Effect of Load Eccentricity on the Strength of Concrete Columns

This research presents a theoretical study to determine the effect of the load eccentricity on the reinforced concrete column strength taking into account the variables: amount of eccentricity ratio (e/h=0.1 and 1.0); amount of longitudinal reinforcement ρ%=1% to 8%; concrete compressive strength ( ) ' 21,28,35,42, ; 63 84 c and MPa f = steel yielding strength ( ) 414 525 ; y f and MPa = the steel reinforcement distance ratiocondition of loading (Uniaxial and Biaxial bending); shape of the cross section (rectangular and circular) and finally the distribution of the reinforcement on two opposite sides and on four sides. Generally the strength of columns is reduced with existing the load eccentricity and amount of losses in strength increased with increasing the eccentricity amount. The average strength ratio in case of biaxial bending condition is about (82%) of the uniaxial condition in case of (e/h=0.1) and become (55%) in case of (e/h=0.1). For uniaxial bending condition, the average relative column strength is about (75%) in case of (e/h=0.1) and (14%) in case of (e/h=0.1); while for biaxial bending condition, the ratio is (60%) in case of (e/h=0.1) and (8%) in case of (e/ h=0.1). Increasing of concrete compressive strength ( ) ' c f , steel yielding strength ( ) s γ , steel distance ratio ( ) s γ and amount of longitudinal reinforcement ( ) % ρ cause increasing in column strength and reducing the losses in column strength. Also the results show great effect of the load eccentricity ratio (e/h) and bending condition (uniaxial and biaxial) on the reduction of column strength. The distribution of the reinforcement on two opposite sides gives upper limit results and maximum column strength, compared with the case of when the reinforcement distributed on four sides and rectangular section with circular distribution of the reinforcement, while circular columns gives lower limit results and minimum column strength compared with other cases mentioned above. *Corresponding author: Ayad Zeki Saber Agha, Department of Civil Engineering, Erbil Polytechnic University, Erbil, Iraq, Tel: +18197620971; E-mail: agha_ayad@epu.edu.krd Received November 29, 2017; Accepted April 06, 2018; Published April 12, 2018 Citation: Agha AZS, Rashid MHF (2018) Effect of Load Eccentricity on the Strength of Concrete Columns. J Civil Environ Eng 8: 308. doi: 10.4172/2165-784X.1000308 Copyright: © 2018 Agha AZS, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Generally the strength of columns is reduced with existing the load eccentricity and amount of losses in strength increased with increasing the eccentricity amount. The average strength ratio in case of biaxial bending condition is about (82%) of the uniaxial condition in case of (e/h=0.1) and become (55%) in case of (e/h=0.1).
For uniaxial bending condition, the average relative column strength is about (75%) in case of (e/h=0.1) and (14%) in case of (e/h=0.1); while for biaxial bending condition, the ratio is (60%) in case of (e/h=0.1) and (8%) in case of (e/ Also the results show great effect of the load eccentricity ratio (e/h) and bending condition (uniaxial and biaxial) on the reduction of column strength. The distribution of the reinforcement on two opposite sides gives upper limit results and maximum column strength, compared with the case of when the reinforcement distributed on four sides and rectangular section with circular distribution of the reinforcement, while circular columns gives lower limit results and minimum column strength compared with other cases mentioned above.

Introduction
Columns are members used primarily to support axial compression loads. In reinforced concrete buildings the joints between concrete beams, floor and columns are fixed, causing some moments in the column due to end restraint. Also perfect vertical alignment of columns in a multi-storey building is not possible, causing loads to be eccentric relative to the center of columns. The eccentric loads will cause moments in columns. Therefore a column subjected to pure axial loads does not exist in concrete buildings. Concrete is used in columns because of high compressive strength and in expansive material.
Column may be classified based on loading conditions to; axially loaded columns, uniaxial loaded columns (combined axial load plus bending moment about one axis) and biaxial loaded columns (combined axial load plus bending moments about both axes). Also columns may be classified based on length of columns to; short columns (where the failure is due to the crushing of concrete or yielding of steel bars) and long columns (where buckling effect and slenderness ratio must be taken into consideration in the design). Columns may be classified according to shape of cross section, square, rectangular, circular or any other shape, also according to the type of confined reinforcement, ties or spiral [1][2][3][4].
