Calculation Method Investigation on Jacketing Reinforcement of RC Eccentric Compressive Column Subjected to Fire

Jinjun Guo1,a, Yan Lu1,b and Pingxian Li1,c

1School of Water Conservancy & Environment Engineering, Zhengzhou University, Zhengzhou, China

aguojinjun@zzu.edu.cn, bluyan@zzu.edu.cn, clipingxian@zzu.edu.cn

Keywords: fire；eccentric compressive column； jacketing reinforcement； the second loaded stage

Abstract. Based on eccentric compressive experiments of reinforced concrete column strengthened with jacketing method, the paper calculated and analyzed jacketing reinforcement of RC eccentric compressive column subjected to fire. The calculation procedure of residual load capacity of compressive member after fire was put forward according to temperature distribution at column section. To distinguish tensile or compressive failure of RC column, the formulas of relative balanced depth of compressive zone of jacketing section were deduced as well as the corresponding applied calculation method of norm section load capacity was presented under the second loaded stage. In addition, the reinforcement design and construction of one fire damaged building was conducted in terms of this paper’s method. The good running status of strengthened columns for many years validates the applicability of this method.

Introduction

Recent years strengthening and repairing technique of concrete structures subjected to various disasters has been focus in engineering. However, the little progress was obtained in theory compared to the engineering application resulting in the situation of theoretical study behind engineering applications. There exist many issues to be researched in reinforcement design. The main structural reinforcement methods in columns include enlarging section method, steel-enveloped method, bonding carbon fiber method, external prestressing method, suspending method and increasing supports method and enlarging section methods are widely used due to simple construction and low cost. The calculation method is relative rough in Chinese Standard GB50367-2006 and is difficult to truly reflect work performance of strengthened concrete members, which may overestimate bearing capacity of reinforced component unsafely [1].

The experimental studies on jacketing reinforcement of concrete columns were few and focused mainly on shear performance of generally strengthened columns domestic and overseas [2-4]. The jacketing reinforcement tests of fire damaged columns were not been reported, and literature [5] represented test and analysis of concrete column damaged by high temperature with one-side enlarging section reinforcement, which is different from jacketing reinforcement method. When structures subjected to fire, temperature difference increased rapidly between surface and interior of member, the non-uniform temperature field was formed resulting in a large temperature gradient, and strength of every point on section was damaged with varying degrees. Therefore, uneven and asymmetric performance on section of fire damaged column is different from general reinforced column. In order to assess bearing capacity of reinforced column damaged by fire accurately and offer technique supports to reinforcement design of compressive members, it is essential to launch studies on jacketing reinforcement calculate method of eccentric compressive columns subjected to fire.

Based on tests research results and calculation program, calculation procedure of residual load capacity of compressive member was put forward after fire, and formulas of relative balanced depth of compressive zone of jacketing section were deduced as well as the corresponding applied formula

of norm section load capacity was presented under the second loaded stage. In addition, the reinforcement of one building subjected to fire was designed and constructed in terms of this paper’s method.

Residual Bearing Capacity of Fire Damaged Concrete Column

In general, majority of building columns are surrounded by fire in fire disaster, which is suitable for jacketing reinforcement method. The residual bearing capacity of fire damaged concrete column is governed by fire hours and ultimate temperature experienced at every point of section. The usual treatment method assumes material strength unchanged and only reduces the section area [6]. This method requires referring relative forms and complex calculation with poor accuracy, which can not truly reflect the loss of material strength.

The paper calculated the residual bearing capacity according to the temperature distribution in concrete column section [7]. For simplification, reduction factor of concrete strength was defined as follows.

cu

Tcu,Tc, f

fK = (1)

Where, Kc,T is reduction factor of concrete strength; fcu,T is cooling compressive strength of concrete suffered high temperature T; fcu is ambient compressive strength of concrete.

Similarly, reduction factor of concrete elastic modulus and steel tensile strength is denoted as Ec,T and Ks,T respectively.

To calculate residual bearing capacity of fire damaged member, the paper assumes areas of concrete and steel section unchanged and reduces its strength.

For concrete, the compressive zone is studied and tensile effect is ignored in norm section load capacity calculation. Firstly concrete compression zone is divided into m×n regular grid along two directions, and the area of each grid is hbA Δ×Δ=Δ . Where, mbb =Δ , nxh =Δ , and x is depth of compression zone. According to temperature distribution and moment balance of section, the depth of compression zone and reduction factor Kc,ij of any grid can be obtained. So the transforming reduction factor Kc,T of overall concrete compression zone is able to be determined.

