BEHAVIOUR OF BIAXIALLY LOADED SHORT

BEHAVIOUR OF BIAXIALLY LOADED SHORT COMPOSITE AND INTERNALLY REINFORCED CONCRETE COLUMNS

By Ahmed Abd El-Aziz Abd El-Hay El-Barbary Under the Supervision of

Dr.Wahba Wahba El-Tahan Associate Professor Structural Engineering Department Cairo University

Dr.Mahmoud Tharwat El-Mihilmy Associate Professor Structural Engineering Department Cairo University

Introduction General : Reinforced concrete columns are sometimes exposed to biaxial bending specially the corner column in flat slab building,in addition to great axial force such as high raise building. These loads increase the size of the cross section of column , which is not satisfied from architectal view. One of solutions to overcome the big size of cross section is to use composite columns, also it possible to use internal reinforced bars beside the outer bars, which placed at the outer perimeter. In this research an attempt has been made to study the behavior of composite or internally reinforced concrete short column subjected to axial compression force accompanied with biaxial bending.

Problem Statement: In this research an important question is need to have an answer. The question is : Under the same loads, eccentricities, material properties is the composite column are similar to the other type of columns with internally reinforced bars in behavior of different? So the inertia and area of steel section used in composite column are similar to those steel bars internally placed instead of steel section in concrete cross section.

Problem Statement: An experimental as well as theoretical approach is pursued to answer the last question.

Experimental approach : Four specimens were prepared for each type to have totally eight specimens. Composite specimens have a symbol (C) and the specimens with internally reinforcement bars have a symbol (R) . The specimens were placed vertically in two forms depending on the applied eccentricity. For small eccentricity the load is applied inside column cross section, while for big eccentricity the load is outside column so two cantilevers are provided to column cross section.

Theoretical Approach : A computer program using Excel sheet was designed to study interaction between compression force and double bending. The computer program is based on strain compatibility according to the Egyptian code of concrete design and practice (ECCS 2001).

Literature Review

Tied short reinforced concrete column under axial compression load and biaxial bending.

Composite columns types and the behavior of composite column under axial load and biaxial bending.

Heavy reinforcement column, which the ratio of the vertical reinforcement in x-section of column is relatively high.

Tied short reinforced concrete column under axial compression load and biaxial bending

Ultimate Strain in Biaxial Bending 

According to the (ECCS 2001), the ultimate strain in concrete sections subjected to flexure or eccentric compression is 0.003 while it is 0.002 for sections subjected to axial compression.



The ultimate compressive strain according to the British standards (B.S.8110) is (0.0035) for flexural members .

(Gurfinkel 1985) In a section with biaxial bending, the neutral axis is inclined to the horizontal therefore the compression zone can taken one of the following six shapes . The amount of inclination is depending on :  The ratio of the bending moments in the two directions. 

(1)

(2)

(3)

(4)

(5)

(6)

The section properties.

Thus the major part of the compressed area is exposed to relatively small strains while only one point is subjected to the ultimate strain, so it is expected that the ultimate moment will develop at higher strain (Zahn and Park 1989).

An extreme concrete fiber with compressive strain of 0.003 gives a conservative estimate for the flexural strength of a section when the maximum strain exists only at the apex of the compression zone (Rotter 1985).

Equivalent Stress Block (E.R.S.B.): The design of R.C columns subjected to biaxial bending is complicated and tedious when using hand calculations. The use of Equivalent rectangular Stress Block could simplify the design process.

(Taylor 1985) The stress block at failure be approximated by a uniform block whose depth varies between 0.85 and 0.65 according to the strength of concrete. In spite of the using of stress block is simple but it can be expressed as an approximate technique, which is because the integration of actual stress-strain curve of the concrete over the compressed area using hand calculation may be complicated and difficult to be achieved in short time. But using computer analysis that make this work be easy.

The use of equivalent stress block (Taylor 1985)

(ECCS 2001) Using the actual stress - strain curve instead of the equivalent rectangular stress block calculate the stress of concrete over the compressed area of sections subjected to biaxial moment for symmetrical and unsymmetrical steel arrangement.

Analytical work Analysis and Design of R.C. Column Under Biaxial Bending: There many approaches for designing biaxially R.F.T concrete columns.

These methods can be generally divided into the following: 1) Methods using design formulae. 2) Methods using design charts. 3) Methods using computer program.

1-Using Design Formula (Bresler 1960 ) Developed interaction equations to design sections subjected to biaxial bending.

1 1 1 1    pu pux puy po Pu = ultimate load under biaxial bending Pux = ultimate load when only eccentricity ex is present Puy = ultimate load when only eccentricity ey is present Po = ultimate load when there is no eccentricity.

1

 Mx    M ux  

 My  M uy 

2

   

 1.0

Mx: Design moment about x-axis. My: Design moment about y-axis. Mux: Uniaxial flexural strength about x-axis at design normal force. Muy: Uniaxial flexural strength about y-axis at design normal force. 12: Coefficients that depends on the Po/Pu Po = 0.45 fcu Ac + 0.75 Aac fy fcu : concrete characteristic compressive strength (kg/cm2). Ac : Area of concrete cross section (cm2). fy : Steel yield strength (kg/ cm2). Aac : total area of steel (cm2). The values of 12 is given in following table.It may be assumed that 1=2 = for rectangular cross sections:

(Pu/Po)  0.2 0.4 0.6  0.8

 1.00 1.33 1.67 2.00

(Prame1966) suggested the following modification for Bresler equation

 Mx     M ux 

(log 0.5/ log  )

My  M  uy

  

(log 0.5/ log  )

 1.0

Where (ß) equals the ordinate of the point at which relative moments are equal.

