III.- RESULTADOS
3.1 Descripción
This chapter corresponds to Section 9 of EN 1994-1-1, which has the following clauses:
g General Clause 9.1
g Detailing provisions Clause 9.2
g Actions and action effects Clause 9.3
g Analysis for internal forces and moments Clause 9.4
g Verification of profiled steel sheeting as shuttering for ultimate limit states Clause 9.5
g Verification of profiled steel sheeting as shuttering for serviceability limit states Clause 9.6
g Verification of composite slabs for ultimate limit states Clause 9.7
g Verification of composite slabs for serviceability limit states Clause 9.8 9.1. General
Composite slabs are a highly efficient form of floor construction, but they are less robust than continuous concrete slabs with two-way reinforcement. Their orthotropic structural properties and staged construction lead to relatively complex rules for design. Some verifications are done by manufacturers of the sheeting and embodied in tables of limiting spans and load levels. A designer using these makes further verifications, but may not be fully aware of the assumptions that underlie the tables.
New entrants to this competitive market should become familiar not just with rules in the Euro-codes but with the extensive guidance provided by the industry – in the UK, for example, by the Steel Construction Institute, among other organisations.
Potential situations that could lead to unsatisfactory or unsafe performance include the following:
g under-prediction of the loads that may be applied during construction
g as-built layouts of profiled sheets that differ from that assumed during design
g the addition of significant line loads (e.g. from partitions) during the life of the building
g the application of repeated travelling loads, as from fork-lift trucks (see clause 9.1.1(3)P)
g unintended location of shear connectors on the ‘unfavourable’ side of troughs in profiled sheeting, which can reduce their slip capacity and shear resistance.
The preceding list is mainly for designers. Problems that could arise during construction (e.g.
unsatisfactory through-deck welding of studs) are outside the scope of this guide.
Scope
The form of construction and the scope of Section 9 are defined in clause 9.1.1. The shape of the steel profile, with ribs running in one direction, and its action as tensile reinforcement for the finished floor, result in a system that effectively spans in one direction only. The slab can also act as the concrete flange of a composite beam spanning in any direction relative to that of the ribs. Provision is made for this in the clauses on the design of beams in Sections 5, 6 and 7.
The ratio of the gap between the webs to the web spacing, br/bs in clause 9.1.1(2)P, is an important property of a composite slab. This notation is as in Figure 9.2 and Figure A.1 in
Clause 9.1.1
Clause 9.1.1(2)P
Clauses 9.1.1(3)P Clauses 9.1.1(4)P Clause 9.1.1(5)
Clause 9.1.2.1(1)P
Clause 9.1.2.2(1)
Clause 9.2.1(1)P Clause 9.2.1(2)P
Clause 9.2.1(4)
Appendix A. If the troughs are too narrow, the shear strength of stud connectors placed within them is reduced (clause 6.6.4), and there may be insufficient resistance to vertical shear. If the web spacing is too wide, the ability of the slab to spread loads across several webs may be inadequate, especially if the thickness of the slab above the sheeting is minimised, to save weight.
Such a wide range of profiles is in use that it was necessary to permit the upper limit to br/bsto be determined nationally. It should probably be a function of the thickness of the slab above the sheeting. The UK’s National Annex states that the recommended value, 0.6, should be used.
No account is taken of any contribution from the top flange of the sheeting to the resistance to bending in the direction transverse to the span of the slab.
The design methods for composite slabs given in Section 9 are based on test procedures described in clause B.3. Although the initial loading is cyclic, the test to failure is under static loading. Thus, if dynamic effects are expected, the detailed design for the particular project must ensure that the integrity of the composite action is maintained (clauses 9.1.1(3)P and 9.1.1(4)P).
Guidance on the degree of lateral restraint provided to steel beams (clause 9.1.1(5)) is available in EN 1993-1-1 and elsewhere (Gardner, 2011). Inverted U-frame action relies also on flexural restraint. This subject is covered in comments on clause 6.4.2.
Because of the wide range of profiles used, the resistance to longitudinal shear has always been based on tests. Slabs made with some profiles have a brittle mode of failure, which is penalised in clause B.3.5(1).
Types of shear connection
As for other types of composite member, bond is not accepted in clause 9.1.2.1(1)P as a reliable method of shear connection. Sheeting without local deformations of the profile is permitted where the profile is such that some lateral pressure will arise from the shrinkage of the concrete (Figure 9.1(b)). Here, the distinction between ‘frictional interlock’ and ‘bond’ is, in effect, that the former is what remains after the 5000 cycles of loading specified in clause B.3.4.
