UNIVERSITY OF ARCHITECTURE, CIVIL … · university of architecture, civil engineering and geodesy faculty of structural engineering department “steel, timber and plastic structures”

UNIVERSITY OF ARCHITECTURE, CIVIL ENGINEERING AND GEODESY

FACULTY OF STRUCTURAL ENGINEERING

DEPARTMENT “STEEL, TIMBER AND PLASTIC STRUCTURES”

eng. Dimo Siderov Zhelev

DUCTILITY OF BEAM-TO-COLUMN JOINT

WITH ENDPLATE CONNECTION

Author's summary of PhD thesis (English version)

For the award of educational

and scientific degree "doctor"

Sofia, 2015

http://uacg.bg/?p=163&l=2&f=2

http://uacg.bg/?p=220&l=2&f=2&dp=21

Ductility of beam-to-column joint with endplate connection (English version of author’s summary) page 2

The thesis is structured in 6 headings and 1 application in total of 246 pages with 276 figures and 62

tables. In heading 1 is grounded the relevance of the study. In heading 2 is researched the T-stub as contains

detailed literature review and results from author’s numerical simulations of isolated T-stubs. In heading 3 are

described researches of the web panel. Heading 4 summarize analytical and numerical research of beam-to-

column joint with endplate connection subjected to cyclic load. In detail are presented results and conclusions

based on 23 by FEA simulated specimens. The material models applied in the FEA are specified in heading 5.

In heading 6 is performed comparison of experimental and author’s numerical results to verify them.

The thesis is discussed at scientific seminar in Department "Steel, Timber and Plastic Structures" at the

UACEG in ………………, 2015 and is targeted for defense.

The author is enrolled as regular doctoral student at Department "Steel, Timber and Plastic Structures" of

UACEG in 21.04.2012 with Protocol № 333 / 21.04.2012.

The public presentation of the thesis will take place on ………………. in Hall ………. of UACEG,

1 Hristo Smirnenski Blvd., 1046 Sofia, Bulgaria from …………. hours

Materials for defense will be available to those interested in the study in office room …….., UACEG, 1

Hristo Smirnenski Blvd., 1046 Sofia, Bulgaria and are uploaded to the website of the university www.uacg.bg.

Author: Eng. Dimo Siderov Zhelev

Title: Ductility of beam-to-column joint with endplate connection


Contents Contents ................................................................................................................................................................................... 3

1 Formulation of thesis ..................................................................................................................................................... 5

2 Equivalent T-stub ........................................................................................................................................................... 5

2.1 FEA of T-stub for tension resistance determination ............................................................................................... 6

2.1.1 Prying force in T-stub .................................................................................................................................... 7

2.2 Designation of the maximum tension resistance of the T-stub. .............................................................................. 8

2.3 Determination of parameters in Richard-Abott formula representing “Force-elongation” in T-stub ..................... 9

2.3.1 Determining the initial stiffness of T-stub with no pretension bolts ............................................................. 9

2.3.2 Determination of the initial stiffness of the T-stub with pretension bolts ................................................... 10

2.3.3 Determination of the elongation at reaching maximum strength u of T-stub ........................................... 10

2.3.4 Determination of the parameter .............................................................................................................. 10

2.3.5 Comparison of the evaluated analytical expression with experimental study [11] ...................................... 11

3 Shear of column web .................................................................................................................................................... 11

3.1 Maximum shear resistance of joint panel ............................................................................................................. 12

4 Numerical and analytical study of stiffened extended end plate connection subjected to monotonic loading ............. 13

4.1 Analytical expressions for determining the rotation capacity of end plate connection ........................................ 13

4.2 Relationship end plate connection resistance and plastic moment of the beam ................................................... 14

4.3 Numerical simulation of isolated end plate connection ........................................................................................ 14

4.3.1 Входни данни за изследването ................................................................................................................. 14

4.3.2 Numerical simulation of end plate connection partial results ...................................................................... 15

4.3.3 Initial stiffness of the end plate connection specimen ................................................................................. 15

4.3.4 Proposal for an analytical expression for determining the rotation capacity of end plate connection ......... 16

5 Numerical and analytical study of beam-to-column joint with end plate connection subjected to cyclic load ............ 17

5.1 Low cycle fatigue literature review ...................................................................................................................... 17

5.2 Research of beam-to-column joint 1 from frame 1 .............................................................................................. 18

5.2.1 Results of beam-to-column joint of Frame 1 ............................................................................................... 20

5.3 Part of results for frame 1 specimen. .................................................................................................................... 22

5.3.1 Specimen N_6_20_24_600 .................................................................................................................................. 22

5.3.2 Fatigue life of simulated specimens, subjected to JISF cyclic load ............................................................. 23

5.3.3 Beam flange local buckling ......................................................................................................................... 25

5.3.4 Joint rotation distribution on the components ............................................................................................. 26

5.3.5 Influence of the end plate connection resistance to the joint hysteresis behavior when subjected to cyclic 27

5.3.6 Influence of Rd on the behavior of partial strength and full strength end plate connections, when subjected

to cyclic load. ............................................................................................................................................................... 30

5.4 Research of beam-to-column joint from frame 2 ................................................................................................. 32

5.4.1 Comparison of the maximum strain in the simulated specimens in frame 2 ............................................... 34

6 Appropriate material models for cyclic loading appication from the ANSYS material library ................................... 35

7 Numerical simulating of experiments .......................................................................................................................... 36


7.1 Bursi and Jaspart [32] experimental study on T-stub loaded on tension. ............................................................ 36

7.2 Gang Shi study on beam-to-column joint with end plate connection, subjected to cyclic loading [29] ............... 37

Bibliography

[1] БДС, БДС EN 1993-1-8: Проектиране на стоманени конструкции Част 1-8: Проектиране на възли, 2007.

[2] J. Jaspart, Etude de la semi-rigidité des noeuds poutre-colonne et son influence sur la résistance et la stabilité des ossatures

en acier, Liège, Belgique: Université de Liège, 1991.

[3] N. Krishnamurthy, "A Fresh Look at Bolted End-Plate Behavior and Design," Engineering Journal, vol. 15, no. 2, pp. 39-

49, 1978.

[4] A. M. G. Coelho, Characterization of the ductility of bolted end plate beam to column steel connections, Universidade de

Coimbra, 2004.

[5] A. Abolmaali, J. H. Matthys, M. Farooqi и Y. Choi, „Development of moment–rotation model equations for flush end-plate

connections,“ Journal of Constructional Steel Research, № 61, p. 1595–1612, 2005.

[6] R. S. Silva, L. S. da и P. J. Cruz, „Cyclic behaviour of end-plate beam-to-column composite joints,“ Steel and Composite

Structures, том 1, № 3, pp. 355-376, 2001.

[7] C. Faella, V. Piluso и G. Rizzano, Structural steel semirigid connections, 2000.

[8] K. Weynand, J.-. P. Jaspart и M. Steenhuis, „The stiffness model of revised annex J of Eurocode 3,“ Connections in Steel

Structures, том III, pp. 441-452, 1995.

[9] SAC Joint Venture, FEMA 350 Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings, 2000.

[10] БДС, БДС EN 1993-1-5: Проектиране на стоманени конструкции Част 1-5: Пълностенни конструктивни елементи,

2007.

[11] D. Dubina, A. Stratan, N. Muntean и D. Graecea, „Dual-Steel T-stub behaviour under monotonic and cyclic loading,“

Connections in steel structures, том VI, 2008.

[12] F. A. Charney и W. M. Downs, „Modeling procedures for panel zone deformations in moment resisting frames,“

Connections in Steel Structures V, pp. 121-130, 2004.

[13] K. Ikarashi, H. Kaneko, H. Yanase и M. Aono, „Hysteresis loop model of joint panels in H-shaped column to bema

connections,“ Journal of Structural and Construction Engineering, № 597, pp. 119-126, 2005.

[14] A. Kawano, H. Asega и H. Hasebe, „An experimental study on ductility of wide - flange steel frame with composite beam

including weak joint panel in different collapse models,“ Journal of structural construction engineering, № 452, pp. 109-

119, 1993.

[15] A. Kawano, „On the effect of structural composition of joint panel on a seismic behaviour of steel frame,“ Journal of

Structural Construction Engineering, том 435, 1992.

[16] SAC Joint Venture, FEMA 355D State of the art report on connection performance, Sacramento, California, 2001.

[17] БДС, БДС EN 1998-1: Проектиране на конструкциите за сеизмични въздействия Част 1: Общи правила, сеизмични

въздействия и правила за сгради.

[18] P. Zoetemeijer, Summary of the research on bolted beam-to-column connections (period 1978-1983), Delft, 1983.

