DESIGN OF RC BEAMS AND FLOORS, BRACING

Transcription

1 BME Department of Mechanics, Materials and Structures Dr András Draskóczy Lecture 5: DESIGN OF RC BEAMS AND FLOORS, BRACING Design of Reinforced Concrete Structures 1 BEAMS, FLOORS, BRACING

2 CONTENT: BEAMS Examples General characteristics Approximate design of beam dimensions Constructional rules R.c. cantilevers used as architectural motifs. FLOORS Characteristic span ranges of reinforced concrete structures Advantages of different floor systems Design of variable height and variable thickness RC floor systems 1 Monolithic solid slabs 2 Partially prefabricated floors 3 Cobiax (or bubble deck) floor slabs 4 Steel-concrete composite floors Design of Reinforced Concrete Structures 2 BEAMS, FLOORS, BRACING

3 5 Post-tensioned floors (lecture of Máté Borbás Pannon Freyssinet Kft.) BRACING Ways of bracing Bracing systems of reinforced concrete load bearing structures. Connection of tilting and bracing Design of Reinforced Concrete Structures 3 BEAMS, FLOORS, BRACING

4 BEAMS Examples Design of Reinforced Concrete Structures 4 BEAMS, FLOORS, BRACING

5 Series of simple supported arched diaphragm beams of Nervi's Orvieto airplane hangars Design of Reinforced Concrete Structures 5 BEAMS, FLOORS, BRACING

6 Monolithic rc cantilever of the Flaminio stadium, Rome by Nervi Design of Reinforced Concrete Structures 6 BEAMS, FLOORS, BRACING

7 Variable section arched continuous rc beams of Calatrava's Lyon railway station Design of Reinforced Concrete Structures 7 BEAMS, FLOORS, BRACING

8 Variable section rc frame beam of Calatrava, Lyon railway station Design of Reinforced Concrete Structures 8 BEAMS, FLOORS, BRACING

9 Metro line 4 Budapest, Fővám square, slurry wall supporting strut-beams Design of Reinforced Concrete Structures 9 BEAMS, FLOORS, BRACING

10 General characteristics of beams DEFINITION, INTERNAL FORCES Beams are linear members generally supporting vertical loads, with their axis running mostly horizontally and mainly being subjected to moments and shear forces along their axis (M+V). Axial force can also act sometimes (N+M: eccentric compression). Try to avoid torsion! TYPES -Geometry -Axis: straight, curved or eventuallypolygonal -Cross-section: constant, variable, haunched near supports, flanged. For ex. when cast integral with the floor slab. The way of variation is mainly in connection with the variation of moments, which can also be exploited for rainwater canalisation (see above) -Static models: Design of Reinforced Concrete Structures 10 BEAMS, FLOORS, BRACING

11 -single span and continuous with or without cantilever -beams can also be part of frames, joining to other members by hinged or rigid joint. Principal beams and secundary beams, joist floors Design of Reinforced Concrete Structures 11 BEAMS, FLOORS, BRACING

12 Estimation of the width (b, bw) and height (h): b, b w is generally determined by technological requirement: b= wall thickness or column width Columns Ribs cm): h estimate by approximate value of the slenderness ratio: l/d l/(h-5 -heavily loaded simple supported beam: l/d 10 to 12 -simple supported beam with low load intensity: l/d 14 to 16 -continuous beam, flanged beam: l/d 16 to 18 -prefabricated prestressed beam: l/d 18 to 22 2 Rigidity check in SLS of deformations (limitation of deflections) w max l /250 l Design of Reinforced Concrete Structures 12 BEAMS, FLOORS, BRACING

13 Simplified check of the deflection by limiting the slenderness ratio l/d / K d ( / d) allowable where: l/k is the distance between 0-moment points, K: tabulated, (l/d) allowable tabulated (see below!) 1 ped M Rd 500 A 2 p M f A qp Ed yk s,prov s,requ α, β: modifying factors p qp = g k + ψ 2 q k quasi permanent load ψ 2 q k long term part of the variable load 500 f yk Design of Reinforced Concrete Structures 13 BEAMS, FLOORS, BRACING

14 Basic values of the allowable slenderness ratio (l/d) allowable for rectangular sections Concrete strength grade p Ed [kn/m 2 ] (by beams b is the width of the beam in m, by slabs b=1,0 m) b C40/ C35/ C30/ C25/ C20/ C16/ beam slab For T-sections and flanged beams use another table of the design aids (DA) In case of applying pre-camber of the extent l/500, we can add Δ(l/d) allow =4 to the values of the previous table, whereas in case of a pre-camber by l/250, Δ(l/d) allow =8 can be added to the tabulated values Design of Reinforced Concrete Structures 14 BEAMS, FLOORS, BRACING

