CBFEM design: verification of components according to Eurocode
CBFEM method combines advantages of general Finite Element Method (FEM) and Component Method (CM) mentioned in EN1993-1-8 [1]. The stresses and internal forces derived from the CBFEM model are used in checks of all components. Individual components are checked according to Eurocode EN 1993-1-8 [1]. In general, all steel materials must be larger than 4mm, which is a limit to fully comply with EN1993-1-1 & EN1993-1-8 [1].
PROFIS determines the design at the level of the connection. Critical sections for design, i.e. buckling, are not determined in the verification of the connection, precisely because PROFIS would need to know more about the surrounding structure, and not only the node.
Anchor verifications
Static load combinations
The user can choose to perform anchor design per following European design codes:
• Eurocode 2-4.
• ETAG 001 Annex C.
• EOTA TR029.
• fib design bulletin 58.
Verifications are performed according to user selected guideline for steel and concrete failure modes.
Required verifications for headed and post-installed fasteners in tension
Required verifications for headed and post-installed fasteners in shear
Per EN1992-4/EOTA TR045, the design resistance of a fastening in case of seismic, shall be performed per failure mode, according to:
Where:
is safety factors related to seismic failure mode
And:
is the basic characteristic resistance for a given failure mode
is defined in product ETA
is defined in the following tables
Reduction factors for αeq in tension, per EN1992-4
Reduction factors for αeq in shear, per EN1992-4
Base plate
The resulting equivalent stress (Von Mises Stress) and plastic strain are calculated on plates as per the FEM model defined in Part 2
Stress
The use of Von Mises stress is also indicated to determine the maximum stress level in the cross section.
PROFIS Engineering and the EN 1993-1-5 [2], App C, Part C.8 Note 1 allow stress slightly higher than fyd, because the steel yielding stress level is not 100% constant. There is a very small increase of stress during this phase.
Example of steel stress
Strains
Ultimate limit state criteria for plated structural elements should verify the principal membrane strains against a limiting value of strain (ε).
Where εlim is defined by the user. PROFIS Engineering presents a default value of εlim, considering a max. value of 5% EN 1993-1-5 [2], App C, Part C.8 Note 1.
Example of plastic strain
The engineer is responsible to check the max. strain limits, and if there are any National regulations for εlim in specific markets. This information would be in the NA for EN 1993-1-5 [2], App C, Part C.8 Note 1. Since the plate elements are divided into 5 layers, elastic/plastic behavior is investigated in each layer separately. A verification of stress level and equivalent plastic strain is performed by the program- the calculation output relates to the most critical verification for all 5 layers.
Equivalent stress and plastic strain
The limiting criteria is 5%- as suggested in Eurocode EN 1993-1-5 [2], App C, Part C.8 Note 1. The connection design does not replace the steel design for critical cross sections, which should be performed outside of PROFIS Engineering.
CBFEM method can provide steel stress higher than the yield strength. The reason is the slight inclination (1) of the plastic branch of the stress-strain diagram which is used in the analysis to improve the stability of interaction calculation.
This is not a problem in practical design. At higher loads, the equivalent plastic strain is rising and the connection fails while exceeding the plastic strain limit.
Profile
A part of the profile is modeled to ensure that the stress distribution in the profile is “settled” in order to be transferred to the welds. However, the software does not replace the verification on the superstructure because is not doing any buckling or stability assessment. But is checking the stresses and strain in a certain section of the profile
Strains
Ultimate limit state criteria for plated structural elements should verify the principal membrane strains against a limiting value of strain (ε).
Where εlim is defined by the user. PROFIS Engineering presents a default value of εlim, considering a max. value of 5% EN 1993-1-5 [2], App C, Part C.8 Note 1.
The engineer is responsible to check the max. strain limits, and if there are any National regulations for εlim in specific markets. This information would be in the NA for EN 1993-1-5 [2], App C, Part C.8 Note 1.
Stress
The use of Von Mises stress is also indicated to determine the maximum stress level in the cross section
Both PROFIS Engineering and the EN 1993-1-5 [2], App C, Part C.8 Note 1 allow stress slightly higher than fyd. This because the steel yielding stress level is not 100% constant. There is a very small increase of stress during this phase.
Stiffeners
Similar the plate and profile components, PROFIS Engineering checks for the stiffeners the equivalent stress (or Von Mises stress) and plastic strain. This check does not replace the frame design which is required for steel structures (including buckling check of the stiffeners).
Strains
Ultimate limit state criteria for plated structural elements should verify the principal membrane strains against a limiting value of strain (ε).
Where εlim is defined by the user. PROFIS Engineering presents a default value of εlim, considering a max. value of 5% EN 1993-1-5 [10], App C, Part C.8 Note 1.
The engineer is responsible to check the max. strain limits, and if there are any National regulations for εlim in specific markets. This information would be in the NA for EN 1993-1-5 [2], App C, Part C.8 Note 1.
Stress
The use of Von Mises stress is also indicated to determine the maximum stress level in the cross section.
PROFIS Engineering and the EN 1993-1-5 [2], App C, Part C.8 Note 1 allow stress slightly higher than fyd, because the steel yielding stress level is not 100% constant. There is a very small increase of stress during this phase.
