estimation method of load-carrying capacity of heavily ... · estimation method of load-carrying...

Estimation Method of Load-Carrying Capacity of Heavily Confined RC Column Considering

Core Concrete Strength under Triaxial Compression

－1－

Estimation Method of Load-Carrying Capacity of Heavily Confined

RC Column Considering Core Concrete Strength under Triaxial

Compression

Shizuka IZAWA*, Makiko TAKANO*, Tadashi ABE**, Tetsukazu KIDA**,

Kiyoshi KATO***, Makoto SUDO**** and Kazuhiko MINAKUCHI**

( Received July 18, 2003 )

Abstract

The authors have already clarified that the upper-bound load-carrying capacity of RC column considering

the buckling of the primary rebar without the lateral confinement is rational both theoretically and experi-

mentally in the basical design concept, and the trinity among the load-carrying capacity, the pitch spacingand the design yield strength of primary rebar has been developed for the first time. This paper deals with the

main, important items as follows:

① The effect of the lateral pressure of core concrete of the RC column on the buckling 1oad of primary

rebar.

② The analysis of the load-carrying capacity of only hollow reinforcement cage.③ Formularizing the load-carrying capacity of confined column considering the buckling of primary

rebar and the triaxial strength of core concrete.

Keyword: Column, Load-carrying capacity, Primary rebar, Buckling, Lateral confinement

ISSN 0386-1678

Report of the Research Institute of Industrial Technology, Nihon University

Number 72, 2004

* Graduate Department of Industrial Technology, Nihon University

** Department of Civil Engineering, College of Industrial Technology, Nihon University

*** University Research Center, Nihon University

**** ingérosec Corporation

1. Introduction

The damages of concrete structures due to the great

earthquakes are the worldwide problem. The honest

researches have been continued and the present authors

also have carried out the fundamental study1) from the

viewpoint of the structural material and the structural

member. Especially, it was clarified quantitatively that

the decrease of the tie bar spacing and the usage of the

higher yield strength primary rebar of the RC column

resulted in its high load-carrying capacity. On the other

hand, the Standard Specification2) ignores the lateral

confinement by tie bars concerning the compressive

load-carrying capacity. To put the design yield strength

Shizuka IZAWA, Makiko TAKANO, Tadashi ABE, Tetsukazu KIDA, Kiyoshi KATO,

Makoto SUDO and Kazuhiko MINAKUCHI

－2－

of primary rebar to a valid use, it also adopts the ser-

viceable limit state designing value of concrete for the

load-sharing capacity. Thus the upper-bound load-car-

rying capacity of RC column has been obtained by

them. Nevertheless, the compressive load-carrying ca-

pacity approaches a definite asymptote according to

enlarging the tie bar spacing1). Therefore, it is rational

to determine the asymptote as the upper-bound com-

pressive load-carrying capacity inherent in the RC col-

umn.

This paper describes mainly the following practical

problems: ① the existence of the effect of the lateral

pressure of core concrete of the RC column subject to

compression on the buckling load of primary rebar, ②the analysis of the load-sharing capacity by virtue of

the reinforcement cage itself, and ③ the general new

formulation of load-carrying capacity of confined RC

column considering the buckling of primary rebar and

the triaxial compressive strength of core concrete.

2. Status quo of upper-bound equation of designload-carrying capacity

2.1. Constitutive Relation

In general when the compression test of the RC col-

umn model, it is an experienced fact that the effect of

primary rebars does not appear remarkably. This rea-

son can be said because of depending on the perfor-

mance that the primary rebars do not show the simple

compressive strength perfectly but those result in the

elastic failure due to those buckling1). Figure 1 illus-

trating a damaged highway bridge pier when Great Han-

Shin Earthquake Disaster in Japan (1995), may mean

a phenomenal fact that the earthquake load was not only

too large but also the load-carrying capacity was too

small beyond estimation. Figure 2 expresses the sim-

plified buckling model of the reinforcement cage post

the spall-off of cover concrete of the bridge pier as

shown in Fig. 1.

