- Original article
- Open Access
Effects of Variation of Axial Load on Seismic Performance of Shear Deficient RC Exterior BCJs
- Mohammed Ali Al-Osta^{1}Email authorView ORCID ID profile,
- Umais Khan^{1},
- Mohammed Hussain Baluch^{1} and
- Muhammad Kalimur Rahman^{2}
https://doi.org/10.1186/s40069-018-0277-0
© The Author(s) 2018
- Received: 13 October 2016
- Accepted: 23 April 2018
- Published: 26 July 2018
Abstract
The focus of this paper is to investigate the effect of column axial load levels on the performance of shear deficient reinforced concrete beam column joints (BCJs) under monotonic and cyclic loading. The problem of interaction between shear stress in BCJ and axial load on column has been addressed in this work by initially postulating a mechanistic model and substantiated by an experimental test program. This was achieved by conducting appropriate tests on seven BCJ sub-assemblies subjected to monotonic and reversed cyclic loading, with varying levels of the column axial load. Experimental results were further validated using a finite element model in an ABAQUS environment. The effect of variation of compressive strength of concrete was considered in a subsequent parametric study, in order to obtain sufficient data, and utilized to develop a new shear strength model for BCJs which includes influences of all the important parameters required to predict the shear strength of BCJs. The results showed that column axial load affects the seismic performance of BCJs significantly. Experimental results demonstrated that at initial stages of loading, increase in axial load enhances the shear capacity of the joint and reduces its ductility. However, when the column axial load/axial strength ratio increases to about 0.6–0.7, shear strength starts to decrease rapidly, leading to pure axial failure of the joint. The magnitude of axial load/axial capacity ratio also dictates the failure mode and development of crack patterns in BCJs. Results of reverse cyclic tests on BCJs showed that high value of axial load/axial capacity ratio increases the initial stiffness of BCJ but rate of stiffness degradation is accelerated after peak strength attenuation.
Keywords
- shear failure
- beam-column joints
- axial load
- monotonic
- reverse cyclic tests
- finite element model
- mechanistic model
1 Introduction
Since the 1970s there have been many developments in the field of earthquake engineering, resulting in advanced seismic design codes and regulations that were developed for different structural components, including beam column joints (BCJs). Many researchers have studied parameters that influence the performance of BCJs such as the aspect ratio, material properties, beam reinforcement ratio, anchorage of beam reinforcement, and the confinement effect of the presence of slab and transverse beams. The influence of these parameters is well understood, and has been incorporated in several joint shear strength models and consequently guidelines for design are available in the current design guidelines. However, effect of magnitude of column axial load, which is a key influencing parameter in predicting shear strength of BCJs, has not been considered explicitly thus far, and its complex effects on the shear strength of the joint remained not well understood.
Sparse information is present in literature regarding the effect of column axial load in predicting seismic performance of BCJ. Research work by Pantelides et al. (2002), Barnes and Jigoral (2008), Wong (2005), Antonopoulos and Triantafillou (2003), Pantelides et al. (2008) and Sarsam and Phillips (1985) concluded that an increase in the column axial load also improves the shear capacity of BCJ. However, the range of column axial load/axial strength ratio considered by above researchers is very narrow and it is usually less than 0.15. The maximum axial load considered and well documented in the form of shear strength equation is 0.42 \(f^{\prime}_c\) A_{g} as in the case of Sarsam and Phillips (1985). Masi et al. (2014) conducted experimental work on full-scale beam-column joints with wide beam to study the effect of axial load on the behavior of BCJ; the values of axial load ratio considered were 0.15 and 0.3. The results showed that the deformation and ductility are affected by the magnitude of column axial load. Li et al. (2015) studied the effect of high axial load on the non-seismically designed RC BCJ with or without strengthening. The ratios of axial load considered were 0.2 and 0.6. Masi et al. (2013) also conducted experimental work on beam-column joints to study influence of a known axial load on the column, dimensions of the beam, and steel on behavior of BCJ. Tran (2016) analyzed data published from literature of a total of 172 experimental works on BCJ. The results showed that the effect of column axial load on the joint shear strength of BCJ was higher for the exterior joint than that of the interior joint. Another group of researchers like Vollum and Newman (1999), Bakir and Boduroglu (2002) believe that the axial load on the column does not affect joint shear strength.
