Composite Floor System

Transcription

1 Composite Floor System

2 INTRODUCTION This manual has been developed in order to assist you in understanding the Hambro Composite Floor System, and for you to have at your fingertips the information necessary for the most efficient and economical use of our Hambro products. Suggested detailing and design information throughout this manual illustrates methods of use. To achieve maximum economy and to save valuable time we suggest that you contact your local Hambro representative. He/she is qualified and prepared to assist in the selection of a Hambro system that is best suited to your project s requirements. 1

3 GENERAL INFORMATION 1. GENERAL INFORMATION DESCRIPTION The Hambro Composite Floor System has been used with different types of construction, i.e. masonry, steel frame buildings, poured in place or precast concrete as well as wood construction. Uses range from the single-family detached house to multistory residential and office complexes. The Hambro Composite Floor System consists of a hybrid concrete/steel T-beam in one direction and an integrated continuous one-way slab in the other direction, and is illustrated in figures 1 and 2. Depending on the span, the loads and the type of form to support concrete poured in place, the Hambro steel joist may have a different configuration at the top chord. PRODUCT SERIES CONFIGURATION D500 TM H MD2000 MD2000 Double Top Chord (DTC) LH Wire mesh draped over top chord to form catenary Poured in place Concrete slab Rollbar Continuous slab over wall or beam forms an accoustical seal Hambro joist with bearing shoe Reusable plywood mm x mm (4 x 8 typ.) forms Handle mm (4-1 1 /4 ) Slots in top chord to support reusable Rollbar (Chord cut for clarity) Rollbar clips temporary bottom chord bracing Rollbar installed and rotated into a locked position into joists, support plywood forms Fig. 1 Hambro D500 Composite Floor System CANADA PATENT N o : U.S.PATENT N os : OTHER U.S. & FOREIGN PATENTS PENDING Cold rolled top chord portion embedded 39 mm (1 1 /2 ) in slab for composite action NOTE: Rollbar are rotated and unlocked for removal of plywood forms 1

4 GENERAL INFORMATION The unique top chord section has four basic functions: 1. It is a compression member component of the Hambro non-composite joist during the concreting stage. The system is not shored. 2. It is a high chair for the welded wire mesh, developing negative moment capacity in the concrete slab where it is required - over the joist top chord. 3. It locks with and supports the slab forming system (Rollbar and forms). 4. It automatically becomes a continuous shear connector for the composite stage. The bottom chord acts as a tension member during both the concreting stage and the service life. The web system, consisting of bent rods, ties the top and bottom chords together and resists the vertical shear in the conventional truss manner. The concrete slab is reinforced with welded wire mesh at the required locations and behaves structurally as a continuous one-way reinforced concrete slab. 65 mm (2 1 /2 ) concrete slab (min.) Shear connector embedded 39 mm (1 1 /2 ) into slab Web Bottom chord mm (4-0 ) plywood sheet Draped mesh Rollbar locked into section Hambro joist spacing* Fig. 2 * Normally mm (4-1 1 /4 ) to accommodate standard mm (4-0 ) wide plywood forms, but can be altered to suit job conditions. The rigid plywood sheets and Rollbar, when locked into the section, not only act as simple forms for placing concrete, but provide the essential lateral and torsional stability to the entire Hambro floor system during the concreting stage. The interaction between the concrete slab and Hambro joist begins to occur once the wet concrete begins to set. The necessary composite interaction for construction loads is achieved once the concrete strength, f c, reaches 7.0 MPa (1 000 psi). This will usually occur within 48 hours. Even in the coldest of concrete pouring conditions, construction heating will maintain the concrete at temperatures necessary for this gain of strength. When in doubt, concrete test cylinders can be used to verify strength. It is important to note that the overall floor stiffness after concreting increases substantially as compared to that during its non-composite condition prior to concreting. The result is a composite floor system having a sound transmission class (STC) of 57 with the addition of a gypsum board ceiling. Fire resistance ratings of up to three hours are easily achieved with the Hambro Composite Floor System by the installation of a gypsum board ceiling directly under the joists. Other types of fire protection could be used: refer to U.L.C. and U.L. publications. The Hambro Composite Floor System has been subjected to many tests both in laboratories and in the field. ADVANTAGES The Hambro joists are custom manufactured to suit particular job conditions and are easily installed. The Hambro joist modular spacing can be adjusted to suit varying conditions. The Hambro forming system provides a rigid working platform. Masonry walls or tie beams may be filled, when required, using the Hambro floor as a working deck. Shallower floor depths can be used because of the increased rigidity of the system resulting from the composite action. The wide Hambro joist spacing allows greater flexibility for mechanical engineers and contractors. Standard pipe lengths can be threaded through the Hambro web system - this means fewer mechanical joints. The ceiling plenum can accommodate all electrical and mechanical ducting, eliminating the need for bulkheading and dropped ceilings. The interlocking of concrete with steel provides excellent lateral diaphragm action with the composite joists acting as stiffeners for the entire system. Other subtrades can closely follow Hambro, thereby shortening completion time. The Rollbar and plywood sheets are reusable. 2

5 APPROVALS AND FIRE RATINGS APPROVALS The Hambro Composite Floor System is approved, classified, listed, recognized, certified or accepted by the following approving bodies or agencies: 1. CCMC No R irc.nrc-cnrc.gc.ca/ccmc/registry/13/06292 f.pdf 2. International Conference of Buildings Officials (ICBO) Report No. PFC files/ubc/pfc2869.pdf 3. Miami-Date County, Florida, Acceptance No The cities of Los Angeles Report No. RR FIRE RATINGS Fire Protection floor/ceiling assemblies using Hambro have been tested by independent laboratories. Fire resistance ratings have been issued by Underwriters Laboratories Inc. and by Underwriters Laboratories of Canada (ULC) which cover gypsum board, accoustical tile and spray on protection systems. Reference to these published listings should be made in detailing ceiling construction. Check your UL directory for the latest updating of these listings, or see the UL website at or ULC website at ulc/online directories.asp 1

