Improvements to classification of haunched rafters to EC3
Tekla Portal Frame Designer
Background:The propensity for the deep end of a haunch to become Class 4 has increased with the adoption of EC3 design [see EN 1993-1-1 Table 5.2 Sheet 1]. This can affect the haunch itself or the rafter section that forms part of the overall haunched section. The primary cause is due to tighter classification limits at the Class 3/Class 4 boundary in EC3 compared with BS 5950.
Under pure bending (S355 steel) the limit changes from 105.6 in BS 5590 to 100.9 in EC3 and for pure compression from 35.2 to 34.2. These are small but significant changes and are exacerbated by the fact that the more onerous pure compression case is approached more quickly in EC3.
One of a number of difficulties in allowing Class 4 haunches is the effect of the movement in the position of the elastic neutral axis when part of the cross-section is deemed ineffective [see EN 1993-1-1, 188.8.131.52 (4)]. This increases the moment on the section due to the axial force not operating at the original centroidal position. This causes a change in the stress distribution which then affects the position of the neutral axis. So the solution is iterative.
A consequent difficulty for haunched sections is that the analysis line is at the centre of the rafter not the haunch as this varies. This gives a dislocation between the assumption in the analysis as to where the axial force is applied and where it might be assumed in design. For compression forces typically found in haunched rafters this is thought to be unconservative.
Rigorous solutions to the above are not simple and so an alternative approach has been adopted in the latest (2021) release of Tekla Portal Frame Designer. That is, to mitigate against the occurrence of Class 4 cross-sections from the outset.
A total of five interventions has been taken to achieve this.
Steps to avoid Class 4:
- An equivalent section is created for each cross-section of the haunch. This cross-section ignores the root radius in order to simplify the calculation of properties such as plastic modulus. Previously this equivalent section was also used in the classification. That is, c/t for the haunch section and rafter section of the haunch use ‘c’ as the depth between the inside of the flanges. The change here then is to incorporate the root radius of the rafter and haunch section as appropriate. A small but sometimes helpful change.
- In order to establish the Class 3/Class 4 boundary we calculate the elastic stresses, and these are used to establish, ψ, for use in one of the following two equations taken from Table 5.2 of EC3:Image
Previously, the stresses used were the sum of the axial and bending stresses. These need to be ‘normalised’ to the yield strength and we increased both the axial and bending stresses equally. However, for classification of all other standard rolled sections and plated sections the bending moment term is increased and the axial term kept constant. One idiosyncrasy can be observed due to the ‘normalisation’ being applied to the compressive stress. Occasionally this can result in the maximum tension stress appearing to exceed yield - this is the condition described in Table 5.2 for ψ < -1.
The approach adopted for all other sections has now been applied to haunches to give a very minor improvement in classification.
- The first check position in the haunch strength checks was previously at the face of the column. The further along the haunch that this first position is checked the less likelihood that the cross section will be Class 4 (for the haunch component). Given that the end plate is as stiff if not more so than the column flange, it is very reasonable to move the first check position to the face of the end plate - typically 20 to 40 mm. A small but sometimes helpful change.
- Previously if the cross-section was established as Class 4 then an error was given, the classification results were available but no other design calculations were carried out. Class 4 can result from the haunch web or the rafter web (in reverse bending). In this latest release, when only the haunch web is Class 4 then a warning (not a fail) is given and all the relevant design checks carried out assuming a ‘truly’ class 3 section. Giving the calculations in this way might allow the designer to justify this approach to the checking authority on a case by case basis. If the rafter web is Class 4 then the status remains as a Fail as here there is little option but to increase the rafter size. This change will allow engineering judgement to be applied in some cases.
- Clause 5.5.2 (9) of EN 1993-1-1 is as follows:
(9) Except as given in (10) Class 4 sections may be treated as Class 3 sections if the width to thickness ratios are less than the limiting proportions for Class 3 obtained from Table 5.2 when ε is increased by [ fy/γM0 /σcom,Ed ]0.5, where σcom,Ed is the maximum design compressive stress in the part taken from first order or where necessary second order analysis.
This clause refers to cross-section strength checks only - the exception given at the start of the clause refers to member (stability) checks. So for member stability checks the normal Class 3/Class 4 rules apply.
You will see two new variables in the output, σcom,Ed and εmod. The latter is the adjusted value of ε to be used in establishing the class limits - see equations quoted in ‘Item 2’.
In many situations the actual maximum compressive stress, σcom,Ed, will be significantly below the yield strength and so the adjustment to the value of ε will be equally significant. This will have a marked effect on the c/t limit at the Class 3/Class 4 boundary. One idiosyncrasy can be observed when the value of σcom,Ed is already above yield. In this case εmod is less than ε and the class limit is ‘tighter’. This is reasonably rational but the cross-section will have failed one or more strength checks anyway.
Outcome:Taken together you should find that the incidence of Class 4 cross-sections is very significantly reduced. Where these might still occur for haunch webs a solution can be sought through engineering discussions.
This will be most apparent in the cross-section strength checks but less so in the member stability checks because ‘Item 5’, the most efficacious, does not apply.