evaluation of diaphragm effect for steel welded box beam and …c).pdf · 2018-01-08 · evaluation...

Steel Structures 8 (2008) 189-198 www.ijoss.org

Evaluation of Diaphragm Effect for Steel Welded Box Beam

and Circular Column Connections

Young-Pil Kim1 and Won-Sup Hwang2*

1Struatural Department, YOOSHIN Eng. CO., 832-40 Yeoksam-Dong Seoul, Korea2Department of Civil Engineering, Inha University, 253 Younghyun-Dong Incheon, Korea

Abstract

This paper investigates the design equations and the strength behavior of the diaphragm for steel box beams and circularcolumn connections. The strength of the connection is decided by the strength of beam and column as well as connectiondiaphragm, because the connection diaphragm supports the concentration forces from the box beam's lower flange. In previousresearches, however, the calculation procedure of the diaphragm stress from the indeterminate curved-girder model is toocomplicated to apply in regular practice. Irrational assumptions exist in deriving the process of the equation. Moreover, noreasonable design has yet been made because the diaphragm's effect on the strength of the connection has not been considered.Therefore, this study examines the strength behavior of a connection with diaphragm details through non-linear FEM analysisof the connection diaphragm. Finally, the connection strength is evaluated by using rigidity capacity of diaphragm, newdiaphragm design method is proposed.

Keywords: box beam and circular column connection, diaphragm, non-linear analysis, strength, rigidity capacity

1. Introduction

Recently, welded steel piers have been widely applied

for pier structures of urban overpasses and elevated

structures in East Asian countries due to their excellent

earthquake resistance capacity, small space requirements,

and short construction term. At the T-type or framed

beam-to-column connections of box-sectioned steel piers,

it has been widely acknowledged that serious shear lag

and stress concentrations may occur due to abrupt

direction changes in member forces, so it is necessary to

handle these problems properly in the design stage.

Instead of box-sectioned steel piers, circular- sectioned

piers have been introduced lately due to high local-

buckling strength, efficient behavior for changing loading

direction, and fine appearances.

In an early study on welded steel connections, Beedle

et al. (1951) proposed a stress and strength evaluation

method for an H-sectioned beam-to- column connection

by assuming that stresses are uniform in flanges and

webs. Fielding and Huang (1971) indicated that the

strength of the beam-to-column connection of H-

sectioned frame is reduced due to the axial force in the

column. However, they did not recognize the shear lag

phenomenon at the flange of connections. By recognizing

the shear lag phenomenon at box -sectioned beam-to-

column connections of the pier structure, Okumura and

Ishizawa (1968) carried out theoretical and experimental

studies using a simple beam model subjected to a

concentrated mid-span load. Instead of using a simple

beam model, Nakai et al. (1992) suggested an equation

for the shear lag stress from a study using an overhanging

beam model with additional moments due to shear

deformation occurring in the connection. Qi and Mimura

(2002) suggest design and strength evaluation method of

welded beam-column connection. Also, Hwang et al.

(2004) suggest shear lag stress evaluation method for

box-sectioned welded connection using the additional

moment of cantilever beam model.

However, almost all researches, except Okumura and

Ishizawa’s, have been limited to box-sectioned connections

only. Also, most researches do not consider that the

behavior of the box beam and circular column connection

is much more efficient than that of H-sectioned or box-

sectioned connections in steel piers. After Okumura and

Ishizawa, There is no reach result on analysis and

experiment of the box beam and circular column

connection. Basic research is carried out from large scale

test of the box beam-to-circular column connection by

Hwang et al. (2002).

Okumura and Ishizawa (1968) suggest stress equation

Note.-Discussion open until February 1, 2009. This manuscript forthis paper was submitted for review and possible publication on July17, 2008; approved on August 30, 2008

*Corresponding authorTel: +82-32-860-7570; Fax: +82-32-873-7560E-mail:[email protected]

190 Young-Pil Kim and Won-Sup Hwang

from indeterminate curved I-girder model for connection

diaphragm of box beam-to circular column connections

as shown in Fig. 1 and Fig. 2. Their equations are very

complicated form and design variable are not precise.

