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1、Chapter 3 Composite floor with steel profiled 压型钢板-混凝土组合楼板,By Professor Shiming Chen Lecture Notes for Presentation 2013,OBJECTIVE/SCOPE To describe the design of one-way spanning composite slabs, formed using profiled steel sheeting and a concrete topping, including consideration of ultimate and se
2、rviceability limit state design for building structures. 压型钢板、压型钢板分类 压型钢板-混凝土组合楼板 应用范围 设计方法 构造,3.1 Introduction,压型钢板-混凝土组合楼板是指将压型钢板与混凝土通过某种构造措施组合成整体而共同工作的受力构件。 Composite flooring system consists of a cold-formed, profiled steel sheet which acts, not only as the permanent formwork for an in-situ cast
3、 concrete slab, but also as the tensile reinforcement The essential composite action between the steel deck and the concrete slab is provided by some form of interlocking device, capable of resisting horizontal shear and preventing vertical separation at the steel/concrete interface.,Composite slab
4、with profiled steel sheet,it provides a working platform for construction. it acts as formwork for the concrete slab. it constitutes bottom reinforcement for the slab.,Profiled Steel sheeting(a pattern of embossments) 板面的齿槽与压痕可提供界面粘结力；界面的摩擦粘结等,Construction stage: place the profiled steel sheeting ov
5、er the support beams,Construction stage: weld studs through the steel sheeting with portable welding gun,Construction stage: place the light steel reinforcement/ steel mesh,Construction stage: cast concrete,Types of Profiled Sheet 压型钢板类型,Re-entrant types 闭口型压型钢板,Trapezoidal types 开口型压型钢板,Advantages
6、identified as the follows: The steel deck acts as permanent shuttering for the in-situ cast concrete slab, with a consequent saving in time and labor. It once in position, immediately provides a platform to support construction loads and a safe, sturdy working surface. It acts as the tensile reinfor
7、cement. The steel deck geometry can result in a reduction of labor about 30% in the amount of concrete fill required for the floor, significant reduction in dead weight loads .,3.2. DESIGN PRINCIPLES 设计验算,Design Situations（设计工况） Two distinct structural states must be checked: firstly, the temporary
8、state of execution, when only the sheeting resists the applied loads（construction stage 施工阶段）; secondly, the permanent state, after the concrete is bonded to the steel giving composite action（composite stage 正常使用阶段）.,Relevant limit states and load cases are considered for both design situations.,a)
9、Steel deck shuttering（施工阶段） Verifications at the ultimate limit and serviceability limit states are required, with respect to the safety and serviceability of the steel deck acting as formwork for the wet concrete. The effects of any temporary props used during execution, must be taken into account
10、in this design situation. b) Composite slabs （正常使用阶段） Verifications at the ultimate limit and serviceability limit states are required, with respect to the safety and the serviceability of the composite slab after composite behaviour has commenced and any props have been removed.,设计考虑因素：Three major
11、aspects identified for consideration during the design of a composite flooring deck: The steel deck itself must be sufficiently strong and rigid to support the weight to wet concrete during casting-construction stage behavior. The steel deck acting compositely with the hardened concrete, and spannin
12、g between the supporting steel beams, must support the imposed live loading-composite slab action. The steel beams, acting compositely with the hardened concrete through the stud shear connectors must support the imposed live loading-composite beam action.,3.2 Criteria for the design of composite fl
13、oors 设计准则,In design, it is necessary to ensure that the strength and deflections both during construction (when the concrete is still green) and in service (when composite action has been achieved) are satisfactory. Construction stage: the profiled steel deck alone withstands the weight of wet concr
14、ete, workman and equipment. Composite slab stage: the hardened concrete slab, acting compositely with the profiled steel sheet, spans between the supporting beams and carries the imposed live loads,Key points for Construction stage -Profiled steel as shuttering,Installation of the sheeting is carrie
15、d out by laying one or more span lengths over the supporting beams. The sheeting behaves as a folded plate structure and, for low load levels, the behavior is similar to simple beam behavior. At higher load levels, buckling of the component plates may occur. The prediction of buckling stresses on th
16、e component plates can be achieved using classical or energy methods.,The sheeting has to have adequate bending strength and stiffness. The section properties of profiled sheets can be computed based on the analytical methods provided by design codes. Manufacturers prefer to carry out load tests on
