThickness, mmSpecific weight, kN/m3Weight, kN/m2Sandstone12200.24Adhesive support5210.105Flooring20220.44Vapors foil0.30.20.00006RC slab115252.875Steel sheeting1780.078Gypsum plaster board12150.18Total3.70c) Partition walls (lightweight walls) 1.0 kN/m2 (of slab). This weight is represented byuniformly distributed load on the floor slabs.d) External walls (lightweight walls) 1.0 kN/m2 (of wall – linear load). We assume thatsecondary beams (for external lightweight walls) will be installed in horizontal position. Theway of installation is shown on the visualization below:Vis.1. Installation of secondary beams for external walls.Therefore, the load from external walls will be applied to columns. In order to apply this loadin ROBOT we will use claddings working in one-way (horizontal) direction.4
2. Variable actions.a) Imposed loads.For residential building according to table 6.1 of EN 1991-1-1, category of use is A (areas fordomestic and residential activities). From this this table we take underlined recommendedcharacteristic values of imposed loads.qk, kN/m2Loaded areaFloorsQk, kN2.02.0In the project we will use only the imposed load on floor (qk 2.0 kN/m2) which is intended fordetermination of global effects. We neglect the loads given for representing of stairs and balconiesas long as they are not considered for calculation in our project.According to table 6.9 of EN 1991-1-1 roof is categorized category H (roofs not accessible exceptfor normal maintenance and repair). Therefore, according to recommended values in table 6.10,imposed load on roof is qk 0.4 kN/m2.b) Wind loads.Surface horizontal load 1.5 kN/m2 in one façade and -0.6 kN/m2 in the opposite façade. Wind loadwill be divided into two orthogonal loads which can not act simultaneously. First wind load will act, second wind load will act with angle. Value of the loads will be takenwith angleidentical in both directions.c) Snow loads.According to EN 1991-1-3 for Iberian Peninsula (Guarda, Portugal, 1056 m a.s.l.) region and statingthat in this region exceptional snow falls and exceptional snow drifts are unlikely to occur we obtain:,;,(for Guarda, Portugal)3. Summary of basic actions.The resulting actions are summarized in following table:Action NoLC2LC3LC4DescriptionSelf-weight of steel structureWeight of floor slabWeight of roof slabWeight of partition wallsWeight of external wallsImposed load on floorImposed load on roofWind load 1 ()ypePermanent actionPermanent actionPermanent actionPermanent actionPermanent actionVariable actionVariable actionVariable actionLC5Wind load 2 (Variable actionLC6Snow loadLC1)Variable actionValueObtained in ROBOT3.70 kN/m24.48 kN/m21.0 kN/m21.0 kN/m22.0 kN/m20.4 kN/m21.5 kN/m2 – one façade;-0.6 kN/m2 – oppositefaçade1.5 kN/m2 – one façade;-0.6 kN/m2 – oppositefaçade1.15 kN/m25
2.2 Load combinations.Ultimate limit state.The design values of the applied forces are obtained from the fundamental combinations, given by(EN 1990):Reduction coefficients for variable actions.Actionψ0Imposed loads (category0.7A)Snow loads (sites located0.7at altitude H 1000 m a.s.l)Wind load0.6According to EN 1990 Table A1.2(A) we consider verification of static equilibrium which involves theresistance of structural members. Permanent actions are considered to be unfavorable part. Followingcoefficients apply to these considerations:The following combinations are considered for the Ultimate Limit State:Combination 1-Imposed load as a leading variable action; wind load -.Combination 2-Imposed load as a leading variable action; wind load Combination 3-Snow load as a leading variable action; wind load -.Combination 4-Snow load as a leading variable action; wind