Then, current design specifications don’t reflect this

equations. Therefore, new design method of connection

diaphragm should be developed by considering practical

diaphragm behavior. In current design specifications and

researches of connection diaphragm, importance of

diaphragm has been neglected, because concentrated

forces of beam lower flange are transferred to circular

column through connection diaphragm. Then, Connection

strength is affected by strength of connection diaphragm.

Also, appropriate reinforcements of diaphragm deficits

area such as working manhole are required. However,

previous research did not consider connection strength

behavior with connection diaphragm shape.

Therefore, to suggest new diaphragm design methods

for the steel box beam and circular column connections.

The strength behavior is examined with the diaphragm

shape from the non-linear FEM analysis. Influence of

diaphragm design parameters is investigated based on

connection strength. Also, required thickness of connection

diaphragm is evaluated with connection diaphragm details.

2. Investigating Existing Researches for Connection Diaphragm

2.1. Calculation of Connection Diaphragm Stress

Previous research (Okumura and Ishizawa, 1968) have

analized stress of connection diaphragm using concept of

stress concentration. Specially, stresses should be calculated

in the point such as ϕ=π, ϕ=π/2, and ϕ=α. Also, normal

and shear stresses of the internal and external fiber are

given as followings.

(1-a)

(1-b)

(1-c)

Where fo and fi is external and internal fiber normal stress.

Also, v is shear stress, Tϕ is axial force, Mϕ is bending

moment, and Qϕ is shear force in any point. In any point,

Tϕ, Mϕ, and Qϕ is given by Table 1. As shown in Table 1.

Okumura’s stress equations are very complicated form.

Then, its practical usage is very difficult in connection

diaphragm design.

2.2. Specifications for connection diaphragm

In current design specifications, the dimension of the

diaphragm should be decided after the review of stress

calculation based on Eq. (1) (KHBDC, 2005; Hanshin

Highway Co., 1985). However, design specifications do

not adopt Eq. (1) due to complicated calculation

procedure. In current stage the stress calculation can be

omitted when following empirical conditions is satisfied.

① Ro≤1500mm, ② tbf≤25mm, ③ r≒Ro/2,

④ td≥b/17, ⑤ tr·br≥250tbf

Where, an each dimension uses a mm unit. Also, a

manhole radius of the diaphragm should be fixed to one

half of column outer radius. A diaphragm thickness tdmust be more thick a flange thickness tbf.

2.3. Investigating of stress equation

Eq. (1) is composed of complicate variables as

described before. Also, assumed condition of deriving

sequence is too finite. Therefore, deriving procedure of

Eq. (1) should be reviewed for normal stress term.

Generally, bending stress of curved girder is given by

Eq. (2) (Ugural and Fenster, 1995).

(2)

Where, Z is variable depending on curvature radius of

curved I-girder. Other variables are defined as Symbols.

For curved girder, variable Z is expressed as followings.

fo

Tϕ

Ar

-----–M

ϕh1

⋅

Are j⋅ ⋅

---------------–=

fi

Tϕ

Ar

-----–M

ϕh2

⋅

Are a⋅ ⋅

---------------+=

νQϕ

Ad

------–=

fTϕ

Ar

-----–M

ϕ

ArR'

---------- 1y

Z R' y+( )-------------------++=

Figure 1. Diaphragm of connections.

Figure 2. Diaphragm details of connections.

Evaluation of Diaphragm Effect for Steel Welded Box Beam and Circular Column Connections 191

(3)

Eccentricity e of Fig. 1 is derived as Eq. (4) from

condition that right term of Eq. (2) equals zero.

(4)

Eq. (4) is rearranged for reciprocal of Z. Eq. (5) is

obtained.

(5)

As Substituting Eq. (5) to Eq. (2), Eq. (6) is obtained.

(6)

When, R' approximate to infinity, Eq. (7) is gained.

(7)

For outer fiber of upper flange Eq. (8) is obtained due

to y=h1 and R+h1=j.

