36 Gregor Steel to Concrete

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STEEL TO CONCRETE

MOMENT CONNECTIONS

Dalibor Gregor

Excon a.s.Czech Republic

E-mail: [email protected]

Frantiek Wald

Czech Technical University in PragueCzech Republic

E-mail: [email protected]

ABSTRACT

The paper describes the work on the analytical prediction model of behaviour of end platejoints connecting the steel beams to concrete structure. Three sets of tests simulating the

beamtocolumn joint components under cycling loading were carried out in the laboratory of

Czech Technical University to observe experimentally the components: the bolt in tension and

the end plate in bending, the anchor bolt in tension and the concrete in compression. An

analytical prediction model for cyclic loading was developed based on component method

taking into account the test results as well as the existing knowledge of the beam-to-column

and the column-base behaviour. The prediction obtained using the model was compared to

the results of the published test and the good accuracy was found.

1 INTRODUCTION

Structural joints are designed assuming to be exposed to the internal forces resulting from the

quasistatic loading. Connections of the structures which are loaded cyclically by live loads or

thermal and seismic actions are further checked separately against fatigue. In many

structures, however, the number of cycles depending on load spectrum may reach 8 10 3105.

In the joint the local yielding could occur. Information about the behaviour of joints

subjected to repeated loading is important namely for connections of elements from different

material but is appropriate for all structures, even for these where quasistatic approach have

been approved in practice, as a good prediction tool. The modified ECCS recommendation

and classification for the cyclic loading procedure is commonly applied to compare the results

of tests of the structural joints and to analyse the results.

A component method was proved to be an effective analytical tool for determination of jointbehaviour. The method is based on the analytical modelling of separated components

(individual parts) of the joint. The behaviour of each component is represented by a spring.

A mechanical model of the joint is composed of these springs and infinitely rigid plates. The

description of behaviour of each component by three basic design characteristics: an initial

(elastic) stiffness, strength (design value) and a deformation capacity enables an application of

the method into the practice. The resulting force-displacement relationship for the joint

design is thus bi-linear. The analytical description of components offers to designer

a freedom of geometrical variants. The extrapolation of the method to combination of both

bolted and welded parts of joints under loading by combination of the internal forces

(bending, shear and normal force) was proved to be sufficiently accurate.


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The cyclic overall behaviour of joints is traditionally predicted by curve-fitting models. For

fitting the model behaviour onto the tests, it is important to select main parameters of the

model properly. The parameters are characterised by constants which are to be defined on a

basis of test results or a sensitivity study by FE analysis. These models are reaching, within a

limited range of applications, the required accuracy. Any extrapolation out of the

experimentally proved geometrical set-up is not possible. In the last decade, the sophisticatedmathematical models for the steel beam-to-column joints were derived for an accurate

prediction of frame behaviour under seismic actions [1] and [2] and for column bases.

Fig. 1: Test of component concrete in compression and

end plate in bending; deformed shape of the plate

Fig. 2: End plate in bending and anchor bolts

in tension; failure mode of the end plate

2 COMPONENT TESTS

Three sets of tests with components were performed. The end plate in bending and the

concrete in compression were tested under repeated loading, see Fig. 1. The tests with

threaded bar cast in the concrete block was designed to analyse its behaviour and prepare the

test of the component end plate in bending and anchor bolts in tension.

The test set-up of experiment concrete in compression and end plate in bending is shownin Fig. 2 [3]. The tests were carried out in two configurations. Three specimens were

attached to upper horizontal surface of the concrete block (representing concrete slab) and

three specimens were tested on vertical side of the block (representing concrete wall). The

surface of the concrete was cleaned and levelled by a thin (less than 1 mm thick) layer of high

strength grout to achieve smooth surface. Two more sets of tests were carried out replacing 1

mm grout layer by 15 mm grout layer with strength 10 MPa and 50 MPa. The steel plate with

nominal dimensions 200 100 10 mm was placed on the fresh grout layer. The steel bar,

nominally 10 10 220 mm, was centred on the plate. The concrete block was positioned

under the head of the hydraulic actuator and a layer of plaster was made under the block to

ensure the level of the top surface to be horizontal and the laboratory floor to be in full contact

with the block. An example of the result of test C1/1 (test on horizontal surface, 1mm grout

layer) is presented in Fig. 3 [4].

The threaded bar cast in the concrete block loaded in tension was tested separately to learn a

local behaviour of the tension part of the connection, see [4]. Threaded bar M20 was cast in

the concrete block 500 500 500 mm. Two hydraulic jacks were placed on the plaster

layer to ensure the vertical position and good transfer of the reactions into the concrete block.

The beam made of two UPN 140 profiles with web stiffeners transfers the forces into the bar

which was fixed to the beam by washer plate with thickness 20 mm.