This equation can be simplified by assuming that the contour lines consist of two lines instead

of exponential contour .

 Mx   My      M ux   M uy

  1       1.0    

2-Using Design Charts (Weber1960) Presented interaction diagrams for square columns subjected to normal force moving along the diagonal only (θ = 45 deg .) Interpolation can be made between uniaxial interaction diagram and Weber’s charts to get the true value of (Mux ) which equal to (Muy )in case of square column. θ = tan –1 (My / Mx)

(Hilal 1991) Produced a simple graphical method for designing short reinforced concrete column according to the ACI 318-83 code ..

(El-Mihilmy 1992) Presented several charts for biaxial reinforced concrete short columns, the charts are divided to two types. 1st type: charts have constant load with different angles of eccentricity which is the result of cutting the failure surface for biaxially loaded column horizontally . 2nd type: charts have constant angle of eccentricity (q) with different loads levels and moments that is the result of cutting the failure surface for biaxially loaded column vertically .

(Horizontal section)

(Vertical section)

3-Using computer program: (Wang and Hsu 1992) Made a typical numerical model for determination of load-moment-curvature- deflection relationships for short columns. The method of analysis is based on dividing the cross section of column into (m) small elements. The origin (O) is located at the centroid of cross section. The strain [K] at the centroid ( xk , yk) of element (K) is assumed to be uniform across the element.

P=

m



fk ak & Mx

k 1

m

=

 fk

m

ak yk & My

=

k 1

k 1

k 1

fk ak xk

Y

m

P =  Ek єk aK



K (xk,yk )

Mx =  Ek єk ak yk k 1

b

m

X O

m

My = Ek єk ak Xk k 1

a

(Ross 1986) Developed a computer program to perform column design. The program initially assumes four reinforcing bars configuration and then determines the strength of the section (P u , Mux , Muy) if it is less than the applied forces, then the program adds reinforcement to the section and satisfies the design requirements.

(Fattah 1990) Developed a computer program to study the case of biaxial bending but the moment is taken about geometric centroid instead of the plastic centroid as state in clause (4-2-1-3) in (ECCS 2001) , also the variation of the safety factor (γc and γs) according to different eccentricities is not employed . It is also restricted to biaxial bending without normal force.

(El-Mihilmy 1992 ) Prepared a computer program to design columns subjected to biaxial bending .The computer program is based on strain compatibility according to the Egyptian code.

Experimental work (Ramamurthy 1983) Performed an experimental work on 45 columns under different eccentricities of axial compression loads. all columns were tested in the vertical position . At each stage of loading, lateral deflections and strains in the concrete using 200mmdemec gage were measured at the top, middle and bottom sections of the column.

In addition to ,the author present a graphical method to determine the ultimate load in L-shape column under biaxial eccentricity by transform L-section to equivalent Square section.

(Hsu 1985 ) Tested the L-shaped and channel shaped and T-shaped reinforced concrete columns under biaxial bending to study the ultimate strength capacity and deformational behavior. These columns have high percentage of area of steel (4.9 %). Also, specimens were tested in the horizontal position that does not simulate the actual position of the column.

(Kashif 1986) Conducted an experimental program consisting of eleven NSC corner tied square columns to study the behavior of the column subjected to biaxial eccentricity . The author also carried out an analytical study to provide design aids and computer program based on the ultimate theory to predict the strength of L-sections and rectangular sections subjected to biaxial bending. The author found that improvement of concrete grade affects the section strength more significantly in the case of square section than that in case of L-section.

(El-Mihilmy 1992) Tested six biaxially loaded NSC short columns in the vertical position. Test variables were steel percentages, value of load eccentricities, distribution of steel bars and ratio moments Mx to My. The experimental value of ultimate strain for biaxially loaded columns is higher than the value specified by the Egyptian Code . The ultimate capacity of biaxially loaded columns with big eccentricity slightly increases with the presence of compression reinforcements.

(Torkey and Shabban 2001) tested eight reinforced HSC columns of dimension to study the strength and deformation behavior under biaxial bending. They tested the columns in the vertical position pin ended of the top of the column only. The parameters were the eccentricity of load in both X and Y directions, ratio and configuration of tie reinforcement, and longitudinal steel percentage. The authors showed that increasing load eccentricity resulted in reducing the ultimate capacity of the studied HSC columns by approximately 15% .In addition, increasing the lateral confinement led to an increase of ultimate capacity by approximately 22%.

Composite columns

Advantages : 1) Increase building resistance to lateral seismic loads . 2) Helps to increase the efficiency of column to carry loads for the same cross section of ordinary column (column without steel core). Classification of composite column due to cross section materials: 1) Cross section strengthen by Fiber-reinforced polymer (FRP) . 2) Concrete-filled steel tubular (CFT) . 3) Steel-reinforced concrete (SRC) .

(Munoz and Hsu 1997) Presented a design equation to predicte and check the ultimate load capacity not only to short column but also it available to long column, to account for the slenderness effects on concrete–encased composite columns under biaxial bending and axial load. 