15 Constructional rules of beams (read through, for information only!) 1. Reinforcement designed for bending Minimum quantity of tensile reinforcement A s,min =ρ min b t d ρ min = max 0,26 f ctm /f yk ; 0,0015 see table below b t medium width of the tension zone Minimum steel ratio min (%o) f yk concrete C12 C16 C20 C25 C30 C35 C40 C45 C ,5 1,5 1,5 1,5 1,51 1,66 1,82 1,98 2, ,5 1,5 1,5 1,69 1,89 2,08 2,28 2,47 2, ,73 2,06 2,38 2,82 3,14 3,47 3,79 4,12 4,44 The allowable maximum quantity of the total steel cross-section: A s,max =0,04A c, where A c is the area of the total concrete cross-section. At overlaps the double of this quantity is allowed. Design of Reinforced Concrete Structures 15 BEAMS, FLOORS, BRACING

16 Partial restraint at beam ends: Partially restrained ends of monolithic beams must be designed for the calculated restrain moment. The respected restrain moment can not be smaller than 15% of maximum moment in the span. The section design for 15% of the span moment should be made even if the beam was considered simply supported. The rule concerning the minimum reinforcement must be respected. Anchorage of bent-up bars with straight end The anchorage length in the tension zone must be at least 1,3l bd, in the compression zone at least 0,7 l bd, which should be measured from the intersection point with the longitudinal reinforcement. Design of Reinforced Concrete Structures 16 BEAMS, FLOORS, BRACING

17 Anchorage of the bottom longitudinal reinforcement above support At least 1/3 of the span reinforcement must be continued beyond the theoretical support point. At extreme support reinforcement must be anchored for the tensile force F Ed given in point , and the anchorage should be measured from the internal face of the support. At intermediate supports one of the solutions indicated below can be applied. The mostly recommended solution is (d). The figures do not indicate the top reinforcement. Values of d b = D min are given in section Shear reinforcement Design of Reinforced Concrete Structures 17 BEAMS, FLOORS, BRACING

18 In case of designed shear reinforcement at least half of the shear force should be equilibrated by links. The shear steel ratio: w =A sw /(s. b. w sin ), where α is the angle between axis of the beam and axis of elements of the shear reinforcement The minimum shear steel ratio: w,min =max 0,08 f yk f ck ;0,001 from the table below. Values of the minimum shear steel ratio: w,min (%o) Concrete f yk C12/ 16 C16/ 20 C20/ 25 C25/ 30 C30/ 37 C35/ 45 C40/ 50 C45/ 55 C50/ ,00 1,00 1,00 1,00 1,00 1,00 1,01 1,07 1, ,00 1,00 1,00 1,00 1,10 1,18 1,26 1,34 1, ,15 1,33 1,48 1,67 1,81 1,95 2,05 2,21 2,33, which can be taken Design of Reinforced Concrete Structures 18 BEAMS, FLOORS, BRACING

19 If b w >h: 0,08 w,min = f yk f ck 0,0007 0,0003h / b 0,001 w 0,0007 0,0003h / b The greatest allowable spacing of elements of the shear reinforcement Maximum spacing of links in general s l,max =0,75d ( 1 cot ) min 1,5b w ;300mm in case of designed compression steel s l 15 [13], [15] * is the smallest diameter of the compression steel perpendicular to the beam axis s l,max =0,75d 1000 mm. Maximum spacing of 45 bent-up bars s b,max =1,5d Detailing of links w, a) b) c) d) e) f) g). Design of Reinforced Concrete Structures 19 BEAMS, FLOORS, BRACING

20 Open links can only be applied in flanged beams, if there is transverse reinforcement in the slab. Links cages can also be bent using spot-welded meshes. Related constructional rules see in point 8.2. At junction of principal and secondary beam the links of the principal beam must go through, at column-beam junctions links of the column must go through. 3. Torsion reinforcement Links must be anchored with overlap. Spacing of links can not be greater than a) 1/8 of the concrete perimeter b) the smaller side length Distance between elements of the longitudinal reinforcement uniformly distributed along the link perimeter must be smaller than 350 mm. (In the cross-section indicated on the figure elements of flexural and torsion reinforcement can also be seen.) Design of Reinforced Concrete Structures 20 BEAMS, FLOORS, BRACING

21 R.c. cantilevers used as architectural motifs Design of Reinforced Concrete Structures 21 BEAMS, FLOORS, BRACING

22 Design of Reinforced Concrete Structures 22 BEAMS, FLOORS, BRACING

23 Some design principles Smaller F c better: h c (Beams) c (Deep beams, walls) 5 c c hc to (Slabs) Greater compression zone better Design of Reinforced Concrete Structures 23 BEAMS, FLOORS, BRACING

