Rotational stiffness characteristics of the steel-timber connection

MIROSLAV ROSMANIT, DAVID MIKOLASEK

Department of Structures and Department of Mechanics

VSB – Technical University of Ostrava

17. Listopadu 15/2172, Ostrava - Poruba, 708 33

CZECH REPUBLIC

miroslav.rosmanit@vsb.cz http://homel.vsb.cz/~ros11/

Abstract: - Paper is focused on the behavior of individual elements on the pin connection of steel and timber

beams and determines the stiffness characteristics of this connection. The connection is repetitively use

on modern bridge structures to ensure the overall stability of the structure. Interaction of all parts of the

connection (components as beams, face plate, bolts, washers and nuts) is numerically modeled using the FEM

program, the stiffness and the deformation behavior of the connection is studied mainly. The problem is also

analytically solved.

Key-Words: - timber, pin connection, stiffness, interaction, FEM model, analytical model

1 Introduction Today, engineers and designers have to cope with

difficult requirements. Economics of the structural

design is being taken into account increasingly;

which leads to further reduction of capacity reserve

margin. The structure must fulfill the requirements

for strength and reliability, but also has to be as

simple and subtle as possible.

Subject of our research activity are a timber

bridges similar to the one on a Fig. 1. Despite its

rural location, the bridge should bear heavy and

special load conditions -lorries, harvesters and other

farm machines. One of the main problems expected

is natural degradation of the glued laminated timber

main beams, which are freely exposed to the

elements: mainly water, snow and sun. Although the

young age of the bridge in Fig. 2 we can see

degradation of a main beam resulting in drought

crack. In the long run, the resistance capacity and

overall stiffness of the main beams can decrease

rapidly; therefore the aim of our research is

prediction of such behavior of the structure.

In this paper the connection of steel and timber

beams and determination of its stiffness behavior is

presented. Both, numerical and analytical solutions

are showed up (Section 3 and 4). The connection is

very important for overall stability of the bridge

structure. For better understanding the connection

was also tested experimentally, see Section 2.

The idea of researching such a problem is not

new; some results were already achieved in

cooperation between Technical Universities in

Žilina and in Ostrava [1], [2].

Fig. 1 Side view of the bridge structure,

Fig. 2 Degradation of the main beams

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ISBN: 978-1-61804-137-1 269

2 Experiments Experiments were performed at the laboratories of

the VSB-TU in Ostrava. The specimens represent

decreased section of the real bridge structure – steel

cross-beams connected with GL timber main beams

using the bolt connection. The model was simplified

for laboratory conditions, see Fig. 3.

Results from the experiments were already

published [4], measured points are marked as

S – overall deformations and T – local deflections.

S7

S5

S10

S9

S8

S11

S9

S8

S4

S2S1 S6, S10

S3

T7

T8

T9

T10

T6T5

T3

T4

T2

T1T0

2001000200

500

S5

S7

Fig. 3 Experiment set-up

3 Numerical model Numerical model was created using FEM program

ANSYS. Experimentally tested structure was

modeled as 3D body composed of SOLID45,

BEAM4 and SHELL63 elements, where SHELL63

elements were used for mesh only. Bolts were

modeled using 1D bar elements for easy

interpretation of the results. Individual parts of the

model cooperate due to contact elements. Numerical

modeling of such a structure needs to have a special

knowledge, see for example [3], [4], [5], [6], [7].

A material for GL timber was considered as

orthotropic with plastic behavior, for steel material

an isotropic and plastic behavior was chosen.

Numerical model allows geometrical and physical

nonlinearities. Main requirement of the numerical

model is correct behavior of the specimen on

meaning of rotational stiffness of the modeled

connection. Overview of the model and mash

density is presented at the Fig. 4.

The numerical model was calibrated using data

from experiments, total deformation on the middle

of the cross-beam (S6) and development of this

deflection due to applied load was observed mainly,

to be similar on both numerical and experimental

models.

Fig. 4 ANSYS FEM numerical model

2.1 Results from numerical modeling At the Fig. 5 is shown behavior of the numerical

model. The deformations are oversized at the figure

to get a better understanding of the collapse

mechanism. Chart at Fig. 6 is clarifying the load-

deflection dependency at the middle span of the

cross-beam. The end part of the curve is influenced

by not good convergences of the numerical solution,

because the plastic behavior of the bolts and on

local elements of the GL timber.

Fig. 5 ANSYS FEM numerical model – collapse

Fig. 6 Load-deflection curve at the middle-span

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ISBN: 978-1-61804-137-1 270

The force about 165 kN is possible to set as

a ultimate load for bolts. The bolts are loaded by

combination of tension and shear forces. Using

Eurocode5 procedure, excluding the influence of

factor kmod (kmod = 1,0), and considering the material

factor as γM = 1,1 – the ultimate shear capacity of

the used bolts is 7,53 kN. Multiplying this value by

number of used bolts and comparing with the

maximum load reached by numerical model it can

be seen approximately 40 % reserve. This

corresponds well with reserves which are included

in the codes.

At the Fig. 7 vertical deflection (slip deforma-

tion) of the bolts is shown. This deformation

occurred because of pressure to the wooden material

mainly, there is also very small influence

of deformation of whole specimen, which can be

neglected. Comparing with the slip deformation

calculated according to German code DIN 1052

it can be shown 78% agreement.

