Cracking

Cracking options Cracking moment Crack widths

Cracking moment Short term properties always used. Strain at point of first crack varies The resulting cracking moments will be very different. The different models measure the cracking strain at different positions. The tension strength (eg fctm) is much bigger than the value of 1.0 used in BS8110. No Tension ACI, AS

Cracking moment analysis 8110 pt 2 The different models measure the cracking strain at different positions. – 8110 measures the strain at the level of the centrod of foce of the tension steel. Whereas the other models measure it at the surface. TN372

Crack widths Crack width formulae are an approximation. They are based on simple section geometry They do not give 0mm crack at the cracking moment. BS8110 & 5400 require accurate modelling of the reinforcement. EC2 methods are not suited to AdSec. ACI/AS codes do not provide a method.

BS Crack width equation Also PD6687 approach for EC2 Section acr The crack width formulae are a weighted interpolation between 2 experimentally observed effects – The value of acr is used to perform the interpolation. And this gives a gradually changing value of crack width around the section as you move further away and closer to bars. Soffit acr is the distance from the point being checked to the nearest bar

AdSec : First find the strain εm due to the applied loads using SLS analysis AdSec changes the strain plane until.... Axial Force Moment Moment angle Match the applied values Here is what AdSec does – it first finds the strains.

AdSec BS crack width post-processor Split section sides into many points Walk round the section Calculate crack width at every point Find the maximum result Display all results graphically The rest is all post processing – and there is no reason why you shouldn’t simply take the worst strains – assess the most vulnerable position by eye and do a hand calc.

AdSec BS crack width post-processor BUT – crack-width formulae are an approximation AdSec includes interpretation +warnings Use the Graphical output to check the results Re-work the crack calc if needed – its only a post-processor!

AdSec BS interpretations (h-x) is interpreted for composite sections with locked in strain planes. cmin - minimum cover is not always the cover to the side in question- but makes answer correct for faceted sections

AdSec BS warnings WARNING: Controlling bar is remote from crack location NOTE: Cover to controlling bar measured to different side from crack location Do we think the results will be ok? YES We can see quickly by eye that the crack width calculated by AdSec will be fine. acr cmin

AdSec BS warnings WARNING: Controlling bar and crack are located on either side of re-entrant corner NOTE: Cover to controlling bar measured to different side from crack location Do we think the results are ok? In this case we probably would need to think carefully about the model. – Do we need more bars? We are clearly outside the realms of the assumptions in the code.

EC2 formulae for crack width ( ) w = s e - e = maximum crack spacing x strain across a crack at a bar k r , max sm cm Simple tension stiffening ( ) s eff p ct t E f k , 6 . 1 r ³ + - = cm sm e Es/Ecm eff p r k c s , 2 1 max 425 . 4 3 f + = A bit of a black box! In order to work out how to minimise the crack width it is best to remember the basic equation. Crack width is crack spacing x crack strain A simple approximation is offered for tension stiffening to calculate the crack strain. This was developed for pure tension. The crack spacing is controlled by the distribution of the reinforcement. In BS8110 & BS5400 and PD6687, the spacing term would vary along the surface of a section. However for EC2 there is an average crack spacing, based on the ratio of bar diameter to proportion of reinforcement in tension zone. This concept requires interpretation for irregular sections. p,eff = As/Act,eff Ratio of reinforcement/effective tension area

Irregular sections = cr Interpretation needed For irregular sections the crack strain can be calculated directly from a cracked and uncracked section analysis using the interpolated method. This gives a lower stiffness/higher crackwidth strain than the simplified formula on the previous slide. The control from the reinforcement will need interpretation within the spirit of the diagrams and text in the code.

Effective reinforcement ratio (7.3.2, Figure 7.1) p,eff = As/Act,eff Act,eff = lesser of: 2.5b(h - d) or b(h - x)/3 or hb/2 (x = neutral axis depth) d h The diagrams in the code are ambiguous and interpretation is needed. This is discussed in th paper in ‘The STRuctural Engineer’ (Handout).

‘Blob Method’ Actually for computerisation this is the kind of diagram that is needed. This will be included in AdSec EVENTUALLY.