6 FIRE RATINGS Hambro Product UL/ULC/cULC Rating (hr.) Slab thickness (3) Ceiling Beam Rating D500 LH (1) MD2000 (2) Design No. (mm) (in.) (hr.) x x - I-506 x x - I /2 Gypboard 1 /2 (12.7 mm) /2 Gypboard 1 /2 (12.7 mm) / /2 Gypboard 1 /2 (12.7 mm) /4-3 Gypboard 1 /2 (12.7 mm) x I Gypboard 1 /2 (12.7 mm) 1 1 /2 x I /2-2 3 /4 Spray on 1 / x /4 Spray on 1 x x /2 Suspended or panel - G x /4 Suspended or panel - x x x G Suspended or panel Suspended or panel 3 x x /2 Suspended or panel 3 G x /4 Suspended or panel 3 x x x G /4 Suspended or panel 2 x x x G Suspended or panel Suspended or panel 3 x x /2 (3) Gypboard 1 /2 (12.7 mm) x G /4 (3) Gypboard 1 /2 (12.7 mm) 2 x x x /2 (3) Gypboard 1 /2 (12.7 mm) 3 x x - G /4 Gypboard 5 /8 (16 mm) 3 x x - G Varies (3) Spray on - x x - G Varies (3) Spray on - (1) For LH Series, add 1 /4 inch concrete for slab thickness (2) For MD2000 series, the thickness shown in this table is above the decking (deck thickness = 1 1 /2 ) (3) Normal and lightweight concrete 2

7 ACOUSTICAL PROPERTIES 3. ACOUSTICAL PROPERTIES SOUND TRANSMISSION Because sound transmission depends upon a number of variables relating to the installation and materials used, Hambro makes no representations about the sound transmission performance of its products as installed. You should consult with a qualified acoustical consultant if you would like information about sound performance. HAMBRO SOUND INFORMATION All product tests were performed at NGC Testing Services, Buffalo NY, SOUND TRANSMISSION CLASS (STC) The STC is a rating that assigns a numerical value to the sound insulation provided by a partition separating rooms or areas. The rating is designed to match subjective impressions of the sound insulation provided against the sounds of speech, music, television, office machines and similar sources of airborne noise that are characteristic of offices and dwellings. STC RATINGS: WHAT THEY MEAN IMPACT INSULATION CLASS (IIC) The Impact Insulation Class (IIC) is a rating designed to measure the impact sound insulation provided by the floor / ceiling construction. The IIC of any assembly is strongly affected by and dependant upon the type of floor finish for its resistance to impact noise transmission. The following chart is provided as a reference only. The calculations of sound rating and design of floor/ceiling assemblies with regard to acoustical properties is a building designer responsibility. Hambro Assemblies STC IIC 2 1/2 slab, 1 layer 1/2 drywall 3 slab, 1 layer 1/2 drywall IMPACT OF FLOOR FINISHES & HAMBRO FLOOR SYSTEM 4 slab, 1 layer 1/2 drywall slab, 2 layers 1/2 drywall Floor Finishes Additional STC Rating Practical Guidelines 25 Normal speech easily understood 30 Normal speech audible, but not intelligible 35 Loud speech audible, fairly understandable 40 Loud speech audible, but not intelligible 45 Loud speech barely audible 50 Shouting barely audible 55 Shouting inaudible IIC points Carpet and Pad 24 Homasote 1/2 comfort base 18 under wood laminate 6 mm cork under engineered hardwood 21 QT scu - QT mm underlayment under ceramic tile Quiet Walk underlayment 19 under laminate flooring Insulayment under engineered wood /2 Maxxon gypsum 28 underlayment over Enkasonic sound control mat with quarry tile over Noble Seal SIS 1 1/2 Maxxon gypsum 29 underlayment over Enkasonic sound control mat with wood laminate floor over silent step 1 1/2 Maxxon gypsum 27 underlayment over Enkasonic sound control mat w/armstong Commissions Plus Sheet Vinyl * All products tested were on a 2 1 /2 Hambro slab with a one layer 1 /2 drywall ceiling. 1

8 ACOUSTICAL PROPERTIES ACOUSTICAL ASSOCIATIONS & CONSULTANTS The following is a list of acoustical associations that may be found on the World Wide Web. National Counsel of Acoustical Consultants Canadian Acoustical Association Acoustical Society of America Institute of noise Control Engineers As a convenience, Hambro is providing the following list of vendors who have worked with this product. This list is not an endorsement. Hambro has no affiliation with these providers, and makes no representations concerning their abilities. Siebein Associates, Inc. 625 NW 60th Street, Suite C Gainesville, FL Telephone : Octave Acoustique, Inc. Christian Martel, M.Sc. Arch 963 Chemin Royal Saint-Laurent-de-l Île-d Orléans, (Québec) Canada G0A 4N0 Telephone : Acousti-Lab Robert Ducharme C.P Ste-Anne-des-Plaines (Québec) Canada J0N 1H0 Telephone :

9 DESIGN PRINCIPLES AND CALCULATIONS 4. DESIGN PRINCIPLES AND CALCULATIONS 4.1 DESIGN THE HAMBRO The slab component of the Hambro Composite Floor System behaves as a continuous one-way slab carrying loads transversely to the joists, and often is required to also act as a diaphragm carrying lateral loads to shear walls or other lateral load resisting elements. The slab design is based on CSA Standard A , Design of Concrete Structures which stipulates that in order to provide adequate safety level, the factored effects shall be less than the factored resistance. S ø R Where = load factor, taking into account the probability of exceeding the specified load S ø R = load effect (dead or live) = performance factor = member resistance Exterior span: M f = W f L 1 2 / 11 Interior span: M f = W f L i 2 / NEGATIVE MOMENT First interior support: M f = W f L 2 / 10 At other interior supports: M f = W f L 2 / SHEAR At face of first interior support: V f = 1.15 W f L 1 / 2 At other interior supports: V f = W f L i / 2... Location... Location... Location... Location... Location... Location EFFECTS OF LOADING The Canadian concrete code (CSA Standard A ) cl requires that we consider dead load to act simultaneously with the live load applied on: i) Adjacent spans (maximum negative moment at support) or ii) Alternate spans (maximum positive moment at mid-span). However, if criteria (a) thru (c) of cl are satisfied, the following approximate value may be used in the design of one-way slabs. Refer to fig. 4 for location of the design moments. Where W f = Total factored design load = 1.25 x dead x live L 1 = First interior span L i = Interior spans L = Average of two adjacent spans Note: L is clear span (mm) S is joist spacing (mm) L = (S) POSITIVE MOMENT Extra mesh at 1 & 2 when required Location indexing numbers 1 S 2 /3 3 3 Spacing S 1 Spacing S 2 Spacing S i Fig. 4 1