  Pn  Pnb    M nx M fx       mfx P  P M nb  o nb   

M ny     mfy M nb 



     

1



1

Where: Pn :nominal axial compressive strength. Pnb :nominal balanced load. Po (  ) : max. axial compressive load of composite x-sec. Po (  ) : max.axial tensile load of composite x-sec.

M nx , M ny :bending moment about X and Y axis. M nb : nominal balanced uniaxial bending moment.

 : coefficient to define load-moment interaction diagram.  : coefficient to define load-contour diagram.  mfx , mfx : Moment magnification factors for x and y bending moment.

(Azizinamini 1997) Made a Developing in (SRC) columns based on the position of column in the building. The arrangement of steel shapes inside R.C core depending on stress applied on each column according its position in the building. Cross sections of SRC members . (a) Interior Columns. (b) External and Corner Columns. (c) Using Single H-Shaped Steel.

(Doval 2001) Studied the circular filled with concrete FRP (Fiber-reinforced polymer) shells . The fiber orientations in the composite are controlled to give the desired strength and stiffness in specified direction. This new structural system improves the shear resistance and confinement of the concrete core. The important disadvantage of this system is the highly cost.

(Lee 2001) Studied the performance and behavior of biaxially and uniaxially loaded two types of column. 1)Concrete-filled steel tubular (CFT) . 2)Steel shapes incased in Reinforced Concrete core (CRC). For 1st type the confinement created by steel casing enhances the material properties of concrete and also the inward buckling of the steel tube is prevented by concrete. The composite action between concrete core and steel tube lead to the increases of the stability , strength , earthquake resistance and high ductility . For 2nd type concrete encased steel construction to make a composite system which has high strength, stiffness, ductility, and fire resistance.

Heavily reinforcement column Using : In some cases, architectal or mechanical design requires a limited cross section of columns. As the same time, the load that should be resisted by the columns is large and this needs increase the column cross-section or increase the vertical reinforcement ratio and keep the cross section as required.

(Diniz 1997) Study the effect of increasing ratio of steel reinforcement on column capacity and behavior . Ratio of steel reinforcement varied from 0.6% to 3.8% where all vertical bars were distributed around he column perimeter .

(Khayat 2001) studied the heavily reinforced columns cast with normal and self-consolidating concrete .the area of steel used was 3.6% and was also distributed around the column diameter.

According to the code of practice requirements the vertical bars should be placed around the outer perimeter of the column and tied with stirrups, but the pouring of concrete in heavy reinforced column becomes difficult due to the small spacing between the vertical bars and increased stirrups branches.

Solution

The designer may oblige to redistribute the vertical bars of the column on outer perimeter and inside the core of column or use composite columns.

(Abd-Elbaky 2004) presented a study on the behavior of heavy reinforcement columns with redistribution of vertical bars around the perimeter and inside the core of column under axial loads only. Eight columns were prepared ,the total area of steel reached (5.12%) for each column from concrete cross section. The author drawn some conclusions: 1. It is recommended to distribute the vertical bars on the outer perimeter and inside the core of the column to facilitate the concrete casting and void concrete honeycombing without any reduction in column capacity. 2. The columns with inner and outer vertical reinforcement exhibited higher load than the columns with outer vertical reinforcement only, where the gain in ultimate loads ranged from 6% to 13%

As = 6 16

As = 6 16

25.00 cm

25.00 cm

25.00

25.00

25.00

25.00

25.00

25.00

As = 6 16

As = 6 16

El-Tahan (under publication) . performed experimental study to compare the response of uniaxially loaded short composite and internally reinforced columns under axial compression and uniaxial bending.10 specimens were prepared, 5 for the composite column and the rest were for internally reinforced concrete with nearly statically equivalent internal steel reinforcement Demec gauges locations

sition of nt Loading

face (3)

face (1)

face (3)

Demec gauges locations face (4)

face (2) Position of Point Loading

Internally reinforced column –Type A

Composite column –Type B

Load –Concrete and Steel strains were recorded at the column mid-height, lateral deformations were recorded along column height using Linear Variable Differential Transformers L.V.D.Ts and displacement dial gauges . Crack pattern and failure mode were recorded

conclusion The behaviour of both composite and internally reinforced composite columns was similar within a range of 20% margin for the capacities.

Experimental Investigation

Composite Sections (C)

Small eccentricity Specimens (C1&C2)

Big eccentricity Specimens (C3&C4)

Internally Reinforced Sections (R)

Small eccentricity Specimens (R1&R2)

Big eccentricity Specimens (R3&R4)

Test parameters:

Eccentricity of the applied load:

1. Eccentricity of the applied load. Column No.

2. Ratio of Mx to My .

ex (cm)

ey (cm)

e (cm)

qo

R-1

C-1

4.30

2.00

4.742

65.0

R-2

C-2

7.35

5.15

8.975

55.0

R-3

C-3

10.00

16.00

18.868

32.0

R-4

C-4

18.00

18.00

25.456

45.0

ex=7.35 cm

ex=4.30 cm

C.Gof column

C.Gof piston

25

25

55° (P) 65°

(P) C.Gof piston

Machine Steel Head plate

Spc.(C2 and R2)

Spc.(C1 and R1)

ey=2.00 cm

C.Gof column

ey=5.15 cm

25

25

55 55 30 18

ex=10cm 10

6.5

(P/2)

16

32°

(P) "C.Gof piston" Applied load

30

18

(P) "C.Gof piston" Applied load

(P/2)

Spc.(C4 and R4)

10.5

(P/2)

6.5

30

55

ey=18cm

(P/2)

55

25

ex=18cm

25 ey=16cm

25

45°

30

25

Spc.(C3 and R3)

Codes limitation on composite columns: According to the Egyptian Code of Practice for steel construction (ECOP) : 1. Composite column is designed as a reinforced concrete column in accordance with ECCS 203-2001.