The ratio of longitudinal steel area to gross concrete area is in the range (0.01 to 0.08), according to ACI-Code [5]. The lower limit is necessary to ensure resistance to bending moments not accounted in the analysis and to reduce the effect of creep and shrinkage of the concrete under sustained compression. Ratios higher than (0.08) are uneconomical and also cause difficulty owing to congestion of the reinforcement. Most of the columns are designed with ratios below 0.04. Larger diameter bars are used to reduce placement cases and to avoid unnecessary congestion. A minimum of four longitudinal bars is required for bars enclosed by rectangular or circular ties and six bar must be used when the bars enclosed by a continuous spiral.

Literature Review
Pharis [6] studied the behaviour and limit state performance of high strength reinforced concrete columns. Fifteen specimens were tested to failure, strength and arrangement longitudinal steel, spacing of ties, amount of load eccentricity and compressive strength of concrete are taken as a main variables of the study. He concluded that relationship between stress-strain is more linear over a greater range and can be approximated by a straight line. Also, HSC is extremely brittle; no further strain capacity can be counted on beyond the strain at peak stress. The modulus of elasticity depends on the type and quantity of coarse aggregate. Generally strain capacity is low for high strength. The strain of maximum stress may be slightly higher for high strength concrete than normal strength concrete, but the total stress at failure is normally less for HSC.
The use of rectangular stress block with maximum strain of 0.003 is not valid for high strength concrete. A triangular stress block is found to be much better approximate for high strength concrete because of the linear stress-strain characteristics of high strength concrete, maximum Available test data indicate that typical stress-strain curves in compression for HSC are characterized by an ascending portion that is primarily linear, with maximum strength achieved at an axial strain between (0.0024 and 0.003). Therefore it may be more appropriate to use a tri-angular compression stress block shown in Figure 1 for HSC columns when ' The Canadian Code [23]; suggested the following modified rectangular stress block: Ibrahim et al. [24] compared the concrete component of the measured load and moment strength of (94) tests of eccentrically loaded columns with concrete strengths ranging up to 130 MPa and they conclude that the max. Concrete strain before spalling was greater than (0.003), and the HSC columns can be designed based on rectangular strain of 0.0025 is taken for analysis to determine ultimate strength of the columns, within a few percentage of error in the measured failure load, while using the rectangular stress block of ACI 318 resulted in overestimate of strength.
Rangar and Bisby [7] studied the effect of eccentricities on the behaviour of FRP (Fiber Reinforced Polymer) confined R.C. columns. They conclude that the strength and deformation capacity of FRP confined concrete columns under eccentric axial load is improved as compared with unconfined columns, reduction in strength is occur with increasing eccentricity.
The benefits of FRP wrapping, both in terms of peak load and lateral deformation at peak load, reduction in capacity due to load eccentricity are more pronounced for FRP confined columns. Clear evidence that axial-flexural interaction reduces the effectiveness of FRP wraps. The loop strain observed in the FRP at failure for both FRP concentric and eccentric columns was less than the failure strain in direct tensile tests on FRP coupons.
Majewski et al. [8] presents a FE (Finite Element) modelling to study failure behaviour of reinforced concrete column under eccentric compression. Concrete was described with an elasto-plastic model using isotropic; hardening and softening. The reinforcement was described with an elastic-ideally plastic constitutive law. The FE results were compared with experimental data found in previous studies and satisfactory agreement was achieved.
Lioy and Rangan [9] studied the behaviour and strength of highstrength concrete columns subjected to axial compression and uniaxial bending; they concluded that strength of columns increased by increasing the compression strength of the concrete and longitudinal reinforcement ratio. The strength is reduced with increasing the load eccentricity and mid-height deflection at failure is increased. The theory based on a simplified stability analysis and strain-stress relationship for high strength concrete predicted the strength of columns well.