The main emphasis of this research work was to investigate the effect of column axial load levels on the performance of reinforced concrete BCJs under monotonic and cyclic loading and to develop shear strength model that considers all important parameters including column axial load, beam reinforcement ratio, concrete compressive strength and aspect ratio of BCJ. Surprisingly, no shear strength model is available in literature that combines all the above influencing parameters together that would yield a more representative and conservative estimate of BCJs shear strength.
2 Evaluation of Existing BCJ’s Shear Strength Models
Several BCJ shear strength models are available in literature to characterize its behavior under seismic loading. In this section, the existing joint shear strength models proposed by several researchers and design guidelines are reviewed.
Vollum and Newman (1999) have developed a shear strength model to predict the shear capacity of exterior BCJs. Their model while considering the influence of anchorage details of beam longitudinal reinforcement into the joint and joint aspect ratio as significant parameters did not explicitly consider the effect of column axial load.
Sarsam and Phillips (1985) proposed a shear strength model based on test databank of exterior BCJs subjected to monotonic loading. Parameters like the aspect ratio of joint, axial load on column and column steel percentage are considered. According to this model, joint shear capacity increases with an increase in an axial load. However, a limit of axial load ratio \( \frac{N}{{A_{g} f^{\prime}_{c} }} \le 0.42 \) was set due to non-availability of experimental results in literature above this limit.
3 Mechanics of BCJ’s
A mechanistic model to predict the shear strength of beam column joints under various levels of column axial load was initially developed by the authors in an earlier project (Al-Osta et al. 2017). The column axial load N creates an axial stress σ_{N} whereas load on beam V creates shear stresses τ_{v} in the joint. These stresses can be converted to principal joint stresses σ_{1} and σ_{2} using Mohr’s circle as:
4 Experimental Program
The experimental program was designed to include load tests on seven 1/3 scale exterior BCJs. Both monotonic and reversed cyclic loading was considered in the test program to estimate the actual shear capacity and to evaluate stiffness degradation pattern under seismic excitation. Monotonic tests were performed on four specimens to monitor the influence of different magnitude of column axial loads on the joint shear strength and failure mechanism, whereas reversed cyclic loading was applied on three BCJs to understand the ductility, strength degradation and energy dissipation capacity of BCJ.
4.1 Specimen Design
Beam and column design details.
Specimen | Dimensions (mm) | Reinforcement | |||||
---|---|---|---|---|---|---|---|
Beam | Column | ||||||
SP1-SP7 | Beam | Column | Top | Bottom | Stirrups | Main | Ties |
200 × 250 | 200 × 250 | 4 Ø20 | 4 Ø20 | Ø8 @ 50 | 6 Ø20 | Ø8 @ 50 |
4.2 Material Properties
Compressive strength test of concrete was conducted on test date of each specimen according to ASTM C39 M at a loading rate of 0.25 MPa/s. Three cylinders were tested for each specimen and the average compressive strengths was calculated as 21 MPa except for specimens SP-6 and SP-7 where it was 30 MPa.
Results of steel tensile test.
Specimen | Bar size (mm) | Stress (MPa) | Strain µε (Micro strain) | ||
---|---|---|---|---|---|
f _{ y} | f _{ u} | ∈ _{ y} | ∈ _{ u} | ||
SP1-SP7 | Ø8 | 580 | 667 | 3000 | 10,500 |
Ø20 | 605 | 695 | 3100 | 10,600 |
4.3 Test Setup Details
4.4 Specimens Instrumentation
Specimen instrumentation targeted the capture of all the required aspects of the experiment including the over-all structural response, local distortions, and strains in concrete and steel. Instrumentation was done in two stages. At first stage electrical strain gauges were installed on steel reinforcement before casting of concrete. Second stage instrumentation was done in laboratory, which comprised of installation of external sensors; like concrete strain gauges, LVDT’s and extensometer. The test setup was also equipped with LVDT’s to measure any possible over-all rigid movements of the specimen.