10 DESIGN PRINCIPLES AND CALCULATIONS CONCENTRATED LOAD In addition to the previous verification, the National Building Code of Canada cl (1) requires consideration of a minimum concentrated load to be applied over an area of 750 mm x 750 mm. The magnitude of the load depends on the occupancy. This loading does not need to beconsidered to act simultaneously with the specified uniform live load. The intensity of concentrated loads on slabs is reduced due to lateral distribution. One of the accepted methods of calculating the effective slab width which is used by Hambro actually appears in Section 317 of the British Standard Code of Practice CP114 and is reproduced in fig. 5. Note that the amount of lateral distribution increases as the load moves closer to mid-span, and reaches a maximum of 0.3L to each side; the effective slab width resisting the load is a maximum of load width + 0.6L. An abbreviated summary of the calculations is shown in tables 6 and 7. A A Load Slab X L Effective width 1.2 (X) ( 1- X L) 0.3L Load width Section A-A Fig. 5 Lateral Distribution of Concentrated Loads 2

11 DESIGN PRINCIPLES AND CALCULATIONS TABLE 6: Concentrated Loads with mm (4-1 1 /4 ) Joist Spacing f c = 20 MPa (3 000 psi), F y = 400 MPa ( psi) for Wire Mesh CONCENTRATED MESH SIZE SPECIAL REMARKS LOAD THICKNESS 152 x 152 (6 x 6) (See fig. 1) MW18.7 x MW18.7 Extra and (6/6) OFFICE BUILDING 70 mm (2 3 /4 ) MW18.7 x MW18.7 Single layer throughout No to (6/6) but S mm chairs on 90 mm (3 1 /2 ) MW25.7 x MW25.7 Single layer throughout Top chord 9 kn on (4/4) 750 mm x 750 mm MW25.7 x MW25.7 Single layer throughout 100 mm (4 ) (4/4) to MW13.3 x MW13.3 (8/8) Double layers throughout 125 mm (5 ) or MW18.7 x MW18.7 (6/6) MW18.7 x MW18.7 Double layers throughout (6/6) PASSENGER CAR * MW25.7 x MW25.7 Extra No (4/4) chairs on 90 mm (3 1 /2 ) to MW25.7 x MW25.7 Single layer throughout Top chord 11 kn on 115 mm (4 (4/4) but S1 /2 ) mm 750 mm x 750 mm MW13.3 x MW13.3 Double layers throughout plus 50 mm asphalt (8/8) + Extra MW13.3 x MW13.3 Double layers throughout (8/8) but S mm MW18.7 x MW18.7 Double layers throughout No PASSENGER CAR * (6/6) chairs on 90 mm (3 1 /2 ) 18 kn on MW25.7 x MW mm x 750 mm to (4/4) Extra and Top chord plus 50 mm asphalt 115 mm (4 1 /2 ) MW25.7 x MW25.7 (4/4) Single layer throughout but S mm * See CAN3-S for Parking Structures Design for more information. TABLE 7: Concentrated Loads with mm (5-1 1 /4 ) Joist Spacing f c = 20 MPa (3 000 psi), F y = 400 MPa ( psi) for Wire Mesh CONCENTRATED MESH SIZE SPECIAL REMARKS LOAD THICKNESS 152 x 152 (6 x 6) (See fig. 4) MW25.7 x MW25.7 Extra OFFICE BUILDING 70 mm (2 3 / 4 ) (4/4) 9 kn on to MW18.7 x MW18.7 Double layers throughout 750 mm x 750 mm 100 mm (4 ) (6/6) PASSENGER CAR * 90 mm (3 1 / 2 ) MW18.7 x MW18.7 Double layers throughout 11 kn on to (6/6) but S mm 750 mm x 750 mm 115 mm (4 1 / 2 ) MW25.7 x MW25.7 Single layer throughout plus 50 mm asphalt (4/4) + Extra and PASSENGER CAR * 90 mm (3 1 / 2 ) MW18.7 x MW18.7 Double layers throughout 18 kn on to (6/6) + Extra and 750 mm x 750 mm 115 mm (4 1 / 2 ) MW25.7 x MW25.7 Double layers throughout plus 50 mm asphalt (4/4) No chairs on Top chord No chairs on Top chord No chairs on Top chord * See CAN3-S for Parking Structures Design for more information. NOTE: For other configurations, please contact your Hambro representative. 3

12 DESIGN PRINCIPLES AND CALCULATIONS MOMENT CAPACITY The factored moment resistance of a reinforced concrete section, using an equivalent rectangular concrete stress distribution is given by: t d M r = ø s A s F y (d - a/2) a = depth of the equivalent concrete stress block = ø s A s F y 1 ø c f c b Where F y = yield strength of reinforcing steel (400 MPa) f c = compressive strength of concrete (20 MPa) A s = area of reinforcing steel in the direction of analysis (mm 2 /m width) 1 = f c 0.67 b = unit slab width (mm) d = distance from extreme compression fiber to centroïd of tension reinforcement (mm) (see tables 8 and 9 on pages 19 and 20) ø s = performance factor of reinforcing steel (0.85) ø c = performance factor of concrete (0.65) SHEAR CAPACITY The shear stress capacity V, which is a measure of diagonal tension, is unaffected by the embedment of the section as this principal tensile crack would be inclined and radiate away from the section. The factored shear capacity is given by: V r = V c = ø c ß f c b w d (CSA A , clause ) Fig. 6 c C T a SERVICEABILITY LIMIT STATES CRACK CONTROL PARAMETER When the specified yield strength, F y, for tension reinforcement exceeds 300 MPa, cross sections of maximum positive and negative moments shall be so proportioned that the quantity Z does not exceed 30 kn/mm for interior exposure and 25 kn/mm for exterior exposure. Ref. CSA A , clause The quantity Z limiting distribution of flexural reinforcement is given by: 3 Z = f s dc A x 10-3 Where f s = stress in reinforcement at specified loads taken as 0.6F y d c = thickness of concrete cover measure from extreme tension fibre to the center of the reinforcing bar located closest thereto (d c 50 mm) Width Bar spacing Fig DEFLECTION CONTROL For one-way slabs not supporting or attached to partitions of other construction likely to be damaged by large deflections, deflection criteria are considered to be satisfied if the following span/depth ratio are met: at location t n/24 at location t n/28 (CSA A , table 9.2) n=space between joists or joist to wall d c d c Where = 1.0 for normal density concrete ß = 0.21 = (CSA A , clause ) b w = b = width of slab And ø c,f c and d are as previously described. 4