[19] I. O. Adegoke и A. R. Kemp, „Moment-rotation relationships of thin end plate connections in steel beams,“ в In

Proceedings of the International Conference on Advances in Structures (ASSCCA’03), 2003.

[20] FEMA, „FEMA 356 prestandard and commentary for the seismic rehabilitation of buildings“.

[21] БДС, БДС EN 1993-1-1 Проектиране на стоманени конструкции Част 1-1: Общи правила и правила за сгради, 2007.

[22] D. Beg, E. Zupancˇicˇ и I. Vayas, „On the rotation capacity of moment connections,“ Journal of Constructional Steel

Research, том 60, № 3-5, pp. 601-620, 2004.

[23] O. Basquin, „The Exponential Law of Endurance Tests,“ American Society for Testing and Materials Proceedings, том 10,

pp. 625-630, 1910.

[24] Det norske veritas as, Determination of Structural Capacity by Non-linear FE analysis Methods, 2013.

[25] F. J. Davila-Arbona, Panel zone behaviour in steel moment resisting frames, 2007.

[26] ECCS, Recommended Testing Procedure for Assessing the Behaviour of Structural Steel Elements under Cyclic Loads,

1986.


[27] A. Ghobarah, A. Osman и R. M. Korol, „Behaviour of extended end-plate connections under cyclic loading,“ Engineering

structures, том 12, pp. 15-27, 1990.

[28] ANSI/AISC, ANSI/AISC 341-10 Seismic Provisions for Structural Steel Buildings, 2010.

[29] S. Gang, Y. Shi and Y. Wang, "Behaviour of end-plate moment connections under earthquake loading," Engineering

structures, vol. 29, no. 5, pp. 703-716, 2007.

[30] ANSYS, „Mechanical APDl (ANSYS) 14.0 Theory manual“.

[31] S. Yongjiu, W. Meng and W. Yuanqing, "Experimental and constitutive model study of structural steel under cyclic

loading," Journal of Constructional Steel Research, vol. 8, no. 67, pp. 1185-1197, 2011.

[32] O. S. Bursi и J. P. Jaspart, „Benchmarks for Finite Element Modelling of Bolted Steel Connections,“ Journal of

Constructional Steel Research, том 43, № 1-3, pp. 17-42, 1997.

[33] J.L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories, International Journal of Plasticity,

Volume 24, Issue 10, 1642–1693, 2008.

1 Formulation of thesis Beam-to-column joint is typically detailed with endplate connection because easy assembly and

low price. The scope of the thesis is research of beam-to-column joint with endplate, subjected to

monotonic or cyclic loading, as the survey will be carried out by numerical simulations.

It is known from the literature that the prying force in the T-stub is not always situated on the

edge of the flange plate. Based on the parametric study of numerical simulations on T-stubs the

position of the prying force will be defined, considering bearing capacity and rigidity of the

components of the T-stub. This will allow proposing an appropriate expression for determining the

prying force position and correct the tension strength of the T-stub.

To evaluate the usefulness and accuracy of FEA for numerical simulation of beam-to-column

joint with endplate connection is necessary to make a comparison between the results of experimental

and numerical studies in applied monotonic or cyclic load. To properly simulate the behavior of steel

under cyclic load is necessary to use proper material model, which should be validated with result

from material cyclic test.

One of the significant advantages of numerical simulations is the low cost of the study and ease

of "what-if" analysis. Because this convenience a detailed study of the beam-to-column joint subjected

to cyclic load can be performed. This will assess the impact of strength and ductility of the individual

components of the beam-to-column joint to the joint ductility.

Typical end plate connection types are stiffened end plate, unstiffened end plate and end plate

with haunch. Even designed with the same resistance, a different performance is expected. By

comparing the strain in the connection subjected to cyclic loading the connection types could be

ranked. The comparison of different solutions for detailing of beam-to-column joint will allow

evaluation of the advantages of some details to others.

2 Equivalent T-stub Equivalent T-piece is formulated by the endplate with adjacent bolt row as in Figure 1. The

endplate is working on bending while the bolts on tension mainly. Typical an equivalent T-stub for

each bolt row is defined. According to [1] the length of the equivalent T-piece effl is such that the

bearing capacity is identical to the capacity of the portion represents. The length of the equivalent T-

piece effl is conditional and does not correspond to the part that represents.

The behavior of T-piece subjected to tension has being researched from the early seventies.

Fundamental interest of researchers is the prying force influence to T-stub resistance. In the literature

are known analytical expressions for determining the bearing capacity of the T-stub, typically based on

http://www.sciencedirect.com/science/journal/0143974X/67/8


plastic analysis. The reader is kindly invited to acquaint with the literature review in the PhD’s first

heading if interested in T-stub analytical models.

a)

b)

c) Figure 1 „Identification of T-stub in endplate connection“

The analytical method for determining the yield resistance of T-stub in [1] assumed that the

prying force is situated at the end of the end plate and calculated with the requirment 1.25*e n m ,

as on Figure 1 c). Jaspart [2] and Krishnamurthy [3] suggest that the prying force should not be

situated at the end T-stub when plate yielding occurs. Based on Figure 2 is proposed eq. (1) for

determining the distance 'n from the axis of the bolt row to the prying force.

' lМn

Q (1)

Figure 2 „Determination of the distance 'n between the prying force and the bolt row“

The value of the bending moment in the endplate lМ and the prying force are Q unknown, but

may be determined by numerical simulation of isolated T-stub. By conducting a parametric study of

numerical simulation of T-stub with variable thickness of endplate and bolt tension resistance also

further knowledge would be gained about T-stub design.

2.1 FEA of T-stub for tension resistance determination

For the numerical study of T-stub are used frame finite elements explained in detail in Table 1

and Figure 3. Modeling of T-stub with frame finite elements is applied by Coelho [4]. This is the

simplest method for numerical simulation of T-stub, but is only suitable for calculating the bearing

strength of the T-piece, not for its initial stiffness. Another benefit of this simplistic approach is that

the effective length effl of the T-piece is initially known.

Variables in the parametric study are the thickness of the endplate pt , dimension ratio /e m , the

bolt diameter and grade. The structural steel is simulated by bilinear material model without hardening

which complies with the assumed steel flowchart in [1].


Figure 3 „Finete element types used in T-stub FE model“

specimen “m” e <1.25m Bolts

pt effl

V1 40mm 40mm М20 grade 8.8 variable 100mm





Table 1“Specimen V1, V2, V3, V4 and V5 dimensions.

The results of the numerical study shows that by increasing the thickness of the endplate pt , the

prying forceQ shifts to the edge of the endplate. Following the above 50 FEA tested T-stubs is

derived formula (2), which gives an expression for the determination of distance 'n from the axis of

the bolt row to the prying force. 4.5

'0.003 , where ' and М in kNcmplM

pl

nn d

n (2)

The relationship between pt and '/n n obtained from the numerical study and eq. (2) is compared

in Figure 4, as reported the influence of n / m, the class and the diameter of the bolt connection. Based

on the comparisons in Figure 4 can be reported that relatively simple expression in eq. (2) well

suggests the numerical results trend.

Figure 4 „Analytical results with eq.(2) compared to FEA results”

2.1.1 Prying force in T-stub

Interesting result of the numerical study of the T-stub is that in first or second mode [1] always

has prying force, contrary to the analytical result obtained by the instructions in BDS EN 1993-1-8 [1].

Therefore it can be assumed that there is always prying force in T-stub endplate connection.

5

10

15

20

25

30

0.30 1.00

tp -

[mm

]

n'/n

Prying force location dependance

from n/m

n/m=1.25

n/m=1

n/m=0.875

аналитичен израз

5

10

15

20

25

30

0.50 1.00

tp -

[mm

]

n'/n


from bolt grade

n/m=0.875 клас 8.8

n/m=0.875 клас 10.9


5

10

15

20

25

30

0.50 1.00

tp -

[mm

]

n'/n


from bolt diameter

n/m=0.875 M20 клас 8.8

n/m=0.875 M16 клас 8.8



2.2 Designation of the maximum tension resistance of the T-stub.

Figure 5„von Mises stresses in Т-stub endplate, subjected to tension load“

Figure 5 shows the von Mises stresses in the endplate, while the T-stub has reached its

maximum tensile resistance, working in first mode (plate yielding only). It is noted that near the web

the endplate end fibers has reached tensile strength, while in the bolt line the yield stress is reached.

Following the concept T-stub solution in [2], the maximum tensile strength of a T-stub can be

expressed by eq. (3) - (5).

Figure 6 „Определяне на максималната якост на опън на Т-парче“

Because of the equilibrium of the forces in Figure 6, equations (3) - (5) can be obtained.