17、their products to assess full capacity and provide load-span tables appropriate to each profile. Propping can dramatically reduce deflections.,Key points for composite stage,The steel deck acts as tensile reinforcement to the slab and the development of composite action depends entirely upon adequat
18、e transference of horizontal shear forces at the steel/concrete interface. To evaluate the shear bond resistance at the interface between the concrete and the profiled deck, Porter and Ekberg (1976) proposed a testing program (shear-bond test) now worldwide adopted in determination of the shear bond
19、 resistance for composite slabs.,3.3 BEHAVIOR AND ANALYSIS,Steel deck（混凝土结硬前：压型钢板） During execution when the concrete is wet, the steel deck alone resists the exterior loads. Its behavior is then comparable to that of profiles used for roof decking. The steel deck is subjected mainly to bending and
20、shear; compression due to bending may arise in either the flanges or the web; shear occurs essentially near the supports.,Once the concrete has hardened the steel deck and concrete combine to form a single structural unit, the composite slab. Behavior of a composite slab is analogous to that of a co
21、nventional reinforced concrete slab. The bond between the steel deck and concrete may not be fully effective and longitudinal slip may occur before the steel deck yields.,Composite slab failure mode types,Failure type I :弯曲破坏(flexural failure)： Failure type II :纵向剪切破坏(longitudinal shear failure, she
22、ar-bond failure.)： Failure type III :垂直剪切破坏(vertical shear failure),Load deflection response of brittle and ductile slabs,The brittle or ductile mode of failure depends on the characteristics of the steel-concrete interface.,Shear bond failure,Brittle behavior in which slip causes a sudden decrease
23、in load carrying capacity as the surface bond is broken. The extent to which the load reduces is dependent on the effectiveness of the mechanical embossments. Ductile behavior in which case the mechanical shear connection is capable of transferring the shear force until failure occurs. This may be f
24、lexural or by longitudinal shear.,Behavior of Composite Slabs,Longitudinal shear in composite slabs Three types of shear connection between a profiled steel sheet and a concrete slab: (1) natural bond between the two, known as frictional interlock (2) mechanical interlock provided by pressing dimple
25、s or ribs into the sheet (3) end anchorage provided by means of shot-fired pins, or by welding studs through the sheeting to the steel flange. Determination of the longitudinal shear strength The m-k or shear-bond test,Mode 1 brittle (or non-ductile) behavior Mode 2 ductile behavior,Empirical method
26、 for evaluating longitudinal shear resistance,The merits of using profiled steel deck composite floors: its efficiencies in construction and its higher load carrying capacity over the traditional steel deck as shuttering. The shear-bond resistance is essential to the interaction between steel sheeti
27、ng and concrete at the sheet-concrete interface, and governs the composite slab design. Shear-bond tests must be carried out to calibrate different types of steel decks. Normally, slabs are tested with no shear connectors.,Relationship between failure mode and span If longitudinal shear resistance o
28、f the slab is not sufficient, it can be increased by the use of some form of end anchorage.,Partial connection method,The partial connection method can also be used for the verification of the resistance to longitudinal shear. (slabs with ductile behavior).,The verification procedure is illustrated
29、in the Figure above for two slabs with different types of loading and span. Resistant moment diagrams and design bending moment diagrams are plotted against Lx on the same axis system. For any cross-section of the span, the design bending moment MSd cannot be higher than the design resistance MRd.,P
30、artial connection method (another expression),The partial connection method can also be used for the verification of the resistance to longitudinal shear.,The partial-interaction design method requires that the mean ultimate shear stress is determined.,Vl design longitudinal shear force of the compo
31、site slab Vu shear bond resistance determined by tests,组合楼板前提：压型钢板与混凝土组合作用，要确保界面黏结强度： Shear-bond strength requirement 纵向抗剪强度验算,Analysis of Composite Slabs（组合楼板受力分析） linear elastic; linear elastic with moment redistribution（线弹性分析、考虑弯矩重分布的线弹性分析）. plastic according to the theory of plastic hinges（极限状态的
32、塑性分析）. Higher order analysis taking into account non-linear behaviour and slip（考虑非线性特性以及滑移的高阶分析）.,Verification of Profiled steel sheeting as shuttering at ultimate limit state (ULS),The sheeting should resist to construction and wet concrete loads. Bending moment resistance of the section is then gi
33、ven by:,Verification of profiled steel sheeting as shuttering at serviceability limit state (SLS),For the ultimate limit states (强度极限状态；uncracked section) For the serviceability limit states（使用极限状态） The slab is comparable to a continuous beam of constant inertia, equal in value to the average inerti