13 DESIGN PRINCIPLES AND CALCULATIONS DESIGN EXAMPLE METRIC Verify the standard Hambro slab under various limit states (strength and serviceability) for residential loading. Dead load: 3 kpa Live load: 2 kpa Slab thickness: 70 mm Joist spacing: mm Concrete strength (f c ): 20 MPa at 28 days Area of steel: 152 x 152 MW18.7 x MW18.7 A s = 123 mm 2 /m 1- Analysis (Per Meter of Slab) a) Factored Load W f = 1.25 x x 2 = 6.75 kn/m 2 b) Maximum Positive Moment at M f + = 6.75 x /11 = 0.88 kn m c) Maximum Negative Moment at M f = 6.75 x /10 = 0.97 kn m d) Maximum Shear V f = 6.75 x 1.15 x 1.25 = 4.85 kn 2 a = ø s A s F y 0.85 x 123 x 400 = 1 ø c f c b 0.82 x 0.65 x 20 x a = 3.92 mm M r = ø s A s F y (d - a/2) M r = 0.85 x 123 x 400 ( ) x M r = 1.61 kn m > M f = 0.97 kn m OK b) Shear Capacity V r = ß ø c f c b w d = 0.21 x 1 x 0.65 x 20 x x 40.4 x 10-3 = kn >> V f = 4.85 kn OK 3- Serviceability a) Crack Control d c = t ø/2 = 29.6 mm 50.0 mm OK A = 2 x d c x 152 = mm 2 f s = 0.6 x 400 = 240 MPa Z = f s 3 d c A x 10-3 Z = 240 x x x 10-3 Z = 15.5 kn/mm < 25.0 kn/mm exterior exposure OK < 30.0 kn/mm interior exposure OK 2- Resistance a) Moment Capacity ø = ø = 4 x A wire π 4 x 18.7 π = 4.88 mm where ø = wire diameter at mid-span: 20 mm concrete cover d = t - (20 + ø/2) = 70 - ( /2) = 47.6 mm at support: 38 mm depth of embedded top chord d = 38 + ø/2 d = /2 = 40.4 mm governs b) Deflection Control Span/depth = 1 250/70 = 18 Exterior span = 18 < 24 Interior span = 18 < 28 OK OK 1 = f c = OK 5

14 DESIGN PRINCIPLES AND CALCULATIONS TABLE 8: Slab Capacity Chart (Total Unfactored Load in kn/m 2 ) * d MESH SIZE (152 mm x 152 mm) mm JOIST SPACING mm JOIST SPACING THICKNESS (t) (mm) f c = 20 MPa, = kg/m 3 Exterior Interior Exterior Interior F y = 400 MPa (1) (1) (1) (1) 70 mm t < 90 mm NO CHAIR 2 layers MW9.1 x MW MW18.7 x MW mm t < 115 mm NO CHAIR 41 MW25.7 x MW MW25.7 x MW layers MW13.3 x MW layers MW18.7 x MW layers MW25.7 x MW mm t 140 mm WITH 75 mm CHAIR INTERIOR AND EXTERIOR EXPOSURE (1) 2 layers MW18.7 x MW layers MW25.7 x MW layers MW34.9 x MW * Loads indicated are the total allowable service load (W s ) that the slab can carry. W s is determined from the conservative equation: W s = (W f D) / D Where W f = factored total load D = minimum dead load (weight of slab + joist) Wire mesh designation: 152 x 152 MW9.1 x MW9.1 = 6 x 6-10/ x 152 MW13.3 x MW13.3 = 6 x 6-8/8 152 x 152 MW18.7 x MW18.7 = 6 x 6-6/6 152 x 152 MW25.7 x MW25.7 = 6 x 6-4/4 152 x 152 MW34.9 x MW34.9 = 6 x 6-2/2 (1) Wire mesh : 1 layer on top chord and 1 layer on high chair Note: Slab capacities are based on mesh over joist raised as indicated. 6

15 DESIGN PRINCIPLES AND CALCULATIONS TABLE 9: Slab Capacity Chart (Total Unfactored Load in psf) * d MESH SIZE (6 x 6 ) /4 JOIST SPACING /4 JOIST SPACING THICKNESS (t) (in.) f c = psi, = 145 lb./sq. ft. Exterior Interior Exterior Interior F y = psi (1) (1) (1) (1) 2 3 / 4 t < 3 1 / 2 NO CHAIR 2 layers 10/ layer 6/ layer 4/ / 2 t 4 1 / 2 NO CHAIR layer 4/ layers 8/ layers 6/ layers 4/ / 2 t 5 1 / 2 WITH 3 CHAIR INTERIOR AND EXTERIOR EXPOSURE (1) 2 layers 6/ layers 4/ layers 2/ * Loads indicated are the total allowable service load (W s ) that the slab can carry. W s is determined from the conservative equation: W s = (W f D) / D Where W f = factored total load D = minimum dead load (weight of slab + joist) (1) Wire mesh : 1 layer on top chord and 1 layer on high chair Note: Slab capacities are based on mesh over joist raised as indicated. 7