_ _1 _* 2* 2* *u Rd pl pl ultF m M M B e (3)

_ _1 2* 2*u RdF Q B (4)

* ' 0.5* * plQ n B e M (5)

Solving the equations (3) to (5) resulted in eq. (6) which sets the maximum tensile strength of T-

stub operating in first mode _ _1u RdF . Should be remind that the distance *0.25e D , where D is the

washer diameter or the average size of the nut/bolt head [1].

_ _1

4* * ' 2* (2* )

2* * *( )

pl ult

u Rd

M n M n eF

m n e m n

(6)

Eq. (7) is known in the literature to define the maximum bending resistance.

2 3

_ 2

* ** 3* * 2* *

12

eff p T y

pl ult T y T u

u

l t E EM E E E

(7)

When considered u y eq. (7) is simplified as eq. (8).

2 2* *

* 2* *12 4

eff p eff p

u y u p

l t l tM f f f (8)

Maximum tension resistance of T-stub in second mode _ _ 2u RdF in eq. (10) can be evaluated

assuming that the bending moment in the endplate is _pl ultM from eq.(9). The bolt tension resistance is

assumed *u ub bB f A .


2

_

2*0.25* * * , като

3

y u

pl ult p eff p p

f fM t l f f

(9)

_

_ _ 2

2* 0.98 * '

'

pl ult u

u Rd

M B nF

m n

(10)

2.3 Determination of parameters in Richard-Abott formula representing “Force-elongation” in

T-stub

Richard-Abott formula is based on a formula proposed to express the elasto-plastic behavior of

certain materials. It was later used to compile dependency "moment-rotation" of beam-to-column joint

subjected to monotonic load [5], [6]. With certain processing the formula is also applied to describe

the hysteresis loops of cyclic loading [6].

Richard-Abott formula is also known as the four power equation, as is defined by four

parameters: the initial stiffness ik , tangent stiffness hk , yielding resistance 0F and parameter

defining the curve radius. Richard-Abott formula is described in detail in Figure 7.

001

0

( )*( ) * , където

*( )1

i hh

i h

i h

k k FF k

k kk k

F

1

ln 2

ln h

y i h

kF

F k k

Figure 7 „Richard–Abott formula“

A numerical study of T-stubs considering the pretension bolt is performed. The endplate is

simulated by element type SHELL188 and the bolt with COMBIN39. The reader is kindly invited to

acquaint with results in the thesis.

2.3.1 Determining the initial stiffness of T-stub with no pretension bolts

Faella [7] have assumed that the initial stiffness of the T-stub can be evaluated as the stiffness of

simple beam with span 2*m, loaded with concentrated force in the middle and the bolts are ignored.

According Faella, the length 'effl of the equivalent T-stub for determining initial stiffness is taken by

eq. (11).

0' 2*eff effl m d l (11)

'effl depends also on the availability of endplate stiffener. The results in numerical study and [1]

suggest that 'effl in T-stub with endplate stiffener could be assumed that ' 0.90*eff effl l .

3

3

* '*0.5*

p eff

i

t l EK

m (12)

The initial stiffness according [1] and [8] is evaluated by eq.(13)


3

3

1

0.63

* '*

i

p eff b

Km

t l E K

(13)

From the results presented in the main text of the dissertation may be noted that in the initial

stiffness test VA1 is 2394kN/cm, while in the test VA3 is 2416kN / cm. The effective length of the

equivalent T-stub in the VA1 is 100mm while in VA3 is 150mm. Obviously, the effective length of for

T-stub should be with similar value in the determination of initial stiffness in both cases, so Faella’s

proposition in (11) is confirmed.

2.3.2 Determination of the initial stiffness of the T-stub with pretension bolts

Bolt pretension in the end plate connection will increase the stiffness and improve the fatigue

behavior of the bolts and the connection. In FEMA 350 [9] is stated that in end plate connection for

beam-to-column joint the bolts must be pretension.

There are known methods in the literature for the precise determination of the initial stiffness of

the T-piece with pretension bolts, but they are inconvenient for practical approach. By comparing the

results of numerical simulation of T-stub with the non-pretension and pretension bolts is revealed the

difference in their initial stiffness is in the range of 2.0 to 3.0. To simplify the initial stiffness

calculation of the T-stub with pretension bolts eq. (14) is proposed.

_ 2.5*i pret iK K (14)

2.3.3 Determination of the elongation at reaching maximum strength u of T-stub

Elongation at reaching maximum strength u can be evaluated by formula (15), which

corresponds to the proposed by Jaspart [2].

_u RD TRDTRD

u

i h

F FF

K K

(15)

The tangent stiffness of the T-stub hK is dependent on the tangent stiffness of the bolt and the

plate. For a simple set at hK , it can be assumed expression as eq. (16).

1*

100h iK K (16)

In [10] it is stated that the tangent modulus is recommended as 0.01 of the elastic modulus and

this is applied in eq.(16).

The elongation u was evaluated with eq. (15) for the numerical simulated T-stubs, but the

results are showing different trend.

2.3.4 Determination of the parameter

From the results of numerical study, presented in the dissertation, it follows that it can be

assumed 1 _0.6* u RdF F . Then the parameter can be defined as in eq. (17).

_

_

0.693

0.6*ln

*

u Rd h

y Rd h y i h

F k

F k k k

(17)


2.3.5 Comparison of the evaluated analytical expression with experimental study [11]

At the Polytechnic University of Timisoara was held extensive experimental research program of

beam-to-column joint in steel frame. In the experimental program is included study of T-subs and

partial of the results are used for comparison of the analytical expressions in this subsection.

Specimen ,expyF yF

max,expF uF max,exp/uF F

max,exp u max,exp/u

kN kN kN kN mm mm

TST-12C-S235 397.8 394 582.6 466 0.80 20.2 9.6 0.48

TST-20C-S235 559.5 607 758.3 722 0.95 5.4 3.3 0.61

TST-10C-S460 423.8 462 550.2 513 0.93 17.6 12 0.68

TST-16C-S460 538.6 619 687.5 695 1.01 8.8 4.3 0.49

TST-8C-S690 379.6 441 474.2 482 1.02 17.9 19 1.06

TST-12C-S690 522.4 613 693.2 666 0.96 6.9 7.5 1.09

Table 2„Comparison between experimental research of T-stub in [39] with analytical”

Table 2 presents the results of experiments [11] and the analytical expressions from 2.3 to

determine the maximum uF tension resistance and the elongation at maximum resistance u of T-

stub. The comparison of results shows that the obtained analytical tensile strength uF is close to the

experimentally determinedmax,expF and can be reported that the results from the proposed analytical

method in 2.2 are correct.

The ratio max,exp/u varies within the range of from 0.48 to 1.09 but analytically resulting

elongation u is less than the experimentally determined max,exp in samples with steel S235, so that the

result is in favor of security. The large range of max,exp/u evaluated by different analytical method is

also reported by Coelho [4].

3 Shear of column web The beam of frame structure transmits the bending moment to column by column web shear. The

relationship between the bending moment and the rotation of joint panel is the subject of much

research. In the literary review of this heading are partial described the researches of Krawlinker,

Ikarashi [13], Kawano [14], [15] and Charney [12].

Figure 8 „Shear in column web“


The relationship between the shear force in the column web and the beam yielding resistance

*be el yM W f is shown in eq. (18), reported that the plastic hinge is located in the beam intersection

with the stiffening ribs according FEMA350 [9] and shown on Figure 8.

1 12* * * *

2*

p

p be

p s p p

L L LV M

L L L H L L H

(18)

Parameter p in eq. (19) between panel shear yielding resistance *y y vcV A and pV

determines the panel participation in the frame yielding mechanism.

y

p

p

V

V (19)

FEMA350 [9] and FEMA355D [16] recommends a balanced design as 0.70 1.10p

(expressed in [16] differ slightly from those used in eq.(18)). BDS EN1998-1 [17] recommended shear

capacity of joint panel to be calculated based of the plastic moment of beams, which significantly

reduces the participation of joint panel in the frame yielding mechanism.

3.1 Maximum shear resistance of joint panel

From Figure 9 it is apparent that the shear stress in the joint panel (in the step of load, at which

reached 20% equivalent strain) does not have non-constant distribution. When averaging the shear

stresses of Figure 9 is obtained eq. (20), wherein the average value of the shear stress was 93% of the

maximum.

With known value of u (20) can easily identify the maximum shear resistance of joint panel

depending on the column web area.