2. It is required that As  0.04Ag where As : area of steel in the cross-section . Ag : area of concrete cross section . 3. Concrete encasement of the steel core should be reinforced with longitudinal bars and stirrups to restrain concrete and prevent cover spalling. 4. The spacing of lateral ties shall not be greater than two thirds of the least dimension of the composite cross section, or 20 cm, whichever is smaller. 5. The minimum cross-sectional area of the lateral ties and longitudinal bars is 0.02 cm2 /cm of bar spacing. 6. The characteristic 28-day cube strength of concrete, fcu, shall not be less than 250 kg/ cm2, nor greater than 500 kg/ cm2.

According to The American Concrete Insatiate (ACI): 1. The minimum thickness of the steel shape is: b

fy

for each face of width (b).

3E s

2. Lateral ties diameter shall not be smaller than No.3 (10 mm) and are not required to be larger than No.5 (16 mm). Also not less than 0.02 times the greatest side dimension of the composite member. 3. Maximum vertical spacing of lateral ties. 16 times longitudinal bar diameters. 48 times tie bar diameters. 0.5 times the least side dimension of the composite member. 4. It is required that 0.08Ag  Asl  0.01Ag where. Asl : area of Longitudinal bars located within the ties . Ag : area of concrete cross section .

5. The spacing between vertical bars not more than one-half the least side dimension of the composite member. 6. The yield strength of structure steel core and reinforcing bars used in calculating the strength of the composite column shall not exceed 50,000 psi. (351.5 N/mm2)

7. The specified compressive strength of concrete shall not less than 2500 psi. (17.58 N/mm2)

The chosen cross section for composite and internally reinforced column : For fair comparison between the composite section and internally reinforcement section for the tested column, the area and inertia of steel x-section should be equal to the area and inertia of reinforced bars

Composite column section

Internally r.f.t column section

Details of test specimens:

Concrete mix specifications : 1)

Maximum aggregate size should be small enough (10 mm) to account for the narrow spacing between the reinforced bars. 2) Concrete mix must have good workability to fill all spacing between reinforced bars without any segregation. Admixture (super plasticizer) could be used to provide enough workability. 3)

Low strength of concrete is needed due to low capacity of test machine in the laboratory. But not less than 250 kg/ cm2 according to E.C.C.S 2001 . Trial concrete mixes : Mix constitutes / m3 Mix No. 1 2 3 4 5 6 7 8

Cement (Kg)

Gravel (Kg)

300 300 300 350 350 350 400 400

1184 1184 1180 1180 1180 1250 1250 1250

Sand (Kg) 643 643 640 640 640 535 535 535

Water (Litre)

Super Plasticiser (Kg)

210 240 213 230 210 185 185 195

------------------------1.97 4.17 4.17 4.17

Compression Strength(Kg/cm2 )

Slum p (cm)

7 Days

21.75 23.50 9.00 16.00 16.00 21.00 19.25 23.50

75 50 100 84 130 208 210 195

28 Days 110 77.5 138 96 205 292 281 296

The chosen concrete mix constitutes (Kg/m3) Cement 400 1

: : :

Slump : 23.5 cm

Sand 535 1.34 ,

: : :

Gravel 1250 3.13

: : :

Water 195 0.49

: : :

Admixture 4.17 0.01

Fcu after 28-days : 296 Kg/cm2

Compressive Strength of specimens : 3 cubes (15.8x15.8x15.8 cm) and 3 cylinders (15cm dia.x 30 cm height) were prepared from the concrete mix for each specimen . Specimen No.

Cylinder strength fc\ (Kg/cm2)

Compression strength fcu (Kg/cm2)

C1

215

332

R1

198

328

C2

221

308

R2

170

261

C3

192

262

R3

182

260

C4

224

355

R4

221

370

Steel shape properties : Dimensions of steel section:

Dimensions B.F.I.B No.

100

Area (cm2)

26

Weight (Kg/m)

20.4

Ix

h.

b.

s.

t.

c.

h-2c.

(mm)

(mm)

(mm)

(mm)

(mm)

(mm)

100

100

6.0

10.0

22.0

56.0

Iy

(cm4)

(cm4)

450.0

167.0

Physical properties of steel section : Dimension Width (mm)

Height (mm)

Spec. Length (mm)

6.00

60.00

600.00

Gage length (mm)

Yield Load (Kg)

Ult. Load (Kg)

Yield Stress (Kg/cm2)

Ult. Stress (Kg/cm2)

Elong. (%)

214.40

11400

15900

3166.67

4416.67

25.20

A

A

Sec.(A-A)

Stress-Strain Relationships of steel bars: No

Dia (mm)

Avg. Dia. (mm)

Cross Section (cm2)

Gage Length (mm)

Yield Load (Kg)

Ult. Load (Kg)

Yield Stress (Kg/cm2)

1

12

12.345

1.197

120

3800.0

6360.0

3174.76

Ult. Stress (Kg/cm2 ) 5313.55

Elong . (%)

2

18

17.950

2.531

180

8520.0

12720.0

3366.83

5026.53

29.4

3

32

32.55

8.321

320

24000

37500.0

2884.16

4506.50

31.6

27.5

Specimens fabrication:

1. The reinforcement steel was assembled on the floor and tied together using steel weirs to form a rigid cage.

2. The steel sections located inside the column reinforced bars by using welding to keep the distance between steel section and column perimeter reinforcement.

