the simple model for welded angle connections in fire · temperature based on the recommendations...

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International Journal of Steel Structures 17(3): 1009-1020 (2017)

DOI 10.1007/s13296-017-9012-y

ISSN 1598-2351 (Print)

ISSN 2093-6311 (Online)

The Simple Model for Welded Angle Connections in Fire

Amir Saedi Daryan*

Assistant Professor, Civil Engineering Department, Shahid Beheshti University,11369, Tehran, Iran

Abstract

Due to the high sensitivity of fire affected steel behavior, fire resistance of steel structures is of great importance. Moreover,since the connections act as the main means of integration of frame members, the behavior of steel connections in fire issignificantly important. Considering the importance of this matter, this paper describes a spring-stiffness model developed topredict the behavior of welded angle connections made of bare-steel at elevated temperature. The joint components areconsidered as springs with predefined mechanical properties i.e. stiffness and strength. The elevated temperature joint’sresponse can be predicted by assembling the stiffness of the components which are assumed to degrade with increasingtemperature based on the recommendations presented in the design code. Comparison of the results from the model withexisting experimental data shows good agreement. The proposed model can be easily modified to describe the elevatedtemperature behavior of other types of joints as well as joints experiencing large rotations.

Keywords: Welded angle connection, Elevated-temperature, Fire, Spring-stiffness model, Rotation-temperature curves,Moment-rotation curves, Experimental test, Isolated joint, Flexure zone, Tension zone, Shear zone, Compression zone

1. Introduction

Beam-to-column joints have been found to be of great

significance in influencing the structural behavior of frame-

works at ambient and elevated temperatures. Observations

from full-scale fire tests and from damage to steel frame

structures due to real fires (Al-Jabri KS 1998, 1999)

confirm that joints have a considerable effect on the

survival time of structural members in fire due to their

ability to distribute forces.

Fire is a disaster that frequently happens in buildings

(Meacham et al., 2016, Aseeva et al., 2014). Since steel

structures are widely used in buildings and susceptible to

fire, much research has focused on studying the influence

of high temperature on the behavior of steel structures. In

recent years, considerable research work has been conducted

to understand the performance of steel beam to column

joints at ambient temperature with both experimental and

analytical study approaches (Qiang et al., 2013, Hu et al.,

2010, Hantouche et al., 2016, Hean et al., 2015). Experimental

tests have been carried out on a wide variety of joints

either in isolation or as part of complete steel-framed

structures in order to understand their behavior. In general,

experimental tests provide reliable results that can describe

the behavior of the beam-to-column connections. However,

in many cases experiments are either not feasible or too

expensive to conduct. Although of high importance, they

are always limited in terms of the number of geometrical

and mechanical parameters studied, which obviously would

not provide comprehensive understanding of connection

performance. Therefore Various forms of analysis and

modeling methods have been suggested including simple

curve-fitting techniques, simplified analytical methods

and sophisticated finite element models for both bare-

steel and composite joints. The European code for the

design of steel structures (EC3: Part 1.8) has adopted a

simplified analytical procedure for the design of joints at

ambient temperature. This method is based on dividing

the joint into its basic components of known mechanical

properties. By assembling the contributions of individual

components which represent the joint as a set of rigid and

deformable elements, the entire behavior of the joint may

be determined. This method is known as the spring-

stiffness or component method. However, due to the lack

of experimental data to describe the joints’ behavior, the

number of elevated temperature component models is

limited. This paper describes a spring-stiffness model

developed in an attempt to use the component method to

predict the behavior of welded angle connections at

elevated temperatures using the mechanical characteristics

of the components that are available in the literature. In

Received July 22, 2016; accepted January 19, 2017;published online September 30, 2017© KSSC and Springer 2017

*Corresponding authorTel: +982129902233, Fax: +982122431919E-mail: [email protected]

1010 Amir Saedi Daryan / International Journal of Steel Structures, 17(3), 1009-1020, 2017

the model, the joint’s components are represented as

springs with known characteristics such as stiffness and

strength. By assembling the characteristics of individual

components, the joints’ response can be predicted with

increasing temperature. Only those parameters representing

the stiffness and strength of the joint are degraded with

increasing temperatures. Comparison of the results from

the model with existing test data demonstrated good

results.