4.5 Loading Procedure
Summary of loading on specimens.
Specimen ID | Magnitude of axial load (kN) | Axial load ratio (ALR), \( \frac{N}{{A_{g} f^{\prime}_{c} }} \) | Test method |
---|---|---|---|
SP-1 | 0 | 0.00 | Monotonic |
SP-2 | 200 | 0.19 | Monotonic |
SP-3 | 600 | 0.57 | Monotonic |
SP-4 | 200 | 0.19 | Reverse cyclic |
SP-5 | 600 | 0.57 | Reverse cyclic |
SP-6 | 1050 | 0.70 | Monotonic |
SP-7 | 1050 | 0.70 | Reverse cyclic |
5 Experimental Results and Discussions
5.1 Effect of Axial Load on Shear Strength of BCJ Subjected to Monotonic Loading
5.2 Effect of Axial Load on Shear Strength of BCJ Subjected to Reverse Cyclic Loading
Pronounced pinching effect of hysteresis is observed due to formation of large number of shear cracks in the joint. The phenomenon of pinching is more prominent at high displacements due to severe shear damage of joint.
Figure 10b displays the hysteresis response of specimen SP-5. The maximum load in the positive and negative direction reached 47.3 and 50.0 kN, corresponding to a shear strength of the joint as 3.43 and 3.50 MPa, respectively.
Pinching effect of hysteresis in this specimen is comparatively less as compared to specimen SP-4 which is due to the fact that high axial load confined the joint against shear failure and therefore reducing the pinching effect.
Figure 10c displays the hysteresis response of specimen SP-7. The maximum load in the positive and negative direction reached 58.9 and 54.0 kN, corresponding to a shear strength of the joint as 4.58 and 4.30 MPa, respectively.
It can be noticed that pinching effect of hysteresis in this specimen is even far less as compared to specimen SP-4 and SP-5. In addition, excessive fine cracks were observed in beam of specimen SP-7 as compared to the specimens SP-4 and SP-5. Although specimen SP-7 failed in joint shear failure mode as reinforcement of both beam and column had not yielded, but slight crushing of concrete at the outer edge of joint was also observed at ultimate failure of joint.
Results summary of test specimens.
Specimen ID | Load | σ_{N} (f’c %) | ICL (kN) | JCL (kN) | P (kN) | T (kN) | V_{u(col)} (kN) | V_{j(Joint)} (kN) | v_{j(Joint)} (MPa) |
---|---|---|---|---|---|---|---|---|---|
SP-1 | M | 0.00 | 16 | 16 | 37 | 166 | 28 | 137 | 2.74 |
SP-2 | M | 0.19 | 29 | 29 | 51 | 212 | 37 | 174 | 3.50 |
SP-3 | M | 0.57 | 38 | 38 | 57 | 254 | 43 | 211 | 4.23 |
SP-6 | M | 0.70 | 45 | 45 | 66 | 310 | 49 | 260 | 5.20 |
SP-4 | RC | 0.19 | 20 | 21 | 41/43 | 182/187 | 31/32 | 152/155 | 2.98/3.09 |
SP-5 | RC | 0.57 | 27 | 36 | 47/50 | 207/210 | 35/37 | 171/172 | 3.43/3.50 |
SP-7 | RC | 0.70 | 51 | 51 | 59/54 | 273/255 | 44/40 | 228/215 | 4.58/4.30 |
6 Numerical Modeling of BCJs
The finite element model presented below delineates the modeling to simulate concrete followed by modeling of reinforcing steel and its bond behavior with concrete. Dynamic explicit approach was adopted to overcome convergence problems associated with softening of concrete in tension. Non-linear finite element software ABAQUS was utilized to implement a finite element model as outlined in the next section.
6.1 Finite Element Model
6.1.1 Models to Simulate Cracking in Concrete
To simulate quasi-brittle nature of reinforced concrete, various conceptual models are available in the literature, which include discrete crack model, smeared crack model and concrete damage plasticity model. In this research, damage plasticity model has been utilized for concrete which is a constitutive model available in non-linear finite element software ABAQUS. In damage plasticity model, compression and tension are two hardening variables that control the evolution of the yield surface. A continuum damage mechanics is used to model the damage by stiffness degradation approach which essentially means that the modulus of elasticity is degraded in the concrete where it cracks.