3. rigid cage for different specimens

4. Wooden forms were prepared as for casting concrete in a vertical position.

5. The concrete mix was placed inside the form and vibrated with an electrical rod type vibrator .

6. The specimens was covered by wet canvas that was sprinkled with water twice a day about 21days in order to obtain the specified concrete strength .

Measuring devices: 1 ) Concrete strain device: Concrete strains were measured by a 200mm. demec gauges, for better accuracy. The demec points were arranged at the mid-height of the column, located on four sides of the columns.

2 ) Steel strain device: Strains of longitudinal reinforcement and steel I-Beam section were measured by electric strain gauges , which has a gauge length of 20 mm . The strain gauge were mounted on the steel reinforcement and steel I-Beam section at the mid length of column before casting concrete.

Note: Four faces of column are divided to compression faces (1), (4) which exposed to compression stresses and tension faces (2), (3) which exposed to tension stresses 0

Composite section

Internally R.F.T section

3 ) lateral deformations device: Lateral column deformations were measured at each stage of loading by using two LVDTs, which were placed to measure tension sides lateral deflection of column. The LVDTs erected at mid height of column, in addition to using one dial gauge (of 0.001 mm accuracy) on each tension side.

Test procedures : 1) 2) 3)

4) 5) 6) 7) 8)

The test specimen was placed between the machine heads. The axis of applied load was centered with machine axis, and the specimen itself was displaced to achieve the specific required eccentricity. To avoid the local failure due to stress concentration at both ends (top and base) for column exposed to small eccentricity group (A) {C-1 & C-2 & R-1 &R-2}, steel bearing plates were surrounds the specimen. All electrical strain gauges wires were connected to the data logger. The initial readings of steel strains, concrete strains and all demec strain gauge dials were taken before the beginning of the test. At every stage of loading, cracks were observed and marked on the column surfaces which were white painted. The load was incrementally applied with an initial rate of 200 kn/min for specimens subjected to small eccentricity loading, and 100 kn/min for specimens subjected to large eccentricity loading. Before failure the rate of loading was reduced to one half of the aforementioned loading rate.

Data logger connected the Data Logger connected to electrical strain gauges.

Mechanical Behavior of Specimens C1&R1:

Comparison Item

Specimen (C1)

Specimen (R1)

33.20

32.80

1170.00

1162.00

2350.00

2025.00

2.00

1.74

Load of first tension crack (Kn)

2300.00

2000.00

Load of first compression crack (Kn)

2350.00

2025.00

Centre

3.58

3.76

Bottom

0.36

3.17

Centre

0.74

1.30

Top

2.21

1.77

Maximum tensile strain of steel using S.G.(A) **

0.000597

0.000184

Maximum compression strain of concrete (Electrical)

0.00217

0.00244

Maximum compression strain of concrete (Mechanical)

0.00156

0.00256

fcu “N/mm2” Theoretical load (Pth) “Kn” * Experimental failure load

(Pf)

“Kn”

(Pf / Pth)

Deflection on face (1) (mm) Deflection on face (4) (mm)

* Theoretical load means ultimate load according ECCS code using biaxial interaction diagram setting partial safety factor (gs and gc) = 1.0. ** Yield strain of the bar, which glued to the electrical strain gauge (A) = 0.001587 .

Mode of failure of (C1&R1) The failure mode of specimens C1 & R1 was compression brittle failure, starting at upper half of specimen (C1) and at the midheight of specimen (R1) at the extreme compression apex and followed by a dramatic loss of load carrying capacity accompanied by spalling of small portions of concrete cover and buckling of reinforcement compression steel bar.

Important notes : 1) The position of maximum compression cracks located at the upper half of specimen (C1) while for specimen (R1) it was at the mid-height of column exactly”where the location of electrical strain gauge”, so this illustrate why value of compression strain of concrete for specimen (R1) higher than (C1). 2) The values of compression strain of concrete for both specimens are within the stipulated limit values by the Egyptian Code of Practice for Concrete Structures (2001) for eccentrically loaded members (0.002- 0.003) . 3) The two provided steel caps at the base and at the top of column make a complete confinement prevent appearance of any cracks in those zones .