Setty and Rangan [10] studied high strength concrete columns subjected to combined axial compression and bending moment. They conclude that the mode of failure of test columns was typically flexure with concrete spalling in the compression zone, the lateral reinforcement provide was adequate to prevent buckling of longitudinal bars in the compression zone. Also they proposed a simplified stability analysis to predict strength of columns and showed good correlation with test results.
Many studies [11][12][13][14][15][16][17] have demonstrated the economy of using high strength concrete in columns of high-rise buildings and low to mid rise buildings. In addition to reducing the column size, and producing a more durable material, the use of high strength concrete has been shown to be advantageous with regard to lateral stiffness and axial shortening and reduction in cost of forms. There is no unique definition of high strength concrete. The Australlian standard for concrete structures AS 3600-1994 [18] is limited to concrete compressive strength up to 50 Mpa, while Razvi and Soatcioglu [19], considered the strength of 41 MPa for normal weight concrete and 27 MPa for light weight concrete to be high strength concrete. This is found to be justifiable and since most of the ready-mix concrete supplied. There is no universal agreement on the applicability of ACI code requirement for calculating flexural strength of high strength concrete columns subjected to combined axial load and bending moment.
Columns are usually designed for combined for combined axial load and bending moment using the rectangular stress block. This stress block was originally derived by Mattock et al. [20].  Figure 1 shows a member loaded to its axis by a compression force (P n ) at eccentricity (e) from the centreline. The assumptions taken into consideration are: the plane sections remain plane after bending and concrete strains vary linearly with distance from the neutral axis with full compatibility of deformations, the steel strains at any location are the same for concrete at the same location. Equilibrium between external and internal axis forces result the ultimate load capacity, and ultimate bending moment capacity is determined by taking moment about the centreline of the section of the internal stresses and forces.  Pn These are the two basic equilibrium relations for rectangular column subjected to eccentric compression load.
At this stage, the steel reinforcement carries larger fraction of the load than the case at lower total load.
The maximum useful strength in tension member is the force that will just cause the stress to reach the yield point. A series of such calculation, each corresponding to a different eccentricity is seen. Vertical axis corresponds to (e=0) and 0 n P is the capacity of the column if concentrically loaded, the horizontal axis corresponds to an infinite value of (e) i.e., pure bending at moment capacity ( ) 0 M . Small eccentricities will produce failure governed by concrete compression, while large eccentricities give a failure governed by yielding of the tension steel. This study presents a theoretical study to determine the effect of the load eccentricity on the column strength taking into account the following variables: 1) Amount of the eccentricity: Two ratios (e/h) are considered (e/h=0.1) and (e/h=1.0). The load corresponds to (e/h=0.1) is termed (P n0.1 ) and the load correspond to (e/h=1.0) is termed (e/h=1.0) as shown in Figure 3.
a) The relative ratio with respect to pure compression, i.e., concentric condition (e=0)  Table 1 shows the value of column strength      The results show that increasing of the eccentricity from (0.1 to 1.0) the column strength ratio reduced from about (75% to 14%) and losses in column strength increased from (25% to 86%) for the uniaxial bending condition, while in biaxial bending condition the column strength ratio reduced from about (4% to 8%) and losses increased from (60% to 92%) for same eccentricity values (0.1 and 1.0).

Result and Discussion
More detail graph is shown in Figure 6 for column with eccentricity  , while in columns with ( ) 0.8 &0.9 γ = the effect of ( ) γ is small and changing in the strength ratio is small, also the column strength ratio increased with increasing the reinforcement distance ratio ( ) γ . In the same column with eccentricity ratio ( )  Table 7   reduced from (78% to 64%) and lost its strength about (18%) when the bending condition changed from uniaxial to biaxial condition, while the ratio ( )  Table  11, the column (case b), where the reinforcement distributed on               the opposite sides gives the maximum column strength and that is (upper limit) for both uniaxial and biaxial bending conditions and at eccentricity ratio ( ) / 0.1 &1.0 e h= , while circular column (case c) gives minimum values of column strength and maximum amount of losses, that is lower limit. The cases can be arranged from maximum column strength to minimum column strength as following: b, a, d, and c.