),,2,1 ;,,2,1( 1 1ijc,

Tc, njmimn

KK

m

i

n

j LL ===∑∑= = （2）

Where, Kc,ij is reduction factor of concrete strength in any grid. The calculation results show that it is appropriate to take the value of ⊿b and ⊿h as 5mm～10mm.

For reinforcement bar, the reduction factor Ks,T of steel strength can be calculated in terms of the temperature at bar position in section [7].

yfKf Ts,Ty, = （3）

Where, fy,T is yield strength of reinforcement bar experienced high temperature T (MPa).

The ultimate compressive strain of concrete can be taken as 0.0033 after high temperature [5]. The relative balanced depth of compression zone of concrete eccentric compression column damaged by fire can be determined as follows.

)0033.0(18.0

Ts,Ty,Tb, Ef+=ξ （4）

So the residual load capacity of fire damaged column can be calculated in terms of related code.

Mechanical Calculation and Analysis for Jacketing Reinforcement of Fire Damaged Eccentric Compression Column

Mechanical Properties of Reinforced Compressive Member. Jacketing reinforcement columns generally belong to second loaded structures, which indicate that original structures keep bearing a certain amount external forces such as dead load, partial live load and construction load during reinforcement process, and then new and old structures start to support service stage load together when design strength of new poured concrete is reached. Clearly, the ultimate bearing capacity of reinforced structure is not a simple superposition of old and new part. There exist preceding phenomenon of bar stress in original column and delaying effect of compressive strain in jacketing concrete. The first loaded level index β governs these effects. The greater β is, the remarkable these effects are. When β is less or equal to 0.75, jacketing concrete and bar can reach its ultimate strength respectively at failure stage [2]. Calculation Hypothesis. (1) Plane hypothesis; (2) Tensile function of concrete is ignored; (3) Bond of new and old concrete is reliable [2,3,8]; (4) The stress resulted from shrinkage and temperature effect of jacketing concrete is ignored and taken as zero before second loaded stage; (5) Stress-strain relationship of fire damaged concrete refers to literature [9]; (6) Stress-strain relationship of bar in fire damaged concrete is taken as ideal elastic plastic model. Yield strength of damaged bar is determined in terms of reduction factor. Calculation Analysis of Second Loaded Stage. Jacketing reinforcement sketch of eccentric compressive column is shown in Fig.1. The strains of concrete and bar in original column are obtained by means of section curvature calculation in first loaded stage. In order to make jacketing reinforced part take effects and avoid original concrete crushed prior to jacketing concrete, the reinforcement size should meet the following conditions.

original concrete

jacketing concrete

As1 A's1

A's2As2h1

b2b1bf

hf hf

h2

bf

as2 a's2

as1 a's1

Fig.1 Sketch of jacketing reinforcement

sy2cu

c1

20

f

Efhh

+>ε

ε （5）

Where, εc1 is concrete strain on the edge of compression zone at first loaded stage; fy2 is yield strength of bar in jacketing concrete; εcu is ultimate compressive strain; Es is elastic modulus of bar; h20=h2-as2，the meanings of symbols such as hf, h2, as2,et al see Fig.1.

For jacketing reinforced column satisfying the above condition, the relative balanced depth of compression zone are given under two balanced failures at the second loaded stage as follows.

(1) When jacketing compression concrete reaches its limit state, tensile bars in jacketing concrete at the same time.

φεεφεε

ξ

2mcu

s22my2b1

5.0)5.0(

1

8.0

hah

−+−++

+= (6)

Where, φ and is curvature and strain at axial position of section at the first loaded stage respectively.

mε

So the strain increment of remote side bar in original column is

)( cuy220

fy2s2 εεεε +−=

hh

（7）

Assuming the yielding strain of bar is equivalent approximately in original column and jacketing

concrete, namely εy1=εy2=εy，the remote side bars can arrive at yielding in original column if steel strains meet the following condition.

)( cuy20

fs1 εεε +≥

hh

（8）

Where εs1 is strain of remote side bars in original column at the first loaded stage.

(2) When jacketing compression concrete reaches its limit state, tensile bars in original column yield at the same time.