0.93* 0.53*

3u u uf f (20)

von Mises stresses в kN/cm2

Actual distribution of shear stresses in joint panel and their

average value

Figure 9 „Shear panel FEA simulation results“

Average shear stress

Actual

distribution of

shear stress


4 Numerical and analytical study of stiffened extended end plate connection subjected

to monotonic loading

4.1 Analytical expressions for determining the rotation capacity of end plate connection

Determining the rotational capacity is important for determining the ductility of the end plate

connection. There are known expressions in the literature for determining the rotational capacity of

end plate connection subjected to monotonic or cyclic load.

Zoetemeijer [18] proposes eq. (21) for determining the rotational capacity of end plate

connection cd subjected to monotonic load.

1

10.6 4*

1.3*

Rdcd

h

(21)

In (22) Rd is the ratio of the end plate bending resistance and bolt tension resistance, while 1h

is the distance from the first bolt row to the center of compression as defined in [1].

2* *

*

eff p y

Rd

tRd

l t f

m F

(22)

Parameter Rd is related to the mechanism of plasticizing T-stub and can be estimated in Figure

10. According Zoetemeijer if T-stub yielding mechanism is first mode (plate yielding only) with

2*

2* 1Rd

the end plate connection will provide significant deformation capacity.

If 2.0Rd end plate will work elastic and connection yielding will be carried out by bolt

yielding, so to avoid such a situation, 1.75Rd

is proposed.

Figure 10 „Yielding mechanism of T-stub“

Adegoke and Kemp [19] conduct analytical and experimental study of thin flange plates and

propose eq. (23) to evaluate the rotational capacity of end plate connection cd.

2

2

* * *1.4* 40*

* * * *

f y f x y

cd

p p mrn

m f m m f

E t h E t h (23)

In eq. (23) 2( )*0.50f epm m m is the average of the distance from the bolt to the beam web

and the flange, while mrnh is the distance between the compression force to resultant tension force in

the connection.


FEMA356 [20] indicates that beam-to-column joint are classified as PR (partial restrained). The

initial stiffness of the joint, if not taken into account the participation of the RC slab is determined by

eq. (24) with MCE as the end plate yielding resistance.

0.005

CEMK (24)

4.2 Relationship end plate connection resistance and plastic moment of the beam

Ratio y in eq. (25) represents the ration between end plate connection resistance and the beam

plastic moment.

_ _ _ _

_ *2*

y e p y e p

ypyRd b

yRd

p s

M M

L LMM

L L L

(25)

4.3 Numerical simulation of isolated end plate connection

4.3.1 Входни данни за изследването

To determine the relationship “Moment-rotation” of end plate connection a FEA is performed on

the fragment in Figure 11.

In the model of the fragment is used axis of symmetry of the connection to reduce the number of

finite elements. The column web will be presented by supports prohibiting transfers in x, y and z.

Transverse stiffeners in the column are accounted for supports in x direction. The lower nodes of the

column web are supported in z.

Figure 11 „Partial joint of MR frame with end plate connection“

Stiffened extended end plate connections with different y and Rd ratios are simulated as

shown in Table 3. The bolt connection is assumed as pretension in half of the specimens.

Within the Abstract are presented only the most important results, the full study can be viewed

in the thesis.


Specimen Bolt

grade

10.9

pt Bolt row yielding

resistance

End plate

connection

yielding

resistance

Beam

plastic

moment

[21]

Rd

y

Non pretension

bolts

Pretension

bolts first second third

mm kN kN kN kNm kNm

F_25_24

Fp_25_24

М24 25 571 591 363 488 299 1.29 1.34

F_20_24 Fp_20_24 М24 20 479 492 340 400 299 0.83 1.14

F_16_24 Fp_16_24 М24 16 413 421 218 331 299 0.53 0.94

F_20_20 Fp_20_20 М20 20 381 394 303 326 299 1.25 0.95

F_16_20 Fp_16_20 М20 16 319 327 213 264 299 0.76 0.75

F_12_20 Fp_12_20 М20 12 266 273 136 193 299 0.49 0.55

Table 3 „Specimens analytical calculated characteristics considered [1]“

4.3.2 Numerical simulation of end plate connection partial results

The reader is kindly invited to examine the detailed results in the main text of the dissertation.

From the results in Figure 12 can be reported that the resultant force of the contact stresses is located

near the beam flange, which meets the guidelines in [1].

The resultant force of the prying force near to the first and second bolt row, however, is near the

bolt so does not meet the assumptions in [1]. This reduce the T-stub tension resistance, at the same

bolt force, and thereafter the resulting end plate yielding capacity is smaller than the designed one.

Figure 12 „Specimen F_20_24 results in rotation 0.06rad”

4.3.3 Initial stiffness of the end plate connection specimen

specimen iK ,i pretK , /i pret iK K

F_25_24 279582 849378 3.04

F_20_24 207710 585394 2.82

F_16_24 180014 456783 2.54

F_20_20 189163 534402 2.83

F_16_20 165145 428204 2.59

F_12_20 126814 332411 2.62

Table 4 „Comparison between the stiffness of the end plate connection with pretension and non-pretensioned

bolts“

Deformation Contact stresses [kN/cm2] End plate strain


By comparison in Table 4 of the initial stiffness of the end plate with pretensioned bolts ,i pretK

and non-pretension bolts iK it can be reported that the bolts pretension have increased the initial

stiffness of the flange connection with 2.5 3.0 times, which confirms the results in Chapter 2.3.2. At

Figure 13 can assess the influence of the pretension of the bolts on the deformation of the end plate.

Non-pretensioned bolts

Pretensioned bolts

Figure 13“ End plate middle section nodes deformation on joint rotation 0.00912rad “

4.3.4 Proposal for an analytical expression for determining the rotation capacity of end plate

connection

According Beg [22] it can be conservatively assumed that the rotation capacity cd of end plate

connection is reached when the maximum load bearing capacity is achieved. Also according Adegoke

and Kemp [19] cd is the rotation at maximum load capacity. In the thesis the end plate rotation

capacity cd in monotonic load is accepted when reached 20% elongation in node from the FE mesh or

at maximum accepted bolt elongation.

The yield rotation y is determined with the known eq. (26).

_ _

y

i

y e p

K

M (26)

The tangent stiffness is assumed 1

*75

h iK K as in [19]. Using Jasper’s proposal cd is

evaluated with eq. (27)

,

_ _ _ _

p cd y

h

u e p y e p

K

M M

(27)

Results in Table 5 have revealed that ,p cd calculated according to Zoetemeijer eq. (21) have

good coincidence with the numerical results. Also ,p cd determined by Adegoke and Kemp eq. (23) is

with good coincidence too. The result from eq. (27) shows large deviation with the numerical result.

-0.005 0.005 0.015 0.025

deformation [cm] F_25_24F_20_24F_16_24F_20_20F_16_20F_12_20

-0.005 0.005 0.015 0.025

deformation, [cm]

Fn_25_24

Fn_20_24

Fn_16_24

Fn_16_20

Fn_12_20


Specimen FEA Analytical

,p cd

,p cd

Eq. (27)

,p cd by

Zoetemeijer eq.(21)

,p cd by Adegoke

and Kemp eq.(27)

[rad] [rad] [rad] [rad]

F_25_24 0.017 0.035 0.014 0.014

F_20_24 0.027 0.030 0.018 0.017

F_16_24 0.030 0.028 0.021 0.021

F_20_20 0.017 0.032 0.015 0.017

F_16_20 0.026 0.028 0.019 0.021

F_12_20 0.024 0.028 0.022 0.028

Table 5 „Determinaton of rotational capacity ,p cd by analytical methods and numerical“

The joint rotational capacity cd in relation with Rd and

y is shown on Figure 14. It can be

reported that in case of partial strength connection with 1.0y higher value of cd is observed at

plate yielding mechanism of the end plate as2* /

2* / 1Rd

n m

n m

. It can be concluded that for 1.0y

plate yielding mechanism is preferable.

Figure 14 “Rotational capacity relationship with Rd and

y “

5 Numerical and analytical study of beam-to-column joint with end plate connection

subjected to cyclic load

5.1 Low cycle fatigue literature review

Fatigue life is defined as the number of cycles required for the occurrence of damage in the

sample. If number of cycles to failure is less than 104 the fatigue is considered as low cyclic. In steel

structures, damage in low cycle fatigue occurs when the load relates to plastic deformation, typical

result from seismic load on ductile structures.

Basquin [23] equation provides a link between the stress range and cycles to failure, typically

applied for high cycle fatigue. If the stress is replace with elastic strain eq. (28) can be evaluated.

'* 2*

Bfae fN

E E

(28)

Coffin and Manson proposed relation between plastic strain range p and number of cycles to

failure fN in eq (29).

0.5

0.75

1

1.25

1.5

0.4 0.6 0.8 1 1.2 1.4

у

Rd

фcd на възела 0.07 фcd на възела 0.05

full strength joint

partial strength joint

first mode

(plate yielding ) second mode

(plate and bolt yilednig)


Basquin- Coffin-Manson eq. (30) is evaluated by sum of the elastic and plastic strain.