load Combination 5-Wind load as a leading variable action;Combination 6-Wind load as a leading variable action;.Serviceability limit state.For serviceability limit state we apply characteristic combinations (irreversible limit states) (EN 1990):Combination 7-Imposed load as a leading variable action; wind load -.Combination 8-Imposed load as a leading variable action; wind load Combination 9-Snow load as a leading variable action; wind load -.Combination 10-Snow load as a leading variable action; wind load Combination 11-Wind load as a leading variable action; wind load Combination 12-Wind load as a leading variable action; wind load -where G LC1; LC2 LC3; LC4; LC5;. LC6.6
Substituting G,obtain:,,,with appropriate actions according to our project we.Combination 7-Imposed load as a leading variable action; wind load Combination 8-Imposed load as a leading variable action; wind load Combination 9-Snow load as a leading variable action; wind load -.Combination 10-Snow load as a leading variable action; wind load Combination 11-Wind load as a leading variable action; wind load Combination 12-Wind load as a leading variable action; wind load -.7
3.Pre-design3.1 Preliminary evaluation of cross sections.60004600036000216000A6000B6000CDIn order to obtain acting internal forces in the ROBOT model we assumed following cross-sections ofmembers:Type of columnsPerimeterCenterType of beamsMain beamsSecondary beamsGridCross-sectionSteel gradeA1, A4, D1, D4, A2,HEA 300S355A3, D2, D3, B1, B4, C1,C4B2, B3, C2, C3HEA 400S 355Tab.100. Initial assumed geometric characteristics of columns.BeamsCross-sectionSteel gradeA1-D1, A2-D2, A3-D3,IPE 300S 355A4-D4A1-A4, B1-B4, C1-C4,IPE 200S 355D1-D4Tab.100. Geometric characteristics of beams on all floors.BracingCross-sectionSteel gradeA1-A2, D1-D2, A3-A4, D3-D4 CHS 168x8S 355Tab.100. Geometric characteristics of bracings.After obtaining internal forces we perform preliminary design of members considering the biggestinternal forces in members of a type:Beams1. Secondary beams.Assuming class 1 or 2 cross sections, the following solution is obtained:8
In order to satisfy this condition IPE 240 section (is selected.2. Main beams.Assuming class 1 or 2 cross sections, the following solution is obtained:In order to satisfy this condition IPE 360 section (is selected. IPEdoes not meet the requirements as long as the moment in cross330 (section increases after changing the cross section in ROBOT model to Med 318 kNm.Columns1. Central columns.Assuming class 1, 2 or 3 cross sections, the following solution is obtained:As it is expected that buckling resistance will govern the member design, a member HEA320 (A 124.4 cm2)2. Perimeter columns.Assuming class 1, 2 or 3 cross sections, the following solution is obtained:As it is expected that buckling resistance will govern the member design, a member HEA220 (A 64.3 cm2)BracingAssuming class 1, 2 or 3 cross sections, the following solution is obtained:In order to satisfy this condition TRON 88x2.5 section (is selected.Pre-design sections are summarized in following table:Type of c lumnsGridCross-sectionSteel gradeMarginalA1, A4, D1, D4, A2,HEA 220S355A3, D2, D3, B1, B4, C1,C4CenterB2, B3, C2, C3HEA 320S 355Tab.100. Geometric characteristics of pre-designed columns.Type of beamsMain beamsBeamsCross-sectionSteel gradeA1-D1, A2-D2, A3-D3,IPE 360S 355A4-D4Secondary beamsA1-A4, B1-B4, C1-C4,IPE 240S 355D1-D4Tab.100. Geometric characteristics of pre-design beams sections.BracingCross-sectionSteel gradeA1-A2, D1-D2, A3-A4, D3-D4 TRON 88x2.5S 355Tab.100. Geometric characteristics of pre-design bracings sections.9