The quality of mechanical interlock is sensitive to the height or depth of the small local deforma-tions of the sheeting, so tight tolerances (clause B.3.3(2)) should be maintained on these during manufacture, with occasional checking on site.
These two standard forms of interlock are sometimes insufficient to provide full shear connection, as defined in clause 9.1.2.2(1). They can be augmented by anchorages at the ends of each sheet, as shown in Figure 9.1, or design can be based on partial shear connection.
The omission in EN 1994-1-1 of the paragraph number, (1), from these two clauses is a drafting error, to be corrected.
9.2. Detailing provisions
The limits to the thickness given in clauses 9.2.1(1)P and 9.2.1(2)P are based on the satisfactory experience of floors with these dimensions. They do not make clear how ‘the main flat surface of the top of the ribs’ should be interpreted where small top ribs are present. If the limits given are related to the shoulder height (comment on clause 6.6.4 is relevant), the concrete slab could be too thin for the detailing rules for stud connectors and slab reinforcement to be followed.
No limits are given for the depth of the profiled sheeting. Its minimum depth will be governed by deflection. For a slab acting compositely with a beam, the minimum depths are increased (clause 9.2.1(2)P) to suit the detailing rules for stud connectors, such as the length of stud that extends above the sheeting and the concrete cover. A slab used as a diaphragm is treated similarly.
Where a slab spans onto a hogging moment region of a composite beam, the minimum reinforce-ment transverse to its span is governed by the rules for the flange of the beam (e.g. Table 7.1), not by the lower amount given in clause 9.2.1(4).
The minimum bearing lengths (clause 9.2.3) are based on accepted good practice. The lengths for bearing onto steel or concrete are identical to those given in BS 5950-4 (British Standards Institution, 1994).
9.3. Actions and action effects Profiled sheeting
Where props are used for profiled sheeting (clause 9.3.1(2)P), care should be taken to set these at the correct level, taking account of any expected deflection of the surface that supports them. If verification relies on the redistribution of moments in the sheeting due to local buckling or yielding, this must be allowed for in the subsequent check on the deflection of the completed floor; but this is, of course, less likely to be critical where propping is used.
For the loading on the profiled sheeting, clause 9.3.2(1) refers to clause 4.11 of EN 1991-1-6 (British Standards Institution, 1991). For working personnel and small site equipment, a note to clause 4.11.1(3) proposes a characteristic distributed load of 1 kN/m2. The UK’s National Annex for EN 1991-1-6 notes that these loads can be determined for individual projects, and gives recommended minimum values.
For the weight density of normal-weight concrete, Annex A of EN 1991-1-1 (British Standards Institution, 2002) recommends 24 kN/m3, increased by 1 kN/m3for ‘normal’ reinforcement and by another 1 kN/m3for unhardened concrete.
In addition to self-weight, clause 4.11.2 of EN 1991-1-6 specifies an imposed load qkof 10% of the weight of the concrete, but not less than 0.75 kN/m2(which usually governs) and not more than 1.5 kN/m2, applied to a working area 3 m 3 m; and 0.75 kN/m2outside this area. The lower limit corresponds to a layer of normal-weight concrete about 30 mm thick, to allow for the mounding that occurs during the delivery of fresh concrete. The upper limit would govern for composite slabs more than 0.6 m thick, which are unlikely in practice. Guidance on the avoidance of overload during construction is available elsewhere (Rackham et al., 2009).
For construction loads due to working personnel, etc., with small site equipment, a note to clause 4.11.1(3) of EN 1991-1-6 recommends an imposed load of 1.0 kN/m2. Whether this should be assumed to be an alternative to qk as given above, or additional to it, may depend on the details of the construction process.
Partial factors for ultimate limit states are recommended in Table A1.2(B) of EN 1990, as 1.35 for permanent actions and 1.5 for variable actions. It would be reasonable to use 1.35 for the whole of the weight density of 26 kN/m3, explained above, even though the extra 1 kN/m3for unhardened concrete is not strictly ‘permanent’.
Sometimes, to increase the speed of construction, the profiled sheeting is not propped. It then carries all these loads. This condition, or the check on the deflection of the finished floor, normally governs its design.
For the serviceability limit state, the deflection of the sheeting when the concrete hardens is important, for use when checking the total deflection of the floor in service. The construction load and the extra loading from mounding are not present at this time, so the deflection is from the permanent load only, and the factors for serviceability, given in Table A.1 of EN 1991-1-6, are not required.
Clause 9.3.2(1) refers to ‘ponding’, and clause 9.3.2(2) gives a condition for its effects to be ignored.