''* 2* * 2*

2

B Cf

f f fN NE

(30)

In the literature eq.(30) is recognized as N curve. The values of the parameters in (30) are

based on performed cycle tests. Evaluating the fatigue life of the specimen in the thesis is performed

by the N curve recommended in [24].

For damage in weld joint in [24] is recommended eq. (31)

0.10 0.50175

* 0.095*2

f f

MPaN N

E

(31)

For damage in the base metal in [24] is recommended eq. (32)

0.10 0.43175

* 0.091*2

f f

MPaN N

E

(32)

Figure 15 „ N curve applied in the thesis by [24]“

5.2 Research of beam-to-column joint 1 from frame 1

Figure 16 „Beam-to-column joint with end plate connection in Frame 1“

' * 2*2

Cp

p f fN

(29)

N при повреда

в основният метал

N при повреда

в заварен възел


Static scheme of Figure 16 for the study of the beam-to-column joint with end plate connection

is selected same as in [12], [25]. A parametric study of the joint subjected to cyclic loading will be

done to determine the influence of different joint components on the behavior of the node. The

parameters to be traced are the thickness of the reinforcing plate spt of the column panel, the thickness

of the end plate pt and the diameter of the bolt bd . Thickness

spt relates to panel ratio pa , pt and bd

relates to end plate resistance ratio ya and to the end plate yielding mechanism Rd .

The initial axial force in the column is assumed 600kN which is 20%of the section axial force

resistance. In [13] Kawano has applied compression force in the column equal to 20% section

resistance, while Ikarashi [12] applies 30%.

Cyclic load by JISF recommendations on

beam-to-column joint on frame 1

Cyclic load by ECCS recommendations on

beam-to-column joint on frame 2 Applied rotation ф on

beam-to-column joint Figure 17 „Cyclic load applied on beam-to-column joint with end plate on frame 1 and frame 2 “

The cyclic load for beam-to-column joint on frame 1 is by JISF recommendations, while the

cyclic load on frame 2 is by the ECCS [26] recommendation. Both load protocols are presented on

Figure 17.

Beam top flange is supported out-of-plane, this is needed to allow the beam to yield without

lateral-torsional buckling to occur [17]. Beam bottom flange is supported at the beam end.

The specimens’ characteristics are specified in Table 6. Panel ratio p is from 0.70 to 1.10. The

end plate connection is designed with 0.94 1.34y , which covers full strength and partial strength

connections. The Rd value is such that the eqivalent T-stub yields in first or second mode, and also

one specimen in third mode.

Specimen

_ _ _ _sp p b colN t t d N spt

,mm

pt ,

mm

bd ,

mm

colN

,kN

Pretensioned

bolt grade 10.9

beam column y

Rd

p

1 N_6_16_24_600 6 16 24 600 М24 IPE360 HEA320 0.94 0.53 0.67

2 N_6_20_24_600 6 20 24 600 М24 IPE360 HEA320 1.14 0.83 0.67

3 N_8_20_24_600 8 20 24 600 М24 IPE360 HEA320 1.14 0.83 0.80

4 N_10_20_24_600 10 20 24 600 М24 IPE360 HEA320 1.14 0.83 0.92

5 N_12_16_24_600 12 16 24 600 М24 IPE360 HEA320 0.94 0.53 1.05

6 N_12_20_24_600 12 20 24 600 М24 IPE360 HEA320 1.14 0.83 1.05

7 N_12_25_24_600 12 25 24 600 М24 IPE360 HEA320 1.34 1.29 1.05

8 N_16_25_24_600 16 25 24 600 М24 IPE360 HEA320 1.34 1.29 1.34

9 N_12_20_20_600 12 20 20 600 М20 IPE360 HEA320 0.95 1.25 1.05

10 N_12_26_20_600 12 26 20 600 М20 IPE360 HEA320 1.14 2.02 1.05

11 N_12_22_22_600 12 22.3 22 600 М22 IPE360 HEA320 1.14 1.20 1.05

12 N_12_26_22_600 12 26 22 600 М22 IPE360 HEA320 1.25 1.51 1.05

13 N_12_23_20_600 12 23 20 600 М20 IPE360 HEA320 1.04 1.58 1.05

Table 6 „Beam-to-column joint specimen characteristics of frame 1“

-0.074-0.0555-0.037

-0.01850

0.01850.037

0.05550.074

0 21ф,

[rad

]

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 29ф,

[rad

]


5.2.1 Results of beam-to-column joint of Frame 1

tp=16mm; tsp=6mm; d=24mm

ay=0.94; ap=0.67; bRd=0.53


ay=1.14; ap=0.67; bRd=0.83


ay=1.14; ap=0.80; bRd=0.83


ay=1.14; ap=0.92; bRd=0.83


ay=0.94; ap=1.05; bRd=0.53


ay=1.14; ap=1.05; bRd=0.83


ay=1.34; ap=1.05; bRd=1.29


ay=1.34; ap=1.34; bRd=1.29


ay=0.95; ap=1.05; bRd=1.25


ay=1.25; ap=1.05; bRd=1.51


ay=1.14; ap=1.05; bRd=1.20


ay=1.25; ap=1.05; bRd=1.51

Figure 18“Hysteresis curves „Moment-rotation“ of frame 1 specimens“

On Figure 18 are presented hysteresis curves “Moment-rotation” of Frame 1 specimens,

subjected to cyclic load according to JISF. Also the values of the parameters y , p and Rd are

shown.

Based on Figure 18 it can be concluded that for 0.92p flange local buckling does not occure

for rotation to 0.056rad. But the specimens with 0.80p has lower resistance than the other

specimens.

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08


Joint panel beam bolt balanced


ay=1.14; ap=0.67; bRd=0.83


ay=1.34; ap=1.34; bRd=1.29


ay=0.95; ap=1.05; bRd=1.25


ay=0.94; ap=1.05; bRd=0.53

Figure 19 „Comparison of beam-to-column joint with end plate connection yielding mechanism from frame 1“

On Figure 19 can be compared yielding mechanisms of beam-to-column joint. Also are

presented deformed schemes of reversal 15 and for better visibilities are increased three times.

When panel ratio p value is 1.0p , joint rotation ф is mainly concentrated in the panel.

According Kawano [13], [14] the panel yielding shows increased ductility compared with the beam

yielding.

FEMA355D [16] recommends a balanced design, wherein beam and joint panel are to yield

simultaneously and is recommended 0.70 1.10p .

BDS EN1998-1 [17] recommends beam yield mechanism and the participation of the joint panel

is limited. With increasing the joint rotation the beam flange local buckling occurs, which results not

only in a reduction of the bearing capacity, but also damage to the beam flage due to the accumulation

of plastic deformation of high value.

Bolt yielding may occur when designing the connection with bolt with insufficient resistance. A

hysteresis pinching is observed in such case which leads to less energy dissipated. Due to the

accumulation of plastic elongation in the bolt is observed bolt damage which leads to reduced fatigue

life.

Yielding in the end plate decreased the demand in the beam and nodal panel, but causes a

decrease in load capacity and stiffness of the beam-to-column joint; this is explained in detail in Figure

31 and the description thereof.

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08

-500

0

500

-0.08 0.00 0.08


5.3 Part of results for frame 1 specimen.

5.3.1 Specimen N_6_20_24_600

The cumulative fatigue damage is evaluated by the Palmgren-Miner rule, and cycle counting is

performed by the rain flow method. For reaching 1.0iD in node form FE mesh is conservative

assumed that the beam-to-column joint have reached the fatigue life of the joint.

rib

number

cycles

fN iD

0.50 0.15 1.63 0.31

1.00 0.14 1.88 0.53

0.50 0.08 5.84 0.09

1.50 0.04 24.00 0.06

iD

=1.0

Figure 20 „Low cycle fatigue analytical solution on specimen N_6_20_24_600“

The beam-to-column joints are examined according to recommended procedure for assessing the

behavior of steel elements under cyclic load ECCS [26]. The results are shown on Figure 20.

Figure 21 „Recording of behavioral parameters by [26] during the cyclic test of specimen N_6_20_24_000“

The yielding moment yM and yielding rotation y are defined by the recommendation in [26],

as shown on Figure 21. The relation 0 /i y is recognized as partial ductility.

The parameters needed for description of the specimen subjected on cyclic load according to

[26] are:

1) Full ductility /i i yR R is the ductility in cyclic loading, and is the relation of the absolute rotation in

the positive (or negative) force range iR to the yielding rotation yR .