(8)

Precisely, Eq. (8) is same equation with Eq. (1-a),

condition is irrational considering R' is from 1.0 m

to 5.0 m in usual practice. Also, connection diaphragm

sections are excessively decided by using empirical

design method. Excessive diaphragm thickness leads to

abrupt collapse of adjacent member in ultimate state.

Then, beam, column, and diaphragm must maintain

strength balance.

3. Diaphragm Analysis Model

3.1. Outline of analysis model

In this study, to investigate influence of diaphragm

design parameters, 4 analysis groups are produced. They

are LD, DH, DR, and DHR models.

A diaphragm location was moved to the downward

direction by the ld in LD model which is be produced to

examine a strength behavior with a diaphragm location.

LD model is same dimension with specimen NC-50. LD-

00 model is same dimension with NC-50 specimen. LD

model’s details are expressed as shown in Table 1. Where

main parameter of LD model is moved distance-to-

thickness ratio ld over td. The ld was changed based on a

diaphragm thickness td from 0mm to 24mm. At this case,

ld/td is changed from 0.0 to 2.0.

DH model was produced to examine a connection

strength behavior according to Db. DH model which

changes diaphragm web depth-to-radius ratio Db/R. into

0.0, 0.13, 0.25, 0.5, 0.75, and 1.0 as shown in Table 2.

Reinforcing rib is not installed in DH model at

connection diaphragm. Central angle α is established

from 40o to 70o. Also, DH model’s last term of notation

means Db/R values.

DR model is introduced to investigate reinforcing rib

Z1

Ar

-----–y

R' y+----------- Ad

A∫=

eZ

Z 1+----------– R'=

1

Z---

R' e+

e-----------–=

fTϕ

Ar

-----–M

ϕ

Ar

-------1

R'----

1

e---

1

R'----+⎝ ⎠

⎛ ⎞ y

R' y+( )---------------++=

fTϕ

Ar

-----–M

ϕ

Ar

-------1

e---⎝ ⎠⎛ ⎞

–y

R' y+( )---------------+=

fo

Tϕ

Ar

-----–M

ϕh1

⋅A

re j⋅ ⋅

---------------–=

R' ∞≅

Table 1. Member forces in any point

Point Forces Stress Equation

In Case ofϕ=α

Axial Force

Bending Moment

Shear Force

In Case of.ϕ=π/2

Axial Force

Bending Moment

Shear Force

In Case ofϕ=π

Axial Force

Bending Moment

Shear Force

Tϕ

To

αcosF

i1

2------- α

απ--- 1–⎝ ⎠⎛ ⎞

sin–=

Mϕ

Mo

R' To1 αcos–( )

Fi1

2-------

2λµ------ 1 αcos–( ) 1

απ---–

3

4---λ–

1

4---λk+⎝ ⎠

⎛ ⎞ αsin+⟨ ⟩–+=

Qϕ

To

αsinF

i1

2-------

1

π--- αsin α αcos–( ) αcos+⟨ ⟩–=

Tϕ

Fi1

4-------=

Mϕ

Mo

ToR' F

i1R'

λπ---

1

4---

λ8--- 3 k–( ) αsin–+⟨ ⟩+ +=

Qϕ

To

Fi1

2π( )⁄+=

Tϕ

T–o

=

Mϕ

Mo

2ToR' F

i1R'

λπ---

1

4---

λ8--- 3 k–( ) αsin–+⟨ ⟩–+=

Qϕ

0=


effect. As shown in Table 3, the width-to-radius ratio br/

R of DR model is changed form 0.25 to 0.75. In current

design specifications (KHBDC, 2005), Db/R od DR

model is fixed to 0.5 because a manhole radius of the

diaphragm should be reserve also the half of a column

outer radius. Also, diaphragm thickness td of DR model is

changed into 12, 15, 18, and 21 mm.

DHR model is similar to DR model. In notation of

DHR model, before hyphen term means Db/R values. Db/

R is defined as 0.25 or 0.75. Also, DR09 and DR12

models mean that each diaphragm thickness td is 9,

12 mm respectively. After hyphen term is central angles

of connections. Last term of notation is value of br/R. br/

R value of DH model and DR model is changed from

0.25 to 0.75.