Vertical cracks start at failure load (C1)

Vertical cracks start at failure load (R1)

Horizontal cracks start at failure load (C1)

Horizontal cracks start at failure load (R1)

Pattern of failure of specimen (C1) and (R1)

Mechanical Behavior of Specimens C2&R2: Comparison Item

Specimen (C2)

Specimen (R2)

fcu “N/mm2”

30.80

26.10

Theoretical load (Pth) “Kn” *

620.00

562.00

1300.00

920.00

2.10

1.64

Load of first tension crack (Kn)

600.00

500.00

Load of first compression crack (Kn)

1250.00

900.00

Centre

8.09

5.43

Bottom

4.35

5.41

Centre

10.05

2.59

Top

8.35

3.75

Maximum tensile strain of steel using S.G.(A) **

0.00163

0.00093

Maximum compression strain of concrete (Electrical)

0.00238

0.00169

Maximum compression strain of concrete (Mechanical)

0.00372

0.00163

Experimental failure load

(Pf)

“Kn”

(Pf / Pth)

Deflection on face (1) (mm) Deflection on face (4) (mm)

* Theoretical load means ultimate load according ECCS code using biaxial interaction diagram setting partial safety factor (gc and gs) = 1.0. ** Yield strain of the bar, which glued to the electrical strain gauge (A) = 0.001587 .

Mode of failure of (C2&R2) Specimens (C2&R2) are subjected to greater eccentricity compare with previous specimens (C1&R1). It noticed that the failure mode of specimen (C2) is completely different from specimen (R2). The mode of failure of specimen (C2) is as expected from the computer analysis using the interaction diagram. Steel bar in tension zone yielded while compression strain of concrete zone was reached up to (0.003) at failure,which is consider balanced failure. 

A local failure was occurred to specimen (R2), cracks start to appear at top and bottom of specimen height far from the mid-height . 

Horizontal cracks start at 46% of failure load (C2)

Vertical cracks start at 95% of failure load (C2)

Pattern failure of column (C2)

Horizontal cracks start at 54% of failure load (R2).

Local failure of column (R2) Pattern of failure of specimen (C2) and (R2)

Mechanical Behavior of Specimens C3&R3: Comparison Item

Specimen (C3)

Specimen (R3)

26.2

26.00

280.00

278.50

550.00

410.00

(Pf / Pth)

1.96

1.47

Load of first tension crack (Kn)

50.00

50.00

Load of first compression crack (Kn)

475.00

350.00

Centre

14.14

15.08

Bottom

13.94

12.32

Centre

21.57

12.87

Top

20.54

7.17

Maximum tensile strain of steel **

0.00162

------- ***

Maximum compression strain of concrete (Electrical)

0.00294

------- ****

Maximum compression strain of concrete (Mechanical)

0.00363

fcu “N/mm2” Theoretical load (Pth) “Kn” * Experimental failure load

(Pf)

Deflection on face (1) (mm) Deflection on face (4) (mm)

“Kn”

* Theoretical load means ultimate load according ECCS code using biaxial interaction diagram setting partial safety factor (gc and gs) = 1.0. ** Yield strain of the bar, which glued to the electrical strain gauge (A) = 0.001587 . *** The strain gauge was damaged . **** A physical error of electrical strain gauges arrangement result in no strain gauge attached to the corner bar.

0.00307

Mode of failure of (C3&R3) Specimens (C3& R3) are subjected to large eccentricity biaxial bending moments. The mode of failure of these specimens is completely “Tension failure”. That is because before crushing of concrete which reach maximum strain the tension cracks due to yielding of steel reinforced bars were appear in very early stag of loading.

Important Notes : 1) The value of compressive concrete strain of C3 was larger than the code limit for eccentrically loaded members (0.003). 2) The lateral deflection corresponding to failure load at both of tension sides was more than those deflections observed at top and bottom of column height. 3) It noticed that the development of cracks at tension faces for both specimens (C3), (R3) starts to propagate very early stage of loading (9-12% of the failure load). 4) The paths of cracks in tension face of column sometimes pass through or intersect with the demec points that made longitudinal tensile strain recorded using mechanical strain gauges is unreliable .

5) No cracks were developed in the base of column or in the two short cantilevers due to the presence of adequate reinforcement and bigger cross sections.

Eccentricity of load on column (C3) & (R3)

Vertical cracks start at 85% of failure load (C3).

Vertical cracks start at 85% of failure load (R3).

Horizontal cracks start at 9% of failure load (C3).

Horizontal cracks start at 12% of failure load (R3).

Note: Path of Horizontal cracks intersects with demec points which affect on demec gauges readings

Pattern of failure of specimen (C3) and (R3)

Mechanical Behavior of Specimens C4&R4: Comparison Item

Specimen (C4)

fcu (N/mm2)

Specimen (R4)

35.50

37.00

Theoretical load (Kn) *

232

202

Experimental failure load (Kn)

450

425

(Failure load / Theoretical load)

1.94

2.10

Load of first tension crack (Kn)

50

50

Load of first compression crack (Kn)

450

425

Deflection on centre of face (1)

(mm)

10.14

7.36

Deflection on centre of face (4)

(mm)

6.26

6.04

Maximum tensile strain of steel **

0.00176

0.00135

Maximum compression strain of concrete (Electrical)

0.00270

0.00257

Maximum compression strain of concrete (Mechanical)

0.00369

0.00310

* Theoretical load means ultimate load according ECCS code using biaxial interaction diagram setting partial safety factor (gc and gs) = 1.0. ** Yield strain of the bar, which glued to the electrical strain gauge (A) = 0.001587 .

Mode of failure of (C4&R4) Specimens (C4& R4) are subjected to large equal eccentricity in both X and Y-directions .These equality reflects on a similarity of mechanical behavior of both specimens. The mode of failure of these specimens is completely “Tension failure”, that is because before crushing of concrete, which reach maximum strain the tension cracks due to yielding of steel reinforced bars were appear in very early stag of loading.