34、a of the cracked and uncracked section（均匀截面模量）. Long-term loading effects on the concrete are taken into account using a variation in the modular ratio Ea/Ec（考虑长期、短期效应时引入混凝土模量系数来简化）. For simplification.,3.4 RESISTANCES OF SECTIONS,Section I: ultimate moment of resistance failure for positive bending
35、. Section II: ultimate moment of resistance failure for negative bending. Section III-IV: ultimate resistance to vertical shear failure. Section V: ultimate resistance to longitudinal shear failure.,Verification of composite slab at ultimate limit state (ULS),Sagging bending resistance. That failure
36、 mode is reached if the steel sheeting yields in tension or if concrete attains its resistance in compression.,composite slab at ultimate limit state,Case 1 Plastic neutral axis above the sheeting Case 2 Plastic neutral axis in steel sheeting,Case 1 Plastic neutral axis above the sheeting,Case 2 Pla
37、stic neutral axis in steel sheeting,Verification of the hogging bending resistance,Bending resistance and deflection,At construction stage: bending resistance of the steel deck is checked as the following: Deflection of the steel deck must satisfy the deflection requirement as:,At composite slab sta
38、ge,Bending resistance, diagonal shear resistance and shear bond resistance should be checked If sufficient shear bond is provided at the interface between concrete and steel sheeting, its bending resistance normal to strong bending direction as the following: Positive bending :,When a composite slab
39、 spans continuously over supporting beams, with negative reinforcement over the internal support region, the negative moment resistance of the slab can be calculated. Negative bending: The bending resistance normal to weak bending direction is treated as reinforced concrete slab.,Vertical shear veri
40、fication,Vertical and punch shear resistance （抗冲切承载力）,punch shear resistance is checked as,Longitudinal shear resistance (纵向抗剪承载力）,To enable a composite slab, the longitudinal shear bond resistance at the interface between the concrete and the profiled deck should be sufficient. Diagonal shear resis
41、tance （斜截面抗剪）,Deflections 组合板挠度，按荷载短期效应组合与荷载长期效应组合计算。 For deflection under short term load（荷载短期效应）, the area of concrete section is divided by a E (a E = E s/E c); for deflection under long term load（荷载长期效应）, divided by 2a E.,3.5 Some detailing requirements （构造要求）,Detailing is to ensure that the ful
42、l strength of components can be developed under the most adverse conditions The effects of corrosion on steel sheets about 1 mm thick are more severe than on thicker sections, so the materials are usually galvanized. The overall depth of a composite slab should not be less than 90 mm, while the dist
43、ance between the top surface of concrete and the top of the steel ribs should not be less than 50 mm. The concrete grade is better over C20.,The required bearing overlaps of composite slabs over the different （构造要求）,When shear studs are welded through steel profiles to the top flange of a steel beam
44、, the diameter of the studs should be 13 to 16 mm if l3 m, and 16 to 19 mm if 3 m l 6 m. Distributing steel mesh is suggested be used to compensate shrinkage and thermal stress in concrete. The minimum steel reinforcement ratio in the two individual directions is 0.002 (rs = As/ bhc).,Negative steel
45、 reinforcement ratio not less than 0.002 for crack width control is required in the top layer of concrete slab at the supports of a simply supported slab, the distance from the edge of the support to the cutting point of the reinforcement should not be less than l/4, and 5 re-bars minimum per meter
46、width.,3.6 Design example floor slab,A one way composite floor with profiled steel sheeting, the slab span is 2.2 m. Steel grade Q235, t = 1mm, As =1700 m2 /m (weight 0.149 kN/m2); I s = 0.96106mm4/m. The depth of concrete above the top ribs is 80 mm, Concrete grade C20, dead load : g k1 = 0.29 kN/m
47、2, live load: qk = 2 kN/m2. Check bending strength, diagonal shear strength and deflection of the slab,Solution: Calculations of load and internal forces Take the unit width b =1m. Dead load (the mean depth of the concrete slab 101 mm) gk = 0.10125+0.149+0.29 = 2.964 kN/m g = 1.22.964 = 3.56 kN/m Li
48、ve load qk = 21 = 2kN/m q = 1.42 = 2.8 kN/m,M = ( g + q )l02 /8= ( 3.56+2.8 )2.22/8 = 3.85 kNm V = ( g + q ) l0 /2= (3.56+2.8) 2.2/2 = 7.0 kN Calculation of moment resistance fsy = 205 N/mm2, Es = 2.06105 N/mm2 fc = 9.6 N/mm2, h0 = 150 70/2 =115 mm mm = 0.81700205(115 36.3/2) = 27.0 kNm M,Diagonal s
49、hear strength,Take one wave length (200 mm) as a checking unit, subjected to shear force as: V1 = V200/1000 = 7.0 200/1000 = 1.4 kN f t = 1.10 N/mm2 (C20) 0.7 f t bbm h0 = 0.71.10(70+50)/2115 = 5.31 kN V1 Calculation of deflection Take one wave length (200 mm) as a checking unit. Elastic modulus of concrete: Ec = 2.55104 N/mm2 aE = E s/E c = 2.06105/2.55104 = 8.08 Deflection under short term loading Equivalent width of concrete slab:,Equivalent width of rib: second moment of area of the transformed section of one wave leng