Where profiled sheeting is continuous over several supports, this check should be made using the most critical arrangement of the imposed load. There is further comment on clause 9.6(2).
Composite slab
The resistances of composite slabs are determined by plastic theory or by empirical factors based on tests in which all of the loading is resisted by the composite section (clause B.3.3(6)). This permits design checks for the ultimate limit state to be made under the whole of the loading (clause 9.3.3(2)).
Clause 9.2.3
Clause 9.3.1(2)P
Clause 9.3.2(1)
Clause 9.3.2(2)
Clause 9.3.3(2)
Clause 9.4.1(1) Clause 9.4.1(2)
Clause 9.4.2(3) Clause 9.4.2(4)
Clause 9.4.3
9.4. Analysis for internal forces and moments Profiled steel sheeting
Clause 9.4.1(1) refers to EN 1993-1-3 (British Standards Institution, 2006), which gives no guidance on the global analysis of continuous members of light-gauge steel. Clause 9.4.1(2) rules out plastic redistribution where propping is used, but not where the sheeting extends over more than one span, as is usual. Subsequent flexure over a permanent support will be in the same direction (hogging) as during construction, whereas at the location of a prop it will be in the opposite direction.
Elastic global analysis can be used, because a safe lower bound to the ultimate resistance is obtained. Elastic moments calculated for uniform stiffness are normally greatest at internal supports, as shown in Figure 9.1 for a two-span slab under distributed loading. The reduction in stiffness due to parts of the cross-section yielding in compression will be greatest in these regions, which will cause redistribution of the moment from the supports to mid-span. In a technical note from 1984, and in a note to clause 5.2 of BS 5950-4 (British Standards Institution, 1994), the redistribution is given as between 5 and 15%. This suggests that redistribution exceeding about 10% should not be used in analyses for design ultimate loads in the absence of supporting evidence from tests.
Redistribution should not be used in analyses for serviceability loads, because of its uncertain effect on deflections.
Composite slab
As the steel sheets are normally continuous over more than one span, and the concrete is cast over this length without joints, the composite slab is in reality continuous. If elastic global analysis is used based on the uncracked stiffness, the resulting moments at internal supports are high, as in the example in Figure 9.1. To resist these moments may require heavy reinforcement. This can be avoided by designing the slab as a series of simply supported spans (clause 9.4.2(5)), provided that crack-width control is not a problem. Other approaches that reduce the quantity of hogging reinforcement needed are the use of the redistribution of moments (clause 9.4.2(3)), and of plastic analysis (clause 9.4.2(4)).
Numerical and experimental research on continuous slabs has been reported (Stark and Brekelmans, 1990). With typical relative values of the moment resistance at internal supports and at mid-span, the maximum design loads calculated by elastic analysis with limited redistri-bution were found to be less than those obtained by treating each span as simply supported.
This arises because the large resistance to sagging moment is not fully utilised.
If the slab is to be treated as continuous, plastic analysis is more advantageous. The studies showed that no check on the rotation capacity need be made, provided the conditions given in clause 9.4.2(4) are satisfied. Where reliance is placed on the contribution of sheeting to the resis-tance to hogging bending, designers should consider whether the layout of the sheets could be modified during construction.
Effective width for concentrated point and line loads
The ability of composite slabs to carry masonry walls or other heavy local loads is limited. The rules of clause 9.4.3 for the effective widths bm, bemand bevare important in practice. They are based on a mixture of simplified analysis, test data and experience (British Standards Institution, 1994), and are further discussed, with a worked example, by Johnson (2004). The effective width depends on the
Figure 9.1. Bending moments for a two-span beam or slab for uniform loading; elastic theory without redistribution
0.125wL2 0.070wL2
L L
ratio between the longitudinal and transverse flexural stiffnesses of the slab. The nature of these slabs results in effective widths narrower than those for solid reinforced concrete slabs.
The rule for the effective width of a slab in clause 9.4.3(2) is related to the level of the bottom reinforcement in the slab. The depth hcin Equation 9.1 should therefore be based on the gross depth of the sheeting, hpg.
The nominal transverse reinforcement given in clause 9.4.3(5) is not generous for a point load of 7.5 kN, and should not be assumed to apply for the ‘largely repetitive’ loads to which clause 9.1.1(3)P refers.
9.5–9.6. Verification of profiled steel sheeting as shuttering
The design checks before composite action is established are done to EN 1993-1-3. Clause 9.5(1) refers to the loss of the effective cross-section that may be caused by deep deformations of the sheeting. This loss and the effects of local buckling are both difficult to determine theoretically.