Important Notes : 1)

It noticed that the development of cracks at tension faces (1), (4) for both specimens (C4), (R4) starts to propagate very early stage of loading (10-11% of the failure load).

2) The paths of cracks in tension face of column sometimes pass through or intersect with the demec points that made longitudinal tensile strain recorded using mechanical strain gauges is unreliable . 3) No cracks were developed in the base of column or in the two short cantilevers due to the presence of adequate reinforcement and bigger cross sections. 4) The location of concrete crushing for the specimen (C4) as expected at middle third of column height, while for specimen (R4) local failure was occurred transfer the location of concrete crushing at upper third of column height.

Vertical cracks start at failure load (C4).

Vertical cracks start at 84% of failure load (R4).

Horizontal cracks start at 11% of failure load of specimen (C4)

Horizontal cracks start at 10% of failure load of specimen (R4).

Pattern of failure of specimen (C4).

Failure of column (R4).

* Average value does not consider the value of failure load of specimen R2 due to local failure Where :

Pult. : Ultimate load according to computer program. Pth. : Theoretical load according to computer program. Pf. : Experimental failure load. y : Pf.(R-type) / Pf.(C-type) k : t (R-type) / t (C-type) t : Pth./ Pult h : l (R-type) / l (C-type) l : Pf. / Pth. p : c (R-type) / c (C-type) c : Pf. / Pult

Commentary: Very good correlation between (failure load / theoretical load) and (failure load / ultimate load) for (R-type) and (C-type) columns respectively, is obtained.

1.40

Load Level (R = P f / (fcu .b.t) )

1.20

1.00

0.80

0.60

0.40

0.20

0.00 C1

R1

C2

R2

C3

R3

C4

R4

Columns

The ratio of the ultimate load level (R) of internally reinforced columns (R-type) and composite (C-type) range between (75% to 94%), the average is about 85%.

Computer Program The program flow chart : Start Input column dimensions, reinforced bars arrangement and properties of materials..

Calculate the plastic centroid

Assume Cx, Cy (inclination of N.A)

Calculate strains and stresses for both concrete and reinforced bars

Calculate forces and moments

Change value of Cx or Cy or both to make new iteration

Print forces and moments

End

Note: The analysis process is depending on the variation of inclination of neutral axis (N.A). Cx and Cy are the horizontal and vertical Components of N.A inclination.

Cx = kx . bx Cy = ky . hy According the values of Cx , Cy four cases are established.

Input Data : Cross section such as dimension .  Concrete and steel stresses.  Steel modulus of elasticity.  The partial factor of safety for both steel and concrete.  Large table of steel bars (locations, area and arrangement in cross section). 

Position of plastic centroid : 1)

Calculate ultimate force Ps(i) and moments Zxs(i) & Zys(i) about X, Y axis of each steel bar. Ps(i) = As(i) fy / gs Zxs(i) = Ps(i) . x(i) Zys(i) = Ps(i) . y(i)

Calculate ultimate force Pc and moments Zxc & Zyc about X, Y axis of concrete. Pc = 0.67 Ac fcu / gc Zxc = Pc . (bx / 2) Zyc = Pc . (hy / 2) 3) Calculate the total ultimate capacity (Pt) 2)

n

Pt = Pc + 4)

 Ps(i) i 1

Calculate the position of P.C from both axes X, Y . Dx = (Zxc + Zxs) / Pt Dy = (Zyc + Zys) / Pt

Note : gc = 1.5 * { [7/6] - [(e/t)/3] } gs = 1.15 * { [7/6] - [(e/t)/3] } due to ECCS 2001 For calculate plastic centroid take gc = 1.750 gs = 1.342

Forces and moments in concrete slices: According to ESSC2001 the actual stress-strain curve used to calculate the compression forces in concrete The height of compression zone is ( Lp ) divided into two zones Zone 1: Rectangular stress block with length (LpA ) and height (0.67fcu/gs),includes 10 slices. Stress in each slice (f) = fc = 0.67fcu/gs Zone 2: Parabolic shape with length (LpB) and varying height (f),includes 20 slices.

Calculation of (f): f = fc – f * f * = Q2. fc  f = fc [1 – Q 2]   H  1 / 3)  Q  1  2 / 3  

& H1 

pos (i ) Lp



Cy (i ) Cy

pos(i) = (i -0.5)* ΔL

Where: i is the slice number (from i=1 to i=30 ) Slice force Cc(i) = slice stress . slide area. slide area = Oo(i) . ΔL , (=Lp/30) Cc(i) = f . Oo(i) . ΔL 30 Total compression force Cc =  Cc(i) i 1

30

Moment about x-axis

M xc  C c (i ) .e y (i ) i 1 30

Moment about y-axis

M yc  C c (i ) .e x (i ) i 1

Forces and moments in concrete slices: The strain at any steel bar could get by this relation:

i 0.003



(L P  Z i ) Z  1  i  1 V LP LP

 i  0.003*(1 V ) If i  ≥ steel yield stain (y)  fs = y * (Es .gs) 6 Where:  i 1 elasticity of steel. Es is the modulus of y is the steel yield strain gs is the steel safety factor gs = 1.15 {[7/6]-[(e/t)/3]} ≥ 1.5