-0.16

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

0.16

4 6 8 10 12 14 16stra

in

reversal

ребро

плоча

пояс

панел

0.90

1.40

1 4 7 10

Resistance ratio

положителен

отрицателен

1.0

18.0

1 4 7 10

Full ductility

0.90

1.00

1 4 7 10

Full ductility ratio

0.20

1.00

1 4 7 10

Absorbed energy ratio

Cycle count by rain flow

method


2) Full ductility ratio / ( ( ))i i y i yR R R R shows the relation between specimen real full ductility and

the ductility of specimen with perfect elasto-plastic behavior.

3) Resistance ratio /i i yQ Q indicates specimen’s hardening and has reached value 1.32i , which

indicates that the resistance has increased due to hardening.

4) Absorbed energy ratio *

i

i

y i y i y

A

F

estimates the relation between the dissipated energy

by the specimen for one half cycle to the energy that could be dissipated in idealized elasto-plastic conditions.

Value of i

indicates well plastic energy absorbing capacity of the reinforced joint.

Figure 22 „Determination of yielding moment and yielding rotation“

5.3.2 Fatigue life of simulated specimens, subjected to JISF cyclic load Specimen

y p Final reversal Cumulative dissipated energy

kNm*rad

Rotational

capacity

5 7 9 11 13 15 краен

N_6_20_24_600 1.14 0.73 12 3 10.3 22.5 49.4 81.5 100.4 0.037

N_8_20_24_600 1.14 0.83 12.3 3.1 10.9 24.2 53.8 89.5 111 0.037

N_10_20_24_600 1.14 1.0 14.2 3.2 11 24.6 55.5 93.1 150.9 0.0556

N_12_16_24_600 1.01 1.15 15.9 2.9 9.7 22.1 50.8 85.7 139.6 198.2 0.0556

N_12_20_24_600 1.14 1.15 16.2 3.6 11.9 26.6 58.6 97.4 157 185.3 0.0556

N_12_25_24_600 1.34 1.15 15 3.7 12.2 27.3 60.1 99.8 160.1 0.0556

N_16_25_24_600 1.34 1.43 14.2 4 13 28 63 104 133 0.0556

Table 7 „Fatigue life of simulated specimens“

В Table 7 е представена дълготрайността на изследваният възел и сумираната дисипирана

енергия до съответен номер на полуцикъл.

Figure 23 „Fatigue life of specimen type N“

-350

0

350

-0.08 0.00 0.08

M

[kN

m]

ф,

[rad]

12

13

14

15

16

17

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

final

hal

f cy

cle

ау

аp

Full strength

connection Partial strength

connection


From Figure 23 and Table 7 is reported, that longer fatigue life when loaded with JISF cyclic

load is observed when panel ratio p is in the interval 0.90 1.20p and end plate ratio y is

0.90 1.30y . In the specimens with с 0.90p is observed damage in the endplate stiffener, but

this damage does not reduce significantly the connection resistance. If ignored the endplate stiffener

damage joints with 0.90p will show longer fatigue life.

Figure 24 „Definition on the joint

component with damage index equal to

1.0 related to ар и ау“

From Figure 24 is observed that damage in the endplate stiffener have occurred when 1.0ya

or 1.0pa , otherwise the beam flange is damaged.

Figure 25 „Cumulative dissipated energy in frame 1 beam-to-column joint specimen”

From Figure 25 is reported, that the cumulative dissipated energy have increased when the

values p и у have increased. If 0.90p and 1.0y the difference in the hysteresis areas

between the strongest and the weakest specimen is in 10%.

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

ay

ap

Damage in

beam flange

Damage in

endplate stiffener

Partial strength

connection Full strength

connection

0

50

100

150

200

5 7 9 11 13 15 17cum

ula

tive

dis

ipat

ed e

ner

gy

[kN

m*

rad

]

reversal

N_6_20_24_600

N_8_20_24_600

N_10_20_24_600

N_12_16_24_600

N_12_20_24_600

N_12_25_24_600

N_16_25_24_600


5.3.3 Beam flange local buckling

Figure 26 „Beam flange local buckling“

Тhe studied specimen shows that after local buckling of beam flange subjected to cyclic loading

the strain is increasing which prerequisite for low cyclic fatigue. The growth of rotation as

indicated in Figure 26 indicates when the local instability is present. The rotation is defined by the

difference of vertical displacements of node 2747 and node 1304 divided by the flange width.

Figure 27 „Comparison of rotation of specimens in dependence of the reversal“

Specimen N_16_25_24_600 with 1.34ya and 1.34pa is designed according to [1] and [17],

while the other samples are within the limits of the recommendations of FEMA355D [16] and

FEMA350 [9]. The comparison of Figure 27 shows that N_16_25_24_600 beam flange local buckling has

occur one cycle before the other specimens.

It can reported that with the increase pa the durability of joint subjected to cyclic load is reduced

because the participation of joint panel in taking the node rotation was reduced which increase the

demand of the beam.

0

0.6

10 20

, [r

ad]

reversal

N_16_25_24

N_10_20_24

N_12_20_24

N_12_25_24

N_8_20_24

N_12_16_24

тс 13

-8

0

8

2 21


5.3.4 Joint rotation distribution on the components

Joint rotation

Beam rotation b

End plate rotation e

Joint panel rotation s

Figure 28 „Rotation definition on joint and on joint components“

Joint rotation is distributed between the beam, the panel and the end plate. Joint rotation in

eq. (33) is equal to the sum of the beam rotation b , end plate rotation e and joint panel rotation s .

b e s (33)

The rotation is the same in the simulated joints, but is distributed in different way in the

specimens’ components.

The end plate rotation e is defined based on the end plate uplift 3xu as shown on Figure 28 and

eq. (34).

3xe

p

u

H (34)

The beam rotation b is written in eq.(35). The rotation 2 1 /x x pu u H is distributed between the

beam and the end plate.

2 1x xb e

p

u u

H

(35)

The moment resistant frame is designed such than the column behaves in elastic manner, due to

the capacity design. The column contribution in the joint rotation can be expressed as eq. (36). It

should be mentioned that the rotation in the column c is much smaller than the other specimen so c

is not considered in the analytical study.

*(0.5* )

2* *

p

c

M H H

E I

(36)

Based on the known values of , e and b joint rotation s can be evaluated based on eq. (37).

s b e (37)

From Figure 29 is reported, that in early stage of the loading is distributed between the

components based on their. When the component with lower resistance has yield the rotation is mainly

in it. The rotation in the balanced design joints is distributed between beam and column, which

allows joint rotation with lower components rotation.


.Joint panel Beam Balanced

Figure 29 „Components rotation in different specimens“

While evaluating the rotation capacity of partial strength joint cd according to БДС EN 1998-1

[17], the panel rotation s is reduced to 30% of the joint rotation cd as shown in eq. (38).

, where 0.30*cd b e s s cd (38)

The limited value of cd in eq. (38) difficult the application of joints with lower value of p в

steel frame in desired high or medium ductility level.

The rotation capacity cd against p и y is shown on Figure 30. From Figure 30 can be

reported that 0.90 1.10p and 1.10y results to balanced design and higher value of cd .

Figure 30 „Rotational capacity of beam-to-column joint with end plate connection [5]“

5.3.5 Influence of the end plate connection resistance to the joint hysteresis behavior when

subjected to cyclic

To express the influence of the stiffened end plate connection to the behavior of the joint under

cyclic load on Figure 31 are compared specimens N_12_16_24 with 0.94y , N_12_20_24 with 1.14y

and N_12_25_24 with 1.34y .

The results shows that the joint resistance is similar with end plate ratio 1.14y and 1.34y

but reduced with 5% in specimen with 0.94y . Also the hysteresis area in specimen 0.94y is

reduced compared to the others. Lower end plate resistance has increased the uplift and reduced the

compression resistance of the tensioned in previous reversal T-stub.

-0.08

0.00

0.08

2 20

rota

tio

n

rad

reversal

N_6_20_24_600

фе

фs

фb -0.08

0.00

0.08

2 20

rota

tio

n

rad

reversal

N_16_25_24_600

фе

фs

фb

-0.08

0.00

0.08

2 20

rota

tio

n

rad

reversal

N_12_16_24_600

фе

фs

фb

0.005

0.015

0.025

0.035

0.045

0.055

0.6 0.8 1 1.2 1.4

Фcd

ay

ap

High ductility level

Low ductility level

Medium ductility level

Partial strength Full strength


Figure 31 “Hysteresis curves M-ф in specimens with different end plate 16mm, 20mm и 25mm and panel ratio

ap=1.05”

На Figure 32 is presented hysteresis curve „Force-elongation“ of T-stub when loaded with

cyclic load but with one full cycle. T-stub first load case is tension load, and then second load case is

performed with compression load. It is observed that the compression T-stub compression resistance is

lower than the tension resistance in position 1. The tension resistance of the bolt rows is not larger than

the T-stub compression resistance, because the forces are in equilibrium. As conclusion it can be

reported that the lower compression resistance of the end plate reduces the moment resistance and

stiffness of end plate connection, subjected to cyclic load.