The load-carrying capacity considering the buckling

of primary rebars depends on the buckling load given

by function of their slenderness ratio. The slenderness

ratio λ is denoted by Eq.(1).

λ =ℓ /(φ /4) (1)

where,ℓ and φ are the length and the diameter of

the primary rebar, respectively.

When both ends of rebar are pin-connections, the

critical slenderness ratio Λ and the buckling stress σs

by the Rankine’s equation3) are given by Eq. (2) and

Eq. (3), respectively.

Λ = (π2Es / f’yd)1/2 (2)

σs = f ’yd/[1+ f’ydλ2/(π2Es)] (3)

where, f ’yd and Es are the design yield strength and

the elastic modulus of the primary rebar, respectively.

Therefore, the upper-bound load-carrying capacity

Fig. 1. A failure mode of damaged bridge pier. Fig. 2. Buckling model of primary rebar.



－3－

N’oub considering the buckling effect, basically, can be

obtain by Eq. (4).

N’oub = Ae f ’c + Asσs (4)

where, Ae and f’c are the core area and the compres-

sive strength, respectively. As is the cross-sectional area

of rebars.

In the practical design, the factor of strength: 0.85,

and (the analytical factor of structure) × (the load fac-

tor) × (the factor of structure): 1.44, etc, should be con-

sidered.

2.2. Load-Carrying Capacity Considering LateralConfinement

It is understood that the “double spacings”, 2s, be-

tween tie bars correspond to the buckling length of fi-

nite elemental primary rebar as supposed from the phe-

nomenal viewpoints of the small size type column

model1) and also the bridge pier model4). Thus the load-

carrying capacity of confined RC column not exceed-

ing the critical pitch spacings2) can be evaluated by

Eq.(3) by virtue of using the “double spacings” as the

hypothetical buckling length of primary rebar, that is,

ℓ≡ 2s. The previous report5) has already revealed that

the “double pitch method” fairly well agrees with the

experimental values as to both the SBPD type rebar

and the SD type one, and on the other hand, the

Mander’s method6) is 1.4 to 1.6 times larger than the

experimental ones as to them; moreover, there is a ten-

dency to coincide with each other according to the ex-

pansion of pitch spacing and they ultimately result in

conversing to the upper-bound load-carrying capacity.

However, the improved equation more accurately ca-

pable of estimating the load-carrying capacity of con-

fined RC column is desired.

3. New load-carrying capacity equation includingfactor of triaxial compressive strength of concrete

3.1. Experimental Verification

3.1.1. Preparation of RC column

D13(φ =12.7mm; SD type below 785N/mm2 of the

design yield strength, f ’yd =333N/mm2) and U13(φ

=13.1mm; SBPD type over 785N/mm2 of the one, f ’yd

=1424N/mm2) for the primary rebars, and U6.4(SBPD

type, 785N/mm2 of the one, f ’yd =1446N/mm2) for the

tie bar were used for preparation of the reinforcement

cages. The specimen size of the column model and the

core size were 150 × 150 × 530mm and 120 × 120mm,

respectively. The nominal pitch spacings were seven

kinds of 25mm, 50mm, 75mm, 125mm, 170mm, 250

mm, and 500mm. Figure 3 represents the examples of

hollow reinforcement cages. The average compressive

strength of the structural concrete with the maximum

size of aggregate of 10mm was f ’c =64N/mm2 under

the 28 days underwater curing. The procedure placing

s=25 s=50 s=75 s=125 s=170 s=250 s=500Fig. 3. Examples of hollow reinforcement cage [s:mm].



－4－

concrete is first to fill up it into the reinforcement cages,

secondly to set down the filled cage into the mould for

flexure, thirdly to pour the screened mortar into the part

of covering and lastly enough to compact the whole in

a body by the vibrator. The compression test was car-

ried out by use of the 5000kN universal type testing

machine.

3.1.2. Buckling mode and load-carrying capacityof hollow reinforcement cage

(1)General buckling mode of hollow reinforcement

cage

Figures 4 and 5 exhibit the buckling modes in cages

of the SD type primary rebar and the SBPD type one,

respectively. In general, the macroscopical deformation

of hollow reinforcement cages develops a tendency to

the first-order type buckling pattern as a whole when

the pitch spacings are more dense but the primary rebars

independently are apt to buckle separately when they

are sparse.