φεεεξ

2mcu

y1b2

5.01

8.0

h−++

= （9）

Therefore, When 20b1hx ξ≤ , remote side bars in jacketing concrete yield at failure and reinforced eccentric

compression member belong to tensile failure type. When 20b1hx ξ> , remote side bars in jacketing concrete don’t yield at failure and reinforced

eccentric compression member belong to compressive failure type. When )( f10b2 hhx +≤ ξ ，remote side bars in original column yield at failure. In limit state of the second loaded stage, compression zone concrete can reach its strength and

preceding phenomenon of steel stress eliminates in original column generally. The failure character of reinforced eccentric compression column under the second loaded stage is almost same as reinforced column with first loaded stage [2,3], which makes transforming section method available simplifying calculation. In terms of transforming principle, namely the value and applying position of resultant force remain unchanged, calculating formulas of norm section load capacity can be deduced.

Engineering Application

Project Introduction. A large mall is four storey reinforced concrete frame structure with an area of 17700 m2. Concrete of frame was designed as C30 and reinforcement bar was used as grade Ⅱbar (in Chinese Standard). The plane sketch of the second floor is shown in Fig. 2. At 20:00 on January 18, 2006, electrical spark in knit store caused a fire at the second floor. The fire started from area of grid A-C-5-7 and spread to the third and forth floor through courtyard and glass curtain wall rapidly. The fire was extinguished at about 22:30. The second floor was damaged seriously due to long fire time resulting in decorated layer dropping and concrete spalling.

64.8

7.2

E

7.2

1.85

A

2.4

1 2

7.2

7.2

B

C

7.2

42.1

D

7.2

3

7.2

4 5

7.2

G

F

5.5

7.8

7.2

6 7

7.2

9 1311

7.27.2

Fig.2 Sketch of the second floor plane (unit: m)

Considering project characteristics, site conditions, service surrounding and cost factor, jacketing reinforced method was selected and applied in columns strengthening. The calculation showed the residual load capacities of most of columns in the second floor were 70%~80% of original design capacity and reinforcement is essential. Reinforced Column Calculation. The paper took column 5-C as example to calculate its load capacity using jacketing reinforcement. Column 5-C: section size 500mm×600mm, C30 concrete, Grade barⅡ (fy=fy′=310N/mm2), 8Ф25 (symmetry), fire hour 2.5h. Reinforced column size 700mm×800mm，reinforced bar in jacketing concrete 8Ф12 (symmetry).

(1) Checking calculation of original design load capacity According to original design documents, the ultimate load capacity of column was calculated as

Nu=1841kN, Mu=545kN.m. (2) Residual load capacity of column The depth of compression zone was calculated as 270mm by program and corresponding reduction

factor Kc,T was 0.672. The temperature at corner bar was 720℃ and reduction factor of bar strength was 0.85. By formulas (4), ξb,T=0.595, ξ =0.482≤ξb,T. The load capacity of column can be calculated in terms of tensile failure type, namely Nu,T=1387kN, Mu,T=410kN.m,

%3.751841/1387uTu, ==NN . So, the residual load capacity of original column can not meet design requirements and the column

should be reinforced. (3) Load capacity of reinforced column The curvature of column section was 0.0024 by calculation under the first loaded stage, and strain

at section centre was 0.00014. So,

00058.021

1 −=−= φεεh

mc (10)

000764.0)2

( 11

1 =−+= φεε sms ah (11)

The formulas (5) is satisfied. Jacketing concrete fails under compression prior to original concrete in limit state. By means of program calculation, the depth of compression zone was 370mm and corresponding reduction factor of concrete strength was 0.742. From formulas (6) and (9), ξb1=0.494, ξb2 =0.586.

Therefore, reinforced column belongs to tensile failure type and remote side bar in original column can yield in limit state. According to simplification method, the load capacity of reinforced column is 3670kN, which is greater than original design 1841kN.

Reinforcement work of this project was completed in 2007. As major business center, the building has operated for four years with good structural performance.

Conclusions

(1) The paper researched calculation method of jacketing reinforced column subjected to fire under the second loaded stage. The calculation procedure of residual load capacity of compressive member was put forward after fire. Formulas of relative balanced depth of compressive zone of jacketing section were deduced as well as the corresponding applied calculation method of norm section load capacity was presented under the second loaded stage.

(2) According to calculation method proposed in this paper, reinforcement of one fire damaged building was designed and constructed. The calculation and engineering applications verified availability and applicability of formulas proposed in reinforcing fire damaged compressive members.

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