Serviceability considerations

Transcription

1 Serviceability considerations Presented by: Jan Wium / John Robberts Stellenbosch University NUCSE

2 Table of contents Stress limitation (Chapter 7) Crack control (Chapter 7) Deflection control (Chapter 7) (Vibrations : not covered in SANS )

3 Stress limitation Applicable for Durability class XD, XF, XS (Table 4.1): XD : Corrosion induced by chlorides XF : Freeze/Thaw attack XS : Corrosion induced by chlorides from sea water The compressive stress in the concrete shall be limited in order to avoid longitudinal cracks, micro-cracks or high levels of creep, where they could result in unacceptable effects on the function of the structure. Longitudinal cracks may occur if the stress exceeds compressive stress 0.6 x f ck RSA: Design value of concrete in compression in any case < 0.6 x f ck stress < 0.6 x f ck then linear creep

4 Crack control (Clause 7.3) Cracking shall be limited : not impair the proper functioning; Impair durability of the structure; cause unacceptable appearance. Cracks may be permitted to form without any attempt to control their width, provided they do not impair the functioning of the structure.

5 Crack width limits (Table 7.1N) Water retaining structures: Other limits apply Refer to SANS including crack width calculation method

6 Minimum reinforcement to prevent cracking If crack control is required, a minimum amount of bonded reinforcement is required to control cracking in areas where tension is expected. In profiled cross sections like T-beams and box girders, minimum reinforcement should be determined for the individual parts of the section (webs, flanges). k = 1.0 (h<300mm), or 0.65 (h>800mm) k c = 1.0 (pure tension); for bending and axial tension (rectangular sections) : eq 7.2; Flanges and T-sections : eq 7.3

7 Effective tension areas

8 Crack control without direct calculation Slabs < 200mm (section 9.3 rules adequate); Tabular form: (bar diameter, spacing), extract (Table 7.2N)

9 Beams and other areas Beams with total depth > 1000mm: (section (3)).: skin reinforcement within links Other to remember: (4) It should be noted that there are particular risks of large cracks occurring in sections where there are sudden changes of stress, e.g. - at changes of section; - near concentrated loads; - positions where bars are curtailed; - areas of high bond stress, particularly at the ends of laps.

10 Calculation of crack width s r,max = max spacing ε sm = strain in reinforcement ε cm = mean strain in concrete between cracks ε sm - ε cm = equation (7.9), with values of k t given in National Annex f ct,eff = σ s k t 1 αeρ ρ p,eff Es p,eff S r,max = k 3 c + k 4 k 1 k 2 φ /ρ p, eff (7.11)

11 Crack width, w, at concrete surface relative to distance from bar

12 Crack prediction Compared crack models of GL, Eurocode and Stellenbosch University proposed model for flexural cracking, own experimental data: One of the few sets of data on long term cracking Found that Eurocode underestimates crack width long term Research at Stellenbosch concludes that: o EN1992 provides crack prediction model: short term vs long term crack behaviour o Relationship between w max and w mean variable o Coefficients in EN1992 crack spacing equation need further investigation o Long term flexural loading model uncertainty higher

13 Deflection control (Clause 7.4) Appropriate limiting values of deflection taking into account the nature of the structure, of the finishes, partitions and fixings and upon the function of the structure should be established. The limiting deflections given in (4) and (5) should generally result in satisfactory performance of buildings such as dwellings, offices, public buildings or factories. Care to be taken to ensure that the limits are appropriate for the particular structure considered and that that there are no special requirements (4) The appearance and general utility of the structure could be impaired when the calculated sag of a beam, slab or cantilever subjected to quasipermanent loads exceeds span/250. Pre-camber may be needed.

14 Deflection control (cont.) (5) Deflections that could damage adjacent parts of the structure should be limited. For the deflection after construction, span/500 is normally an appropriate limit for quasi-permanent loads. The limit state of deformation may be checked by either: - by limiting the span/depth ratio, according to or - by comparing a calculated deflection, according to 7.4.3, with a limit value Provided that reinforced concrete beams or slabs in buildings are dimensioned so that they comply with the limits of span to depth ratio given in this clause, their deflections may be considered as not exceeding the limits set out (4) and (5) above.

15 Deflection control by span/depth limits 7.16a 7.16b K takes account of structural system; ρ 0 = reference reinforcement ratio ρ = required tension reinforcement ρ = required compression reinforcement (NOTE f ck in CYLINDER STRENGTH)

16 Deflection L/d limitations Note: Calculation of equations is based on a serviceability steel stress of 310 MPa (yield stress assumed 500 MPa). Correction needed for 450 MPa steel: (7.17) Corrections for flanged beams (0.8 as in SANS ) Corrections for span > 7m (note > 10m in SANS ) Corrections for flat slabs with span > 8.5m

17 Span/effective depth comparison : EN and SANS Implication on slabs

18 Table 7.4N: L/d ratios Structural system Simply supported beam, one- or two-way spanning simply supported slab End span of continuous beam or one-way continuous slab or twoway spanning slab continuous over one long side Interior span of beam or one-way or two-way spanning slab Slab supported on columns without beams (flat slab) (based on longer span) K Concrete highly stressed = 1,5 % EN Concrete lightly stressed = 0,5 % EN Concrete lightly stressed = 0,25 % Obtained using SANS , , , ,

19 Calculated deflections Rules given for the effect of : Cracked and un-cracked conditions: α1 and α11 can be the parameter being calculated, such as deflection, for cracked and un-cracked conditions. may be replaced by M cr /M for flexure (or N) Equation then because similar to that in SANS β = (1.0 for short term; 0.5 for long term loading)

20 Deflection calculation (cont.) Allow for effective Young s Modulus: Allow for shrinkage curvature (similar to SANS ):

21 The end