Serviceability limit states (SLS)

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2020 revision

Serviceability limit states (SLS) - generallyMotto: structure should be safe, but also service-able (usable).Design for serviceability is largely connected with ensuring that thefunction of the structure (not safety as by ULS) is not impaired by theaverage performance of the structure.Serviceability criteria will therefore depend upon the actual function ofthe structure. Since all design functions cannot be caught by a code, thedesigner and his client have the ultimate responsibility for choosingappropriate limits. The limitations given in EN 1992-1-1 are applicable inmost normal circumstances. The responsibility of the designer to checkthat 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 1992-1-1 comprise only: stress limitation, crack control, deflection control.

For serviceability in general we can formulate simple condition

reliability: Sc ≤ SclimWhere Sc is choosen manifestation of serviceability and Sclim it’s limit.

Where is: Gk,j - characteristic value of j - permanent load, Qk,i -characteristic value of i -variable load, Qk,1 - characteristic value of leading variable load, 0,i , 1,i , 2,i , – combination coefficients for variable loads.

SLS need for determining of a safety level not 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

ii

ij

j QQG k,1

,0k,11

,k "+" "+"

EN formula 6.14b – used for irreversible limit states. Frequent combination

ii

ij

j QQG k,1

,2k,1 11

,k "+" "+"

EN formula 6.15b – used for reversible limit states. Quasipermanent combination

ii

ij

j QG k,1

,21

,k "+"

EN formula No. 6.16b – used for long term effects and appearance.

WithoutEquationdetails

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Resistance: Material properties by SLSPartial safety factor applied to material properties should generally be 1.0(compare with fcd = fck/1,5 or fyd = fyk/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 - ES=200 GPa,the modulus of elasticity of the concrete Ec,m- depends on strength class,as the creep coefficient 0, the shrinkage strain and esh,the tensile strength of the concrete fctk.05.05.2020

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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.

Models of load – structure interaction

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Limits to compressive stress (concrete)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 creep of the concrete. By the creep is the limit in discussion, now. Commonly is the limit to 0,45 fck 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.

Limitation of stresses (under serviceability conditions)Actually these SLS has been added due to several countries, which have not fulladopted 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).

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Limitation of tensile stresses (rfcmt)In the case of reinforcement, it seems reasonable to ensure thatinelastic deformations of the steel are avoided under serviceloads. (not under ultimate load!) Such deformations wouldinvalidate any calculations of cracking or deflections whichassume that the reinforcement behaves elastically and couldresult in excessively large cracks.It is supposed to be fulfilled, if

ss ≤ 0,8fykLimitation of tensile stress has greater importance byprestressing steels/tendons, so this is not a deal for BL015subject. Stresses in CS can be calculated as by an elastic material- see next page.

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Calculation of stress in Cross Section (CS)1. Can be based on the linear theory of elasticity, so for bended CSthe stress of marginal fibres is s = M/W or M/(J.y) where:J is the second moment of CS (moment of inertia)W is the section modulusM is acting momenty is the distance of tested (marginal) position from the centroid.2.By RC cross-sections as transformed (idealized) CS have to be used! In this case the (concrete + Fe) material of CS is transformed to one→

concrete, ae = ES/Ec more by deflection control.

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Control of cracking – what does it mean?Occurring of cracks at allAs important primary knowledge for determining of CS/member stiffness. Case of deflection control. (later.)

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 colapse.

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Designer's problem

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 mm are shown, only.

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The main EC detailing rules for crack controlAccording to Eurocode 2, prescribed minimum reinforcement As,min must be placed in areas of a concrete member where tensile stresses are expected, if crack control is required. As,min will be derived from the equation:

For more see practice manual (not for memorizing).05.05.2020

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.

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TASK: Try to understand relation between diameter, spacing and stress and apply them by ULS design!

Stress ss in rfcmt. [MPa]

Limit diameter fs [mm]wk=0,4 mm wk=0,3 mm wk=0,2

mm

Stress ss in rfcmt. [MPa]

Maximal distance smax. [mm]wk=0,4 mm wk=0,3 mm wk=0,2

mm

160 40 32 25 160 300 300 200

200 32 25 16 200 300 250 150

240 20 16 12 240 250 200 100

280 16 12 8 280 200 150 50

320 12 10 6 320 150 100 -

360 10 8 5 360 100 50 -

400 8 6 4 - - - -

450 6 5 - - - - -

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End of SLS1

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