FE-MODELLING OF A BOLTED LAP CONNECTION USING A SIMPLIFIED BOLT MODEL

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FE-MODELLING OF A BOLTED LAP

CONNECTION USING A SIMPLIFIED BOLT MODEL

Rafał Grzejda

Katedra Mechaniki i PKM, Zachodniopomorski Uniwersytet Technologiczny w Szczecinie rafal.grzejda@zut.edu.pl

Summary

Modelling and calculations of a bolted lap connection are presented. Analysis of forces acting on the bolts based on the theoretical formulas and using the finite element method (FEM) is performed. In the case of theoretical calculations the recommendations given in the standard PN-EN 1993-1-8 are applied. For a case of numerical calculations a simplified model of the bolt is used. The obtained results of calculations are checked in terms of fulfil- ment of the adopted criterion for load capacity of the connection. Selected results of simulation studies of the bolted lap connection FEM-model in the form of a displacement map and a reduced stress map of the model under specified external load are pointed out. Based on the comparison of the theoretical and numerical analyses results, usefulness of the simplified bolt model for calculations of operational forces in the bolts in bolted lap connections is determined.

Keywords: bolted lap connection, FE-modelling, Eurocode 3

MODELOWANIE MES ZAKŁADKOWEGO POŁĄCZENIA ŚRUBOWEGO Z ZASTOSOWANIEM UPROSZCZONEGO MODELU ŚRUBY

Streszczenie

Przedstawiono modelowanie i obliczenia zakładkowego połączenia śrubowego. Przeprowadzono analizę sił wystę- pujących w śrubach na podstawie wzorów teoretycznych oraz za pomocą metody elementów skończonych (MES).

W obliczeniach teoretycznych zastosowano zalecenia podane w normie PN-EN 1993-1-8. W obliczeniach numerycznych wykorzystano uproszczony model śruby. Otrzymane wyniki sprawdzono pod kątem spełnienia przyjętego kryterium nośności połączenia. Przedstawiono wybrane wyniki badań numerycznych modelu połączenia w postaci mapy przemieszczeń i mapy naprężeń zredukowanych modelu wywołanych zadanym obciążeniem zewnętrznym.

Na podstawie porównania wyników obliczeń teoretycznych oraz wyników obliczeń numerycznych określono przy- datność uproszczonego modelu śruby do obliczeń sił roboczych w śrubach w połączeniach zakładkowych.

Słowa kluczowe: zakładkowe połączenie śrubowe, modelowanie MES, Eurokod 3

1. INTRODUCTION

Depending on the aim of modelling, bolted lap connections may be calculated according to various methods.

For engineering design of this type of connections the standards PN-EN 1993-1-1 [17] and PN-EN 1993-1-8 [18]

are appropriable. However, they cannot be used for connections loaded by dynamic forces [2, 11]. In more complex analyses it is common to use the finite element

method and three-dimensional models of the connections. In these cases the problems of both single-bolted lap connections [3, 4, 20, 21, 24, 25] and multi-bolted lap connections [1, 9, 19, 22, 23] are taken into account.

Between the mentioned calculation methods, the FE- modelling bolted lap connections using simplified bolt models can be positioned. These include models such as:

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- rigid elements without the bolt head [10, 12], - rigid body bolt models with a flexible shank of the

bolt and a rigid bolt head [7, 16], - beam elements [13, 14, 15], - spider bolt elements [5, 6].

Application of simplified bolt models enables to achieve satisfactory calculation results in a much shorter time than in the case of entire three-dimensional models.

Pursuant to the standard [18], bolted lap connections can be subdivided as follows:

- bearing type connections of category A,

- slip-resistant connections at the serviceability limit state of category B,

- slip-resistant connections at the ultimate limit state of category C.

Bolted lap connections of category B and C in this classification belong to the connections that are pre- loaded by the force Fm, which is defined according to the formula [2]

= 0.7 ∙ ∙ (1)

where:

fub – the ultimate tensile strength for bolts [MPa], As – the tensile stress area of the bolt [mm2].

Bolted lap connections can also be divided on the grounds of their geometry. In this classification the following types of the connections can be distinguished:

- simple connections (single-shear joints and double- shear joints),

- complex connections (beam-column joints).

In the paper the theme of modelling bolted lap connections using the Midas NFX 2014 FEM program has been undertaken. The aim of the study is assessment and evaluation the usefulness of a simplified model of the bolt embedded in this system to load analysis of bolted lap connections. The results of numerical calculations are compared with results of calculations under the standards [17, 18].

2. DESCRIPTION OF THE TESTED BOLTED LAP CONNECTION

The subject of research is a complex bolted lap connection show in Fig.1, which has been designed as a slip- resistant connection at the serviceability limit state of category B. It is created with a cantilever beam mounted to a column by means of four M20 bolts made in the mechanical property class 10.9. The joined elements are performed by using channel sections 300E made of S235 structural steel. The connection is loaded by the external force Ft equal to 48 kN. Calculations were made for both the non-preloaded connection and the connection preloaded by the force Fm equal to 171.5 kN designated from the formula (1).