2. Spring-stiffness Modeling

The basis of the ‘Component Method’ is to consider

any steel beam-to-column joint as a set of individual

components. A beam-to-column joint using the welded

angle connection can be divided into four major zones i.e.

flexure, tension, shear and compression zones. Each zone

of the joint can be further divided into a number of

components, each of which is simply a nonlinear spring,

Figure 1. Mechanical model of flange and web angle connections.

The Simple Model for Welded Angle Connections in Fire 1011

possessing its own strength and stiffness in flexure, tension,

compression or shear that degrades with elevating

temperature.

For each component, the initial stiffness and ultimate

capacity is determined and assembled to form a spring

model, which is adopted to simulate the rotational

behavior of the whole joint. To simulate the rotational

behavior of the welded angle connection, rotational

stiffness and rotational resistance should be calculated

initially.

3. Prediction of Rotational Stiffness

In order to further develop component approach for

prediction of the rotational behavior of welded angle

connections in this section attention is paid to the

prediction of the joint rotational stiffness. The joint

components involved in the evaluation of the initial

rotational stiffness are (Fig. 1):

Column web in compression (Kcwc)

Column web in shear (Kcws)

Column flange in bending (Kcfb)

Column web in tension (Kcwt)

Angle in bending (top angle Kta and web angle Kwa)

Weld in tension Kw

Weld in shear (top angle Kwsta, seat angle Kwssa, web

angle Kwswa)

Plate in bearing (top angle Ktab, seat angle Ksab, beam

flange Kbfb, beam web Kbwb, web angle Kwab)

In the above list the symbols in parentheses represent

the stiffness of the spring element corresponding to each

component, which can be modeled as an elastic perfectly

-plastic spring (Fig 2).

In particular as shown in Fig. 1, four components

(column web in compression, column web in shear, weld

of seat angle in shear, seat angle in bearing) are independent

of weld line connecting the angles to the column flange,

while the other components are dependent on it. The first

step for prediction of the rotational stiffness is to evaluate

the equivalent stiffness of each weld line. It can be seen

from Fig. 1 that the web angle is connected to the column

flange by means of weld line and thus, the values of K2,

K3 should be calculated in reference to these weld lines.

The values of K2, K3 are equal and can be calculated as

follows:

(1)

In particular, four sources of deformation (i.e, the top

angle in bending (ta), the welds of top beam flange in

shear (ws) , the top angle in bearing (tab) and the beam

flange in bearing (bfb) are considered to be located at the

level of the mid-thickness of the top angle leg adjacent to

the beam flange. Therefore, the equivalent stiffness of the

weld line connecting the top angle to column flange has

to account for the need to move the contribution of these

components to the level of the weld line which connects

the top angle to the column flange. For this purpose, the

stiffness of these four components is modified by means

of the following relationships:

(2)

(3)

(4)

(5)

where K are the stiffness matrices of the spring acting at

the weld line that connects the top angle to the column

flange level, hsa is the distance between the center of

compression and the mid-thickness of the top angle leg

adjacent to the beam tensile flange and h1 is the distance

between the center of compression and the weld line

which connects the top angle to the column flange. The

parameter K1 can now be calculated by the following

equation:

(6)

The second step of the procedure is the calculation of

the lever arm hi which represents the distance between the

resultant tensile force and the center of compression.