3.2. Analysis method

In this study, boundary condition of analysis model is

Table 2. Dimensions of LD model

LD modelα

(deg)R

(mm)tbf

(mm)tc

(mm)ld

(mm)tw

(mm)b

(mm)db

(mm)ld/td

LD-00LD-05LD-10LD-15LD-20

50 12 12 12

06121824

12 450 488

0.00.51.01.52.0

Table 3. Dimensions of DH model

DH modelα

(deg)R

(mm)tc

(mm)tbf

(mm)tw

(mm)td

(mm)db

(mm)L

(mm)b

(mm)Db/R br/R

DH12-40series

DH12-4000DH12-4013DH12-4025DH12-4050DH12-4075DH12-4010

40 294 12 12 12 12 448 2000 380

0.000.130.250.500.751.00

0.0

DH09-50series

DH09-5000DH09-5013DH09-5025DH09-5050DH09-5075DH09-5010

50 294 12 12 12 9 448 2000 450

0.000.130.250.500.751.00

0.0

DH12-50series

DH12-5000DH12-5013DH12-5025DH12-5050DH12-5075DH12-5010

50 294 12 12 12 12 448 2000 450

0.000.130.250.500.751.00

0.0

DH12-60 series

DH12-6000DH12-6025DH12-6050DH12-6075DH12-6010

60 294 12 12 12 12 448 2000 510

0.000.250.500.751.00

0.0

DH12-70series

DH12-7000DH12-7025DH12-7050DH12-7075DH12-7010

70 294 12 12 12 12 448 2000 550

0.000.250.500.751.00

0.0


given by Fig. 3(b) based on one of test setup as shown in

Fig. 3(a). Concentrated load P is loaded to the upper roller.

Table 4. Dimensions of reinforcing rib model

DR modelα

(deg)R

(mm)tc

(mm)tbf

(mm)tw

(mm)td

(mm)db

(mm)L

(mm)b

(mm)Db/R br/R

DR09 series

DR09-5025DR09-5050DR09-5075

50 294 12 12 12 9 448 2000 450 0.50.250.500.75

DR12 series

DR12-5025DR12-5050DR12-5075

50 294 12 12 12 12 448 2000 450 0.50.250.500.75

DR15 series

DR15-5025DR15-5050DR15-5075

50 294 12 12 12 15 448 2000 450 0.50.250.500.75

DR18 series

DR18-5025DR18-5050DR18-4075

50 294 12 12 12 18 448 2000 450 0.50.250.500.75

DHR0925series

DHR0925-5025DHR0925-5050DHR0925-5075

50 294 12 12 12 9 448 2000 450 0.250.250.500.75

DHR1225series

DHR1225-5025DHR1225-5050DHR1225-5075

50 294 12 12 12 12 448 2000 450 0.250.250.500.75

DHR0975series

DHR0975-5025DHR0975-5050DHR0975-5075

50 294 12 12 12 9 448 2000 450 0.750.250.500.75

DHR1275series

DHR1275-5025DHR1275-5050DHR1275-5075

50 294 12 12 12 12 448 2000 450 0.750.250.500.75

Figure 3. Boundary condition of test and anlaysis.

Figure 4. Residual stress distribution.


Nishimura (1998)’s material constitutive laws were

applied to non-linear F.E.M analysis in this study. Initial

imperfections such as initial deflection and residual stress

are considered. Specially, residual stress of connection

member is applied to box beam and circular column as

shown in Fig. 4(a) and Fig. 4(b). Compression residual

stress is assumed by (-)0.4 fy or (-)0.5fy. Tensile residual

stress is assumed by (+)1.0fy. Figure 5 shows diaphragm

mesh division of diaphragm model and reinforcing rib

model case. Also, diaphragm web and rib details are

shown in Fig. 6.

3.3. Verification of analysis results

To verify analysis method, analysis results of NC-40,

NC-50, NC-60, and NC-70 model compare with test

result. Table 5 shows dimension of test specimens.

Where, notation of test model is indicated under Table 5.