T-stub subjected to

cyclic load

Contact stress Hysteresis curve F-Uz of the tested T-stub

Figure 32 „T-stub behavior if loaded with one cycle loading“

-500

0

500

-0.08 0.00 0.08

Hysteresis curves

М-ф

N_12_25_24 N_12_20_24 N_12_16_24

0

500

0.00 0.06

мом

ент

kN

m

ротация

Envelope of hysreresis curves

0

40

5 17

kN

m*

rad

reversal

cumulative dissipated energy

Tension in T-stub

Compression in T-stub


0.94ya , 16pt mm 1.14ya , 20pt mm 1.34ya , 25pt mm

Figure 33 „von Mises strain in end plate in reversal 15“

On Figure 33 is presented the von Mises strain in half cycle 15. It is reported that increasing ya

value will reduce the strain. The results indicate that the first and second bolt row of the specimen with

0.94ya yields in first mode.

Figure 34“Bolt strain at specimens

subjected to cyclic loading “

From the specimen comparison on Figure 34 it can be reported that bolt damage is not expected

due to bolt strain value under 0.08. Interesting observation is that when reducing end plate ratio ya the

bolt strain is increasing, but this is expected because reducing ya increases the end plate demand.

Figure 35 „Strain at end plate“

0

0.01

0.02

0.03

2 21

stra

in a

t b

olt

in

bo

lt r

ow

1

reversal

аy=0.94

аy=1.14

аy=1.34

0

0.02

0.04

0.06

0.08

2 21

stra

int

in n

od

e F

E m

esh

reversal

ay=0.94

ay=1.14

ay=1.34


5.3.6 Influence of Rd on the behavior of partial strength and full strength end plate connections,

when subjected to cyclic load.

According to [1] specimens N_12_20_20 and N_12_16_24 are partial strength connection because

0.94 1.0y . Further the panel ratio is 1.05p . The end plate ratio 0.94y corresponds to the

requirements of ANSI/AISC 341-10 [28], in which 0.80y , but it should be mentioned that in

FEMA350 [9] is not recommended 1.0y .

Specimen N_12_20_20

1.25; 0.94;

1.05

Rd y

p

Specimen N_12_16_24

0.53; 0.94;

1.05

Rd y

p

Figure 36 „Comparison of specimen N_12_20_20 and N_12_16_24, designed with the same end plate and joint panel

resistance, but with different end plate yielding mechanism“

Based on [18] is evaluated Rd =1.25 for specimen N_12_20_20 and Rd =0.53 for specimen

N_12_16_24. In this specific case 0.654Rd is the limit between first and second mode, so the end plate

connection in specimen N_12_20_20 yields in second mode (bolt and plate yielding), and in N_12_16_24

yields in first mode (plate yielding).

On Figure 36 is recognisable the hysteresis curves pinching on specimen N_12_20_20, compared

with N_12_16_24, which indicatesd that the application of partial strength connection with end plate

yielding in second mode is not recommended design practice for moment resistant steel frame

structure.

Figure 37 „Comparison of bolt at first bolt

row strain at specimens N_12_20_20 and

N_12_16_24“

The strain of bolt М20 in N_12_20_20 is with higher value than the strain of bolt M24 from

N_12_16_24, as presented on Figure 37. The specimens have the same calculated yielding resistance but

the bolts with lower resistance have higher elongation. Further the bolts are damaged in reversal 13 at

bolt strain 0.08, which also leads to early connection failure.

-500

0

500

-0.04 -0.02 0.00 0.02 0.04 0.06

М,

[kN

m]

ф, [rad]

M_N_12_20_20

M_N_12_16_24

bolt

pretension

0.00

0.04

0.08

0.12

0.16

0.20

0 2 4 6 8 10 12 14

bo

lt s

trai

n

reversal

N_12_20_20

N_12_16_24


Specimens N_12_26_20 and N_12_20_24 compared on Figure 38 are full strength joints, with equal

values of the end plate ratio 1.14y and panel ratio 1.05p . But bolt tension resistance and the

end plate thickness differs, and Rd =2.02 for N_12_26_20 and Rd =0.83 for N_12_20_24. First two bolt rows

on specimen N_12_26_20 yields in third mode (bolt yield) with Rd >2.0, but N_12_20_24 yields in second

mode.

Hysteresis curve of the specimen N_12_26_20 with 2.02Rd have significant pinching because

the large bolt elongation, and the premature bolt yielding has reduced the joint fatigue life. It can be

concluded that T-stub yielding in third mode is not recommended, even for full strength end plate

connection.

Specimen N_12_20_24

0.83; 1.14;

1.05

Rd y

p

Specimen N_12_26_20

2.02; 1.14;

1.05

Rd y

p

Figure 38 „Comparison of full strength joints N_12_20_24 и N_12_26_20“

Based on the results in Heading 5.3 are defined certain limits for y and Rd for end plate

connection design, shown on Figure 39. In the recommended zone the rotation capacity is mainly

determined by the beam (panel ratio 1.05pa ), and in the not recommended zone the rotational

capacity is determined by the bolts yielding.

Figure 39 „Recommended

values for y и Rd for

determination of the yielding

mechanism of beam-to-column

joint with end plate connection“

Eq. (39) and (40) are describing the recommended zone on Figure 39.

-500

0

500

-0.04 -0.02 0.00 0.02 0.04 0.06

огъ

ващ

мом

ент,

[kN

m]

ротация,

[rad]

N_12_26_20

N_12_20_24

0.90

1.00

1.10

1.20

1.30

1.40

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

ay

bRd

Болтове с достатъчна носимоспособност

Болтове с недостатъчна носимоспособност

first

mode second

mode third

mode

full strength

partial strength Not recommended

Recommended


Rd I (39)

If

1.0

1.75

y

Rd

, then 0.2* 1

1.75

Rd Iy

I

(40)

, where 2* /

2* / 1I

n m

n m

. Because of lack of simulation in the thesis of specimen with lower

value of y is assumed that 0.94y . Further to increase the rotational capacity of the joint 1.10y

as explained in 5.3.4.

Non recommended zone on Figure 38 can be evaluated with eq. (41) и (42). For specimen with

Rd and y in the non-recommended zone the numerical simulation shows that joint yielding

mechanism is bolt yielding which is not good connection design approach.

1.75 и 1.0Rd I y (41)

1.30.15* 1

0.7

Rdy

, ако

1.0

1.75 1.3

y

Rd

(42)

5.4 Research of beam-to-column joint from frame 2

Typical end plate connections for detailing beam-to-column joint are extended unstiffened end

plate, extended stiffened end plate and end plate with haunch. Even if they are designed with the same

resistance, different behavior is noticed when subjected to cyclic load.

The beam-to-column joint on Figure 40 is simulated in the current part of the thesis, as applied

the indicated connections types. The joint yielding resistance is analytically determined in Table 8

according to [1].

Static scheme of the joint with out-of-plane restrainsindicated

Series H

Series He

Series Hrib

Series Hh

Figure 40 „Beam-to-column joint form frame 2“

The used static scheme of the simulated beam-to-column joint corresponds to the used in the

literature. The beam top flange is restrained out-of-plane, which typically is provided from the RC slab

and the dowel connection. This restrain is required to ensure that the beam can yield when subjected to

cyclic load without lateral-torsional buckling to occur [17].


In first load case is applied bolt pretension, and in second load case the column is loaded with

1200kN axial force, assumed as 20% of column section resistance. In the following load cases is

applied the horizontal load, which corresponds to recommendations in ECCS [26]. образец Нe_5_22 Нe_5_28 Нe_8_28 Нe_10_32 Н_8_22 Н_10_28 Н_16_28 НRib_10_28 Нh_4_28 Нh_7_28

yRdM kNm 643 643 643 643 643 643 643 643 643 643

_y bM

kNm 673 673 673 673 679 679 679 679 679 679

pt mm 22 28 28 32 22 28 28 28 28 28

spt mm 5 5 8 10 8 10 16 10 8 (1бр.) 7

_ _y e pM

kNm 584 637 637 641 805 992 992 992 732 732

y - 0.869 0.947 0.947 0.954 1.19 1.47 1.47 1.47 0.94 0.94

ysV kN 1691 1691 2113 2395 2113 2395 3241 2395 1550 1973

pV kN 2164 2164 2164 2164 2164 2172 2172 2172 1637 1637

p - 0.781 0.781 0.977 1.11 0.977 1.097 1.492 1.097 0.971 1.236

Table 8 „Analytically determination of joint of frame 2 resistances “

Hysteresis curves “Moment-rotation” from the ten performed simulations are shown in Figure

41, and detailed description of the results is available in the thesis.