Assuming that the center of compression is located at the

mid-thickness of the seat angle leg adjacent to the beam

compressed flange and taking into account the location of

each weld line, the lever arm ht is computed by means of

the following relationship:

(7)

wswwabbwbwacfbcwt KKKKKKKKK

/1/1/1/1/1/1/1

132

++++++

==

2

1

' )/( hhKKsa

tata=

2

1

' )/( hhKKsa

wsws

=

2

1

' )/( hhKKsatabtab

=

2

1

')/( hhKK sabfbbfb =

bfbtabwstawcfbcwt KKKKKKKK

/1/1/1/1/1/1/1

11

++++++

=

∑

∑

=

=

=

3

1

3

1

2

i

ii

i

ii

t

hk

hk

h

Figure 2. Spring behavior.


where hi is the distance between the i’th weld line and the

center of compression. Therefore, as the third step of the

procedure, the overall contribution of the weld lines is

represented by means of spring acting at the tension

center level, whose stiffness is given by:

(8)

Finally, the contribution of all the components is

obtained by combining the stiffnesses of the four components,

indecent of the weld line, with the overall contribution Kt

of the components, depending on the weld line. Therefore,

taking into account that this final spring is located at the

tension center level defined by the lever arm ht, the

rotational stiffness of the joint is obtained by means the

following relationship:

(9)

Since the weld stiffness is very high, it is proposed that

the weld stiffness in all equations be assumed to be equal

to ∞.

3.1. Calculate the stiffness of components

In this part, the stiffness of each connection component

that is necessary for calculation of Kϕ is presented

(Azizinamini, A 1987, 1989, Kishi, N 1990). It should be

noted that due to the existence of numerous equations in

this part, the calculation of stiffness for the components

that have negligible effect on rotational stiffness of

connection are not presented herein.

3.1.1. Column flange in bending

(10)

where:

(11)

(12)

(13)

(14)

(15)

2.2.2. Angle in bending

(16)

where:

(17)

(18)

(19)

(20)

(21)

(22)

(23)

where:

(24)

(25)

(26)

(27)

(28)

(29)

t

i

ii

t

h

hk

k

∑=

=

3

1

tsabsawscwscwc

t

KKKKK

hK

/1/1/1/1/1.

2

++++

=ϕ

3

2

,5.0

cf

cfcfbeff

cfbm

tbEk ψ=

{ }2,,1,,,

,min cfbeffcfbeffcfbeff bbb =

cfbhcfbeffmdb 2

1,,+=

cccwcf

cfbeff retb

b 8.022

22,,−−+=

157.0

28.1

≥

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

−

b

cf

b

cf

d

md

tψ

cw

cwcfbeff

cwtd

tbEk

,

=

⎟⎟⎠

⎞⎜⎜⎝

⎛×

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛×=

1

3

3

,

7

45.0

h

h

m

tbEk

b

ta

tataeff

ta ψ

157.0

28.1

≥

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

−

b

ta

b

ta

d

md

tψ

{ }3,,2,,1,,,

,,min taefftaefftaefftaeff bbbb =

tabhtaeff mdb 21,,

+=

222,,

wm

db ta

bhtaeff ++=

23,,

tataeff

bb =

tatatataetLm −−= 5.0

⎟⎠

⎞⎜⎝

⎛=

7

45.0

3

3

,

wa

wawaeff

wam

tbEk ϕ

157.0

28.1

≥

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

−

b

wa

b

wa

d

md

tϕ

{ }4,,3,,2,,1,,,

,,,min waeffwaeffwaeffwaeffwaeff bbbbb =

wabhwaeff mdb 21,,

+=

222,,

wawa

bhwaeff m

db

ρ++=

xwwabh

waeff emd

b ++=

23,,

24,,

waxwwaeff eb

ρ+=


3.1.3. Column web in compression

(30)

where tsa is the seat angle thickness, rsa is the fillet radius

of the seat angle, s = rc for rolled column section or

for welded column section (ac is the weld

throat thickness and dwc is the clear depth of the column

web and rc is the radius of the fillet of the web-to-flange

connection of the column)

3.1.4. Column web in tension

(31)

where beffcwt is computed according to the same criteria

given in section 3.1.1. “column flange in bending”.