3.2 Consideration of horizontal and vertical deformations.In this chapter the verification of horizontal deformations in the building will be made. Limitingvalues for horizontal displacements in frames:This verification is made for serviceability limit states.H 12 m 1200 cm H/500 2.4 cmHi 4 m 400 cm Hi/300 1.33 cmVertical deformations in beams.Limiting value for main and secondary beams:L/250 600/250 2.4 cmThe structure with the members which were chosen in pre-design stage do not satisfy therequirements of horizontal and vertical deformations.Therefore, we change the cross section of members to satisfy the deformation requirements.LimitvaluesIPE 360IPE 450HEA 450HEA 300TRON139x8BracingHorizontal deflection (Δ)2Secondary beamMain beamCentral columnPerimeter column2.4Horizontal deflectionfirst floor (δ1)1.31.33Horizontal deflectionfirst floor (δ2)0.51.33Horizontal deflectionfirst floor (δ2)0.21.33Vertical deflection mainbeam22.4Vertical deflectionsecondary beam2.32.410
4. Structural analysisThe structural model for the analysis was created in software ROBOT. Following input data isused for model consideration:1. Beams in plane xz are rigidly connected to the steel columns.2. The beams in plane yz are hinged at both ends. Releases for hinged connections areindicated in following directions: Ry, Rz.3. Elements defining bracing system are also hinged at both ends.4. Supports are pinned. Fixed directions of pinned support: Ux, Uy, Uz, Rz.5. Bracings in axis A1-A2, D1-D2, A3-A4, D3-D4 are represented by one bar per frameassuming that it will work in tension and compression.6. The concrete slab has a strong influence on the global stiffness of the structure. InROBOT 3D model concrete slab was modeled by a horizontal bracing system, connectedto main columns. Connection of these bracings are hinged.To identify the type of analysis which should be performed (1st or 2nd order) wecalculate αcr for ultimate limit state combinations.αcr (mode 1)Combination 110.95Combination 210.95Combination 311.46Combination 411.46Combination 511.66Combination 611.66In all combinations αcr 10. Therefore, according to EN 1993-1-1 1st order elasticanalysis should be performed.11
5. Checking of elements5.1 Verification of beams5.1.1 Secondary beams (IPE 360)Cross section characteristicsh 360mmd 298.6mmb 170mmIy 16270cm4tw 8mm3Wel.y 904cmtf 12.7mm3Wpl.y 1019cmr 18mm2A1 72.7cmhi 334.6mmLbeam 6miy 15cm2Avz 35.1cmfyd 355MPaγM0 1.0Internal forcesMEd 129.56kN m12
VEd 86.37kNFy and Fz are low so we can neglect them.Cross section classificationAs long as steel class of the beam is S355 weobtain:N2352mmε 0.814fydWeb in bending:cw dcw 37.325 72ε 58.58twWeb is class 1Flanges in compression:cf b tw 2r 63 mm2cf 4.961tf 9ε 7.323Flanges are class 1The class of cross section is class 1Resistance of cross section1. Bending momentFor class 1 the design resistance for bending according to EC3-1-1 chapter 6.2.5:Wpl.y fydMRd 361.745 kN mγM0MEd 0.358 1MRd13
2. Shear resistance according to EC3-1-1 chapter 6.2.6:Design plastic shear resistance:VRd VEdVRd Avz fyd γM0 3 719.407 kN 0.12 1Shear buckling resistance classification:η 1 (conservatively taken)h 45 tw72ε 58.58ηTherefore, shear buckling resistance of the web does not have to be verified3. Bending and shear force according to EC3-1-1 chapter 6.2.8:VEd 86.37 kN 0.5VRd 359.704 kNTherefore, effect of shear force on te moment resistance can be neglectedLateral torsional bucklingSecondary beam is not susceptible to lateral-torsional buckling as long as it is laterally restrained withreinforced concrete slabs on the floor and roof. The slab prevents lateral displacements of the compressparts of the cross section.Verification of serviceability limit stateThe verification of the maximum vertical deflection is performed using deformations from ROBOTsoffor serviceability limit states. For floors general limiting value for the vertical displacement according1990 Annex A1.4, National annex, figure A1.1 is following:δmax Lbeam250For IPE 360:δmax 2.3cm Lbeam250 2.4 cmCross section size is governed by deformation requirements. As long as verticaldeformation values are 2.3 2.4, the cross section satisfies the requirement and can notbe reduced more.Cross section IPE 360 verifies ULS and SLS requirements14