Table 6 shows mechanical properties of materials. SS400

steel class is applied to analysis and test model. Elastic

modulus E is 1.99×106 MPa and yield strength fy is 286

MPa. Figure 7 shows comparison of between analysis

results and test results. P-δ relationship of analysis agree

well with one of test less than about 100 mm displacement

that bursting of welding part is occurred. After bursting of

welding part, connection strength is reduced rapidly in

test results. However, two results have good agreement in

view of yield load. Therefore, it is judged that propriety

of non-linear FEM analysis procedure is ensured in this

study.

Figure 5. Mesh division of analysis model.

Figure 6. Analysis model detail of connections.

Figure 7. Comparison of analysis results and test Results.

Table 5. Dimensions of connection specimens

Modelá

(deg.)R

(mm)tc

(mm)tfb

(mm)tw

(mm)db

(mm)d2

(mm)L

(mm)B

(mm)

NC-40NC-50NC-60NC-70

40516069

290286292293

11.8311.9111.8611.88

11.8311.9111.8611.88

11.8311.9111.8611.88

485484486488

444359293212

1997199419951995

377445504547

Table 6. Mechanical properties of materials

fy (MPa) fu (MPa) E (×105 MPa) fy/fu Steel Class

286 464 1.9992 0.62 SS400


4. Investigation of Design Parameter

4.1. Influence of diaphragm location

Figure 8 shows strength ratio and displacement relationship.

The strength ratio is defined by P-to-Po(NC-50) ratio. Where

Po(NC-50) means yield load of test specimen NC-50 (Lee

and Lu, 1989). As ld increasing, strength ratio decrease.

When ld is 24 mm, strength ratio reduced about 20%.

Strength of NC-50 model is located between strength of

LD-15 and LD-20. Therefore, NC-50 could be analogized

to relocation of diaphragm about 20 mm. At this case, ld/

td equals 1.67. Figure 9 shows ld/td and yield strength ratio

P-to-Po(NC-50) relationship. Connection strength is linearly

increased with increment of ld/td. When ld/td is 2.0, 20%

strength reduction is occurred comparing with LD-00.

4.2. Influence of diaphragm web depth

Figures 10 and 11 show strength ratio DH model with

diaphragm web depth-to-radius ratio Db/R. Strength ratio

Po/Po(NC-40) is defined by Po-to-Po(NC-40) ratio. However,

Po(NC-50) value is selected as yield load of DH-50100

model instead of NC-50 model yield strength due to

diaphragm location effect. As shown in Figure 10,

strength of NC-40 agrees with one of connection which

diaphragm is not installed. Also, Strength ratio Po/Po(NC-40)

of connection model which Db/R is 0.75 is obtained

sufficiently comparing NC-40 model. However, Po/Po(NC-

40) is reduces gradually when Db/R is smaller than 0.75.

Then, strength ratio Po/Po(NC-40) of DH12-4000 model

becomes 0.45. Similarly, Db/R effect of 50o models has

almost same trend comparing 40o models. Specially,

strength ratio Po/Po(NC-50) of DH12-5000 model becomes

0.60. strength ratio shows upward tendency with increase

of central angle due to reinforcement effect of beam web.

Therefore, Figure 12 shows Db/R vs strength ratio with

central angle. Strength ratio develop gradually with

increase of central angle. However, strength ratio of

connection is enough to use without reinforcement when

Db/R is more than 0.75.

4.3. Influence of Influence of rib

DR12 model is br/R is changed as diaphragm depth Db

is fixed to 0.5R and td=tbf. In Db/R=0.5, strength ratio of

rib installed connection is 0.96. strength ratio of non-rib

Figure 8. P-δ relationship of LD model.

Figure 9. Yield load ratio with diaphragm location.

Figure 10. Influence of diaphragm web depth (α=40o).

Figure 11. Influence of diaphragm web depth (α=50o).


installed connection is 0.86. Then, strength ratio of DR12

models is smaller than one of DH12-50100 which

diaphragm manhole is not installed as shown in Figure

13. However, increasing of yield strength is not occurred

with increase br/R as shown in Figure 14. Figure 15

shows strength ratio with diaphragm web thickness. The

diaphragm thickness td is thicker, the connection strength

is stronger. Diaphragm web thickness td must be increased

instead of reinforcing rib width br to develop diaphragm

strength.