(2)Load-sharing capacity of single hollow reinforce-

ment cage

Equation(5) signifies the relationship between the

any load-carrying capacity ratio of hollow reinforce-

ment cage to the theoretical one and the any pitch spac-

ing ratio to the minimum lateral size 200mm for the tie

bar column2), inclusively in spite of the quality differ-

ence of the SD and SBPD types. But the load-carrying

capacity ratio characteristically is structure-insensitive

to the pitch spacing ratio. These relation, also, can be

expressed by Eq. (5), as the function of the natural loga-

s=25 s=50 s=75 s=125 s=170 s=250 s=500Fig. 4. Buckling modes of hollow reinforcement cages when SD type [s:mm].

s=25 s=50 s=75 s=125 s=170 s=250 s=500Fig. 5. Buckling modes of hollow reinforcement cages when SBPD type [s:mm].



－5－

rithm, LN.

β = 1.397 – 0.075 4LN(s/Do) (5)

where, β is N’ous /TN’ous , N’ou is any compressive

load-carrying capacity of only reinforcement cage,

TN’ous is the theoretical one considering the first-order

buckling of primary rebars with both ends of pin-con-

nections, s is the pitch spacing and Do is the minimum

width size of tie bar column.

3.1.3. Failure mode and load-carrying capacity ofconfined RC column model

(1)Failure mode of column model

Figures 6 and 7 show the failure modes in each pitch

spacing for the SD type primary rebar and for the SBPD

type one, respectively. In general, the spall-off of cov-

ering concrete is distinguished severely and the effec-

tive cross-sectional area happens to suffer a deeper loss

with increase of the pitch spacing as reported previ-

ously7). Especially, a large attention must be paid to

the fact that the buckling primary rebar is not in con-

tact with the core concrete at the mid-spacing above

the pitch spacing of 170mm and therefore the confin-

ing lateral pressure by virtue of tie bars unquestion-

ably seems not to function effectively. The individual

characteristics as above-mentioned are classified into

the three deformation categories as follows:

25mm s < 50mm ••••• “Most ductile”

50mm s < 125mm ••••• “Moderately ductile”

125mm s 500mm ••••• “Brittle”

(250mm s 500mm ••••• “Especially most brittle”)

s=25 s=50 s=75 s=125 s=170 s=250 s=500Fig. 6. Failure modes of SD type column [s:mm].

s=25 s=50 s=75 s=125 s=170 s=250 s=500Fig. 7. Failure modes of SBPD type column [s:mm].



－6－

3.1.4. Comparison of load-carrying capacity of RCcolumn model with that of hollow reinforcementcage

The load-carrying capacity of hollow reinforcement

cage is plotted in Fig. 9, together; so, it is no more than

av. 8.3% for the SBPD type and 6.6% for the SD type

of the RC column models. Therefore, the fact has been

found out for the first time that there is hardly the

confinement effect to the primary rebars of single

reinforcement cage, without regard for the difference

between their qualities. Thus, the relationship between

the load-carrying capacities of hol1ow reinforcement

cages for both the SBPD type primary rebar and the

SD type one and the tie bar spacing had better be dealt

with macroscopically due to the statistical treatment;

so, the inclusive expression by virtue of using Eq. (5)

may be evaluated to be effective enough.

Ultimately, the whole column model so confined

more densely results in developing into the first order

buckling as exhibited in Fig. 8, although the elemental

primary rebar apparently looks to buckle up between

the tie bars.

