stiffened end plates in structural steel connections

7/22/2019 Stiffened End Plates in Structural Steel Connections

1/5

1; No. 38

STIFFENED END PLATES IN STRUCTURAL STEEL CONNECTIONS

Martina Eliov1, Fernando C. T. Gomes2, Frantiek Wald1

1Department of Steel Structures, CTU, Thkurova 7, 166 29 Prague 6, Czech Republic

2 Department of Civil Engineering, University of Coimbra, 3049 Coimbra, Portugal

Keywords: Beam to column connection, End plate with stiffener, Equivalent T-stub,

Effective length, Plastic analysis, Kinematic method of plastic yield lines.

Abstract: In the steel structures are very often used end-plate connections which are designed

according to applied yield line theory [1]. Six tests of the steel end-plate with stiffeners

connected by the bolts were performed to check the typical connection behaviour. Based on

the experimental results and theoretical model the simplification of Eurocode 3 proposal is

presented.

1 INTRODUCTION

Design of steel structures is based on plastic analysis, see [1]. Design of different

structural details are a typical application of plastic analysis. Bolted end plates with stiffener

are often used for beam to column connections. Annex J [1] represents the European tool for

design of structural details. Procedure is transferring to the solution of the equivalent T-stub

in tension area. The effective length of equivalent T-stub depends on the boundary conditions.

The most significant boundary conditions are stiffeners of a plate. The equivalent free length

is assessed by a graph, Fig. 3, according the Eurocode 3. The graphical representation is not

suitable for using at the computers programmes. The main aim of this study is development of

simplified expression for determination of the effective length. This proposed analytical

functions were compared with results obtained by theoretical model, Eurocode 3 model and

experimental results.

2 MODELLING

2.1 Theoretical background

Design resistance can be predict by the rigid - plastic analysis of plates. Procedure of

calculation is formed on the principle of kinematic method of plastic yield lines to

determinate plastic limit load Fpl. This method sets the upper bound to plastic limit loads.

Results corresponding to various possible collapse patterns are mutually compared to find the

smallest value of the limit load. The plastic limit load Fpl can be easily determined by

equating the virtual works of the external and internal forces at the instant of rigid-plasticcollapse

!"!i

mwj

F iipl,jjpl, # , (1)

where Fpl,jand wjare plastic limit loads and displacement in the points jof action of loads,

mpl,iand #i- plastic resistances and rotation angle of yield line.

On the simplified model of the stiffened end plate, see Fig. 1, is demonstrated thecalculation

of the plastic limit load Fpl which was chosen from a family of the kinematically feasible

plastic mechanisms. For determining of the plastic limit Fpl is considered only fourth of the

end plate with one bolt. It is assumed, that the tension force are acting on the stiffener, in the

middle of the end plate. It was necessary to solve various failure modes according to the shape

of the plate, location of the bolt, its distances from the edge and stiffener. An example offeasible collapse patterns are shown in Fig. 2. The critical failure mechanism was found


2/5

2; No. 38

through the comparison of individual limit loadsFpl,j.

P8-170x170

Fig. 1 Test specimen of simplified model of the stiffened end plate

$"%

#y

$"%

#y

Fig. 2 Failure mechanism

2.2 Application in Eurocode 3

For calculation of end plate type of connections is used rigid-plastic analysis in

Annex J of the Eurocode 3. The resistance of the column flange or end plate in tension area is

transferred to calculation of resistance of equivalent T-stub with one row of the bolts.Effective lengthLeffof this T-stub is determined by the kinematic method of plastic yields line

for every row of the bolts. Resulting value of Leffdepends on coefficient ' that was derived

from numerical and analytical studies. Coefficient 'varies to the distances of the bolt from

stiffeners. In [1] the coefficient 'is given in a graph, see Fig.3, based onparametersem

m1

(") ,

em

m22

(") . (2)

Effective length of equivalent T-stub for the bolts in the corner of stiffeners is estimated for

the one bolt asLeff= ' mand for the group of the bolts asLeff= 0,5p + ' m - 2m - 0,625e.

2.3 Algorithmisation

The graphical representation of the coefficient ' is not acceptable for algorithmisation of a

procedure. The effort was intent on creating the procedure that would be useful for computers


3/5

3; No. 38

m2

0,8 x 1,4 x awe

e m0,8 r

1

tpc

twc

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

)2

)1

= 8a *2 5,5 4,75 4,45

0

0,5

1,4

0 0,4 0,9

)2

)1

= 8 a

4,45

a

a

a

b

c

a

a

=h2

h1

h3

Fig. 3 Graph for determination of effective lengthLeff

programmes [2], [4], [5]. Curves in graph, Fig. 3, were substituted by function, see [2], in a

form

+ ,+ ,C1

C

2

21

!B1

!AKONST!

(

(" . (3)

Parameters KONST, A, B and C of this function were determined by a method of least

squares. Insetting of function (3) with these points by method of least squares leads to

equation

+ ,+ ,KON ST

A

BC C

(

(

-

.

/

0000

1

2

3333

"! )

)

)2

2

1

2

1

1

*min . (4)

Equation (4) is minimum when the derivations by the parameters of selecting function are

zero. From fourth equations it is possible to evaluate parametersKONST, A, Band C.

2.4 Simplified determination of

Between two modes of failure, for one independent bolt and for two bolts, can be

interpolate the approximation of the solution which gives a procedure below. It is expected

)2

)1

0,4

0,6

0,8

0,3 0,5 0,7 0,9

= 7 2 6 5,5 5 4,75 4,5 = 4,45*'

0,9

0,3

'

21=

21

21>

stiffened end plates in structural steel connections

Documents