5. Design Equation of connection Diaphragm

Okumura’s diaphragm stress equation based on curved

girder model is very complicated and difficult to apply

usual practice. Also, strength of diaphragm web and rib is

unreasonably evaluated. Then, more reasonable design

method of connection diaphragm is required. This study

introduces moment inertia of diaphragm from circular

column axis to consider diaphragm rigidity. Id/I could be

introduced by using diaphragm rigidity Id in connection

which manhole is not installed. Also, connection strength

is expressed by P/Po(DH-50100), Where Po(DH-50100) is yield

strength of connection which manhole is not installed.

Analysis results of 50o models are selected based on

central angle range of design specification, i.e. 45-55o.

Analysis results are rearranged by Id/I and P/Po(DH-50100)

relationship as shown Fig. 16. As Id/I is more than 1.0,

connection yield strength ratio is reduced rapidly.

However, connection yield strength ratio is more than 1.0

when Id/I is smaller than 1.0. This trend is expressed as

followings.

for

(9)

for

Id/I 1.0 condition should be confirmed to maintain

diaphragm strength because strength ratio decrease

remarkably as Id/I is more than 1.0. When Id/I equals 1.0,

P

Po

----- 1.0= IdI⁄ 1.0≥

1.0

IdI⁄( )

1.25-------------------= I

dI⁄ 1.0<

Figure 12. Db/R and strength ratio relationship.

Figure 13. Influence of reinforcing rib width (DR12).

Figure 14. Influence of reinforcing rib width (DR21).

Figure 15. Strength ratio with diaphragm web thickness.


Required diaphragm thickness treq with Db/R is obtained

by numerical solution as shown in Fig. 17. When Db/

R=1.0, treq/td=1.0. treq/td equals 1.1 at Db/R=0.5. Also,

treq/td increases by geometric progression when Db/R is

smaller than 0.25. It is recommended that Db/R of

connection diaphragm should be more than 0.25. Also,

numerical solution such as Fig. 17 is difficult to apply

practical usage. Then, treq is suggested by function of

fourth order Db/R as followings.

(10)

Figure 18 shows comparison of numerical solution and

Eq. (10) that is proposed. Eq. (10) agrees well with

numerical solution of Db/R versus treq/td. Where Eq.(10) is

rearranged by considering flange yielding condition td≥tbf

.

(11)

As a result, required diaphragm thickness-to-flange

thickness ratio treq/tbf could be expressed by fourth order

Db/R as shown in Eq. (11). Required diaphragm thickness

treq could be calculated from Eq. (11) with diaphragm web

depth Db. It is simpler than Okumura’s stress equation.

Also, more reasonable design of connection diaphragm

could be possible.

6. Conclusions

This paper investigates problems of existing design

specification and proposes a newly diaphragm design

method in order to develop the design method of steel

piers. From this study, the following conclusions can be

drawn:

(1) Connection strength reduces linearly with increase

of diaphragm moved length ld. When ld equals two times

of diaphragm thickness td, connection strength reduced by

20%.

(2) Diaphragm web depth Db should be designed over

0.75R in case of diaphragm model in order to confirm

connection strength.

(3) Variation of connection strength is negligible with

the reinforcing rib width.

(4) In view of connection strength, It is judged that

diaphragm web depth is the most important variable.

(5) Equation of required diaphragm web thickness treq

is proposed based on diaphragm web depth Db.

Acknowledgments

This work is a part of a research project supported by

Korea Ministry of Construction & Transportation (MOCT)

through Korea Bridge Design & Engineering Research

Center at Seoul National University. The authors wish to

express their gratitude for the financial support.

References

Beedle, L.S., Topractsoglou, A.A., Jonhston, B.G. (1951),

“Connection for welded continuous portal frames”,

Welding Journal, Vol. 30, pp. 354s-84s.