AdSec ‘Local crack check’ hc,ef distance to edge of section half bar spacing Ac,eff neutral axis ‘Approximate Local Crack Check’ This calculation uses a simplified tension area local to the governing bar. AdSec finds the 2 bars with the highest strain If there are more than 2 bars with the same strain, AdSec will choose the two with the lowest bar numbers. Can anyone see different features from the BS calcs? -THE Calculation is based on bar positons, not the surface -The Result wont vary continuously around the section. When the local check is carried out, AdSec finds the two bars (or tendons) with the highest strain (excluding prestress strain) under the loading conditions being considered. If there are more than two bars with the same highest strain, AdSec will choose the two with the lowest bar numbers. A local value for Ac,eff (see clause 7.3.2 (3)) is allocated to each of these bars, which allows a value of rp,eff to be calculated and used to predict the crack width, wk, according to expression (7.8). The Ac,eff areas allocated to the two bars are plotted onto the section view once the SLS analysis has been carried out. This method assumes that the largest crack width occurs within the areas controlled by these two bars, which in some cases may not be true. The possibility of worse cases occurring in other locations within the section should be assessed by the user, who may use the plotted Ac,eff areas to help consider this.

EC2 Cracking between bars Slab soffit (h - x) 1.3 (h - x)(sm - cm) (3.4c+ 0.17/peff )(sm -cm) W 5(c + /2) EC2 formulae predict These 2 values of crack width EC2 calculates an average crack spacing for a whole zone of the surface, so the crack width only varies with the strain – unless some of the surface can’t be controlled by the bars. In this case (> 5(c + /2)/2) from a bar there is a step in the predicted value and the crack is only controlled by the neutral axis position. This illustrates cracking in the soffit of a reinforced concrete slab. The red line indicates the variation in design crack width depending upon proximity of the point considered to the nearest longitudinal bar. The curve is similar to what would be predicted by the formula in Part 2 of BS8110. It is interesting to note that this variation in crack width is accepted as correct by the Eurocode, from which the figure has been redrawn. The Eurocode 2 formulae do not attempt to give this variation in crack width between bars but to give a typical result in the general region of the bar. The formulae do not apply where the bar spacing is wide and the crack width is being considered near mid spacing. For this situation, the Eurocode gives an alternative formula for crack spacing of 1.3(h - x). This can be compared with the limiting crack spacing given in BS8110 for cases where acr approaches infinity of 1.5(h - x). BS8110 – 5400 prediction

M 2.5(c + /2) hc,ef neutral axis c What might be happening here? How could we solve it? For this moment angle the distribution of steel across the bottom doesn’t matter. Could adjust the arrangement of bars. Or ignore the result for the side bar.

bar with maximum strain adjacent bar Ac,eff w1 w2 c hc,ef b sv hc,ef = min[2.5(c+/2), (c+/2+b)/3, c+/2+sv/2 ] Ac,eff = min[5(c+ /2), (w1+ w2)] * hc,ef neutral axis What should we check? Could take the bar strain from AdSec and do a hand calc for ACef for the red bar - based on judgement Its probably good enough within the intention of the code. I would definitely try out one of the BS approaches for comparison.

distance to edge of section hc,ef Ac,eff neutral axis Bar no: 1 2 3 4 half bar spacing distance to edge of section hc,ef Ac,eff neutral axis What should be done here? Renumbering the bars would mean that bar 4 was used by the programme. However the cover will still be odd. Could do an easy hand calc. Shouldn’t we add a bar in the nib?

A B What could go wrong here? AdSec wont ‘see’ the composite section. Need to do a hand calc based on total geometry?

Approximate Local Crack Check Warning: ... The governing bar is selected based on bar strain. The results may not be the maximum crack width in the following cases: Governing bar does not have the greatest cover in the section Governing bar does not have the widest spacing in the section The calculation meets the boundary between components Bar spacing > 5(c+f/2) - where this condition affects the governing bar it is identified There are no checks for situations remote from bars (where expression (7.14) applies) - these may occur away from the governing bar and hence will not be identified..

Cracking in EC2 ARUP have proposed modifications to EC2 The UK national documents present an alternative. AdSec may give higher crack widths than hand calcs to EC2 AdSec EC2 crackwidths should be checked using the graphic view.