Eurocode based design method for flange-plate connections of tubes under
Eurocode based design method for flange-plate connections of tubes under
tension
tension
Pál Turán Pál TuránBME Department of Structural Engineering,
BME Department of Structural Engineering, e-mail: [email protected]: [email protected]
Abstract Abstract
In this paper an analytical model will be described to determine the resistance of flange-plate pipe joints in tension. This model is In this paper an analytical model will be described to determine the resistance of flange-plate pipe joints in tension. This model is based on the
based on the Eurocode Eurocode T - stub model. Later, an experimentally verified 3D finite element model will be presented. The results of T - stub model. Later, an experimentally verified 3D finite element model will be presented. The results of
the numerical and the analytical models will be compared. Two configurations were investigated with different geometry and the numerical and the analytical models will be compared. Two configurations were investigated with different geometry and welding type. In the first, there is no hole in the middle of the flange-plate; in the other there is a hole, which size is equal to the welding type. In the first, there is no hole in the middle of the flange-plate; in the other there is a hole, which size is equal to the diameter of tube. In the second connection type there is two-sided fillet welding, while in the other there is only one-sided diameter of tube. In the second connection type there is two-sided fillet welding, while in the other there is only one-sided welding. Finally a statistical evaluation was carried out.
welding. Finally a statistical evaluation was carried out.
1. Introduction 1. Introduction
Nowadays load-bearing structures made from tubes (CHS –
Nowadays load-bearing structures made from tubes (CHS – Circular Hollow SectionCircular Hollow Section) are very commonly) are very commonly
used because of their aesthetic appearance and favourable behaviour. Currently, for dimensioning of the used because of their aesthetic appearance and favourable behaviour. Currently, for dimensioning of the flange-plate pipe connections the
flange-plate pipe connections the Euro Eurocodecode does not contain design method. The purpose of the present does not contain design method. The purpose of the present
article is to demonstrate an analytical model that bases on the
article is to demonstrate an analytical model that bases on the Eurocode Eurocode T-stub model. The results of the T-stub model. The results of the
proposed new model will be compared to the result of a 3D finite element model. Furthermore a statistical proposed new model will be compared to the result of a 3D finite element model. Furthermore a statistical evaluation will be performed.
evaluation will be performed.
2. The Eurocode based model 2. The Eurocode based model
The
The Eur Eurocodeocode 3 (EC 3) volume relation to the design of joints [1], [5] does not contain design method for the 3 (EC 3) volume relation to the design of joints [1], [5] does not contain design method for the
calculation of the resistance of flange-plate tube connections under tension. The proposed
calculation of the resistance of flange-plate tube connections under tension. The proposed Eur Eurocode ocode basedbased model
model (in the later: (in the later: ECBM ECBM ) which will be described bases on the L-stub model from the) which will be described bases on the L-stub model from the Eurocode Eurocode standard standard
[5]. This L-stub model has been used to calculate the resistance of end-plate connection of I-beams, this [5]. This L-stub model has been used to calculate the resistance of end-plate connection of I-beams, this model is a modification of the T-stub model. The details of the connection and the derivation of L-stub can model is a modification of the T-stub model. The details of the connection and the derivation of L-stub can be seen in
be seen in Fig. 1.Fig. 1. The main idea is taken from The main idea is taken from KatulaKatula [2], where the main principles and a conceptual [2], where the main principles and a conceptual
drawings without details are described. drawings without details are described.
Fig. 1.
Fig. 1. Details of the bolted connection, the evaluation of L-s Details of the bolted connection, the evaluation of L-stub model [2]tub model [2]
The L-stub model contains two plates, a weld, and a bolt. In this connection model there are three failure The L-stub model contains two plates, a weld, and a bolt. In this connection model there are three failure modes (see in
modes (see in Fig. 2.Fig. 2.): 1. complete yielding of the flange, 2. bolt failure with yielding of the flange, 3. bolt): 1. complete yielding of the flange, 2. bolt failure with yielding of the flange, 3. bolt
failure. failure.
The connections of tubes are generally point symmetrical; it is assumed that both the yield patterns and the The connections of tubes are generally point symmetrical; it is assumed that both the yield patterns and the
behaviour of the bolts are also symmetrical. The supposed failure patterns can be seen in Fig. 3. The following formulas have been derived based on the Eurocode standard.
NT,Rd NT,Rd+Q Q NT,Rd Q NT,Rd ΣBi ΣBi Mpl Mpl Mpl MEd<Mpl 1. 2. 3.