Hanshin Highway Corporation (1985), Design standard. No.

treq

td

------- 1.8Db

R------ 1–⎝ ⎠⎛ ⎞

4

1Db

R------+ 0.25≥ ≥

treq

tbf

------- 1.8Db

R------ 1–⎝ ⎠⎛ ⎞

4

1Db

R------+ 0.25≥ ≥

Figure 16. Relationship of diaphragm rigidity capacityratio versus strength ratio.

Figure 17. Relationship of Db/R versus treq/td.

Figure 18. Comparison between treq/td and Eq. (10).


2 - design of structure (part of bridge)

Hwang W.S., Kim Y.P. and Park Y.M. (2004), “Evaluation of

Shear Lag Parameters for Beam-to-Column Connections

in Steel Piers”, Structural Engineering and Mechanics,

Vol. 17, No. 5, pp. 691-706.

Korea Highway Transportation Association (2005), Korea

Highway Bridge Design Code.

Kim, Y. P., Choi, W. K., Hwang, M. O., and Hwang, W.

S.(2002), “Experiment of circular column-box beam

connections in steel piers”, KSCE, Vol. 22, No. 2-A, pp.

403-412 (in Korean).

Lee, S. J. and Lu, L.W. (1989), “Cyclic Tests of Full Scale

Composite Joint Sub-Assemblages”, Journal of

Structural Engineering, ASCE, 115(8), pp. 1977-1998.

Meichi Highway Corporation (1984), Design standard of

steel structure.

Nishimura, N., Ikeuchi, T., and Taniguchi, N. (1998)

“Numerical Simulation on Damage to Pipe Piers in

Hyogoken-Nanbu Earthquake”, Engineering Structures,

Vol. 20, No. 4-6, pp. 291-299.

Nakai, H., Miki, T. and Hashimoto, Y. (1992), “On limit

state design method considering shear lag phenomenon of

corner parts of steel rigid frames”, JSCE, 455, 95-104 (in

Japanese).

Okumura, T. and Ishizawa, N. (1968), “The design of knee

joints for rigid steel frames with thin walled section”,

JSCE, 153, 1-17 (in Japanese).

Ugural, A.C. and Fenster, S.K. (1995), Advanced Strength

and Applied Elasticity Third Edition, PTR.

Qi, W. B. and Mimura, H. (2002), “Welded Beam-Column

Connection SCGO Design and Evalution”, International

Journal of Steel Structures, Vol. 2, No. 2, pp. 87-93.

Symbols

Stresses

fo: external fiber normal stress

fi: internal fiber normal stress

v: shear stress

Forces

Tϕ: axial force in any point.

Mϕ: bending moment in any point.

Qϕ: shear force in any point.

To: indeterminate axial force

Mo: indeterminate bending moment

Structural dimension

br: reinforcing rib width

Dd: diaphragm web depth

dd: net diaphragm web depth

td: diaphragm web thickness

tc: circular column thickness

tr: diaphragm rib thickness

tr: diaphragm rib thickness

R: radius of circular column

R': distance between axis of circular column and

neutral axis of diaphragm

Ro: external radius of circular column

Sectional property

b3: effective width of circular column (=td+1.56 )

r: distance between the central axis of circular

column and neutral axis of curved girder

(=Ar/[brln(d/a)+tdln(g/d)+b3ln(j/g)])

Ar: sectional area of diaphragm (=brtr+tddd+b3tc)

Ad: sectional area of diaphragm web (=tddd)

e: eccentricity (=R'−r)

k: non-dimensional variable considering shear lag

stress (=(2fi1−fs1)/(2fi1))

λ: ratio of j and R' (=R/R'=j/R')

Id: moment inertia of connection diaphragm for the

central axis of circular column. Where, diaphragm

has not manhole like test specimen.

I: moment inertia of connection diaphragm for the

central axis of circular column. Where, manhole is

installed in diaphragm. Reinforcing rib is neglected

in calculation of moment inertia)

Rtc

evaluation of diaphragm effect for steel welded box beam and …c).pdf · 2018-01-08 · evaluation...

Documents