Specemen Hе

Specimen H

Specimen Hrib

Specimen Hh

ay=0.947; ap=0.781

ay=0.947; ap=0.977

ay=1.19; ap=0.977

ay=0.94 ap=0.971

ay=0.954 ap=1.11

ay=1.47 ap=1.097

ay=1.47 ap=1.097

ay=0.94 ap=1.236

Figure 41 „Hysteresis curves „M-ф“ of frame 2 specimens“

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10

-900

0

900

-0.06 0.10


5.4.1 Comparison of the maximum strain in the simulated specimens in frame 2

A suitable criterion for comparison of different joint types is the value of the equivalent strain

due to the reversals, as in Figure 42. High value predispose to damage due to low cycle fatigue.

Figure 42„Comparison of equivalent strain of frame 2 specimens“

The comparisson between the results for specimens Н_10_28 and НRib_10_28 leads to the conclusion,

that the beam web ribs prevented the flange buckling when the rotation is more than 0.04 but has

increased the strain in the joint for the smaller rotation. It can be concluded that these ribs are not

necessary.

In specimens series Hh the haunch has increased the joint resistance with translating the plastic

hinge away from the column face.

Figure 43„Comparison of connection resistance Mh and equivalent strain of frame 2 specimens“

From Figure 43 can be reported that specimen series Hh has higher resistance than the other

specimens. Further in Figure 42 is visible that the strain in the end plate with haunch is with lower

value, which have increased the joint fatigue life.

The presence of end plate stiffener in specimen Hh has increased the end plate resistance, but the

strain in the rib are with high value, which will lead to rib damage from low cycle fatigue. It is

reasonable to assume that the end plate stiffener works as connection defence [29].

The application of unstiffened extended end plate is less favorable, because a damage will occur

in the beam flange, without developing the beam full rotational capacity.

0.002

0.003

0.006

0.012

0.024

0.048

0.096

0.192

0.384 7 9 11 13 15 17 19 21 23 25

stra

in

(log

sca

le)

reversal

Нe_5_22

Нe_5_28

Нe_8_28

Нe_10_32

Н_8_22

Н_10_28

Н_16_28

НRib_10_28

Нh_4_28

Нh_7_28

0,04rad 0,02rad 0,06rad

300

350

400

450

500

550

600

650

700

750

0.0015 0.003 0.006 0.012 0.024 0.048 0.096 0.192 0.384

ben

din

mo

men

t M

h,

[kN

m]

equivalent strain (log scale)

Нe_5_22

Нe_5_28

Нe_8_28

Нe_10_32

Н_8_22

Н_10_28

Н_16_28

НRib_10_28

Нh_4_28

Нh_7_28


It appears that end plate conection with haunch has lower strain values but higher resistance, so

this makes it a better connection for detailing steel frame.

6 Appropriate material models for cyclic loading appication from the ANSYS material

library The initial behavior of structural steel is linearly elastic and isotropic. When the material starts to

yield, it can be described by the von Mises criterion and normality yield law. Structure steel in

monotonic load application can be simulated by material model with isotropic or kinematic hardening.

In cyclic load application is suitable kinematic hardening and also combined hardening (kinematic and

isotropic). The kinematic hardening rule involves a shifting of the yield surface due to a reversal of

loading and is preferred for analyses involving cyclic loading [30].

The Chaboche nonlinear kinematic hardening model is suitable for describing cyclic metal

material behavior and is applied in the simulation.

The yield function f is expressed in eq. (43).

2( )f I X k (43)

Moreover in eq. (43) is understood that is the stress tensor, 2I is the second invariant of the

deviatoric stress tensor, and k is the initial yield surface size

The simplest way to present kinematic hardening is by using Prager’s model [5], in which the

kinematic variable tensor X is collinear with the evolution of the plastic strain pl eq. (44).

2* *

3pldX C d (44)

The linearity associated with the stress–strain response is rarely observed. A better description is

given by the model proposed initially by Armstrong and Frederick introducing a recall term, called

dynamic recovery:

2* * * *

3pldX C d X dp (45)

The increment of the kinematic hardening tensor dX is expressed by two parameters, the initial

hardening modulus C and the nonlinear recovery parameter , which controls the rate at which the

hardening modulus decreases to zero. In eq. (45) the first term is the hardening modulus, and the

second term is the recall term that produces a nonlinear effect.

The increment of the accumulated plastic strain p is shown in eq. (46).

2:

3pl pldp d d (46)

For a selection of material model in the thesis is performed comparison of numerical simulation

of different material models and the experimental studies in [31]. In [31] Shi explores specimens from

structural steel Q345B and Q235B used in China. The specimens were tested in a monotonic and

cyclic load, using different protocols for cyclic loading.

The comparison on Figure 44 between numerical simulation with combined hardening and the

experimental test results from [31] shows well coincidence between the hysteresis curves.

Based on the accurate comparison is concluded that the experimental test results are accurately

predicted when used combined hardening with Chaboche nonlinear kinematic hardening and Voce

isotropic hardening.


Figure 44 „Comparison from hysteresis curves from experimental study and from numerical study for steel

Q345B“

With applied displacement on tension/compression with the same value the specimen is tested

for shake down. The experimental and the numerical results are compared on Figure 45 with well

coincidence.

Experimental [31]

Numerical with material models of

Chaboche and Voce

Figure 45 „Comparison with shake down from hysteresis curves from experimental study and from numerical

study for steel Q345B“

7 Numerical simulating of experiments

7.1 Bursi and Jaspart [32] experimental study on T-stub loaded on tension.

The authors report T-stubs loaded on tension. One group of the T-stub specimens is cut from hot

rolled section IPE300, and the other from HEB220. Bolts are assembled as pretensioned and non-

pretensioned in the specimens. In this study is performed and presented in detail material tension test,

so it is convenient for numerical simulation.

In Figure 46 are presented the applied in the model finite elements types from ANSYS element

library [30]. The end plate and web is modeled with planar shell elements SHELL181, while the bolt is

simulated with LINK180. The interference between the knee brace element and the plates is simulated

by contact pairs with surface target elements TARGE170 and surface-to-surface contact elements

CONTA174.

Cyclic load protocol

Experimental [31]

Numerical with material models

of Chaboche and Voce

Cyclic load


SHELL181 – planar objects

LINK180 - bolt

MPC184

TARGE170 and CONTA174

–contact pairs

Figure 46 „T-stub FE discretization “

The T-stub tension-elongation comparison on Figure 47 between experimental and numerical

results indicates well coincidence regard the applied finite elements types.

Figure 47 „T-stub tension resistance comparison between experimental [31] and numerical test“

7.2 Gang Shi study on beam-to-column joint with end plate connection, subjected to cyclic

loading [29]

Gang Shi [29] tests eight specimens on beam-to-column joints with end plate connections in

Figure 47, subjected to cyclic loading.

Authors reported that joint with end plate connection can provide enough rotational capacity and

ductility. They recommended stiffened extended end plate connection, while flush end plate is not

recommended.

Figure 48 „Experimental setting in [29]“

0

50

100

150

200

250

0.00 0.25 0.50 0.75 1.00

T-s

tub

ten

sion

res

ista

nce

[kN

]

elongation - [cm]

експеримент Т1 - ненапрегнат

числов модел - болт с LINK180

LINK180

MPC184


On Figure 48 is observed good coincidence between the hysteresis curves from the experiment

and from the numerical simulation. The conclusion is that the performed simulation can predict well

the behavior of beam-to-column joint with end plate connection regard the applied finite elements

types.

Experimental [29]

Numerical

Figure 49 „Numerical and experimental hysteresis curve of beam-to-column joint with end plate connection

comparison”

Authors publications related to the thesis Published to 26.03.2015г.:

1. Zhelev D., Numerical simulation of cyclic load on end plate connection”, Proceedings of the METNET Seminar 2014 in

Moscow.

Sent for publishing to 26.03.2015г.:

1. Желев Д., Числени модели за определяне на носимоспособността на огъващ момент на възел ригел–колона,

решен с фланцево съединение, Годишник на УАСГ.

2. Желев Д., Лостови ефект при еквивалентно Т-парче, Годишник Advances in Bulgarian Science 2014.

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UNIVERSITY OF ARCHITECTURE, CIVIL … · university of architecture, civil engineering and geodesy faculty of structural engineering department “steel, timber and plastic structures”