Design recommendations provided by manufacturers are based in part on the results of loading tests on the sheeting concerned. The data should include the nominal cross-sectional area of the sheeting (Ap) and the positions of the elastic and plastic neutral axes of the profile, denoted e and ep, respectively (Figure 9.6).
Sheeting also has an effective cross-section (Ape) slightly less than Apbecause the embossed parts of the cross-section (provided to improve shear connection) may reduce the stiffness and the resistance to longitudinal force. All four of the preceding properties are required for calculations to clause 9.7.4.
The maximum deflection of L/180 given in the note to clause 9.6(2) is accepted good practice. It is confirmed in the UK’s National Annex with the addition of upper limits: 20 mm where the loads from ponding are ignored (see clause 9.3.2(2)) and 30 mm where they are included.
9.7. Verification of composite slabs for the ultimate limit states 9.7.1 Design criterion
No comment is needed.
9.7.2 Flexure
The rules in clause 9.7.2 are based on research reported by Stark and Brekelmans (1990).
Clause 9.7.2(3) states that deformed areas of sheeting should be ignored in calculations of section properties, unless tests show otherwise. No guidance on relevant testing is given. Test results are also influenced by local buckling within the flat parts of the steel profile, and by the enhanced yield strength at cold-formed corners.
For a composite slab in sagging bending, tests can be done in which the shear span is long enough, or the end anchorage is sufficient, for flexural failure to occur. If the strengths of the materials are known, the effective area of the sheeting, when in tension, can be calculated from the moment resisted. An estimate made by reducing Apby half of the embossed areas is sometimes used.
For a composite slab in hogging bending, the contribution from the sheeting is usually ignored, because it may not be continuous. Where sheeting is continuous, the area of tensile reinforcement is usually small compared with the effective area of the sheeting, so that a conservative estimate of the latter (e.g. excluding embossed areas) may reduce only slightly the calculated resistance to bending. Alternatively, a value found from a bending test on the sheeting alone could be used.
Tests on hogging regions of continuous composite slabs have been reported (Guo and Bailey, 2007).
The effective widths in clause 9.7.2(4) for local buckling take account of the restraint provided to one side of the sheeting by the concrete.
Bending resistances of composite slabs are based on rectangular stress blocks (clauses 9.7.2(5) to 9.7.2(7)). In the design of reinforced concrete beams, the compressive strain in concrete is limited, to prevent premature crushing of the concrete before the reinforcement yields. There is no similar
Clause 9.4.3(2)
Clause 9.4.3(5)
Clause 9.5(1)
Clause 9.6(2)
Clause 9.7.2(3)
Clause 9.7.2(4)
Clause 9.7.2(5)
Clause 9.7.2(6)
Clause 9.7.3
Clause 9.7.3(2)
restriction for composite slabs. The design yield strength of the profiled sheeting, typically between 280 and 420 N/mm2 in Europe (lower than that of reinforcement), and its own bending resistance make composite slabs less sensitive to premature crushing of concrete.
However, it could be a problem where stronger sheeting is used, as in Australia.
For stress in concrete, the 0.85 factor is included, as discussed in the comments on clause 3.1(1).
The drafting of clause 9.7.2 is over-reliant on Figures 9.5 and 9.6, which do not show the small top ribs that many sheetings now have. The profile depth hpis replaced by depths hpn(net) and hpg
(gross), as explained in the comment on clause 6.6.4.
It is assumed that a depth xpl(Figure 9.5) is calculated from 0.85xplbfcd¼ Apefyp,d
where Apeis the effective area of a width b of sheeting.
If xpl h hpg, clause 9.7.2(5) and Figure 9.5 apply.
If xpl> h hpn, clause 9.7.2(6) applies. If the top ribs are ‘small’ (see the comment on clause 6.6.4), xplcan be replaced by hc(¼ h hpn); otherwise, hc(¼ h hpg) should be used. In both cases, the calculation of the level of the plastic neutral axis becomes complex. Use of the simplified Equations(9.5) and (9.6) in clause 9.7.2(6) is recommended.
Where the depth xplis within the top rib, use of any of the alternatives above should be accurate enough.
The derivation of the simplified equations is on record (Stark and Brekelmans, 1990). Equation (9.6) gives the bending resistance Mprof the profiled sheeting, reduced below its plastic resistance to bending, Mpa, by the axial compression Ncf. If xplis less than hc, then Ncf¼ Apefyp,d, and the
The derivation of the simplified equations is on record (Stark and Brekelmans, 1990). Equation (9.6) gives the bending resistance Mprof the profiled sheeting, reduced below its plastic resistance to bending, Mpa, by the axial compression Ncf. If xplis less than hc, then Ncf¼ Apefyp,d, and the