Fig. 2. The failure modes of L-stub model Fig. 3. Failure patterns
2.1. Complete yielding of the flange (Mode 1.)
In the calculation of effective lengths the following formulas can be conducted, based on the Eurocode [5],
assumed extended end-plate (Table 6.6. in [5]) (nbolt is the total number of the bolts in the connection): • Individual bolt, non-circular pattern: , , 4( 2 0,8 2 ) 1, 25 1
eff nc egy w
l = e − a + e
• Individual bolt, circular pattern: , , 2 ( 2 0,8 2 )
eff cp egy w
l = π e − a
• Bolt group, non-circular pattern:
, , ( 2 )1 eff nc csop hs bolt l d e n π = +
• Bolt group, non-circular pattern: , , (2 2 )1
eff cp csop hs bolt l d e n π = +
The total effective length:
,1 min( , , ; , , ; , , ; , , )
eff eff nc egy eff nc csop eff cp egy eff cp csop bolt
l l l l l n
Σ = ⋅
The resistance to the failure mode 1.:
,1, , ,1 1 2 0,8 2 pl Rd t Rd w M N e a = − Where: 2 ,1 ,1, 0 0,25 eff fp yk pl Rd M l t f M γ Σ = ;
f yk – yield strength of the plate,
γ M0 – partial factor to the complete yielding.
2.2. Bolt failure with yielding of the flange (Mode 2.)
The total effective length:
,2 min( , , ; , , )
eff eff nc egy eff nc csop csav
l l l n
Σ = ⋅
The resistance to the failure mode 2.:
,2, 2 , , ,2 1 2 0,5 0,8 2 pl Rd i d t Rd w M e B N e e a + Σ = + −
Where: 2 ,2 ,2, 0 0,25 eff fp yk pl Rd M l t f M γ Σ = ; , , i d csav t Rd B n F Σ = , , 2 0,9 ub s t Rd M f A F γ =
f ub – tensile strength of bolt;
As – the tensile stress area of bolt;
γ M2 – partial factor to fracture.
2.3. Bolt failure (Mode 3.)
Resistance of the bolt failure can be calculated on the basis of individual bolt capacity, taking into account the number of screws placed in the joint:
, ,3 ,
t Rd csav t Rd
N =n F
2.4. The resistance of connection
The resistance of connection bases on the three failure mode:
, min( , ,1; , ,2; , ,3)
t Rd t Rd t Rd t Rd
N = N N N
The resistance of welding and profile’s resistance need to be separately checked.
3. Numerical model
To evaluate the analytical model a numerical model of the joint in the ANSYS finite element software has been built. Two models with different geometry were developed. In the first model there is no hole in the flange-plates and one-sided fillet welding was used (see Fig. 4.b). In the case of other geometry there is a
hole in the middle of flange-plates with double-sided fillet weld (see Fig 4.c). The throat thickness of the
one-sided fillet weld is equal to the thickness of CHS. At the two sided weld, the thickness of the welding is equal to the wall thickness. The gaps between the elements have been taken into account (see Fig 4.d ).
Fig. 4. Geometry model
The steel components have been discretized with SOLID185 element type, the contact was modelled with CONTA173 and TARGE170 elements. Axial displacement at the end of the tube has been used for loading. The verification of the model was carried out by using laboratory tests results. The experiments were
performed in the BME Laboratory of the Department of Structural Engineering. The measured properties are shown in Table 1.
In every cases E = 210000 N/mm2 was assumed as the initial elastic modulus for steel. The bilinear material
model for bolts has 830 MPa yield strength and 2100 N/mm2 hardening modulus, based on tensile tests. For
the 4 mm and 8 mm thickness plates multilinear material models have been used (see Table 2.) based om
laboratory tests.
Specimens tfp[mm] dhs[mm] lCs[mm] ths[mm] dfp[mm] aw[mm] Bolts
A-01 3,94 60,34 254, 6,58 140,32 5 8pcs M16
A-02 8,50 60,57 254 6,51 140,41 5 6pcs M16
A-03 11,95 60,44 252 6,63 140,31 6 6pcs M16
Table 1. Geometry measurements
σ [MPa] 0 291 292 370 420 440 445 4 mm ε [-] 0 0,00141 0,025 0,05 0,1 0,15 0,25 σ [MPa] 0 300 301 346 383 396 -8 mm ε [-] 0 0,00146 0,027 0,047 0,1 0,28
-Table 2. Material models for flange plates
During the experiments the force in the connection, and the size of the gaps between the two flange-plates were measured at four places (see Fig 5.). The measured and calculated values can be seen in Fig. 6-8 .