5.1.2 Main beam (IPE 450)h 450mmd 378.8mmb 190mmIy 33740cm4tw 9.4mm3Wel.y 1500cmtf 14.6mm3Wpl.y 1702cmr 21mm2A1 98.8cmhi 420.8mmLbeam 6miy 18.5cm2Avz 50.9cmfyd 355MPaγM0 1.0Internal forcesMEd 275.78kN m15
VEd 132.62kNNEd 22.63kNValue of axial force is low so we can neglect it.Cross section classificationAs long as steel class of the beam is S355 we obtain:235ε Nmm2fyd 0.814Web in bending:cw dcw 40.298 72ε 58.58twWeb is class 1Flanges in compression:b tw 2rcf 69.3 mm2cf 4.747 9ε 7.323tfFlanges are class 1The class of cross section is class 116
Resistance of cross section1. Bending momentFor class 1 the design resistance for bending according to EC3-1-1 chapter 6.2.5:MRd Wpl.y fyd 604.21 kN mγM0MEd 0.456 1MRd2. Shear resistance according to EC3-1-1 chapter 6.2.6:Design plastic shear resistance:VRd VEdVRd Avz fyd γM0 33 1.043 10 kN 0.127 1Shear buckling resistance classification:η 1 (conservatively taken)h 47.872 tw72ε 58.58ηTherefore, shear buckling resistance of the web does not have to be verified3. Bending and shear force according to EC3-1-1 chapter 6.2.8:VEd 132.62 kN 0.5VRd 521.622 kNTherefore, effect of shear force on te moment resistance can be neglectedLaterral torsional bucklingSecondary beam is not susceptible to lateral-torsional buckling as long as it is laterallyrestrained with reinforced concrete slabs on the floor and roof. The slab preventslateral displacements of the compressed parts of the cross section.Verification of serviceability limit stateThe verification of the maximum vertical deflection is performed usingdeformations from ROBOTsoftware for serviceability limit states. For floorsgeneral limiting value for the vertical displacement according to EN 1990 AnnexA1.4, National annex, figure A1.1 is following:Lbeamδmax 25017
For IPE 450:δmax 2.0cm Lbeam250 2.4 cmCross section size is governed by deformation requirements. The deformation can not beincreased till 2.4 cm because it results in increase of deformations in secondary beams.Deformation in secondary beams can not be increased (this is verified in verification ofsecondary beam).Cross section IPE 450 verifies ULS and SLS requirements18
5.2 Verification of columns5.2.1 Central column (HEA 450)Cross section characteristicsh 440mm3b 300mmtw 11.5mmWpl.y 3216cmtf 21mmr 27mmAvz 65.78 cmiy 18.92 cm24Iz 9465cm2A1 178cm3Wel.z 631cmhi 398mm3Wpl.z 965.5 cmd 344mmiz 7.29 cm4Iy 63720cm63Wel.y 2896cmIw 4148000cm4It 243.8 cmCoefficients and other valuesγM0 1γM1 1Lcolumn 4mHbuilding 12mE 210000MPaν 0.3G 80700MPa19
Internal forcesMyEd 291.07kN mNEd 1072.62 kNVEd 72.77 kNMzEd 020
Cross section classification 235MPa f yd fyd 355MPa ε 1. Flange in compression:cf b tw 2r2 117.25 mmcf 5.583 9ε 7.323tfFlange is Class 12. Web in bending and compressioncw d 1 h N Ed α tf r 0.882 d 2 2 tw fyd 1as long as α 0.875 0.5cw 29.913 tw( 396ε) 30.78913α 1Therefore, web is Class 1Cross section is Class 1.Buckling length of the columnAs long as the column is pinned we obtain following buckling length:Lz.cr Lcolumn 4 mLy.cr Lcolumn 4 mVerification of cross section resistance1. Axial forceNpl.Rd NEdNpl.Rd A1 fyd γM0 6.319 103 kN 0.17 12. Axial force and bendingAccording to EN1993-1-1 chapter 6.2.9.1NEd 1.073 103 kN 0.25 N pl.Rd 1.58 103 kN21
