Serviceability and Ductility The Other Limit States Cracking

Serviceability and Ductility The Other Limit States Cracking, Deflections and Ductility Code Provisions and Recent Research October 2006

Cracking, Deflections and Ductility Code Provisions and Recent Research l Overview – Code provisions for ductility – Background to the study – Codes: AS 3600, AS 5100, EC 2, BS 5400, BS 8110, CEB-FIP 1990, ACI 318 – Background to prediction of cracking and deflections – Code provisions for crack widths and stress limits – Code provisions for deflections – Recent research – Conclusions

Code provisions for ductility

Background to the study l Prediction of cracking and deflection: – Why is it important? – Why is it difficult? – What do the codes say?

Prediction of Cracking and Deflections Why is it important? l l l l l Second order effects Load distribution and transfer Loads on non-structural members Durability Code compliance Contract conditions Client expectations Aesthetics Clearances, ponding etc.

Why is it difficult? l l l Uncertain or unknown material properties Inconsistent and incomplete code provisions Inherently random nature of cracking Unknown manufacture procedures and construction programme Variations in curing procedures and environmental effects Complex loading history

Uncertain or unknown material properties l l Concrete tensile strength; creep rupture? Concrete stiffness under tension; nonlinearity? Concrete creep and shrinkage properties Concrete behaviour under unloading/ reloading

Inconsistent and incomplete code provisions l l l Tensile strength of concrete Effect of shrinkage on tensile strength Tension stiffening Loss of tension stiffening Effect of uncracked parts of structure Effect of shrinkage

Unknown manufacture procedures and construction programme l l l Concrete age at loading? Time before application of loads or restraints? Effect of steam curing – Locked in thermal stresses? l Storage, curing – Differential shrinkage?

Complex loading history l l l Critical sections subject to may be sagging, hogging, sagging, hogging Effect of axial load Calculation of non-recoverable deflections (eg creep)

What do the codes say? l l l Compare AS 3600, AS 5100, EC 2, BS 5400, BS 8110, CEB-FIP 1990, ACI 318 Differing and inconsistent provisions No one code covers all significant effects

Background to prediction of cracking and deflections l l Formation and propagation of cracks Relationship between cracking and section stiffness – Tension stiffening – Loss of tension stiffening l Time related effects – Creep – Shrinkage – Differential shrinkage l Calculating deflections from section stiffness

Background to prediction of cracking and deflections l Recommended reading: Concrete Structures – Stresses and Deformations – Ghali Favre and Elbadry

Formation and propagation of cracks

Relationship between cracking and section stiffness l Tension stiffening l Displacement of Neutral Axis l Loss of tension stiffening

Time related effects l Creep – General agreement on mechanism and analysis approach – Amount and rate of creep variable l Shrinkage – Affects both section curvature and effective cracking stress – No agreed approach to analysis of either effect l Differential shrinkage – May have a large effect on section curvature and deflections – Not specifically covered by any of the codes studied

Calculating deflections from section stiffness l Two approaches in codes – “Effective stiffness” approach (ACI and Australian codes) - Branston equation – Average of cracked and uncracked section stiffness. – Integrate section curvature along the length of the member.

Code provisions for stress limits l AS 3600, AS 5100 and EC 2 – Crack control by stress limits governed by bar diameter and spacing – AS 5100 has much lower stress limits applicable to stresses due to permanent loads in exposure classifications B 2, C or U – EC 2 limits related to specified crack widths under quasistatic loading – AS 3600 limits similar to EC 2 limits for 0. 4 mm crack width for bar diameter, and 0. 3 mm for bar spacing – AS 5100 limits for exposure classification B 2 and higher similar to EC 2 limits for 0. 2 mm crack width – The specified stress limits will result in substantially higher design crack widths with increased cover.