(2)Relation between load-carrying capacity and tie bars-

spacing

Figure 9 displays the relationship between the load-

carrying capacity and the tie bars-spacing. The load-

carrying capacity increases with decrease of the pitch

spacing; in addition this tendency is eminent over the

range of heavy confinement. Strengthening the primary

rebar links up with the higher load-carrying capacity

due to accompanying the appropriate lateral confine-

ment by virtue of the “1attice effect” of both the pri-

mary rebars and the tie bars7). Similarly as the previ-

ous report1), the load-carrying capacity gradually ap-

proaches “an asymptote,” that is, the “upper-bound one”

in spite of the difference in quality of primary rebars

of RC column; so, such an experimental fact indicates

that the critical loads for the different materials are equal

because the buckling load is independent on the strength

of materials, if the size and the elastic modulus of col-

umns are identical. When the pitch spacing widens

beyond 300mm, the lateral confinement displays no

longer its distinguished effect, and both curves for the

SD type and the SBPD type approach the upper-bound

load-carrying capacity given by Eqs. (3) and (4), as a

fundamental design equation for the tied column.

SBPD type

[In case of confined RC column model, N’ou]

[In case of hollow reinforcement cage, N’ou]

Pitch spacing, s(mm)

SD type

SBPD typeSD type

Loa

d-ca

rryi

ng c

apac

ity (

kN)

3000

2800

2600

2400

2200

2000

1800

1600

1400

1200

1000

800

600

400

200

00 100 200 300 400 500

Fig. 9. Relationship between load-carrying capacityand pitch spacing.

Fig. 8. First-order buckling of heavily confined RCcolumn.



－7－

3.1.5. Analysis concerning influence of lateralpressure on buckling of primary rebar

The internal pressure due to the Poisson’s effect of

core concrete must be certified concerning the influence

on the buckling of primary rebar of the RC column.

(1)When without lateral pressure

Figure 10 (a) displays the schematic diagram of the

buckling of primary rebar without the internally lateral

pressure; therefore, it may result in a buckling phenom-

enon due to only the axial force P. The first-order buck-

ling load Pk can be obtained as follows.

M = py

d2y/dx2 + η2y = 0

where, η2 ≡ P/(EI), M is the flexural moment at any

point x, E is the elastic modulus of member, I is the

moment of inertia of its cross-section, y is the deflec-

tion at any point x, and ℓ is the length of member.

Thus, x = 0, y = 0; x = ℓ , y = 0; A ≠ 0

y = Asin ηx; sin ηℓ = 0

ηℓ = π; so, Pk = π2 EI/ℓ 2 (8)

(2)When with lateral pressure

Figure 10 (b) illustrates the schematic diagram of

the buckling of primary rebar with the internally 1ateral

pressure q; accordingly, the supporting reaction qℓ/2

is cumulated on the loading system of Fig. 10 (a). The

first-order buckling load Pk can be expressed as

follows8).

M = Py + qℓ x/2–q x2/2

d2y/dx2 + η2y + qx(ℓ –x)/(2EI) = 0

where, η2 ≡ P/(EI).

Thus, the general solution can be given as follows.

y = C1cos ηx + C2sinηx + q/(2EIη2)•(x2–ℓ x–2/η2)

where, C1 and C2 are the integral constants.

Here, x = 0, y = 0; x = ℓ , y = 0

Then, y = q/(EIη4)•(cos ηx + tan ηℓ /2•sin ηx)•q/

(2EIη2)•(x2–ℓ x–2/η2) (9)

Then, the buckling condition of Eq. (9) is assumed as

follows.

tan ηℓ /2 = ± ∞, y = ∞

In case of the first-order buckling,

ηℓ /2 = π/2; so, Pk = π2 EI/ℓ2 (10)

(3)Existence for influence of lateral pressure on buck-

ling

It can be said analytically that the uniform lateral

pressure gives no influence on the buckling load, be-

cause Eq. (10) agrees with Eq. (8).

3.2. Load-Carrying Capacity of RC ColumnConsidering Triaxial Strength of CoreConcrete

3.2.1. Apparent confined compressive strength ofcore concrete

Figure 11 plots the relationship between the appar-

ent confined compressive strength of core concrete and

ll

P P

P

x

y y

x

Pqr/2

qr/2

q

(a) Without lateral stress (b) With lateral stress

Fig. 10. Analytical buckling of primary rebar.Fig. 11. Relationship between confined core concrete

strength ratio and pitch spacing.