16 DESIGN PRINCIPLES AND CALCULATIONS 4.2 NON-COMPOSITE DESIGN TOP CHORD PROPERTIES - D500 TM 2 N.A. of top chord C r Y 17 mm (0.68 ) Y D d T r Fig. 8 The top chord must be verified for the loads applied at the non-composite stage. From the previous example, we have the following results: 1- Factored Loading Dead load: 70 mm slab: 1.65 kn/m 2 Formwork and joist: 0.24 kn/m kn/m 2 x 1.25 = 2.36 kpa Live load: Construction live load: 0.95* kn/m 2 x 1.5 = 1.43 kpa Total factored load = 3.79 kpa * Reduces beyond mm span at a rate of 0.05 kn/m 2 each 760 mm of span. 2- Factored moment resistance M r nc =C r d or T r d i.e. W nc L 2 =C r d or T r d, whichever is the lesser 8 W nc = 3.79 x joist spacing = kn/m L = clear span mm C = area of top chord (mm 2 ) x factored compressive resistance (MPa) T = area of bottom chord (mm 2 ) x factored tensile resistance (MPa) d = effective lever arm (m) = (D + 2 mm - y) /1 000 From the above formula, the maximum limiting span may be computed for the non-composite (construction stage) condition. For spans beyond this value, the top chord must be strengthened or joist propped. Strengthening of the top chord, when required, is usually accomplished by installing one or two rods in the curvatures of the S part of the top chord. The bottom chord is sized for the total factored load which is more critical than the construction load. Hambro top chord properties are provided to assist you in computing the non-composite joist capacities. 2 mm (0.08 ) X Top Chord F y Bottom Chord F y Top Chord F y Bottom Chord F y Fig. 9 METRIC t = 2.3 mm A net * = 361 mm 2 I x = 2.74 x 10 5 mm 4 = 350 MPa = 380 MPa IMPERIAL t = in. A net * = in. 2 I x = in. 4 = 50 ksi = 55 ksi A net *= Effective area according to CAN3-S Y t X 8

17 DESIGN PRINCIPLES AND CALCULATIONS TOP CHORD PROPERTIES - MD TOP CHORD PROPERTIES - LH Y Y 11.6 mm (0.45 ) 3.5 mm (0.14 ) X X X X t 5.3 mm (0.21 ) t Y Fig. 10 Y Fig. 11 METRIC t = 2.3 mm A net * = 422 mm 2 I x = 3.65 x 10 5 mm 4 METRIC t = 2.3 mm A net * = 623 mm 2 I x = 2.56 x 10 5 mm 4 Top Chord F y = 350 MPa Top Chord F y = 350 MPa Bottom Chord F y = 380 MPa Bottom Chord F y = 380 MPa IMPERIAL t = in. A net * = in. 2 I x = in. 4 IMPERIAL t = in. A net * = in. 2 I x = in. 4 Top Chord F y = 50 ksi Top Chord F y = 50 ksi Bottom Chord F y = 55 ksi Bottom Chord F y = 55 ksi A net *= Effective area according to CAN3-S

18 DESIGN PRINCIPLES AND CALCULATIONS 4.3 COMPOSITE DESIGN FLEXURE DESIGN In the past, conventional analysis of composite beam sections has been linearly elastic. Concrete and steel stresses have been determined by transforming the composite section to a section of one material, usually steel, from which stresses are then determined with the familiar formula, f = My/I, and then compared to some limiting values which have been set to ensure an adequate level of safety. Although this procedure is familiar to most engineers, it does not predict the level of safety with as much accuracy as does an ultimate strength approach which is based on the actual failure strengths of the component materials. It is now known that the flexural behavior at ultimate failure stages of composite concrete/steel beams and joists is similar to that of reinforced concrete beams - the elastic neutral axis begins to rise under increasing load as the component materials are stressed into their inelastic ranges. The typical stress-strain characteristics of the concrete and steel components are shown in fig. 12. The various loading stages of the Hambro composite joist are indicated in fig. 13. As load is first applied to the composite joist, the strains are linear. The elastic neutral axis, concrete and steel stresses can be predicted from the conventional transformed area method. Generally speaking, the Hambro composite joist behaves in this elastic manner when subjected to the total working loads. With increasing load, failure always begins initially with yielding of the bottom chord. In (a), all of the bottom chord has just reached the yield stress, F y. The maximum concrete strains will likely have just progressed into the inelastic concrete range, but the maximum concrete stress will still be less than 1 f c. With a further increase in load, large inelastic strains occur in the bottom chord and the ultimate tensile force, T u, remains equal to A s F y. The strain neutral axis rises, as does the centroid of the compresssion force. Part (b) depicts the stage when the maximum concrete stress has just reached 1 f c. At this stage, the ultimate resisting moment has increased slightly due to a small increase in Iever arm. f c Steel stress Concrete stress Elastic range Inelastic range Concrete strain F u F y Inelastic range Elastic range E y Steel strain Fig. 12 Concrete and Steel Stress - Strain Curves 10

19 DESIGN PRINCIPLES AND CALCULATIONS VARIOUS FLEXURE FAILURE STAGES 1 f c 1 f c 1 ø c f c f c C f a C u C t Simplified concrete stress block Joist depth d Strain line e T u = A s F y T u = A s F y T u = A s F y E y Elastic strain E y Inelastic strain Elastic strain Inelastic strain (a) Initial steel yield (b) Secondary yield stages (c) Ultimate stage Fig. 13 Upon additional load application, the steel and concrete strains progress further into their inelastic ranges. The strain neutral axis continues to rise and the lever arm continues to increase as the centroid of compression force continues to rise. In (c), final failure occurs with crushing of the upper concrete fibres. At this point, the maximum fever arm e, has been reached. In load capacity calculations, the simplified concrete stress block as shown in (c) is universally used. According to CAN3-S16.1-M01 (cl ) and CSA A (cl ), the factored resisting moment of the composite section is given by: M rc = ø s A s F y e = T r e Note: F y = yield point of steel ø c = concrete performance factor = 0.65 f c = concrete compressive strength b e = effective width of concrete top flange = the lesser of - joist spacing, or - span /4. To determine the total allowable service load W s (see load tables), we convert the factored moment into a factored linear loading. M f = W f L 2 (single span moment) 8 Where e = d + slab thickness a/2 y d = joist depth a = T r / 1 ø c f c b e ø s = steel performance factor = 0.90 A s = area of bottom chord y = neutral axis of bottom chord W f = 8 M f L 2 And W s = (W f D) + D 1.5 Where D = weight of (slab + joist) 11