4. Prediction of the Flexural Resistance

In this part, the flexural resistance of each connection

component is presented (Kishi, N 1987(a), 1987(b), Liew,

J.Y.R, 1993)

4.1. Column web in shear

(32)

where β = 1 for this case and VcwsRd is the design

resistance of the column web in shear.

4.2. Column web in compression

(33)

where: φ =0.9

4.3. Column web in tension and column flange in

bending

(34)

For top angle weld line

(35)

For web angle weld line (36)

4.4. Top angle in bending

(37)

(38)

(39)

where Mpl,Rdy is the plastic moment of the top angle leg

with the effective width (beffta= bta /2) and eta is the length

of weld line along the vertical leg of angle.

4.5. Web angle in bending

(40)

In this case

(41)

4.6. Welds force

(42)

(43)

4.7. Plate in tension

(44)

4.8. Plate in compression

(45)

where bsa and tsa are the width and the thickness of the

seat angle leg

4.9. Beam web in tension

(46)

4.10. Beam flange and web in compression

(47)

5. Prediction of Connection Rotation

To calculate the connection rotation, the general

deformation of the connection should be determined. The

general deformation of connection ΔT is equal to the sum

of deformation of each component. The deformation of

each component can be calculated by dividing the

component force by its stiffness. These equations can be

written as:

(48)

wc

wcfcsasa

wc

wceffcwc

cwcd

tstrtE

d

tbEK

)](26.02[ +++

==

s 2ac=

wc

wceffcwt

cwtd

tbEK =

β

rDCWS

Rdcws

VF

.

.

=

effcwcwcycwcwcRd btfF φ=

ycwcwteffRdcwt ftbF,,

=

)(5, ccfbfcwteff rttb ++=

cfbeffcwteffbb

,,

=

ta

Rdpl

Rdtam

MF

,

1,,

4=

ytata

Rdpl ftb

M4

2

,=

tatatataetLm −−= 5.0

wa

plRd

waRdm

MF

'

4=

wawa mm =

'

wawacwartgm 8.0−−=

wwwRdRLF =

)3.0(uew

FtR ϕ=

yRdt AfF =,

ysasasacRd ftbF =

ywbeffbwtbwtRd ftbF =

fbb

bRdbfcRd

th

MF

−

=

∑∑

=Δ

i

iRd

TK

F


(49)

Considering the mentioned equations, after obtaining

the stiffness and ultimate load of each component,

moment-rotation relation may be obtained from the

following equation (Yee KL, 1986):

(50)

where the ultimate moment of the joint can be estimated

using the following expression:

(51)

and KpT can be expressed as 0.02Kj. A zero value is

recommended for C (Yee KL, 1986).

6. Degradation of the Joint’s Characteristics at Elevated Temperature

When a steel welded angle connection is subjected to

fire, the temperature of the joint will be increased to a

high level. At elevated temperatures, the elastic modulus

and strength of steel will be reduced. The reduction of

stiffness and strength of the components were adopted

from temperature dependent structural steel properties of

EC3: Part 1.2 as shown in Table 1.

To calculate steel properties at different temperatures in

order to determine connection rotation, it is sufficient to

obtain steel properties according to the related temperature

from Eq. (8).

7. Accuracy Calibration of the Proposed Model

In order to evaluate and verify the accuracy of the

spring-stiffness model under fire conditions, four samples

of the welded angle connections from experimental report

presented by Saedi Daryan et al. (Saedi Daryan A, 2006,

2009(a), 2009(b), 2009(c), 2013) are used.

7.1. Specimen details

All specimens consisted of a symmetric cruciform

arrangement with a single 800 mm long column made of

IPE300 section connected to two 2400 mm long cantilever

beams made of IPE 220 sections. The load was applied at

a point 200 cm away from the column flange. A series of

eight experimental tests were performed on two types of

welded angle connections. The connections were defined

as the follows:

Connection group 1: Specimen without a web angle

(SOW).

t

T

T

h

Δ=θ

TpT

pT

TTpt

pTT KM

CKKMM θ

θθϕ +

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−−−=

)(exp1

∑=

=

n

i

iiRdpT hFM

1

,.