0.5 h tw fyd 3NEd 1.073 10 kN γM0 898.15 kNAs a result, axial force has an effect on plastic moment resistance.The resistance to bending combined with axial force is obtained from followingexpressions according to clause 6.2.9.1:n a NEdNpl.Rd 0.17 A1 2 b tf 0.292 A10.5fydMpl.y.Rd Wpl.y 1.142 103 kN mγM0Reduced plastic resistance is given by:( 1 n)Mn.y.Rd Mpl.y.Rd 1.11 103 kN m1 0.5 aMyEd 291.07 kN m Mn.y.Rd 1.11 103 kN m3. Shear forceVpl.Rd VEdVpl.Rd Avz fyd γM0 3 1.348 103 kN 0.054 1Shear buckling resistance classification:η 1(conservatively taken)h 38.261 tw72εη 58.58Therefore, shear buckling resistance of the web does not have to be verified4. Bending and shear forceVEd 72.77 kN 0.5 Vpl.Rd 674.111 kNTherefore, effect of shear force on te moment resistance can be neglected22
Verification of the stability of the memberAccording to EN 1993-1-1 chapter 6.3.3 members which are subjected tocombined bending and axial compression should satisfy:As long as members with open sections are susceptible to torsional deformationverification of lateral-tersional buckling is needed.Deternination of the reduction factor due to lateral-torsional bucklingkz 1c1 1.77c2 0c3 0kw 1 kz 2 Iw kz Lcolumn 2 G It Mcr c1 2 k2 π E Iz kz Lcolumn w Iz π E Iz0.5 1.69 103 kN mAccording to EN1993-1-1 chapter 6.3.2.2:Wpl.y fydλLT 0.822 non-dimensional slendernessMcr h 1.467 2 we use buckling curve ab(from table 6.4)For buckling curve aαLT 0.21 (from table 6.3) LT 0.5 1 αLT λLT 0.2 λLT 0.903χLT 1LT 2LT λLT22 0.783 butχLT 1Determination of the reduction factors due to flexural bucklingCalculation of non-dimensional slenderness for flexural buckling accordinf toEN1993-1-1 chapter 6.3.1.323
235MPa λ1 93.9 76.399fyd λy λz Ly.criy λ1Lz.criz λ1for class 1 0.277 0.718Calculation of the reduction factor χy and χz according to chapter 6.3.1.2h 1.467 1.2btf 21 mm 100 mmAs a result for y-y we use curve b, for z-z curve c (table 6.2 EC3-1-1)αy 0.34αz 0.49 2 z 0.5 1 αz λz 0.2 λz 0.8852 y 0.5 1 αy λy 0.2 λy 0.551χy χz y z 1 0.973 0.713 y λy 221 z λz 22Calculation of Nrk, Mi,rk for class 1NRk fyd A1 6.319 106 NMyRk fyd Wpl.y 1.142 103 kN mMzRk fyd Wpl.z 342.753 kN mCalculation of interaction factors according to Method 2Calculation is made according to Annex B EC3-1-1.ψ 0 because of triangular shape of bending moment diagramCmy 0.6Cmz 0.6CmLt 0.624
NEd kyy.1 Cmy 1 λy 0.2 0.608 χy NRk γM1 NEd kyy.2 Cmy 1 0.8 0.684 χy NRk γM1 then kyy 0.608 NEd kzz.1 Cmz 1 2λz 0.6 0.719 χz NRk γM1 NEd kzz.2 Cmz 1 1.4 0.8 χz NRk γM1 then kzz 0.721kyz 0.6 kzz 0.433kzy1 1 0.1 kzy2 1 0.1 λz NEd NRk 0.25 C mLt χz γ M1 NEd NRk CmLt 0.25 χz γ M1 0.951 0.932kzy1 kzy2then kzy 0.95125
Based on the determined parameters we obtain:NEdχy NRkγM1NEdχz NRkγM1kyy MyEd χLT MyRkγM1kzy MyEdχLT MyRkγM1 kyz MzEdχLT MzRkγM1kzz MzEdχLT MzRkγM1 0.373 1 0.548 1The stability of column with cross section HEA 450 is verified.Verification of serviceability limit stateThe verification of the maximum horizontal deflection is performed usingdeformations from ROBOTsoftware for serviceability limit states. Followinglimiting values apply for horizontal displacement:1. Verification of horizontal displacement for the whole building height (H 12 m):HbuildingΔ 2.0 2.4 cm5002. Verification of horizontal displacement for the each floor:Lcolumnfirst floor - δ1 1.3 1.333 cm300second floor - δ2 0.5 third floor -δ3 0.2 Lcolumn300Lcolumn300 1.333 cm 1.333 cmDue to the horizontal displacement on the first floor which are very close to thelimit section can not be reduced. Moreover, decreasing of column section results inincrease of the displacement in secondary beams which are also close to the limit.Cross section HEA 450 for column verifies the reuirements of ULS and SLS.26