20 DESIGN PRINCIPLES AND CALCULATIONS 4.4 INTERFACE SHEAR The Hambro joist comprises a composite concrete slabsteel joist system with composite action achieved by the shear connection developed by two means: (i) by anchorage provided at the joist ends by means of a steel angle which acts both as a bearing shoe and as anchorage for the end diagonal, thereby producing horizontal bearing forces. This horizontal force is closely associated with the concrete strength and the vertical size of the steel angle plate on the shoe. (ii) by bond or friction between the partially embedded specially profiled top chord. Composite action between the section and the concrete slab exists because of the unique shear resistance developed along the interface between the two materials. This shear resistance, which has been called bond or interface shear is primarily the result of a locking or clamping action in the longitudinal direction between the concrete and the section when the composite joist is deflected under load. Another contributing factor to the shear resistance is the lateral compression stress or poisson s effect which results from slab continuity in the lateral direction. This continuity prevents lateral expansion from occuring as a result of longitudinal compression stresses and thus lateral compression stress results. However, this effect has been ignored in determining interface shear capacity which has been based on full scale testing of spandrel joists having only a 150 mm slab overhang on one side for its entire span length. A cross-section of a test specimen is illustrated in fig mm (2 3 /4 ) 150 mm (6 ) mm (4-1 1 /4 ) mm (4-1 1 /4 ) 150 mm (6 ) It was decided to base the limiting interface shear value on this most critical condition as this could often occur in practice with large duct openings. Also, one would expect some additional shear resistance to occur due to some form of friction (or plain bond ) mechanism, however, full scale tests have not shown any significant differences in results among specimens whose section were unpainted or painted. Shear resistance of the steel-concrete interface can be evaluated by either elastic or ultimate strength procedures; both methods have shown good correlation with the test results. The interface shear force resulting from superimposed loads on the composite joist may be computed, using the elastic approach, by the well known equation:... (A) Where q = horizontal shear flow per mm of length (N/mm) V = vertical shear force at the section (N) due to superimposed loads Q = statical moment of the effective concrete in compression (hatched area) about the elastic N.A. of the composite section (mm 3 ) I C = moment of inertia of the composite joist (mm 4 ) And Q = by (Y c - y/2) and y = y c but t n Where b = effective concrete flange width (mm) = smallest of L/4 or joist spacing n = modular ratio = E s /E c = 9.4 for f c = 20MPa t = slab thickness (mm) Y c = depth of N.A. from top of concrete slab y = Y c when N.A. lies within slab = t when N.A. lies outside slab case 1: N.A. within slab (y = Y c ) t q = VQ I C y b N.A. Y c D Fig. 14 case 2: N.A. outside slab (y = t) b y = t N.A. Fig. 15 Y c 12

21 DESIGN PRINCIPLES AND CALCULATIONS For a uniformly loaded joist, the average interface shear s, at ultimate load when calculated by ultimate strength principles, would be: s = 2T u L... (B) and would represent the average shear force, per unit length, between the points of zero and maximum moment. Some modification to this formula would occur when the strain neutral axis at failure would be located within the section. As this modification is slight and would only occur with bottom chord areas greater that mm 2, it is neglected. The following compares the elastic and ultimate approaches: Since M u = T u d u equation (B) can be rewritten: s = 2M u d u L... (C) Also, for a uniformly distributed load, M u = V u L 4... (D) This verifies that q and s are closely related and that the interface shear force does, in fact, vary from a maximum at zero moment (maximum vertical shear) to a minimum at maximum moment (zero vertical shear). The more recent full testing programs have consistently established a failure value for the horizontal bearing forces and the friction between steel and concrete. An additional contributing factor is a hole in the section at each 178 mm on the length. (i) (ii) Horizontal bearing forces The test has defined an ultimate value for the end bearing shoe B u = 222 kn for a concrete strength = 20 MPa Friction between steel and top chord The failure value for the interface shear q u = 36.9 N/mm. This is sometimes converted to bond stress u = q / embedded S perimeter = q /178 mm. Hence, the ultimate bond stress u = 36.9 / 178 = 207 kpa. The safety limiting interface shear is defined by using a safety factor of 2 on point (i) and (ii). Subscipts u, are added to equation (A) to represent the arbitrary q force at failure: q u = V u Q I c... (E) Combining (C) and (E) results in: q u = d u L x V u Q s... (F) 2M u I c and, substituting (D) into equation (F), q u = 2Qd u s I c... (G) The value I c /Qd u has been calculated for the various Hambro composite joist sizes. It is constant, and = 1.1. Substituting this in (G), gives: q u = 1.82 s 13

22 T1 T2 T3 T4 DESIGN PRINCIPLES AND CALCULATIONS 4.5 WEB DESIGN VERTICAL SHEAR The web of the steel joist is designed according to CAN3-S16.1-M01. Clause requires the web system to be proportioned to carry the total vertical shear V f. The loading applied to the joist is as follows: a) A uniformly distributed load equal to the total dead and live loads. b) An unbalanced load with 100% of the total dead load and live loads on any continuous portion of the joist and 25% of the total dead and live loads on the remainder to produce the most critical effect on any component. c) A factored concentrated load of 13.5 kn (3.0 kips) applied at any panel point. The above loadings need not be applied simultaneously. These assumptions result in calculated bar forces which have been shown by test to be as much as 15% higher than the actual values because the slab, acting compositely with the ~ section, is stiff enough to transmit some load directly to the support. This is particularly true for web members at the joist ends those which are subjected to the highest vertical shear. However, the slab shear contribution is disregarded when designing the webs. Due consideration of the total end reaction being concentrated at the shoe shall be taken by the specifying engineer or architect in the design of supporting members EFFECTIVE LENGTH OF COMPRESSION DIAGONAL The webs are dimensioned using cl for tension members and cl for compression member. The effective length of web member KL is taken as 1.0 times the distance between the intersection of the axis of the web and the chords. Except for continuous web member. Note: The web members are sized for the loading specified including concentrated loads where applicable. Furthermore, the webs are designed according to the latest recommendations of the Canadian Institute of Steel Construction (CISC). V f1 V f2 V f3 V f4 V f5 V f H 1 R C 1 C 2 W 1 W 2 W C W C W C W C (Clear span mm or 1 /2 ) C 3 C 4 T5 C 5 d Fig. 16 D500 TM and MD2000 Geometry 14