Table 1. Properties of structural steel at elevated temperature

θs

(°C )

Reduction factors

20 1 1

100 1 1

200 1 0.9

300 1 0.8

400 1 0.7

500 0.78 0.6

600 0.47 0.31

700 0.23 0.13

800 0.11 0.09

900 0.06 0.0675

1000 0.04 0.045

1100 0.02 0.0225

1200 0 0

θs: steel temperature, fy: yield stress, Es: Young’s modulus

ky θ, fy θ, fy⁄= kE θ, Es θ, Es⁄=

Figure 4. Specimen details for the SWW connection group.

Figure 3. Specimen details for the SOW connection group.


Connection group 2: Specimen with a web angle

(SWW).

Connection group 1 (SOW) consisted of two angles.

One of the angles was welded to the top flange of the

beam, and the other was welded to the bottom flange.

This assembly was welded to the flange of the column as

shown in Fig. 3.

For connection group 2 (SWW), in addition to the two

SOW angles, two more angles were welded to the web of

the beam and to the flange of the column. The web angles

used in all specimens were 100*100*10 mm, and are

shown in Fig. 4.

Considering the connection specimens tested by Saedi

Daryan et al. four connection specimens were selected.

Two of these connections were selected from the first

connection group and the other two were selected from

the second connection group. The connection geometries

are presented in Table 2.

7.1.1. Specimen loading and material properties

The values of applied moment to each specimen in the

tests are presented in Table 3. As it can be seen, first the

rotation capacity of connection is theoretically calculated

and then the applied moment is selected as a coefficient

of connection rotation capacity and is applied to the

specimens during the test.

Material properties were measured by coupon for all

specimens, and dimensions were recorded before starting

the tests. The results of the Mill test for this grade of steel

are given in Table 4. The values presented in the mentioned

table are the same, since the results of mill test is

Figure 5. Comparison of temperature-rotation for spring-stiffness model and experimental tests (Saedi Daryan, 2009(c)).

Table 2. Connection geometrical details

Test NO Connection group Size of angle (mm)

S2 1 150*100*15

S3 2 150*100*15

S8 1 100*100*10

S9 2 100*100*10

Table 3. The value of applied moment for each specimenin the tests carried out by Saedi et al.

Specimen number

Group number

Moment (M) level

Applied M(kN m)

Average recorded M

(kN m)

S2 1 .6*Mcc 8.5 8.55

S3 2 .4*Mcc 8.5 8.47

S8 1 .5Mcc 4.25 4.26

S9 2 .5*Mcc 6.5 6.53

Table 4. Material properties

Material Yield stress (N/mm2) Ultimate stress (N/mm2) Modulus of elasticity (N/mm2)

Beam & Column & Angle 235 420 2.06×105


presented for all specimens.

The effectiveness of the spring-stiffness model for

simulating the behavior of the welded angle joints subjected

to fire may be validated with the experiments. In Fig. 5

temperature-rotation curves obtained by experimental tests

(Saedi Daryan, 2009(c)) are compared with the results of

spring-stiffness model. In Fig. 6., moment-rotation curves

presented by Saedi Daryan, 2013 are compared with the

result of spring-stiffness model. It can be seen that the

predicted and the measured results of specimens agree

well with each other. In the case of low number specimens,

some differences between the results are observed which

may be due to the different rates of temperature increase.

The rate of temperature increase has some influence on

the creep strain of steel. So variation of the fire rate may

have an impact on the response of connections. Further

study of the influence of creep strain on the behavior of

welded angle joints will be performed in the next stage of

research. The good agreement between analytical models

with the test results demonstrates that the spring-stiffness

model represents well the welded angle connections

behavior. The spring-stiffness model can be used to predict

the response of connections as well as of structures with

welded angle joints at elevated temperatures.

