78. Cracking

79. Cracking options
Cracking moment
Crack widths

80. 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

81. 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

82. 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.

83. 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

84. 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.

85. 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.

86. 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!

87. 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

88. 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

89. 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.

90. 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 + - = 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

91. 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.

92. 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).

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

94. 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 (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.

95. 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 BS 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

96. 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.

97. 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.

98. 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?

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

100. 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..

101. 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.