23 DESIGN PRINCIPLES AND CALCULATIONS 4.6 DIAPHRAGM DESIGN THE HAMBRO AS A DIAPHRAGM With the increasing use of the Hambro system for floor of buildings in earthquake prone areas such as Anchorage, Los Angeles, Vancouver, Montreal and Quebec City or in hurricane prone areas such as Florida as well as for multistorey buildings where shear transfer could occur at some level of the building due to the reduction of the floor plan, it is important to develop an understanding of how the slabs will be able to transmit horizontal loads while being part of the Hambro floor system. The floor slab, part of the Hambro system, must be designed by the project structural engineer as a diaphragm to resist horizontal loads and transmit them to the vertical bracing system. Any diaphragm has the following limit states: 1) Shear strength between the supports 2) Out of plane buckling 3) In plane deflection of the diaphragm 4) Shear transmission at the supports A diaphragm works as the web of a beam spanning between or extending beyond the supports. In the case of a floor slab, the slab is the web of the beam spanning between or extending beyond the vertical elements designed to transmit to the foundations the horizontal loads produced by earthquake or wind. We will use a simple example of wind load acting on a diaphragm part of a horizontal beam forming a single span between end walls. The structural engineer responsible for the design of the building shall establish the horizontal loads that must be resisted at each floor of the building for the wind and earthquake conditions prevailing at the building location. The structural engineer must also identify the vertical elements that will transmit the horizontal loads to the foundations in order to calculate the shear that must be resisted by the floor slab SHEAR STRENGTH BETWEEN SUPPORTS A series of fourteen specimens of concrete slabs, part of a Hambro floor system, were tested in the laboratories of Carleton University in Ottawa. The purpose of the tests was to identify the variables affecting the in plane shear strength of the concrete slab reinforced with welded wire mesh. The specimens were made of slabs with a concrete thickness of 63 mm (2.5 ) or 70 mm (2.75 ) forming a beam with a span of 610 mm (24 ) and a depth of 610 mm (24 ). This beam was loaded with two equal concentrated loads at 152 mm (6 ) from the supports. The other variables were: 1) The size of the wire mesh 2) The presence or absence of the Hambro joist embedded top chord parallel to the load in the shear zone 3) The concrete strength It was found that the shear resistance of the slab is minimized when the shear stress is parallel to the Hambro joist embedded top chord. A conservative assumption could be made that the concrete confined steel wire mesh is the only element that will transmit the shear load over the embedded top chord. In the following example of the design procedure, we will take into account that the steel of the wire mesh is already under tension stresses produced by the continuity of the slab over the Hambro joist, and that the remaining capacity of the steel wire mesh will be the limiting factor for the shear strength of the slab. The largest bending moment is over the embedded top chord and is calculated for one meter width. In using the example from section page 5, the non factored moment is: Dead load*: Mf d = 3KPa x (1.2m) 2 / 10 = 0.43 kn m Live load*: Mf L = 2KPa x (1.2m) 2 / 10 = 0.29 kn m. 1) Loads Factored dead load: Factored live load: Factored total load: 1.25 x 3.0 = 3.75 kpa 1.50 x 2.0 = 3.00 kpa 6.75 kpa And thus the factored live load accounts for 44% of the factored total load. 2) Bending moment in the slab between joists due to gravity loads The smallest lever arm between the compression concrete surface and the tension steel of the wire mesh is also over the embedded top chord. This dimension allows us to calculate the factored bending capacity of the slab to be M r = 1.61 kn m*. To establish the shear capacity of steel wire mesh for a slab unit width of one meter, we use the following formula adapted from CSA A clause 11.5 and simplified to calculate the resistance of the reinforcing steel only, considering a shear crack developing at a 45 degree angle and intersecting the wire mesh in both directions. V r = ø s x A s x F y x cos (45 ) = 0.85 x 2 x 123 x 400 x 0.707/1 000 = 59.1 kn for a meter width of slab * See page 5 for calculation. 15

24 DESIGN PRINCIPLES AND CALCULATIONS DESIGN EXAMPLE METRIC Wind load = 1.2 kn/m 2 First Hambro Joist B = mm L = mm Fig. 17 From figure 17 we can establish the horizontal shear that the floor diaphragm will have to resist in order to transfer the horizontal load from the walls facing the wind to the perpendicular walls where a vertical bracing system will bring that load down to the foundation. Total wind pressure load from leeward and windward faces: Storey height: Span of the beam with the floor slab acting as the web: Length of the walls parallel to the horizontal force: 1.2 kpa 3.7 m 35.5 m 18.3 m For the purpose of our example the factored wind load is the maximum horizontal load calculated according to the provisions of the local building code, but earthquake load shall also be calculated by the structural design engineer of the project and the maximum of the two loads should be used in the calculation. V f = w f x span / 2 = 3.7 x 1.2 x 35.5 / 2 = 78.8 kn In our example, the end reaction is distributed along the whole length of the end wall used to transfer the load, 18.3 m in our example. V f = 78.8 / 18.3 = 4.3 kn for a meter width of slab Considering the reduction factor from the National Building Code 2005 for the simultaneity of gravity live load and horizontal wind load for our example, the structural engineer of the project could verify the diaphragm capacity of the floor slab and it s reinforcing by verifying that the moment and shear interaction formulas used below are less than unity: Load Combinaison 1: 1.25 x M fd x M fl M r M r Doesn t control Load Combinaison 2: 1.25 x Mfd x MfL x V f 1 M r M r V r (1.25 x 0.43) + (1.5 x 0.29 ) x 4.3 = OK (Controls) Load Combinaison 3: 1.25 x M fd x M fl x V f 1 M r M r V r (1.25 x 0.43) + (0.5 x 0.29) x 4.3 = OK These verifications indicate that the wire mesh imbedded in the slab would provide enough shear strength to transfer those horizontal loads OUT OF PLANE BUCKLING The floor slab, when submitted to a horizontal shear load, may tend to buckle out of plane like a sheet of paper being twisted. The minimum thickness of Hambro concrete slab of 65 mm (2 1 /2 ) is properly held in place by the Hambro joists spaced at a maximum mm (5-1 1 /4 ) and who are attached at their ends to prevent vertical movement, so the buckling length of the slab itself will be limited to the spacing of the joist and the buckling of a floor will normally not be a factor in the design of the slab as a diaphragm IN PLANE DEFLECTION OF THE DIAPHRAGM As for every slab used as a diaphragm, the deflection of the floor as a horizontal member between the supports provided by the vertical bracing system shall be investigated by the structural engineer of the building to verify that the horizontal deflection remains within the allowed limits SHEAR TRANSMISSION TO THE VERTICAL BRACING SYSTEM The structural engineer of the project shall design and indicate on his drawings proper methods and/or reinforcing to attach the slab to the vertical bracing system over such a length as to prevent local overstress of the slab capacity to transfer shear. 16