8. Conclusion

This research was carried out to simulate the behavior

of welded angle connections in fire with spring-stiffness

model. The model is developed according to the specifications

of test data and temperature dependent properties of the

steel. Comparisons of the spring-stiffness method with

experimental results confirm predicted and measured

responses both in elastic and plastic ranges. This method

is capable of predicting the results of the welded angle

connection at elevated temperatures with desirable accuracy.

However the proposed model requires further development

to support following topics which could have an important

effect on the connection behavior in high temperature:

(1) The applicability of the model to predict the joint

behavior at higher levels of moment than those presented;

(2) The model was developed based on isolated joint

test. As observed in Cardington fire tests, since the effects

of axial restraint on the joint behavior can have a

significant influence on the behavior of the structure in

fire, this needs to be addressed in the model. Moreover,

the joint behavior during the cooling phase needs to be

investigated.

Figure 6. Comparison of moment-rotation for spring-stiffness model and reference (Saedi Daryan 2013).


Nomenclature

θT : Rotation of connection at temperature T.

K : Stiffnesses of the spring acting at the weld

line which connects the top angle to the

column flange

Kcwc : Column web stiffness in compression

Kcws : Column web stiffness in shear

Kcfb : Column flange stiffness in bending

Kcwt : Column web stiffness in tension

Kta : Top angle stiffness in bending

Kwa : Web angle stiffness in bending

Kw : Weld stiffness in tension

Kwata : Weld stiffness in shear (top angle)

Kwssa : Weld stiffness in shear (seat angle)

Kwswa : Weld stiffness in shear (web angle)

Ktab : Plate stiffness in bearing (top angle)

Ksab : Plate stiffness in bearing (seat angle)

Kbfb : Plate stiffness in bearing (beam flange)

Kbwb : Plate stiffness in bearing (beam web)

Kwab : Plate stiffness in bearing (web angle)

Kφ : Rotation stiffness of the connection

Kwa : Web angle stiffness

Kcfb : Column flange stiffness

Kcwt : Column web stiffness

Kta : Top angle stiffness

KPT : Connection Plastic stiffness

hsa : Distance between the center of compression

and the mid-thickness of the top angle leg

adjacent to the beam tensile flange

h1 : Distance between the center of compression

and the weld line which connects the top

angle to the column flange

hi : Distance between the weld line and the

center of compression

ht : Distance between center of rotation and

top of the seat angle

hb : Height of beam

MPT : Plastic moment of the connection

MT : Moment of the connection at temperature

T

Fwa,Rd : Web angle force

FwRd : Welds force

Fwat,Rd : Tensile force in web angle

Fbwb,Rd : Beam web bending force

Fsac,Rd : Compressive force in seat angle

Fbwt,Rd : Tensile force in beam web

Fbfc,Rd : Compressive force in beam flange

Fcwt,Rd : Tensile force in column web

Fcws,Rd : Shear force in column web

Vcws,Rd : Design resistance of the column web in

shear

Fcwc,Rd : Compressive force in column web

Fta,Rd : Force in top angle

Ftat,Rd : Tensile force in top angle

Mpl,Rdy : Plastic moment of the top angle leg with

the effective width

ΔT : Sum of deformation of each component

gc : Length of the Weld connecting the column

flange to the beam web

tbf : Beam flange thickness

tcf : Column flange thickness

tcw : Column web thickness

tsa : Seat angle thickness

tta : Top angle thickness

tbw : Beam web thickness

twa : Web angle thickness

Lwa : Web angle length

Lta : Top angle length

eta : Weld line length along the vertical leg of

angle

exw : Web angle edge distance to the weld

connecting web angle to the beam

e2c : Distance between the weld connecting

web angle to column flange edge

s=rc : Column section root radius

rwa : Web angle root radius

rsa : Seat angle fillet radius

bsa : Seat angle width

bcf : Column flange width

bta : Top angle width

bwa : Web angle width

ac : Weld throat thickness

fy : Yield stress of connection components

fu : Ultimate stress of connection components

E : Steel modulus of elasticity for connection

components

υ : Poisson’s ratio

dcw : Column web height

dwa : Vertical distance of web angle to the first

bolt in web angle

A : Section area of angle

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Appendix

The main purpose of this section is to propose a proper and applicable model for describing the behavior of angle