Taking into account the measurement uncertainty the calculated and measured data show a good agreement. It can be stated that, the behaviour of the model is appropriate and it is verified.
Fig 5. Locations of measuring
Fig 6. Force-displacement curve, A-1
The base distance for distance measurements for the force – displacement curves in the following were the twice of the diameter of CHS profiles in every cases in the numerical analyses. The force-displacement curve of this type of connection can be modelled by two straight lines and an arch between the linear (see Fig. 9.).
In the Fig. 9. can be seen the force – displacement curve for the case of (C1) configuration with 8 mm plate
thickness.
Fig. 9. Force-displacement curve, test specimen A-02 Fig. 10. Stress state ratio (the red areas are in plastic state); configuration (C1), test specimen A--02
This curve can be approximated with the following formula (where: F – force; e – displacement; AE 0 –
initial stiffness; b – ratio of the initial and residual stiffness; F m – intersection of the two linear; R number
referring to arched part):
0 0 1 0 (1 ) ( ) 1 R R m AE b e F e AE b e e AE F ⋅ − ⋅ = ⋅ ⋅ + +
This formula is based on the Menegotto-Pinto material model [3], with redefining the used quantity in the
equation. In every case to the force-displacement points from the finite element analyses a curve has been fitted. The two lines intersection point has been projected to the force displacement curve, and this obtained point was ordered to the resistance force (see Fig. 9.). In Fig. 10. can be seen the stress state ratio diagram at 185 kN for the test specimen A-02. The failure mode in this case is the bolt failure with the yielding of
flange-plate.
Parametric study
To investigate the effect of the hole in the flange-plate and evaluate the analytical model, a parametric study was performed. In every case the calculation was performed with six different flange-plate thickness: t fp = 8;
12; 16; 20; 25 and 30 mm. The used material was S235 for plates and 8.8 for bolts in each case. In the finite
element analysis 210000 N/mm2 initial elastic and 2100 N/mm2 hardening modulus were used based on the Eurocode [4]. All of the calculations were carried out with and without hole in the flange-plate. The data of
the used configurations are in the Table 3.
In the analytical calculations the resistance of the bolts were determined with the f yb As equation, so the
analytical and numerical model can be compared with each other. Each quantity has been applied with its nominal value, without partial factors.
In the Fig. 11. and 12. the resistance for the three failure modes can be seen, depending on the flange-plate
thickness. In case of ECBM all of the failure mode can be significant.
In theFig 13. the resistance values can be seen depending on the flange-plate thickness with the two type of
significant difference between the two types of flange-plate configuration. In most of the cases, the plate without hole has more favourable behaviour. The reason is that the membrane forces can be mobilized and the flange-plate inner the tube increase the bending stiffness. If the number of bolts is high ((A3), (B3), (C3)) and the flange-plate is thick enough, the plate with hole can have better behaviour. In these cases the flange has enough stiffness, the welding and the bolts determine the behaviour of the joint. Furthermore, when the thickness of the flange-plate is less than the bolt diameter, the ECBM results show a good agreement with the
FEM model with hole, the FEM model without hole is conservative.
ID dhs [mm] ths [mm] aw [mm] Bolt type e1 [mm] e2 [mm] nbolt [db] ID dhs [mm] ths [mm] aw [mm] Bolt type e1 [mm] e2 [mm] nbolt [db] A1 168,3 6 6 M16 30 25 4 D1 244,5 8 8 M16 30 25 4 B1 168,3 6 6 M16 30 25 6 E1 244,5 8 8 M16 30 25 6 C1 168,3 6 6 M16 30 25 8 F1 244,5 8 8 M16 30 25 8 A2 168,3 6 6 M20 30 25 4 D2 244,5 8 8 M20 30 25 4 B2 168,3 6 6 M20 30 25 6 E2 244,5 8 8 M20 30 25 6 C2 168,3 6 6 M20 30 25 8 F2 244,5 8 8 M20 30 25 8 A3 168,3 10 10 M24 40 35 4 D3 244,5 10 10 M24 40 35 4 B3 168,3 10 10 M24 40 35 6 E3 244,5 10 10 M24 40 35 6 C3 168,3 10 10 M24 40 35 8 F3 244,5 10 10 M24 40 35 8
Table 3. Geometries of different configurations
Fig. 11. ECBM results (A3) Fig. 12. ECBM results (C3)
In the Fig 14. and 15. the comparison of analytical and numerical results have been shown. If there is no
hole in the plate, in most cases the analytical resistance value is on the safe side compared to FEM. If there is a hole in the flange, in some cases the analytical model gives higher resistances, but the most of the result are around the line, where analytical results equal to numerical ones (continuous line in the figures).