Fig. 7 Bolt vertical deflections, (oversized)

Because the experiments have been done in the

laboratory and the collapse was reached due to

short-term loading it is not necessarily to check the

slip stiffness at the connection more carefully.

Different situation will be in practical live, where

this phenomenon will influence behavior of the

whole detail. In that case it will be necessarily to

implement influence of the surrounding and type

and history of a load to reach right results for both

ultimate and serviceability limit states.

Furthermore, at Fig. 7 is shown the overall

behavior of the connection, the force redistribution

mainly. Top row of the bolts is loaded by tension

forces primarily comparing with the bottom row of

the bolts which is loaded by shear forces. The face

plate is relatively stiff enough to transform the

compression forces at the bottom part of the

connection. This leads to idea for analytical solution

of the model as a semi-rigid connection with elastic

redistribution of the forces. The development of the

tension forces at the bolts it can be shown, Fig. 8.

Fig. 8 Development of the normal forces at the bolts

4 Analytical solution In this Section there will be shown how it can be

easily describe behavior of the studied connection

using theory of elasticity and some simplified

assumptions. The goal is to have such a model

which will correspond to numerical analysis results

well but gives us little bit more insight of the

problem.

Simplified schema of the behavior of the

connection can be described, as it shown at the

Fig. 9. The formulas describing that behavior can be

express by the theory of equilibrium forces, for

a simply supported beam with not-movable supports

with semi-rigid rotational supports, as follows:

EI

Fl

k

Fl

k

lX

k

X

k

X

EI

lX

EI

X

822

2

22

2

2

1

1

1

2

21 =−++++ϕϕϕϕ

(1)

EI

Fl

k

Fl

k

lX

k

lX

EI

lX

EI

lX

48

5

20

32

2

2

2

2

2

2

2

1

3

2

2

1 =−++++ϕϕϕ

(2)

where:

X1 moment at the semi-rigid connection [Nm]

kφ rotational stiffness [Nmrad-1

]

F load [N]

l span [m]

EI stiffness of the cross-beam [Nm2]

The equations above are valid only if following

conditions are satisfied:

• Glued-laminated timber member have only

negligible deformations due to bending moment at

the semi-rigid connection.

• The top and bottom stiffeners are stiff enough to

stabilize wooden beams.

• Steel cross-beam with the face plate has small

deformations comparing with those obtained on

bolts (lengthening of the bolts along with

deformations of GL timber member at the contact

with the washers and nuts.

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ISBN: 978-1-61804-137-1 271

This leads to 3-times statically indefinite, but, in

our case, symmetrical problem (kφ1 = kφ1; X2 = F/2;

X3 (axial normal force) = 0). Considered all higher

mentioned requirements the Eq. (1) and (2) can be

simplified to:

( )EIlk

kFlX

+=

ϕ

ϕ

8

2

1 (3)

Fig. 9 Simplified deformation of the face plate

Fig. 10 Moment and deformation diagram of

a cross-beam with semi-rigid support

Fig. 11 Overview of the FEM simulation result and

of two experiment record

Using presented numerical model it can be

shown that rotational stiffness of the connection is

kφ = 1.447 MNmrad-1, moment at the connection

then will be X1 = 7.77 kNm. The axial force at the

top row bolts then will be F1 = 10.4 kN, which

corresponds with the results obtained from the

numerical calculation (F1,ANSYS = 12.2 kN). This

can be accepted as a good approximation,

considered all mentioned simplifications.

Finally the overall deformation of the cross-beam

can be compared with those obtained from the

numerical model, as is shown at the Figs. 10 and 11.

5 Conclusion It has been shown, that rotational capacity of the

timber – steel connection can be calculated using

different methods. Most simple method is an

analytical solution which can lead to acceptable

results, good simplifications and boundary

conditions are needed to take into account. More

advance possibility is FEM numerical modeling

which can be used for deep recognition of the

problem. Anyway the experiments are needed to

prove both numerical and analytical solutions and

help on better understanding the problem.

Designing a simple structure the presented

analytical model (or a procedure) can be used for

acquisition of data, as rotational stiffness of

a connection, which are needed for advanced

numerical models.

References:

[1] Lokaj, A. & all., Drevostavby a drevene

konstrukce, Brno: Akademicke nakladatelstvi

CERM, 2010. 309 p. ISBN 978-80-7204-732-1

[2] Vican, J., Gocal, J., Odrobinak, J., Kombinacia

dreva a ocele pri navrhu lavok pre chodcov

a mostov malach rozpati, Drevostavby,

Oscadnica, 2009, p. 41-48.

[3] Schmidt, J., Kaliske, M., Models for numerical

failure analysis of wooden structures,

Engineering Structures 31, 2009, p. 571-579

[4] Jorissen, A., Fragiacomo, M., General notes on

ductility in timber structures, Engineering

Structures 33, 2011, p. 2987–2997

[5] Malo, K.A., Ellingsbø, P., On Connections for

Timber Bridges, Publisher: Tapir Akademisk

Forlag, 2010, p. 297-312, ISBN/ISBN2

9788251926805

[6] EN 338. Structural timber—strength classes,

rue de Stassart, 36 B-1050. Brussels (Belgium):

Published by Comité Européen de

Normalisation, CEN; 2008

[7] ANSYS Reference manual: Release 12.0,

Documentation for ANSYS Workbench and

ANSYS APDL

Recent Advances in Engineering

ISBN: 978-1-61804-137-1 272