For the component end plate in bending and anchor bolts in tension, two threaded bars M20,

540 mm long were cast into the concrete block. The T-stub was positioned at the concrete

surface four hours after the casting to ensure proper contact with the concrete surface.

No grout was used. The nuts were tightened before the test, after 120 days from casting, by


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torque of 40 Nm to simulate the hand tightening. Two hydraulic jacks were placed on the

block on plaster layer. The beam of two UPN 140 profiles transferred the tensile force into the

T-stub. Three sets of specimens were tested. An example of the result of a set of tests is

presented in Fig. 4.

0

100

200

300

400

500

600

-2-10

Experiment C1/1

Prediction

Force, kN

Deformation, mm

Fig. 3: Comparison of the predicted and measured displacement at centre of the plate for

the component the concrete in compression and end plate in bending, test C1/1

0

20

40

60

80

100

120

140

160

0 1 2 3 4 6 7 8 9 10 11

Experiment TC1

Prediction

Failure load for TC1

5

Force, kN

Deformation, mm

Fig. 4: Comparison of the predicted and measured displacement of the top of the T-stub,

the component end plate in bending and anchor bolts in tension, test TC1

3 MODELLING

Due to hysteretic character of behaviour it is not possible to determine a given point of the

force-displacement or moment-rotation curve without information about the load history. For

the component model under cyclic loading, the degradation of material and the history of

yielding in the precedent cycle are taken into account, see [5]. The degradation phenomena

may be described in the models of each component, see [6]. The step-by-step procedure isused to establish the force-displacement or moment-rotation curves, allowing in each step for


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the cumulative degradation of the material and the deterioration of stiffness. The curves are

simplified by use of linear approach.

The tests with components were published in [3], and [4]. The knowledge developed for base

plates and applied in European structural steel practice may be used for connections between

steel frame and reinforced concrete part of the structure, columns and walls. Two approaches

may be distinguished for the component in compression (the plate in bending and the concrete

in compression): concrete in compression under rigid plate and effective area of flexible plate.

Stiffness and resistance of the concrete in compression is limited by crushing of the concrete

surface. The behaviour is influenced by the concrete quality, the thickness and area of the

plate, the grout quality and thickness, the location of the plate on the concrete structure, the

size of the concrete structure, and its reinforcement as well. The component plate in bending

and anchor bolt in tension is solved by T-stub analogy. The stiffness and resistance are

predisposed by elongation of the anchor bolts, which prevents development of prying forces

and guided failure modes became different to the steel beam-to-column connections. The

prediction of component behaviour in Fig. 3 and 4 is based on the measured values of yield

strength fy and ultimate strength fu of the steel and average measured value of concretestrength. The simple step-by-step procedure with constant increment of 1/1000 of

deformation was applied to achieve the description of the working diagram of each

component as well as of the whole assembly. The unloading part of working diagram of each

deformable component was studied separately and models were developed using a weakening

factor. A simplification adapting the initial stiffness seems to be acceptable even for the

advanced prediction.

16 300 16

SP1

35

54

4x53

54

3580

d e

c

d e

c

Fig. 5: Test setup of the joint assembly [7]

4 COMPARISON TO TESTThe prediction model was developed based on the component models for initial stiffness and

strength known for the monotonic loads and these models are adapted to the repeated loading

using the results of the tests of components, see [3] and [4]. The model was compared to the

available test of the whole assembly. The Fig. 5 shows the test performed by Dunai at al. [7],

the bars transferred the tensile forces and the studs the shear as well as tensile forces. Fig. 6

shows the comparison of the calculation to the test on the moment-rotation diagram. The

springs c represent the compressed part behaviour, springs d the bars, and e the deformed

T-stub in compression. The model was loaded by cyclic actions based on the test records. The

measured values of the material were applied in presented simulation. The first, second and

six cycles together show a good agreement of the model prediction to the test.


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-120

-80

-40

0

40

80

120

-20 -15 -10 -5

0 5 10 15 20

Rotation, mrad

Moment, kNm

Test

Model

Fig. 6a: Comparison of the model to test,

first cycle

-120

-80

-40

0

40

80

120

-20 -15 -10 -5

0 5 10 15 20

Rotation, mrad

Moment, kNm

Test

Model

Fig. 6b: Comparison of the model to test,

second cycle

-120

-80

-40

0

40

80

120

-25 -20 -15 -10 -5

0 5 10 15 20 25

Rotation, mrad

Moment, kNm

Test

Model

Fig. 6c: Comparison of the model to test, six cycles

Fig. 7: The parameters for the comparison of the model to test by the resistance ratio

The ECCS classification of the joint characteristics under cyclic loading may help to comparethe prediction to the test results. The geometrical variables observed by each cycle of the