Code provisions for stress limits Stress Limits for Maximum Bar Diameter

Code provisions for stress limits Stress Limits for Maximum Bar Spacing

Code provisions for stress limits Design crack widths for maximum stress

Code provisions for stress limits Design crack widths for maximum stress

Code provisions for stress limits Design crack widths for maximum stress

Code provisions for crack widths l AS 3600 and AS 5100 – No requirement for calculation of crack widths

Code provisions for crack widths l EC 2

Code provisions for crack widths -EC 2

Code provisions for crack widths l EC 2 - Notes: – Crack spacing is mainly related to cover depth – Crack width is directly proportional to crack spacing – Tension stiffening is limited to 40% of steel strain without stiffening – Coefficient for long term tension stiffening is reduced by 1/3 (0. 6 to 0. 4)

Code provisions for crack widths Design surface crack width: BS 5400 BS 8110

Code provisions for crack widths CEB-FIP 1990 (MC 90) Design crack width: Length over which slip between concrete and steel occurs Steel strain at the crack Steel strain under a force causing stress equal to concrete tensile strength over concrete tension area x empirical coefficient Free shrinkage of concrete (generally negative)

Code provisions for crack widths ACI 318 - 89, 99, Gergely-Lutz equation ACI requirements based on stress limits derived from the Gergely-Lutz equation:

Code provisions for deflections l AS 3600, AS 5100, and ACI 318

Code provisions for deflections l AS 3600, AS 5100, and ACI 318 - Notes – Code provisions based on the “Branson Equation” ACI 318 is differently formulated, but gives the same results. – Ief is the average effective stiffness, applied over the full length of the member. – Ms is determined at the critical section(s) specified in the code. – AS 5100 provisions are identical to AS 3600, (other than a typographical mistake!) – In the Australian codes the cracking moment is reduced by a factor dependent on the concrete shrinkage. ACI 318 makes no adjustment to the cracking moment. – AS 3600 and AS 5100 provide a factor kcs to account for the effects of creep and shrinkage: l kcs = [2 - 1. 2(Asc / Ast )] >= 0. 8

Code provisions for deflections l AS 5400 and 8110 – Deflections calculated from integration of section curvatures – Cracking moment and curvature of cracked sections allows for a short term concrete tensile stress of 1 MPa, reducing to 0. 55 MPa in the long term. – Shrinkage curvature determined from the free shrinkage strain, and the first moment of area of the reinforcement about the cracked or uncracked section, as appropriate. – BS 5400 tabulates factors based on the compression and tension reinforcement ratios.

Code provisions for deflections l l Eurocode 2 and CEB-FIP 1990 (MC 90) Members which are expected to crack should behave in a manner intermediate between the uncracked and fully cracked conditions and, for members subjected mainly to flexure, an adequate prediction of behaviour is given by Expression (7. 18):

Code provisions for deflections l Eurocode 2 and CEB-FIP 1990 (MC 90)

Code provisions for deflections l l Eurocode 2 and CEB-FIP 1990 (MC 90) Shrinkage curvatures may be assessed using Expression (7. 21):

Code provisions for deflections l Summary – Australian and American codes based on the Branson equation, using a uniform average effective stiffness value. – Australian codes allow for loss of tension stiffening through a reduction of the cracking moment related to the free concrete shrinkage. – Allowance for shrinkage curvature in the Australian codes is simplified and will underestimate curvature in symmetricaly reinforced sections. – British codes allow only a low tension value for cracked sections, which is further reduced for long term deflections – European codes adopt an intermediate approach for cracked sections, with an allowance for loss of tension stiffening. – British and European code provisions for shrinkage curvature are essentially the same

l Code provisions for deflections Summary – None of the codes included in this study make specific provision for differential shrinkage for monolithic construction. – Recent research suggests that loss of tension stiffening takes place within a few days, and reduced tension stiffening values should be used in almost all cases

l Recent Research Beeby, Scott and Jones – Loss of tension occurs much more quickly than has previously been assumed, within 20 -30 days – Mechanism is cumulative damage, resulting from loss of tensile strength under load, creep plays an insignificant part – Evidence that final tension stiffening may be largely independent of concrete strength.

l l l Conclusions Cracking and deflections may be highly variable, even under nominally identical conditions Codes do not make specific provisions for all the relevant factors AS 3600 and AS 5100 stress limits may result in substantially greater crack widths than allowed in other codes

Conclusions l l l In spite of similar approaches, different code methods for crack width calculation give highly variable results. Eurocode 2 appears to be the most consistent Predicted deflections are also highly variable. Shrinkage effects are significant, even in symmetrically reinforced sections. Allow for loss of tension stiffening Consider the possibility of differential shrinkage