Fig. 14. Comparing of analytical and numerical results Fig. 15. Comparing of analytical and numerical results
A statistical evaluation has been conducted according to MSZ EN 1990 Annex D [6]. The following coefficients of variation were used in the evaluation (the data were gathered from [7]):
• V d= 0.005variant coefficient for diameter;
• V fy= V fu=0.07 variant coefficient for yield and tensile strength; • V t= 0.05 variant coefficient for plate thickness;
• V e1= V e2= 0.005 variant coefficient for distances.
The resistance is a function of the d hs, f y, t fp, e1 and e2, taking into consideration these variables, the variant
coefficient for the analytical model become V δ =0,0866 . Forming subsets according to the failure modes 1 to
3 the calculated quantities are in the Table 4. The b is the correction factor; with that factor we can get the
bests-fit slope, where the numerical results are almost equal to the analytical results. The V δ variant
coefficient gives the scatter of data. The γ M partial factor is the ratio of the characteristic, and design values.
Because in the calculations usually the geometric dimensions are represented with their mean values as nominal values, we have to use a k c correction factor to get the appropriate factor(γ M *). With the γ M * partial
factor the mean geometry and characteristic strength values can be used in the design. Full description from the used statistical evaluation method can be found in [6] and [8].
The scatter of the analytical model results is lower when there is a hole in the middle of flange-plate, but the
b correction factor has lower values, too. If there is no hole in the flange, the scatter is higher, but theb factor
higher as well. If we evaluate all results for the flange without hole, and we modify the partial factor with the model correction factor, we get γ M * /b = 1.49. Taking into account the subsets, the necessary factor is about
1.25. In some way, with hole in the middle of plate, the needed γ M *
/b factor is about 1.60, except the failure mode 2. subset, where the value is 1.3. The reason of the relatively high partial factors are the strongly conservative approximation how the resistance based on the FEM has been determined. With that approximation we get a resistance force value around the end of the linear behaviour of connection, but
ECBM assume complete yielding. The other reason is that the effective length calculation formulas have not
been derived originally for this type of joints. With proper formulas, the scatter of data can be reduced. More investigation is needed to determine the applicability terms and conditions.
was taken into consideration, because of the continuum model. Subset n b V δδ δ δ γ γγ γ M k c γ γγ γ M * γ γγ γ M * /b All 108 1,0778 0,1566 1,341 1,197 1,605 1,49 Mode 1. 16 1,2625 0,1237 1,346 1,161 1,562 1,238 Mode 2. 72 1,1306 0,1167 1,262 1,122 1,412 1,253 Flange-plate without hole Mode 3. 14 0,927 0,0175 1,132 1,007 1,140 1,230 All 108 0,897 0,1333 1,294 1,152 1,49 1,661 Mode 1. 16 1,0536 0,0942 1,262 1,093 1,379 1,309 Mode 2. 72 0,917 0,1296 1,287 1,145 1,474 1,606 Flange-plate with hole Mode 3. 14 0,807 0,0928 1,237 1,093 1,351 1,675
Table 4. Results of statistical evaluation
Summary
An analytical model ECBM based on the T-stub element of Eurocode standard was derived. An
experimentally verified FEM model is presented which was used to evaluate this analytical ECBM model.
The numerical model is discretized with 3D brick elements, between the touching surfaces contact elements have been used, the model contains the gaps too. Both type of flange-plate connection with and without hole in the middle of the plate were examined. Based on the FEM analysis, the configuration without hole has better mechanical behaviour; the needed partial factor is less in that case. More investigation is needed to determine the applicability terms and conditions. For more accurate calculations the effective length formulas have to been modified in the future.
Acknowledgement
The work reported in the paper has been developed in the framework of the project „Talent care and cultivation in the scientific workshops of BME" project. This project is supported by the grant TÁMOP-4.2.2.B-10/1--2010-0009.
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