24 Pile foundation or heavy mass foundation may be necessary to anchor F t! Downloading by G better ( G Ft ) 2 Design of Reinforced Concrete Structures 24 BEAMS, FLOORS, BRACING

25 Greater restrain length better: Symmetric arrangement better: < restrain length > Design of Reinforced Concrete Structures 25 BEAMS, FLOORS, BRACING

26 Storey-high cantilever (deep beam cantilever) better: Design of Reinforced Concrete Structures 26 BEAMS, FLOORS, BRACING

27 FLOORS Characteristic span ranges of reinforced concrete structures Advantages of different floor systems Design problems of variable height and variable thickness RC floor systems 1 Monolithic solid slabs 2 Partially prefabricated floors 3 Cobiax (or bubble deck) floor slabs 4 Steel-concrete composite floors 5 Post-tensioned floors Design of Reinforced Concrete Structures 27 BEAMS, FLOORS, BRACING

28 CHARACTERISTIC SPAN RANGES OF RC FLOOR STRUCTURAL SYSTEMS Construction one-way Approximate maximum span l(m) type two-way 5 7, , , >35 Char. slender ness l/d monolithic rc one-way solid slab two-way prefab. one-way prestressed hollow core floor panels monolithic rc one-way beams solid flat slab two-way prestressed one-way solid slab prestressed two-way solid flat slab hollow core two-way (flat) slab prestr. hollow core flat slab two-way Design of Reinforced Concrete Structures 28 BEAMS, FLOORS, BRACING

29 CHARACTERISTIC SPAN RANGES OF RC FLOOR STRUCTURAL SYSTEMS (cont.) Construction one-way, Approximate maximum span (m) type two way 5 7, , , >35 prestressed rc beams (used in building construction) prestressed rc beams (used in bridge construction) Char. slender ness l/d one-way one-way deep beams one-way 5 prefabricated box-culvert construction with posttensioning one-way Design of Reinforced Concrete Structures 29 BEAMS, FLOORS, BRACING

30 ADVANTAGES OF DIFFERENT FLOOR SYSTEMS monolithic or prefabricated floors? Cheaper, mainly if manpower is cheaper More rapid construction Increases safety through better structural integrity Better possibilities for individual design Higher level of weather independency No problem in jointing members Partial pre-fabrication can integrate well all advantages! one-way or two-way floors? Mass production by application of hollow Load intensity and moment reduction core pre-stressed floor panels Deflection reduction structural height reduction normal or pre-stressed floor structures? Cheaper Deflection reduction Better possibilities for individual design structural height reduction Design of Reinforced Concrete Structures 30 BEAMS, FLOORS, BRACING

31 DESIGN OF VARIABLE HEIGHT AND VARIABLE THICKNESS Beams Variable beam height for rainwater canalization (cca 5% fall) from flat roof of an industrial hall Favourable effect: shear capacity increase a) variation on side of the compression zone, V V N tan Ed Ed, b) variation on side of the tension zone VEd VEd Ns tan s c Design of Reinforced Concrete Structures 31 BEAMS, FLOORS, BRACING

32 Slabs Favourable effects of the self weight reduction of cantilever slabs achieved by 50% reduction of the thickness at the free extremity The 33% moment and deflection reduction can also be exploited by cca 10 to 13% reduction of the slab thickness itself. The floor slab becoming thin looks lighter, having also a positive aesthetical effect. Design of Reinforced Concrete Structures 32 BEAMS, FLOORS, BRACING

33 RC STRUCTURAL FLOOR SYSTEMS 1 MONOLITHIC SOLID SLABS Design of Reinforced Concrete Structures 33 BEAMS, FLOORS, BRACING

34 Design of Reinforced Concrete Structures 34 BEAMS, FLOORS, BRACING

35 Design of Reinforced Concrete Structures 35 BEAMS, FLOORS, BRACING

36 Design of Reinforced Concrete Structures 36 BEAMS, FLOORS, BRACING

37 2 PARTIALLY PREFABRICATED FLOORS Omnia floors 5 to 6 cm thick prefab formwork panels strengthened by lattice-like reinforcement, provisory supported at 1,5 to 2 m axis distances during constr. Design of Reinforced Concrete Structures 37 BEAMS, FLOORS, BRACING

