Serviceability limit states (SLS)

Transcription

1 Serviceability limit states (SLS) Serviceability limit states (SLS) - generally Motto: structure should be safe, but also service-able (usable). Design for serviceability is largely connected with ensuring that the function of the structure (not safety as by ULS) is not impaired by the average performance of the structure. Serviceability criteria will therefore depend upon the actual function of the structure. Since all design functions cannot be caught by a code, the designer and his client have the ultimate responsibility for choosing appropriate limits. The limitations given in EN are applicable in most normal circumstances. The responsibility of the designer to check that they are appropriate for the particular structure is not touched. Sometimes are vibrations, sound transmissivity, distributions work, special conditions for precision machinery, etc. of great importance. Serviceability checks in EN comprise only: stress limitation, crack control, deflection control. For serviceability we can formulate once more simple condition reliability: Sc Sc lim 1

2 SLS need for determining of a safety levelnot so great as by ULS this touches both side of condition of reliability. Actions: EN 1990 defines three combinations of actions, which may need to be considered, when designing for a serviceability limit state. These are: Characteristic combination G k, j "+" Q k,1 "+" ψ 0, i Q k, i j 1 i > 1 EN formula 6.14b used for irreversible limit states. Frequent combination G k, j "+" ψ 1 Q k,1 "+" ψ 2, i Q k, i j 1 i > 1 EN formula 6.15b used for reversible limit states. Quasipermanent combination G k, j "+" ψ 2, i Q k, i j 1 i> 1 EN formula No. 6.16b used for long term effects and appearance. Where is: G k,j -characteristic value of j - permanent load, Q k,i - characteristic value of i-variable load, Q k,1 -characteristic value of leading variable load, ψ 0, i, ψ 1, i, ψ 2, i, combination coefficients for variable loads. Without Equation details Resistance: Material properties by SLS Partial safety factor applied to material properties should generally be 1.0 (compare with f ck /1,5 or f sk /1,15 by ULS) so characteristic or mean values are used. The properties of materials, which are normally significant in serviceability calculations, are: the modulus of elasticity of the reinforcement -E S =200 GPa, the modulus of elasticity of the concrete E C,m -depends on strength class, the creep coefficient ϕ 0, the shrinkage strain and ε sh, the tensile strength of the concrete f ctk. 2

3 Models of load structure interaction Stresses in cross-sections Three models of an internal forces distribution of CS by SLS can be used: 1. Section without crack with full stress both in tensile and compressive part. 2. Section with crack and compressive part with stress. 3. Fully cracked CS, (without compressive part). Internal forces (tension) are concentrated into the reinforcement. Elastic behavior of concrete prior cracking is assumed. Limitation of stresses (under serviceability conditions) Actually these SLS has been added due to several countries, which have not full adopted their codes to EN. E.g. ULS is calculated by presumption of elastic condition of concrete. Applying of this rule should improve structure safety and economy. All at all two limits need to be considered: Compressive stress limits (concrete) and tensile stress limits (reinforcement). Limits to compressive stress Why limit the compressive stress? Two reasons are usually put forward : (1) To avoid the formation of micro-cracks in the concrete which might reduce durability It is commonly accepted that micro-cracking will start to develop in concrete when the compressive stress exceeds about 70% of the compressive strength. By last tests some micro-cracking by 60% of c. strength was found so this limit is recommended for structures/members applied into aggressive environment. (2) To avoid excessive creepof the concrete. By the creep is the limit in discussion, now. Commonly is the limit to 0,45 f ck accepted, now. (When the creep is essential for the structure safety.) The reason is that up to this limit depends creep linearly on the stress and can be easy predicted. Over this limit increases creep over linear value and it is hard to predict. 3

4 Limitation of tensile stresses In the case of reinforcement, it seems reasonable to ensure that inelastic deformations of the steel are avoided under service loads. (not under ultimate load!) Such deformations would invalidate any calculations of cracking or deflections which assume that the reinforcement behaves elastically and could result in excessively large cracks. It is supposed to befulfilled, if σ s 0,8f yk Limitation of tensile stress has greater importance by prestressing steels/tendons, but this is not a deal for BL015 subject. Stresses in CS can be calculated as by an elastic material -see next page. Calculation of stress in Cross Section (CS) 1. Can be based on the linear theory of elasticity, so for bended CS the stress of marginal fibres is σ = M/W or M/(J.y) where: J is the second moment of CS (moment of inertia) W is the section modulus M y is acting moment is the distance of tested (marginal) position from the centroid. 2.By RC cross-sections an transformed (idealized) CS have to be used! In this case the (Conc. + Fe) material of CS is transformed to one concrete, α e = E S /E c more by deflection control. 4

5 04/04/2018 Control of cracking what does it mean? Occurring of cracks at all As important primary knowledge for determining of CS/member stiffness. Case of deflection control. Crack width limits (hairy cracks, micro-cracks) There are many reasons for wishing to limit the widths of cracks. Among the most commonly cited reasons are: to avoid possible corrosion damage to the reinforcement due to aggressive substances penetrating to the reinforcement down the cracks, to avoid, or limit, leakage through cracks - this is commonly a critical design consideration in water retaining structures, to avoid an unsightly appearance. The figure is real but it s a joke a little bit. In the reality it documents failure at ULS! Total crash. Designer's problem 5

6 Technique of cracking control In the principle there are two ways for control: 1. To calculate the width of a crack (more or less accurate ) and compare it with the given limits. 2. To respect prescribed detailing for relevant member. In the code itself there is stated, that even the accurate calculation is very inaccurate (mostly due to very variable quantities of concrete tensile strength and bond strength). Therefore, there is recommended here to use detailing instead of accurate calculation. For an illustration the limits in mmare shown, only. The main EC detailing rules for crack control According to Eurocode 2, prescribed minimum reinforcement must be placed in areas of a concrete member where tensile stresses are expected, if crack control is required For more see practice manual (not for memorizing). 6

7 Besides minimum reinforcement area there are two other rules, only: Maximal allowed diameter of used main reinforcement bars Maximal allowed spacing of used reinforcement bars 7

8 TASK: Try to understand relation between diameter, spacing and stress and apply them by ULS design! Stress σs in rfcmt. [MPa] Limit diameter φs [mm] wk=0,4 mm wk=0,3 mm wk=0,2 mm Stress σs in rfcmt. [MPa] Maximal distance smax. [mm] wk=0,4 mm wk=0,3 mm wk=0,2 mm

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