connections at elevated temperatures. Thus, the first assumption in this section is that the intended angle connections are

properly designed according to the criteria of current codes. By considering this assumption, use of the proposed spring

stiffness model can provide reliable results about the moment-rotation-temperature behavior for these connections. One

of the items that can prevent the proposed spring stiffness model to function correctly, is the occurrence of local failures

in beams and columns. The occurrences of these failures include local buckling, local crippling and local bending of web

and flange of column and beam. In this appendix, the required controls for preventing these items are presented.

In angle connections the majority of the force transmitted from beam to column is the reaction force R. This force is

transmitted to column due to flexible behavior of seat angle. Thus, the critical moment section in angle connections is

located at the beginning of arc area between the horizontal and the vertical stems of the angle.

To determine the bending moment in a-a section, the reaction force R should be multiplied by the distance between

the acting point and a-a section location. The key point here is to determine the length of contact area between bottom

beam flange and horizontal angle stem (N). Based on the studies carried out by Blodget (1966), the contact length

between bottom beam flange and horizontal angle stem is calculated using the equation proposed for preventing local

web yielding. The equation for checking web local yielding under reaction force R is presented as:

(A1)

where R, Fyw, tbw, Z, and N are respectively reaction force, beam web yield stress, beam web thickness, distance between

beam flange surface to end of arc area of flange web connection root in rolled profile or (distance between beam flange

surface to end of fillet weld connecting web and flange in the profile made by plates) and length of seat angle. It is clear

that Eq. (1) prevents beam web local yielding.

Based on the studies carried out by Johnston and Kubo (1941), web crippling should be controlled by the following

equations:

(A2)

(A3)

In Eqs. (2) and (3), E is elasticity modulus of steel, tbf is beam flange thickness and hb is the beam depth.

Controlling of the above equations prevents web crippling.

( )2.5yw bwR F t N Z= × × +

1.5

2 30.2 0.4 1

yw bfbwbw

b b f bw

EF ttN NR t

h h t t

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥≤ → = × + ⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦

1.5

2 40.2 0.4 1 0.2

yw bfbwbw

b b bf bw

EF ttN NR t

h h t t

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥> → = × + −⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

Figure A1. force R and a-a section in angle connection.


Another item that is important in angle connection design is column local bending. Investigations of Tamboli (1999)

have shown that when angles are connected to column flange and the columns are designed for transferring beam loads

to the structure foundation, local bending checks are not needed during angle connection design. However, if the angles

are connected to column web, column web bending should be checked. In this case, the column web is vulnerable to

local bending induced by eccentricity of reaction force. Tamboli (1999) have presented a method for determination of

column web strength based on fracture lines. In Fig. 2, Kc is distance between column flange surface and end of arc area

of flange-to column web root. Using fracture lines theory, nominal coefficient of column web can be calculated by Eq.

(4):

(A4)

Lwa, b and c are shown in Fig. A2 and ef is the eccentricity of reaction force R from column flange weld. The plastic

moment Mp in Eq. (4) is calculated from Eq. (5):

(A5)

where tcw and Fyc are respectively column web thickness and column yield stress. Finally, equation 5 should satisfy the

following condition:

(A6)

Based on Eq. 6, column web nominal capacity should be larger or equal to support reaction force.

At the end, it should be noted that checking the above equations at the initial step of the angle connection design is

required to prevent local damages including local buckling, local crippling and local bending in beam and column

members such that the connection can play its anticipated role.

22

2

p wax

f wa

M Lc cR

e b L b

⎡ ⎤= + +⎢ ⎥

⎣ ⎦

20.25

p cw wa ycM t L F= × ×

xR R≤

Figure A2. Steel column web rupture lines in flexible top and seat angle connections.

the simple model for welded angle connections in fire · temperature based on the recommendations...

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