6.1.2 Modelling of Concrete
- 1.
Uniaxial stress–strain relation of concrete under compressive and tensile loading.
- 2.
Damage parameters d_{c} and d_{t} for compressive and tensile stress states, respectively.
Figure 15b shows the tensile stress–strain relationship with related parameters.
Concrete parameters used in the plastic damage model.
Concrete strength (MPa) | Mass density (tonne/mm^{3}) | Young’s modulus (MPa) | Poisson’s ratio | Dilation angle Ψ (degrees) | Plastic potential eccentricity ϵ | f_{bo}/f_{co} | b _{ c} /b _{ t} |
---|---|---|---|---|---|---|---|
Varies | 2.4E−009 | Varies^{a} | 0.19–0.20 | 36 | 0.1 | 1.16 | 0.7 |
6.1.3 Modelling of Reinforcing Steel and its Bond with Concrete
Parameters used to define reinforcing steel.
Elastic modulus (MPa) | 193600/195161 |
---|---|
Poisson’s ratio | 0.3 |
Mass density (tonne/mm^{3}) | 7.85E−009 |
Yield stress (MPa) | 580/605 |
Steel reinforcement is bonded with concrete as an embedded element in ABAQUS. Embedment technique allows number of elements to be embedded inside another element known as host element. Thus, modeling of interaction surface between the embedded and the host element is not required, which eradicates numerically costly iterations linked with surface formulations. Essentially, perfect bond is assumed between concrete and the reinforcement in this model, as there was no experimental evidence of any bond slip during the testing of the specimens.
6.2 Validation of Finite Element Model
The FE model described above has been validated with experimental results. A comparison of experimental results and FE model prediction is presented next to validate its competency to envisage the failure load, mode of failure and overall behavior of BCJs.
6.2.1 Specimen SP-1
6.2.2 Specimen SP-2
6.2.3 Specimen SP-3
Failure load predicted by FEM is 58.78 kN corresponding to displacement of 18.23 mm against experimental value of 56.87 kN at a displacement of 17.86 mm. In general, the load displacement curve predicted by FEM is in good agreement with that obtained from the experiment as shown in Fig. 17c. The predicted failure mode of observed is joint failure and the crack pattern of the experiment and FE prediction is shown in Fig. 18c where cracks are at greater inclination than the previous two cases. Figure 19c shows the steel strains at failure load of specimen SP-3. The average maximum strain in beam’s top bars is obtained as 0.00106 mm/mm against experimental value of 0.00098 mm/mm. The joint shear stress predicted by FEM is 4.43 MPa in contrast to the experimental value of 4.23 MPa.
6.2.4 Specimen SP-6
Failure load predicted by FEM is 68.66 kN corresponding to displacement of 5.81 mm against experimental value of 66.94 kN at a displacement of 6.98 mm. In general, the load displacement curve predicted by FEM is in close agreement with that of the experiment as shown in Fig. 17d. The predicted failure mode of specimen SP-6 is joint shear failure. The crack pattern of the experiment and FE prediction is shown in Fig. 18d where joint shear cracks are almost vertical. Figure 19d shows the steel strains at failure load of specimen SP-6. The average maximum strain in beam’s top longitudinal bars is obtained as 0.00127 mm/mm which closely matches with the experimental value of 0.00119 mm/mm. The shear stress calculated with FEM results is 5.36 MPa against 5.06 MPa as obtained experimentally.
6.3 Parametric Study Using Finite Element Modeling
Based on validation of FE model using experimental results as discussed in the previous section, the calibrated FE model is used to extend the research work for different concrete strengths in order to acquire sufficient data corresponding to various concrete strengths and levels of column axial load.
Layout of finite element models.