01.0

1.5

2.0

2.5

3.0

100(0.5)

200(1.0)

300(1.5)

400(2.0)

500(2.5)

App

aren

t con

fine

d co

re c

oncr

ete

stre

ngth

ra

tio, α

= ƒ

’ cc/ƒ

’ c

Pitch spacing, s(s/Do) [Do =200mm]

SBPD typeSD typeAverage



－8－

the pitch spacing ratio s/Do of confined RC column;

moreover it is understood that the confined concrete

strength stands higher as the confinement is heavier and

the relation between both the factors does not more

strongly depend on the strength of primary rebar, there-

fore, their average being to be adopted. The apparent

confined compressive strength ratio α can be defined

as follows.

α = f ’cc /f ’c (11)

where, f ’cc is the apparent confined compressive

strength of core concrete, and f ’c is the simple com-

pressive strength of structural concrete.

[EX.1] When the structural concrete strength f ’c =

30Nmm2 and the pitch spacing s =100mm (s /Do =100

/200 = 0.5), the apparent confined compressive strength

f ’cc = ?

Solution: α = f ’cc /f ’c = 1.75 from Fig. 11;

so, f ’cc = αf ’c = 1.75 × 30 = 53N/mm2

Then, an example9) of the confined strength f ’cc of

concrete9), 10) obtained by the triaxial compression test,

consisting of the function of the lateral pressure f ’ℓ has

been already given by Fig. 12.

[EX.2] When the apparent confined compressive

strength ratio α = 1.75 and the structural concrete

strength f ’c = 30N/mm2, the lateral pressure f ’ℓ = ?

Solution: The lateral pressure ratio ξ= f’ℓ / f’c = 0.2 for

α =1.75 in Fig. 12;

so, f ’ℓ = ξ f ’c = 0.2 × 30 = 6.0N/mm2

The relationship between the lateral pressure ratio ξ

and the pitch spacing from Figs. 11 and 12 can be ex-

pressed by Fig. 13 and also by Eq. 12 as follows;

ξ ≡ f ’ℓ/ f ’c = 0.179 – 0.061LN(s/Do)(γ = –0.906)

(12)

It may safety be said that the lateral pressure at the

ultimate load-carrying capacity of RC column confined

by the tie bars with the pitch spacings from 50mm to

250mm results from approx. 20% of the simple com-

pressive strength of structural concrete. The phenom-

enal fact like this means that (a) the lateral pressure in

detail increases gradually with strengthening concrete

and (b) the confined concrete strength increases with

reducing the pitch spacings in spite of the same con-

crete strength.

3.2.2. Formulation or load-carrying capacity of RCcolumn considering stress-sharing capacity

(1)Formulation

The load-carrying capacity of confined RC column

on the basis of the above-mentioned consideration can

be formulated as follows, considering the stress-shar-

ing capacities of the constituent materials.

Referring to Eqs. (4), (5) and (11);

N’ou = N’ouc + N’ous

= α • f ’cAe + β • T N’ous (13)

where, N’ouc and T N’ous are the load-carrying capac-

ity of core concrete and the theoretical buckling load

of reinforcement cage, respectively, and α, f ’e, Ae, and

β are as above-mentioned.

(2)Confirmation of rationality

Table 1 signifies the comparison between the ex-Fig. 12. Relationship between confined strength and

lateral pressure.

Fig. 13. Relationship between lateral pressure andpitch spacing.



－9－

perimental load-carrying capacity N’ou and the theo-

retical one T N’ous of confined RC column as to the

data base of paragraphs 3.1.1 to 3.1.3. It has been clari-

fied that the proposed method is very eminent to esti-

mate the load-carrying capacity of RC column because

the incremental relative ratio is smaller than one per-

cent and the coefficient of variation is approx. two per-

cent , too, from Table 1.