If i  < steel yield stain (y) fs = i * Es Note

i : is considered negative in case of tension and positive in case of compression

Force in each bar : F(i) = fs(i) x bar Area A(i). Total force

ST =

Moment about x-axis Moment about y-axis 6

M xs   F(i ) .y (i ) i 1 6

M ys   F(i ) .x (i ) i 1

F(i)

Total Forces and moments : The total force at plastic centroid : Moment about x-axis at (origin point O) : Moment about x-axis at (origin point O) :

Pu = Cc +ST Mux = Pu x Dy – ( Mxc +Mxs) Muy = Pu x Dx – ( Myc +Mys)

Note : Dx , Dy : are the distance from the plastic centroid to the principle axes gc , gs : reduction factors of material safety depend on value of (e/t).

where

2

2

& ey 

M ux Pu

e  e   ey    x    t b   t 

ex 

M uy Pu

Mn : is the resultant moment

q : is angle between two moment

M n  (M ux )2  (M uy )2  M uy    M ux 

q  tan 1 

Conclusions Theoretical investigation: Comparing the ultimate and the theoretical load capacity of the internally reinforced column (R-type) and their corresponding ultimate capacities of composite columns (C-type) the ratio is (89%:99%), the average value is (94%) using both “PCACOL Program” and the “Excel Spread Sheet”.



Experimental tests: 

The average ratio of load level (R) of (R-type) and (C-type) columns is about 85%,that indicates that (C-type) has a better efficiency in resisting applied loads.



The experimental value of the ultimate strain for biaxially loaded column reached 0.00369, which is higher than (0.0030)- the value specified by (ECCS 2001)-.



The usage of the mechanical strain gauges to measure concrete strains have a low accuracy due to the existence of entire hair cracks, which sometimes pass through or intersect with the demec points of the mechanical type.



The concrete compression strains for both (C-type) and (R-type) were similar , which reflects the similarity of the behavior of both two types in compression zone of concrete cross section.



The usage of steel caps, which surround the top and bottom of the specimens with small eccentricities, prevent cracks to be developed and provide a good confinement to specimens.



The recorded concrete strains measured using mechanical strain gauge were approximately linear with respect to the distance to the neutral axis as, thus the assumption of plane section before bending remains plane after bending is valid just before concrete crushing. .



The horizontal tension and the vertical compression cracks appeared early at the specimens of large eccentricities while it were delayed for the case of the specimens of small eccentricities of both types



The failure modes of all specimens can be classified into three modes i) Compression sudden failure for specimen C1 and R1. ii) Balanced failure for specimen C2. iii) Tension failure for C3, R3, C4 and R4.

Recommendations for further Researches: 

The strength and behavior of long composite columns subjected to compressive force and biaxial bending.



The effect of shape on the behavior of biaxially loaded columns by studying L-sections, [-sections and rectangular section with different rectangularity ratios.



The behavior and strength of high strength concrete composite columns subjected to compression force with uniaxial and biaxial bending.



The effect of steel bars arrangement on the behavior and strength of column subjected to biaxial bending.

Conclusion 1.

2.

3.  

The experimental value of ultimate strain for biaxially loaded column reached 0.00369 such as specimen (C4) which is higher than the value specified by ESSC 203-2001 for eccentrically loaded member (0.0030). This may be attributed to the fact that the extreme compression fibers are represented only by one point, which is the extreme apex. The experimental maximum capacity of columns with biaxial bending is higher than the theoretical computed value according to strain compatibility based on the ECCS 203-2001. The failure modes can be classified to two modes: i) Compression sudden failure such specimen C1, R1 ii) Tension failure such as C2, C3, C4, R2, R3, R4

4. low capacity of test machine lead to decreases the cross section of specimen and increases the ratio of steel in the cross section (5.6%). 5. The small distances between steel bars due to high ratio of steel in cross section cause the possibility of some micro air voids inside concrete which have two effects: i) The change of the expected location of plastic hinge far from the middle third of column height , Such as specimens(R2&R4). ii) The capacity of composite section is rather higher than of internally steel bars inside core 6. It was clear from the measurements of lateral deflections along all specimens that the increase of eccentricity leads to increase in lateral deflection values.

7. The paths of cracks in both compression and tension faces of column sometimes pass through or intersect with the demec points, that made: i. Longitudinal tensile strain recorded using mechanical strain gauges is unreliable to calculate actual tensile concrete strain. ii. Longitudinal compressive strain recorded using mechanical strain gauges is too higher than the longitudinal compressive strain recorded using electrical strain gauges 8. Ultimate load and moment derived by Excel spreaded sheet based on ESSC 203-2001 code are more than 90% compatible with ACI Code, that give the Excel sheet enough verification. 9. The capacity of specimens of type (R) ≈ 80% capacity of specimens of type (C), and this is the answer, which was required to be known.

Further Researches 1. The strength and behavior of long composite columns subjected to compressive force with biaxial bending. 2. The effect of shape on the behavior of biaxially loaded columns by studying circular sections, L-sections, [-sections and rectangular section with different rectangularity ratios. 3. The behavior and strength of repaired collapsed columns under the action of biaxial bending. 4. The behavior and strength of high strength concrete columns subjected to biaxial bending.

5. The behavior and strength of the effect of steel bars arrangement inside concrete core by studying different arrangements with the same area of steel but with different inertias.