5.2.2 Perimeter column HEA 300Cross section characteristicsh 290 mm3Wpl.y 1383cmb 300 mmtw 8.5mmiy 12.74 cm2Avz 37.28 cmtf 14mmr 27mm4Iz 6310cm23A1 112.5 cmhi 262 mmWel.z 420.6 cm3Wpl.z 641.2 cmiz 7.49cmd 208 mm46Iy 18260 cmIw 1200000 cm3Wel.y 1260cm4It 85.17 cmMaterialγM0 1γM1 1E 210000MPaν 0.3G 80700MPaBuildingLcolumn 4mHbuilding 12m27
Internal forcesMyEd 117.37kN mNEd 694.3 kNVerification of perimetr column will be made using SemiComp software. For input data we need tocalculate Mcr.Deternination of critical moment:kzc1c2c3 11.7700kw 1 kz 2 Iw kz Lcolumn 2 G It Mcr c1 2 k2 π E Iz kz Lcolumn w Iz π E IzFollowing verification were obtained (using Method 2):0.5 762.666 kN m28
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Verification of serviceability limit stateThe verification of the maximum horizontal deflection is performed using deformations fromROBOTsoftware for serviceability limit states. Following limiting values apply for horizontal displace1. Verification of horizontal displacement for the whole building height(H 12 m):Δ 2.0 Hbuilding500 2.4 cm2. Verification of horizontal displacement for the each floor:first floor -δ1 1.3 second floor -third floor -Lcolumnδ2 0.5 δ3 0.2 300 1.333 cmLcolumn300Lcolumn300 1.333 cm 1.333 cmDue to the horizontal displacement on the first floor which are very close to thelimit section can not be reduced. Moreover, decreasing of column section results inincrease of the displacement in secondary beams which are also close to the limit.Cross section HEA 300 for column verifies the reuirements of ULS and SLS.32
5.3 BracingCross section characteristics TRON 139x82Ax 33.1cm - cross section area4Iy 720.29 cm - moment of inertia of a section around y-axis4Iz 720.29cm - moment of inertia of a section around y-axish 14cm diametert 0.8 cm - web thicknessLb 7.21m - length of bracing elementMaterialfyd 355MPaγM0 1γM1 1E 210000MPaInternal forcesNEd 216.8 kNCross section classification235MPa ε fyd Section in compressionh2 17.5 50ε 33.099tThe cross section is class 1.33
Cross section resistanceAxial forceNEd fydNcRd Ax 1.175 103 kNγM0216.8 kN Verification of buckling resistanceFlexural bucklingλ1 π E 76.409fydLE 1 Lb 7.21 m - buckling lengthIy 4.665 cm - radius of girationAxi λ LEλn i 154.559λ 2.023 - nondimensional skenderness coefficientλ1hot finished hollow section curve a, soα1 0.21 2 0.5 1 α1 λn 0.2 λn 2.737 1χ NbRd 0.1972 λnχ Ax fydγM1NEd 216.8 kN 231.494 kNNbRd 231.494 kNSo section TRON 139x8 is adopted.34
6. Verification of joints6.1 Column baseThe design of column base joint is performed in software ROBOT.a) Pinned column base joint for column HEA 450.For designing was chosen a column with the maximum axial load.Axial force diagramShear force diagramFor anchoring of the column two anchor bolts are sufficient. However, for better execution it ischosen to install 4 anchor bolts.Results of calculation can be found in Annex 1.35
6.2 Beam-beam connectionThe design of beam-beam joint is performed in software ROBOT.Connection is made for two secondary beams IPE 360 and main beam IPE 450.As long as the secondary beam has pinned connection to main beam the governing internal forceis shear. Therefore, we chose the beam with maximum shear force for design.Shear force diagram for right secondary beam IPE 360.Shear force diagram for left secondary beam IPE 360.Results of calculation can be found in Annex 2.36
6.3 Beam-to-column connectionThe design of beam-beam joint is performed in software ROBOT.a) Connection of column HEA 300 (flange) to beam IPE 450.This joint is a moment resisting one. We chose the connection with the biggest moment andshear force.Moment diagram of column37