SBPD type SD type

N’ou TN’ou N’ou N’ou TN’ou N’ou

(kN) (kN) TN’ou (kN) (kN) TN’ou

25 2600 2612 0.995 1920 1937 0.991

50 2100 2053 1.023 1840 1767 1.041

75 1900 1914 0.993 1670 1701 0.982

125 1870 1816 1.030 1620 1650 0.982

170 1690 1721 0.982 1540 1611 0.956

250 1670 1672 0.999 1580 1600 0.988

500 1580 1583 0.998 1570 1558 1.008

Av. 1.003 Av. 0.993

C.V. 1.72% C.V. 2.66%

Total Av. 0.998, C.V. 2.20%

Pitch

spacing

(mm)

4. Conclusions

From the new viewpoint of materials science with

regard to the stress-sharing capacities of constituent

materials in the confined RC column, the present pa-

per has formulated its compressive load-carrying ca-

pacity taking in the triaxial strength of core concrete

and verified the validity of constitutive equation; then,

the obtained results are as follows.

(1) The usual upper-bound equation for compressive

load-carrying capacity of the RC column is at-

tended with danger because it gives the excessive

one in general; so, the rational equation consider-

ing the buckling of primary rebar including “the

double pitch spacing method” has been already

proposed by the present authors.

(2) The more accurate estimation method from the

view-point of the materials science has been de-

veloped by virtue of taking in the triaxial strength

of core concrete of confined RC column.

(3) The hollow reinforcement cage in spite of the qual-

ity of rebars develops a tendency to the first-order

type buckling as a whole.

(4) Although the load-carrying capacity ratio β is fairly

structure-insensitive to the pitch spacing ratio s/

Do, these relative equation can be given as follows;

β = 1.397 – 0.0754LN( s/Do)

(5) The failure modes of confined RC column are clas-

sified into the three deformation categories of

“most ductile,” “moderately ductile” and “brittle”

including “especially most brittle” as the function

of the pitch spacing.

(6) Strengthening the primary rebar links up with the

higher load-carrying capacity due to accompany-

ing the enough confinement by virtue of “the lat-

tice effect.”

(7) The lateral confinement displays no longer the

distinguished effect, with the pitch spacing above

300mm.

(8) The load-sharing capacity of hollow reinforcement

cage as a simple substance is no more than approx.

8% of the load-carrying capacity of confined RC

column without regard to the kinds of primary rebar

types; therefore, the inclusive expression by Eq. (5)

becomes effective for evaluation.

(9) Speaking analytically, the uniform lateral pressure

due to the expansion of core concrete has no in-

fluence on the buckling load of primary rebars.

(10) The relationship between the confined compres-

sive strength ratio α = f ’cc/ f ’c of core concrete

and the pitch spacing ratio has been clarified.

(11) The relationship between the lateral pressure and

the pitch spacing has been obtained quantitatively;

in addition, macroscopically the former results

from approx. 20% of the simple compressive

strength of structural concrete.

(12) The load-carrying capacity N’ou of confined RC

column can be formulated as follows, consider-

ing the triaxial strength of its core and the theo-

retical load-sharing TN’ous of hollow reinforcement

cage:

N’ou = α • f’c Ae + β • TN’ous

(13) It has been confined that the proposed method

agrees well with the experimental load-carrying

capacity of confined RC column.

Table 1. Comparison between experimental and theoreti-cal load-carrying capacities of confined RCcolumn (T: Theoretical)



－10－

References

1. M. Sudo, T. Kida, K. Kato, T. Abe, I. Kuroda, and

N. Kato, “Upper-Bound Equation of Compressive

Load-Carrying Capacity of RC Column Consider-

ing Characteristic of Material and Buckling of Pri-

mary Reinforcement,” Mater. Sci. Res. Int., 7,2

(2001), 96-102.

2. JSCE Concrete Committee, “Standard Specifica-

tion of Concrete” [Design], (2000).

3. S. Higuchi, “Elasticity and Material Mechanics,”

(Yokendo, 1966), 112.

4. K. Kamisawa, “Experiment Liable for Bridge”, Con-

crete Engineering, 39, 9(2001), 78-83.

5. M. Sudo, T. Kida, K. Kato, K. Minakuchi, T. Abe,

N. Kato and T. Kamisawa, “Load-Carrying Capac-

ity of Laterally Confined RC Column Considering

Buckling of Primary Rebar,” Theor. and Appl. Mech.,

50(2001), 115-123.