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loading are summarised in Fig. 7. The cycle parameters may be represented by a partial

ductility, which is defined as

ioi

y

e

e

+

+

+= ; i

oi

y

e

e

= (1)

a full ductility

ii

y

e

e

+

+

+

= ; i

i

y

e

e

= (2)

a resistance ratio

ii

y

F

F

+

+

+= ; i

i

y

F

F

= (3)

a rigidity ratio

( )( )

i

i

y

tg

tg

+

+

+= ;

( )( )

i

i

y

tg

tg

= (4)

and an absorbed energy ratio

( )i

i

y i y i y

A

F e e e e

+

+

+ + + =

+ ;

( )i

i

y i y i y

A

F e e e e

+ + =

+ (5)

The functions derived from each cycle parameters depends on the partial ductility as full

ductility function

( )o , see Fig. 8a, relative rigidity function

( )o , see Fig. 8b, and

relative absorbed energy function ( )o , see Fig. 8c. On the functions it may be seen a good

description of tendencies in positive hemi-cycle, on the right side of the diagrams, and on

negative hemi-cycle, on the left one. The particular accuracy of the prediction is limited

compare to the curve fitting prediction.

0,2

0,6

1,0

1,4

1,8

2,2

2,6

-12 -10 -8 -6 -4 -2 0 8

Experiment SP-1

Prediction with

2 4 6

fyPrediction with

fu

Experiment SP-1

Prediction with f

yPrediction with f

u

Partial ductility

Resistance ration

Fig. 8a: Comparison of the model to test by the resistance ratio


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0

Experiment SP-1

Prediction with

2 4 6

fy

Prediction with fu

Partial ductility

Ductility ration

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

-12 -10 -8 -6 -4 -2

Experiment SP-1

Prediction withfy

Prediction with fu

Fig. 8b: Comparison of the model to test by the rigidity ratio

0

Experiment SP-1

Prediction with

2 4 6

fyPrediction with

fu

Partial ductility

Experiment SP-1

Prediction with

fyPrediction with

fu

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

-12 -10 -8 -6 -4 -2

Absorbed energy ratio

Fig. 8c: Comparison of the model to test by the absorbed energy ratio

5 SUMMARY

The behaviour of connections loaded by cyclic forces may be predicted by component model.

Component prediction brings higher understanding of each connection parts influence. Themethod exhibits good quality of prediction based on input data description as well as chosen

accuracy in detailing of model. The calculation is handicapped by the step-by-step procedure

for the each component as well as whole joint assembly, which is on the other hand natural in

today analyses supported by informatics. Based on analytical nature the method enables to go

to prediction of new developments.

The description of steel-to-concrete connection is based on set of tests with components. The

prediction of experiment from literature shows a good quality of prediction. The important

influence of shear forces is expected to be incorporated in the nest step of the model.


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ACKNOWLEDGMENT

The work has been supported by grant COST C12.10 of Czech Ministry of Education, Youth

and Sport.

REFERENCES

[1] Mazzolani, F.M., Mathematical model for semi-rigid joints under cyclic loads.Connections in Steel Structures: Behaviour, Strength and Design, Elsevier Applied

Science Publisher, London, 1988, pp. 112-120

[2] Della Corte G., De Matteis, G. Landolfo, R., A mathematical model interpreting thecyclic behaviour of steel beam-to-column joints. Proc. 17. kongres C.T.A. - Settimana

della construzione in acciaio,Napoli, 1999, pp. 115-126

[3] Gregor D., Wald F., Eliov M., Jrovsk I., Joints for mixed building technology withview to experiments of component steel plate in bending and concrete in compression, in

Eurosteel 2002, Coimbra 2002, pp. 977-986, ISBN 972-98376-3-5

[4] Gregor D., Wald F., Sokol Z., Experiments with End Plate Joints for Mixed BuildingTechnology, in Experimental Investigation of Building Materials and Technologies, ed.Konvalinka P., Luxemburg F., VUT, Praha 2003, pp. 65-82, ISBN 80-01-02835-6

[5] Rassati G.A., No S., Leon, R.T.,PR Composite joints under cyclic and dynamic loadingconditions: The component model approach, in Proc. 4th AISC International Workshop

on Connections in Steel Structures, Roanoke, 2000, pp. 213-222

[6] Bernuzzi C., Balado, L., Castiglioni, C.A., Steel beem to column joints: Failure criteriaand cumulative damage models. Proc. STESSA ed. F.M. Mazzolani and H. Akiyama,

Kyoto, 1997, pp. 538-545

[7] Dunai L., Ohtani Y., Fukumoto Y., Experimental Study of Steel-to-Concrete End-PlateConnections under Combined Thrust and Bending, Technology Reports of Osaka

University, Vol. 44, No. 2197, Osaka 1994

KEYWORDS

Mixed building technology, Steel to concrete connections, Structural joints, Experimental

observations, Prediction model, Component method, Quasistatic loading, Cyclic loading.

36 Gregor Steel to Concrete

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