Shear force diagram of column.Moment diagram of beamShear diagram for beamResults of calculation can be found in Annex 3.38
b) Connection of column HEA 300 (web) to two secondary beams IPE 360.As long as the secondary beam has pinned connection to column, the governing internal force isshear. Therefore, we chose the beam with maximum shear force for design.Shear force diagram of the left secondary beam IPE 360.Shear force diagram of the right secondary beam IPE 360.Results of calculation can be found in Annex 4.39
6.4 Bracing joint (gusset plate connection)The gusset plate is welded to the beam using double fillet welds. Joint is designed in a way to minimizthe eccentricity between the bracing member and the column axis.Main joint data:Column - HEA 300, S355Beam - IPE 360, S355Bracing - TRON 139x8, S355Type - plate welded to bracing and then bolted to gusset plate; gusset plate is weldedto beam.Cross section characteristics TRON 139x82Ax 33.1cm - cross section area4Iy 720.29 cm - moment of inertia of a section around y-axis4Iz 720.29cm - moment of inertia of a section around y-axish 14cm diametert 0.8 cm - web thicknessLb 7.21m - length of bracing elementMaterialfyd 355MPafu 470MPaγM0 1γM1 1γM2 1.25Internal forcesNEd 216.8 kN40
Shear resistance of boltsIn order to evaluate the tpe and quantity of bolts for fastening the bracing plate to gusset plate we usetable 3.4 EN 1993-1-8.Shear resistance per shear plane:αv fub AbFvRd γM2We choose class of bolts 8.8. As a result we obtain following input data:αv 0.6 - for class 8.8N- for class 8.8fub 8002mmFvRd 216.8 kNWe obtain the required cross section of the bolts:Ab FvRd γM2αv fub 564.583 mm2Taking the bolts with d 20mm, class 8.8 required quantity of bolts:2A 314mm - area of one bolt with d 20mm in accordance with EN ISO 898.20n Ab 1.798A20As a result we take 2 bolts class 8.8,d 20mmd0 d 2mm 22 mmNowAb1 2 A20 628 mm2Shear resistance of bolts:αv fub Ab1FvRd 241.152 kNγM2NEdFvRd 0.899 1Verification of bearing resistanceFbRd k1 αb fuac d tpγM241
Characteristics of bolts location:e1 40mme2 40mmp2 80mme1αb 0.6063d0 2.8 e2k1 min d0 1.7 2.5 2.5 tp 10mm - thickness of plate welded to bracingtg 15mm - thickness of gusset plateFbRd k1 αb fu d tpγM2 113.939 kNShear force for one bolt:NEdNEd1 108.4 kN 2FbRd 113.939 kNBearing resistance is sufficient.Weld designWeld design is as follows:1. The gusset plate is welded to the beam using double fillets.a)Weld design for gusset plate and a beam according to simplified method:we proposea 4mmβw 0.95lc 320mmNrdw 2FwRd lFwRd fvw afuN3fvw 228.509 2βw γM2mmNFwRd fvw a 914.037mmNrdw 2FwRd lc 584.983 kNIt supports the horizontal component of the force acting in the bracing:NEdhor NEd sin ( 56deg) 179.735 kNTherefore, the horizontal weld is OK.42
2. The bracing is welded to the plate bolted to the gusset plate.we proposea3 4mmβw3 0.95l3 150mmfuN3fvw3 228.509 2βw3 γM2mmNFwRd3 fvw a3 914.037mmNrdw3 4FwRd lc 1.17 103 kNNEd 216.8 kN Nrdw3 1.17 103 kNSo the welding is OK.43
7. References.1. Simoes da Silva L., Simoes R., Gervasio H.: Design of steel structures. ECCSEurocode Design Manuals, ECCS and Ernst & Sohn, 2010, 438 p.2. Jaspart J.P. and Weynand K.: Design of joints for steel and steel-concrete structures,ECCS, Ernst & Sohn and Wiley, 2012.3. EN 1993-1-1 Design of steel structures – Part 1.1: General rules and
A1-A2, D1-D2, A3-A4, D3-D4 TRON 88x2.5 S 355 Tab.100. Geometric characteristics of pre-design bracings sections. 10 3.2 Consideration of horizontal and vertical deformations. In this chapter the verification of horiz
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