Group | M-21 | M-30 | M-36 | M-50 | M-65 |
---|---|---|---|---|---|
f’c | 21 | 30 | 36 | 50 | 65 |
ALR | |||||
0.00 | M-21-00 | M-30-00 | M-36-00 | M-50-00 | M-65-00 |
0.10 | – | M-30-10 | M-36-10 | M-50-10 | M-65-10 |
0.20 | M-21-19 | M-30-20 | M-36-20 | M-50-20 | M-65-20 |
0.30 | – | M-30-30 | M-36-30 | M-50-30 | M-65-30 |
0.40 | – | M-30-40 | M-36-40 | M-50-40 | M-65-40 |
0.50 | – | M-30-50 | M-36-50 | M-50-50 | M-65-50 |
0.60 | M-21-57 | M-30-60 | M-36-60 | M-50-60 | M-65-60 |
0.70 | – | M-30-70 | M-36-70 | M-50-70 | M-65-70 |
0.80 | M-21-80 | M-30-80 | M-36-80 | M-50-80 | M-65-80 |
0.90 | – | M-30-90 | M-36-90 | M-50-90 | M-65-90 |
1.00 | – | M-30-100 | M-36-100 | M-50-100 | – |
1.05 | – | – | – | – | M-65-AC |
1.08 | – | – | – | M-50-AC | – |
1.10 | M-21-AC | M-30-AC | M-36-110 | – | – |
1.13 | – | – | M-36-AC | – | – |
7 Shear Strength Equation for BCJs
7.1 Development of Shear Strength Equation
Therefore, interactions between axial stress on column and corresponding shear strength of BCJs obtained from experimental and FE modeling is used to develop shear strength equations. The effects of aspect ratio and beam reinforcement are evaluated independently.
7.2 Proposed Shear Strength Equation for BCJs
Values of joint shear co-efficient.
Axial load ratio \( \frac{N}{{A_{g} f^{\prime}_{c} }} \) | Shear co-efficient | ||
---|---|---|---|
α | β | γ | |
0.00 < ALR ≤ 0.50 | 351 | 100 | 0.21 |
0.50 < ALR ≤ 0.70 | 4 | 0.03 | 1 |
0.70 < ALR ≤ 0.90 | 425 | − 5 | 0.25 |
7.3 Validation of Shear Strength Equation
Validation of proposed shear strength equation.
Researchers | Specimens | Joint type | Joint aspect ratio | \(f^{\prime}_c\) (MPa) | Beam | Axial load ratio (ALR) | V_{Test} (MPa) | V_{Predicted} (MPa) | \( \frac{{V_{\text{Predicted}} }}{{V_{\text{Test}} }} \) | ||
---|---|---|---|---|---|---|---|---|---|---|---|
ρ_{bb} (%) | ρ_{tb} (%) | f_{yb} (MPa) | |||||||||
Hakuto et al. (2000) | 06 | Exterior | 1.1 | 31 | 0.66 | 1 | 308 | 0 | 3.75 | 3.23 | 0.86 |
07 | Exterior | 1.1 | 31 | 0.66 | 1 | 308 | 0 | 4.05 | 3.23 | 0.80 | |
Clyde et al. (2000) | SP 2 | Exterior | 0.89 | 46.2 | 2.45 | 2.45 | 454 | 0.10 | 6.26 | 6.31 | 1.01 |
SP 6 | Exterior | 0.89 | 40.9 | 2.45 | 2.45 | 454 | 0.10 | 6.26 | 5.85 | 0.93 | |
SP 4 | Exterior | 0.89 | 37.0 | 2.45 | 2.45 | 454 | 0.25 | 7.07 | 6.20 | 0.88 | |
SP 5 | Exterior | 0.89 | 40.1 | 2.45 | 2.45 | 454 | 0.25 | 6.83 | 6.54 | 0.96 | |
Pantelides et al. (2008) | SP 1 | Exterior | 1.00 | 33.0 | 1.90 | 1.90 | 459 | 0.10 | 5.39 | 4.65 | 0.86 |
SP 2 | Exterior | 1.00 | 33.0 | 1.90 | 1.90 | 459 | 0.25 | 5.24 | 5.22 | 0.99 | |
SP 3 | Exterior | 1.00 | 34.0 | 1.90 | 1.90 | 459 | 0.10 | 5.08 | 4.74 | 0.93 | |
SP 4 | Exterior | 1.00 | 34.0 | 1.90 | 1.90 | 459 | 0.25 | 5.66 | 5.32 | 0.94 | |
SP 5 | Exterior | 1.00 | 31.6 | 1.90 | 1.90 | 459 | 0.10 | 5.46 | 4.53 | 0.83 | |
SP 6 | Exterior | 1.00 | 31.6 | 1.90 | 1.90 | 459 | 0.25 | 5.46 | 5.07 | 0.93 | |