Fig. 1. Beam to column bolted lap connection

The fasteners are modelled as hybrid components consist of (for a review, see [8]):

- a flexible shank of the bolt in the form of a beam, - rigid head of the bolt and a rigid nut (Fig. 2).

Fig. 2. Model of the bolt

For modelling of a contact zone between the cantilever beam and the column general surface to surface contact elements available in the Midas NFX 2014 program are applied. The parameters of the contact elements are collected in Tab. 1. In the data table the following designations are used:

- kn – the coefficient of the normal contact stiffness, - kt – the coefficient of the tangent contact stiffness, - µ – the coefficient of the static friction.

The FEM model of the bolted lap connection is shown in Fig. 3.

Tab. 1. Parameters of the contact elements

Parameter Value

kn 1.0

kt 0.1

µ 0.4

Rigid head

Rigid nut Flexible shank

Ft

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Fig. 3. FEM model of the beam to column bolted lap conne tion

3. CALCULATION RESULTS

In the case of the analysed connection the most exerted fasteners are fasteners marked with numbers 1 and 2 (Fig. 3). In the next part of the paper the discussion will be limited to the fastener No. 1. The maximum value of the operational force in the bolt No. 1 determined on the basis of the formulas given in the standard [18] is 81.6 kN (for a review, see [11]). This value of the operational force fulfils the condition of capacity of the bolt on the pressure [18]. The value of this operational force by th FEM model of the connection is equal to 68.9

therefore lower compared to the value for the theoretical model by about 16 %. The difference in the force values can be explained by the fact that in the theoretical calculations it is assumed that the bolted lap connection is a rigid connection. However, in the FEM calculations the flexibility of contact zone between the cantilever beam and the column is taken into account. Increasing the rigidity of the contact joint in the FEM model of the connection by changing the coefficient of the normal contact stiffness kn to the value of 1.45 and the coeff cient of the tangent contact stiffness kt

0.145 one achieves the operational force in the bolt No. 1 equal to 81.9 kN.

After performing the calculations in a FEM program it is also possible to generate maps of displacements and reduced stresses for a given system. It is an undoubted advantage of this type of calculations in comparison with theoretical calculations. An example of the distr bution of the resultant displacements of the preloaded and externally loaded bolted lap connection FEM model in shown in Fig. 4.

A A

1 3 2 4

FEM model of the beam to column bolted lap connec-

CALCULATION RESULTS

In the case of the analysed connection the most exerted fasteners are fasteners marked with numbers 1 and 2 3). In the next part of the paper the discussion will be limited to the fastener No. 1. The maximum value of No. 1 determined on the formulas given in the standard [18] is 81.6 ]). This value of the operational force fulfils the condition of capacity of the bolt on the operational force by the FEM model of the connection is equal to 68.9 kN. It is therefore lower compared to the value for the theoretical

%. The difference in the force values can be explained by the fact that in the theoretical the bolted lap connection is a rigid connection. However, in the FEM calculations the flexibility of contact zone between the cantilever beam and the column is taken into account. Increasing the rigidity of the contact joint in the FEM model of the ion by changing the coefficient of the normal to the value of 1.45 and the coeffi-

kt to the value of 0.145 one achieves the operational force in the bolt No. 1

the calculations in a FEM program it is also possible to generate maps of displacements and reduced stresses for a given system. It is an undoubted advantage of this type of calculations in comparison with theoretical calculations. An example of the distribution of the resultant displacements of the preloaded and externally loaded bolted lap connection FEM model

Fig. 4. Distribution of the resultant displacements of the preloaded and externally loaded bolted lap connection FEM model

In contrast, Fig. 5 shows the distribution of the reduced stresses of the connection FEM model for the same load case. The maximum value of the reduced stress amounts to 256.3 MPA and does not exceed the ultimate tensile strength for the steel adopted for th

and the column.

Fig. 5. Distribution of the reduced stresses of the preloaded and externally loaded bolted lap connection FEM model

4. CONCLUSIONS

Analysing the results of work the following conclusions were put forward:

1. If the FEM tests of bolted lap connections are ca ried out to study the selected parameters

ample in order to determine forces acting on the bolts and joined elements –

simplified models of the bolts and the connections.

This considerably increases the efficiency of the modelling and shortens the time of numerical calc lations.

2. The use of theoretical formulas (which are included in the standards) for the appointment of operational forces in the bolts can lead to results inconsistent with reality.

Distribution of the resultant displacements of the preloaded and externally loaded bolted lap connection FEM

5 shows the distribution of the reduced stresses of the connection FEM model for the same load case. The maximum value of the reduced stress amounts to 256.3 MPA and does not exceed the ultimate tensile strength for the steel adopted for the cantilever beam

Distribution of the reduced stresses of the preloaded and externally loaded bolted lap connection FEM model

Analysing the results of work the following conclusions

of bolted lap connections are car- ried out to study the selected parameters – for example in order to determine forces acting on the

it is proposed to use simplified models of the bolts and the connections.

eases the efficiency of the modelling and shortens the time of numerical calcu-

The use of theoretical formulas (which are included in the standards) for the appointment of operational forces in the bolts can lead to results inconsistent

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