25 DESIGN PRINCIPLES AND CALCULATIONS 4.7 LATERAL LOAD DISTRIBUTION Line loads are often encountered in construction, i.e. a concrete block wall or even a load bearing concrete block wall. It is always desirable to have a floor system that is stiff enough to allow these line loads to be distributed to adjacent joists rather than be carried by the joist that happens to be directly under it. The Hambro Composite Floor System provides the designer with this desirable feature. This was conclusively proven by randomly selecting a sample of five similar adjacent joists in a bay in an apartment structure and line loading the centre one. The joists were 300 mm (12 ) deep, had a clear span of mm (21-4 ) and a 75 mm (3 ) thick slab. The loads were applied using brick pallets. At every load stage, steel strains as well as deflections were measured. The distribution of load to each of the five joists can be determined by comparing deflections or stresses at similar locations in the five joists under investigation. Tests have demonstrated that for a line load applied to a typical joist in a bay, the actual distribution of load to that joist is approximately 40% of the applied load. The distribution of load to the adjacent joist on either side is approximately 21% of the applied load and to the next adjacent joist approximately 9% of the applied load. 17

26 DESIGN PRINCIPLES AND CALCULATIONS 4.8 MINI-JOISTS H SERIES The standard Hambro section, being 95 mm (3 3 /4 ) deep, possesses sufficient flexural strength to become the major steel component of the mini-joist series. The three sizes that are currently being used are illustrated in the figure below and spans beyond mm (8 ) can be achieved with the heavier SRTC unit. Other sizes are also available. The composite capacities of the TC, RTC & SRTC units are calculated on the basis of elastic tee beam analysis. The effective flange width, b, equals the lesser of span/4, or joist spacing. With the mini-joist spaced at mm (4-1 1 /4 ), b is dictated by span/4. The load table lists total unfactored load capacity in kn/m (plf) for span up to 2.64 m (8-8 ). Full scale tests have demonstrated consistently that shoe plates are not required for TC and RTC - the section is simply notched at each bearing end with the lower horizontal portion of the becoming the actual bearing surface. Note that where the non-composite end reaction exceeds 4.5 kn (1.0 kip) the notched ends are reinforced with a 12.7 mm ( 1 /2 ) diameter bar 200 mm (8 ) long. This is to prevent the section from straightening out at the bearing ends. It is interesting to note that this is not a problem during the composite service stage, even with its higher total loads, as the 70 mm (2 3 /4 ) slab carries the vertical shears. TABLE 10: Mini-joist H Series Span Chart TC RTC SRTC PROPERTIES Fig. 18 TYPE CONDITIONS I S MAXIMUM CLEAR SPAN (m) mm 4 x 10 6 mm 3 x 10 3 TC COMPOSITE NON-COMP UP TO 1.25 m RTC COMPOSITE NON-COMP UP TO 1.68 m SRTC COMPOSITE NON-COMP UP TO 2.44 m TABLE 11: Mini-joist H Series Span Chart PROPERTIES TYPE CONDITIONS I S MAXIMUM CLEAR SPAN (ft.) in. 4 in. 3 TC COMPOSITE NON-COMP UP TO 4-1 RTC COMPOSITE NON-COMP UP TO 5-6 SRTC COMPOSITE b = NON-COMP. b = UP TO

27 DESIGN PRINCIPLES AND CALCULATIONS MD2000 SERIES The standard Hambro MD2000 section, being 95 mm (3 3 /4 ) deep, possesses sufficient flexural strength to become the major steel component of the mini-joist series. The two sizes that are currently being used are illustrated in the figure below and spans beyond mm (8 ) can be achieved with the heavier RMD unit. Other sizes are also available. The composite capacities of the MD & RMD units are calculated on the basis of elastic tee beam analysis. The effective flange width, b, equals the lesser of span/4 or joist spacing. With the mini-joist spaced at mm (4-1 1 /4 ), b is dictated by span/4. The load table lists total unfactored load capacity in kn/m (plf) for span up to 2.64 m (8-8 ). Full scale tests have demonstrated consistently that shoe plates are not required - the section is simply notched at each bearing end with the lower horizontal portion of the becoming the actual bearing surface. Note that where the non-composite end reaction exceeds 4.5 kn (1.0 kip) the notched ends are reinforced with a 12.7 mm ( 1 /2 ) diameter bar 200 mm (8 ) long. This is to prevent the section from straightening out at the bearing ends. It is interesting to note that this is not a problem during the composite service stage, even with its higher total loads, as the 70 mm (2 3 /4 ) nominal slab carries the vertical shears. 1 /2 φ rod L 1 5 /8 x 2 x 0.09 LLH 3 /4 φ rod x 3 length at each end L 1 5 /8 x 2 x 0.09 LLH 3 /4 φ rod x 3 length at each end and at each 24 c/c MD Fig. 19 RMD TABLE 12: Mini-joist MD2000 Series Span Chart TYPE CONDITIONS PROPERTIES MAXIMUM CLEAR SPAN (m) I S t= 70mm t=70mm t=85mm t=85mm DL = 3.2 Kpa DL = 3.2 Kpa DL = 3.55 Kpa DL = 3.55 Kpa mm 4 x 10 6 mm 3 x 10 3 LL = 1.9 Kpa LL = 4.8 Kpa LL = 1.9 Kpa LL = 4.8 Kpa MD COMPOSITE NON-COMP RMD COMPOSITE NON-COMP TABLE 13: Mini-joist MD2000 Series Span Chart t = Thickness above steel deck TYPE CONDITIONS PROPERTIES MAXIMUM CLEAR SPAN (ft.) I S t= 2 3 /4 t = 2 3 /4 t = 3 1 /4 t = 3 1 /4 DL = 67 psf DL = 67 psf DL = 74 psf DL = 74 psf in. 4 in. 3 LL = 40 psf LL = 100 psf LL = 40 psf LL = 100 psf MD COMPOSITE NON-COMP RMD COMPOSITE NON-COMP t = Thickness above steel deck 19