Wong (2005) | BS-L | Exterior | 1.50 | 30.8 | 0.94 | 0.94 | 520 | 0.15 | 4.05 | 3.47 | 0.86 |
BS-U | Exterior | 1.50 | 30.9 | 0.94 | 0.94 | 520 | 0.15 | 4.06 | 3.47 | 0.86 | |
BS-LL | Exterior | 1.50 | 42.1 | 0.94 | 0.94 | 520 | 0.15 | 5.39 | 4.22 | 0.78 | |
BS-L-LS | Exterior | 1.50 | 31.6 | 0.94 | 0.94 | 520 | 0.15 | 5.06 | 3.52 | 0.70 | |
BS-V2T10 | Exterior | 1.50 | 32.6 | 0.94 | 0.94 | 520 | 0.15 | 3.19 | 3.59 | 1.13 | |
BS-V4T10 | Exterior | 1.50 | 28.3 | 0.94 | 0.94 | 520 | 0.15 | 4.76 | 3.29 | 0.69 | |
BS-L600 | Exterior | 2.00 | 36.4 | 0.68 | 0.68 | 520 | 0.15 | 3.38 | 3.26 | 0.97 | |
Ghobarah and Said (2001) | T 1 | Exterior | 1.00 | 30.9 | 1.20 | 1.20 | 425 | 0.19 | 5.58 | 4.27 | 0.77 |
T 2 | Exterior | 1.00 | 30.9 | 1.20 | 1.20 | 425 | 0.10 | 5.63 | 3.97 | 0.70 | |
Antonopoulos and Triantafillou (2003) | C1 | Exterior | 1.50 | 19.4 | 0.77 | 0.77 | 585 | 0.05 | 2.57 | 2.30 | 0.90 |
C2 | Exterior | 1.50 | 23.7 | 0.77 | 0.77 | 585 | 0.05 | 2.95 | 2.57 | 0.87 | |
Average = 0.88 | |||||||||||
Standard deviation = 0.10 |
7.4 Discussion on Proposed and Previous Shear Strength Equations
Several shear strength equations available in literature including present design guidelines are deficient in predicting shear strength of unconfined joints in one or another way. For example Vollum and Newman (1999) model considered the effect of aspect ratio and \(f^{\prime}_c\) but did not account for the important influencing parameters such as column axial load and beam reinforcement ratio. Bakir and Boduroglu (2002) considered the effect of beam reinforcement ratio, aspect ratio and \(f^{\prime}_c\) but did not account for the column axial load which is a key influencing parameter in determining joint shear strength. Sarsam and Phillips (1985) considered the effect of aspect ratio of joint, column reinforcement ratio and axial load on column up to ALR of 0.42 but did not include the effect of beam reinforcement ratio. Current design guidelines of ACI-ASCE Committee 352 (2002) at first assumes that tension steel yields and further, these guidelines do not take into account key parameters like aspect ratio, beam reinforcement ratio and column axial load in estimating shear strength of joint. The shear strength model proposed in this work considers all the effects including column axial load, concrete compressive strength, joint aspect ratio and beam reinforcement ratio and has been validated with experimental database of unconfined joints, giving an average of V_{Predicted}/V_{Test} of 0.88 with standard deviation of 0.10 as compared to V_{ACI}/V_{Test} = 0.64 with standard deviation of 0.32. Thus, it is concluded that proposed shear strength equation gives representative and conservative estimates of joint shear strength.
8 Conclusions
- 1.
Increasing the column axial load from zero to 0.60 \(f^{\prime}_c\)A_{g} enhances the shear strength of BCJ by 42% of the joint strength at zero axial load.
- 2.