6. J.B.Mander, M.J.N. Priestly, and R. Park, “Theo-

retical Stress-Strain Model for Confined Concrete,”

Jour. Struc. Eng., 114, 8(1998), 1804-1826.

7. K. Kato, N. Kato, and N. Iwasaka, “Improvement of

Loading Capacity of RC Column Confined by Heavy

Reinforcement,” Proc. 38th Japan Cong. Mat. Res.,

(1995), 272-279.

8. M. Sudo, T. Kida, K. Kato, K. Minakuchi, T. Abe,

and N. Kato, “Load-Carrying Capacity of Laterally

Confined RC Column with High-Strength Primary

Rebars,” 51st Nat. Cong. of Theor, and Appl, Mech.,

(2002), 253-254.

9. Z. Tokumitsu, H. Matsushita and S. Yamamoto,

“Concrete Strength under Triaxial Stress,” Cement

and Concrete, 39(1973), 21-25.

10. A. M. Nevile, “Properites of Concrete,” (Pitman,

1963).



－11－

三軸圧縮状態下のコア・コンクリート強度を考慮した

重拘束RC柱の耐力推定に関する研究

伊澤閑，高野真希子，阿部忠，木田哲量，加藤清志，須藤誠，水口和彦

概　　要

1999年だけでも，コロンビア，トルコ，ギリシア，台湾，メキシコなどの大地震，ベネズエラの大洪水等によるコンクリート構造物の被害は世界的な課題である。よって，多くの真摯な研究が続けられており，筆者らも構造材料および構造材の視点から基礎的研究を行ってきた。とくに，RC柱の帯鉄筋間隔の縮小および高強度主筋の活用は，その高耐力化に直接的に連係することを明らかにした。一方，標準示方書では，RC柱の上方限界耐力式に関し，帯鉄筋による横拘束効果を無視しており，また，コンクリートに使用限界状態設計用値を，主筋には設計降伏強度を使用し，設計用値に関し基本コンセプトに整合性がない。しかし，圧縮耐力は帯鉄筋間隔の増大とともにある一定の漸近値に近づく。それゆえ，RC柱に固有の上方圧縮耐力としての漸近値を決定することは合理的である。本論文は次の実用的な問題を論じている。①圧縮載荷状態のRC柱のコア･コンクリートの側圧が主

筋の座屈荷重に及ぼす影響の存在，②鉄筋かご自体の荷重分担能の解析，③主筋の座屈およびコア･コ

ンクリートの三軸圧縮強度を考慮した拘束RC柱耐力の一般式の定式化。



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Biographical Sketches of the Authors

Shizuka Izawa majors in the doctor course of Graduate School of Industrial Technol-

ogy, Nihon University. He was born in Tokyo, Japan, on October 7, 1949. He received

his degrees of B. Eng. in 1972 and M. Eng. in 1974 from Nihon University, Tokyo. He

is a member of Japan Society of Civil Engineers (JSCE), having reported some practi-

cal papers. He is an active engineer in the field of Prestressed Concrete Structure.

Miss Makiko Takano graduated from Department of Civil Engineering, College of

Industrial Technology in 1999, and obtained her degree of M. Eng. in 2002, from Nihon

University. She majors now in the formularization of concrete shear strength and the

structural concrete engineering in the doctor course of Industrial Technology, Nihon

University, being a student member of JSCE, Japan Concrete Institute (JCI) and the

Japan Society of Materials Science (JSMS), having already reported leading papers on

the shear strength of concrete and the RC structure.

Tadashi Abe is Associate Professor of College of Industrial Technology, Nihon Uni-

versity. He was born in Iwate, Japan, on May 23, 1948. He received his degree of B.

Eng. from Nihon University, Japan, in 1972. He is engaged in the study of Structural

Mechanics, Structural Concrete Engineering and Bridge Engineering. He is a member

of JSCE, JSMS and JCI, having reported many technical papers in the fields of the

impact problem and the carbon fiber sheet-reinforced slab under the running load.

Tetsukazu Kida is Professor of College of Industrial Technology, Nihon University.