38 Stadium Debrecen Design of Reinforced Concrete Structures 38 BEAMS, FLOORS, BRACING

39 Details of Omnia floors Design of Reinforced Concrete Structures 39 BEAMS, FLOORS, BRACING

40 Slim-floor construction details Hollow core rc floor panels supported by flanged steel beams to reduce the overall structural height of the floor. In situ concreting constitutes the compression zone and impreves fire resistance. With use of bent-up bars F90 fire resistance can be achieved Design of Reinforced Concrete Structures 40 BEAMS, FLOORS, BRACING

41 3 COBIAX (OR BUBBLE DECK) FLOOR SLABS Design of Reinforced Concrete Structures 41 BEAMS, FLOORS, BRACING

42 Installation guide Post-tensioning Mainova Frankfort, Germany Design of Reinforced Concrete Structures 42 BEAMS, FLOORS, BRACING

43 SPAN RANGE SPHERE DIAMETER LOAD INTENSITY DIAGRAM OF COBIAX FLOORS Loads [kn/m2 2 ] 16 Spans [m] with the same slab thickness 22 C B A d = deck thickness dia. = sphere diameter A d 23.0 cm / dia cm B d 40.0 cm / dia cm C d 58.0 cm / dia cm Design of Reinforced Concrete Structures 43 BEAMS, FLOORS, BRACING

44 Omnia products incorporate the triangular Omnia lattice girder that is attached to a lower layer of reinforcement before wet concrete is poured to create the Omnia panel The same principle can be applied to partially prefabricated two way - Cobiax floor panels: Design of Reinforced Concrete Structures 44 BEAMS, FLOORS, BRACING

45 The wet-method The dry-method THREE ALTERNATIVES OF PARTIAL PREFABRICATION AND MOUNTING The in situ-method Design of Reinforced Concrete Structures 45 BEAMS, FLOORS, BRACING

46 Lifting of the ready-assambled floor panel by application of the dry construction method. Design of Reinforced Concrete Structures 46 BEAMS, FLOORS, BRACING

47 Mayor advantages of COBIAX (Bubble-deck) floors: - up to 18 m span without beams - biaxial load-bearing, reduced deflections - up to 30% selfweight reduction - unification of the advantages of prefabrication and monolithic technology STEEL-CONCRETE COMPOSITE FLOORS Design of Reinforced Concrete Structures 47 BEAMS, FLOORS, BRACING

48 4 STEEL CONCRETE COMPOSITE FLOORS Headed stud shear connectors The design shear resistance of a headed stud: 2 0,8f d / 4 2 y 0,29 d fckecm PRd min(, ) (N) V V h where: 0,2( sc 1) 1 d d is the diameter of the shank of the stud, 16 mm d 25 mm; fy is the specified ultimate tensile strength of the material of the stud but not greater than 500 N/mm2; fck is the characteristic cylinder compressive strength of the concrete at the age considered, of density not less than 1750 kg/m3; hsc is the overall nominal height of the stud. partial safety factor, recommended value: 1,25 V Design of Reinforced Concrete Structures 48 BEAMS, FLOORS, BRACING

49 Flexural resistance of encased steel beam Alternative solutions Design of Reinforced Concrete Structures 49 BEAMS, FLOORS, BRACING

50 5 PRESETRESSED RC SLABS WITH BOUNDED AND UNBOUNDED TENDONS 50 cm thick transition slab with unbounded post-tensioned cables, Jerusalem Design of Reinforced Concrete Structures 50 BEAMS, FLOORS, BRACING

51 Design of Reinforced Concrete Structures 51 BEAMS, FLOORS, BRACING

52 The manual pre-stressing jack Design of Reinforced Concrete Structures 52 BEAMS, FLOORS, BRACING

53 BRACING Ways of bracing Beside solid sheared-walls, bracing of buildings can be assured by use of diagonals rigid frames frame filling walls (Andrew-crosses, characteristic for steel constructions) Design of Reinforced Concrete Structures 53 BEAMS, FLOORS, BRACING

54 EXAMPLE: ORVIETO AIRPLANE HANGAR BY NERVI Design of Reinforced Concrete Structures 54 BEAMS, FLOORS, BRACING

55 Bracing systems of reinforced concrete loadbearing structures Not good: a, b, c, d Good: e, f, g, h, i, j May be acceptable: k, l Design of Reinforced Concrete Structures 55 BEAMS, FLOORS, BRACING

56 Design of Reinforced Concrete Structures 56 BEAMS, FLOORS, BRACING

57 Design of Reinforced Concrete Structures 57 BEAMS, FLOORS, BRACING

58 Connection of tilting and bracing Design of Reinforced Concrete Structures 58 BEAMS, FLOORS, BRACING

59 END Design of Reinforced Concrete Structures 59 BEAMS, FLOORS, BRACING