FE-MODELLING OF A BOLTED LAP CONNECTION · PDF fileFE-MODELLING OF A BOLTED LAP CONNECTION...

MODELOWANIE INŻYNIERSKIE 2017 nr 62, ISSN 1896-771X

24

FE-MODELLING OF A BOLTED LAP

CONNECTION USING A SIMPLIFIED BOLT

MODEL

Rafał Grzejda

Katedra Mechaniki i PKM, Zachodniopomorski Uniwersytet Technologiczny w Szczecinie

[email protected]

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 cal-

culations 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 un-

der specified external load are pointed out. Based on the comparison of the theoretical and numerical analyses re-

sults, usefulness of the simplified bolt model for calculations of operational forces in the bolts in bolted lap con-

nections 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 nume-

rycznych 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 connec-

tions 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 connec-

tions. 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:

Rafał Grzejda

25

- 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 connec-

tions 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 connec-

tion 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 ele-

ments 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

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

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

2 3

4

BOLTED LAP CONNECTION USING A SIMPLIFIED BOLT MODEL

26

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 distri-

bution 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 ex-

ample 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

Rafał Grzejda

27

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Artykuł dostępny na podstawie licencji Creative Commons Uznanie autorstwa 3.0 Polska.

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