Concrete block
The resistance of concrete in 3D compression is determined based on EN 1993-1-8 [1] by calculating the design bearing strength of concrete in the connection, fjd, under the effective area, Aeff, of the base plate. The design bearing strength of the joint, fjd, is evaluated according to Cl. 6.2.5 in EN 1993-1-8 [1] and Cl. 6.7 in EN 1992-1-1. The grout quality and thickness is introduced by the connection coefficient, βjd. For grout quality equal or better than the quality of the concrete block, βjd=1.0 is expected. The effective area, A(eff,cm) under the base plate is estimated to be of the shape of the column cross-section increased by additional bearing width, c.
where t is the thickness of the base plate, fy is the base plate yield strength and γM0 is the partial safety factor for steel.
The effective area is calculated by iteration until the difference between the additional bearing widths of current and previous iteration |ci–ci–1| is less than 1 mm.
The area where the concrete is in compression is taken from results of FEA. This area in compression, A(eff,FEM), allows determining the position of the neutral axis.
The intersection of the area in compression, A(eff,FEM), and the effective area, A(eff,cm), allows to assess the resistance for generally loaded column base of any column shape with any stiffeners and is labeled Aeff. The average stress σ on the effective area, Aeff, is determined as the compression force divided by the effective area. Check of the component is in stresses σ≤fjd
Concrete resistance at concentrated compression: 
Average stress under the base plate: 
Utilization in compression [%]: 
Where:
Contact stress in concrete
Mesh sensitivity
This procedure of assessing the resistance of the concrete in compression is independent on the mesh of the base plate as can be seen in the figures bellow. It is shown in the example of concrete in compression assessment according to EC.
Two cases were investigated: loading by pure compression of 1200 kN and loading by a combination of compressive force 1200 kN and bending moment 90 kN.
Influence of number of elements on prediction of resistance of concrete in compression in case of pure compression
The influence of number of elements on prediction of resistance of concrete in compression in case of compression and bending
Welds
Three welding options are available, considering weld materials as per EN 1991-1 [5]. User may select to model the connection between profile / stiffeners and plate.
No welds
If the steel components are not welded together, then it is assumed that there is no transfer of loads between them. Thus, the weld is not modelled – the elements don’t share nodes.
Fillet welds
All loads are transferred via the weld. The fillet weld is modelled as a special weld element, which has an equivalent cross section area as the weld.
Design resistance:
The plastic strain in weld is limited to 5% as in the plate (EN1993-1-5 [2], App. C, Par. C.8, Note 1). The stress in the throat section of a fillet weld is determined according to EN 1993-1-8 [1], Cl. 4.5.3. using the directional method. Stresses are calculated from the stresses in weld element. Bending moment around the weld longitudinal axis is not considered.
Weld utilisation
Where:
The plastic strain in weld is limited to 5% as in the plate EN1993-1-5 [2], App. C, Par. C.8, Note 1. The stress in the throat section of a fillet weld is determined according to EN 1993-1-8 [1]. Stresses are calculated from the stresses in weld element. Bending moment around the weld longitudinal axis is not considered.
All values required for check are printed in tables. Ut is the utilization of the most stressed element. Since plastic redistribution of stress in weld is used, it is the decisive utilization. Utc provides information about utilization along the weld length. It is the ratio of actual stress at all elements of the weld to the design resistance of the stress of the whole length of the weld, [3].
Decomposition of weld loads, source [3]
Butt welds
User can select butt welds, which correspond to full penetration.
According to Eurocode 3-1-8, section 4.7.1 for full penetration butt welds the design is implicitly verified by the resistance of the weakest element in the connection.
Deformations
PROFIS Engineering calculates and provides the deformations in every point of the connection including the location of the anchors. Since the anchors are joined with the plate, the deformation on the plate is the same as the deformation on the anchors. A check on deformations can be done by including SLS loads and verifying the displacements. If a user wants to calculate the deformations under the SLS load combination, it’s a question of inputting the SLS load combination into PROFIS Engineering and check these displacements.
Deformation
Detailing
Detailing checks of minimum distance between anchors are performed always. Hilti Anchor ETAs prescribe dimensions from:
• Minimum distance between anchors
• Minimum distance between anchors and concrete edge . These options may not be changed by the user. The minimum distances guarantee that the Hilti Anchor is able to resist the loads, including concrete related failure modes (e.g. concrete edge failure).
Program settings prescribe dimensions from:
• Minimum distance between anchor and edge of plate
• Minimum distance between anchor and profile
The default values for min. end distance are compliant with EN 1993-1-8
If you would like to start using PROFIS Engineering and start design as per EC2 visit our webpage clicking here
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References
[1] Technical Commitee CEN/TC 250, Eurocode 3: Design of steel structures - Part 1-8: Design of joints, 2009.
[2] Technical Commitee CEN/TC 250, Eurocode 3: Design of steel structures - Part 1-5: Desing of steel structures, 2006.
[3] IDEA StatiCa, General theoretical background; https://resources.ideastatica. com/Content/02_Steel/Theoretical_background/1_General.htm, Version used 10/2018.
[4] Technical Commitee, Eurocode 3: Design of steel structure - Part 1-1: General rules and rules for buildings, 2005.
[5] Technical Commitee CEN/TC 250, Eurocode 1: Actions on structures - Part 1-1: General actions - Densities, self-weight, imposed loads for buildings, 2009.