He was born in Hokkaido, Japan on July 3, 1942. He received his degrees of B. Eng. in

1967, M. Eng. in 1969 and Dr. Eng. in 1989 from Nihon University, Japan. He majors

in the study of Structural Mechanics, Structural Concrete Engineering and Bridge Engi-

neering, having reported many technical papers. He is a member of JSCE, Prestressed

Concrete Engineering Association (PCEA) and JCI. He has been Dean of Dept. of Civil

Eng., College of Industrial Tech., Nihon Univ., for many years.

Kiyoshi Kato is Professor of University Research Center, Nihon University and Emeri-

tus Professor of National Defense Academy, since 2000. He graduated from Depart-

ment of Civil Engineering, Faculty of Technology, Hokkaido University, 1958, and af-

ter that had achieved Research Associate, Assistant Professor, Associate Professor and

Professor till May 2000. The degree of Dr. Eng. was conferred to him by Hokkaido

University, 1973. One of the many social activities was an appraiser of the Shizuoka

court and also he is the author of many academic and technical papers and books. He

majors in the physical property of structural concrete and the concrete structure, being a

member of JSCE, JCI and so on.



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Makoto Sudo is Vice President of ingérosec Corporation. He was born in Tokyo,

Japan on January 1, 1945. He received his degrees of B. Eng. in 1967, M. Eng. in 1969

and Dr. Eng. in 2002 from Nihon University. He has the licenses of Consulting Engi-

neer, Architect and APEC Engineer. He has reported many practical and academic pa-

pers on the most leading design and construction technologies in the field of Prestressed

Concrete Engineering, now consulting the RC bridge and PC structures over the world.

He is a member of JSCE, Federation International du Beton (fib) and International As-

sociation for Bridge and Structural Engineering (IABSE).

Kazuhiko Minakuchi is a research fellow of College of Industrial Technology, Nihon

University. He was born in Ehime, Japan on July 23, 1974. He received his degrees of

B. Eng. in 1998, M. Eng. in 2000 and Dr. Eng. in 2003 from Nihon University. He has

interest in strengthening techniques and the seismic design. He is a member of JSCE,

JSMS and JCI, has already reported several valuable technical papers on repairing meth-

ods for the concrete column in the field of Structural Mechanics.

The List of the Cumulative Contents of Report of the Research Institute of Industrial Technology, NihonUniversity Recently Published.

No.62, February, 2000Y. Fujiya: The Study of KaoruYamada and Residential Area Development at Fuji Sanroku

No.63, March, 2001K. Nakazawa and T. Miyazaki: An Analysis of the Mingled Combination of Land Uses on the CoastalZone in TOKYO BAY Metropolitan Area for Its Complex Use

No.64, March, 2002M. Itamoto, H. Shiokawa and K. Miyauchi: Study on Airflow and Sound Characteristics of DoubleLined Elbows

No.65, July, 2002H. Tsunasima: Dinamic Analysis of Automated Guideway Transit Vehicle with Single-axle Bogies

No.66, March, 2003H. Tsunasima: A New Three-dimensional Image Processing Method for Limited Cone-Beam X-ray CTfor Dental Use

No. 67, April, 2003Ichiro Hirata, Tetsuo Matsuyama, Makoto Kanda and Eizo Maruta: New Hybrid Vibration Tech-nique for Simulating Aerodynamic Vibration of Structures in a Wind Tunnel

No. 68, July, 2003Takakimi Ohki and Makoto Imano: A Study on Slope protection by Grand Anchor for the ToukaiEarthquake

No. 69, September, 2003Goichi Ben and Akiko Shouji: Development of Pultrusion Technique of Phenolic Foam Composites

No. 70, December, 2003Noriaki Kimura: On universal higher order Bernoulli numbers and polynomials

No. 71, December, 2003Goroh Momoki, Isao Tonozuka and Takayuki Matsuzawa: Neutron-neutron interactions and mag-netic moments in light Sn isotopes

These publications are issued at irregular intervals.The authors alone are responsible for the contents of these reports.All communication relating to these reports should be addressed to

Research Institute of Industrial Technology, Nihon University.2-1 Izumi-cho 1-chome, Narashino-shi, Chiba, 275-8575, Japan

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