Shear strength of joint in range of column axial load from 0.60 \(f^{\prime}_c\)A_{g} to 0.70 \(f^{\prime}_c\)A_{g} was found to be almost invariant.
- 3.
Increase in column axial load above a level of 0.70 \(f^{\prime}_c\)A_{g} was found to decrease the shear strength of joint rapidly, leading to a failure of the joint driven purely by the column axial load at magnitude of 1.00 \(f^{\prime}_c\)A_{g}–1.10 \(f^{\prime}_c\)A_{g.}
- 4.
High column axial load was noted to increase the inclination of joint shear cracks at failure. Such increase in crack orientation matches those predicted by traditional concrete failure theories such as Mohr–Coulomb.
- 5.
An average reduction in shear strength of BCJ due to reverse cyclic loading was found to be around 14% as compared to its monotonic loading counterpart.
- 6.
High axial load was noted to delay the initiation of first shear and beam-joint interface crack.
- 7.
Ductility of BCJ was found to reduce with an increase in axial load on column. This effect was more pronounced for column axial loads of 0.60 \(f^{\prime}_c\)A_{g} and greater.
- 8.
Above column axial load of 0.60 \(f^{\prime}_c\)A_{g}, the rate of stiffness degradation was found to increase drastically due to greater deterioration caused by local crushing.
- 9.
The proposed shear strength equation has taken into account the influence of important variables including the effect of column axial load, concrete compressive strength, joint aspect ratio and beam reinforcement ratio in predicting the joint shear strength.
- 10.
It is found that the proposed shear strength model is capable of predicting results from several other research contributions, including the influence of column axial load magnitude and other important variables. Therefore, it is believed that the proposed model gives representative and conservative estimates of joint shear strength for unconfined joints.
Notes
Declarations
Authors’ contributions
MAA-O and MHB conceived of the presented idea. UK with help and support from MAA-O conducted the experiments and performed the numerical simulations. MAA-O, MHB, and MKR developed the mechanistic model. UK and MAA-O developed the manuscript with support from MHB and MKR. All authors read and approved the final manuscript.
Acknowledgements
The authors would like to acknowledge the support provided by the Deanship of Scienti1c Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, Saudi Arabia, for funding this work through Project No. IN 131052. The support provided by the Department of Civil and Environmental Engineering is also acknowledged.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- ACI Committee, 318-14. (2014). Building code requirements for structural concrete and commentary.Google Scholar
- ACI-ASCE Committee 352. (2002). Recommendations for design of beam-column connections in monolithic reinforced concrete structures. Farmington Hills: American Concrete Institute.Google Scholar
- Al-Osta, M., Al-Khatib, A., Baluch, M., Azad, A., & Rahman, M. (2017). Performance of hybrid beam-column joint cast with high strength concrete. Earthquakes and Structures, 12(6), 603–617.Google Scholar
- Antonopoulos, C. P., & Triantafillou, T. C. (2003). Experimental investigation of FRP strengthened RC beam-column joints. ACSE Journal of Composites for Construction, 7(1), 39–49.View ArticleGoogle Scholar
- Bakir, P. G., & Boduroglu, H. M. (2002). A new design equation for predicting the joint shear strength of monotonically loaded exterior beam-column joints. Engineering Structures, 24(8), 1105–1117.View ArticleGoogle Scholar
- Barnes, M. & Jigoral, S. (2008). Exterior non-ductile beam column joints. University of California, Berkeley, PEER/NEESREU Research Report.Google Scholar
- Birtel V., & Mark P. (2006). Parameterized finite element modeling of RC beam shear failure. ABAQUS Users’ Conference.Google Scholar
- Clyde, C., Pantelides, C. P., & Reaveley, L. D. (2000). Performance-based evaluation of exterior reinforced concrete building joints for seismic excitation. PEER Report 2000/05 University of California, Berkeley.Google Scholar
- Ghobarah, A., & Said, A. (2001). Seismic rehabilitation of beam-column joints using FRP laminates. Journal of Earthquake Engineering, 5(1), 113–129.Google Scholar
- Hakuto, S., Park, R., & Tanaka, H. (2000). Seismic load tests on interior and exterior beam-column joints with substandard reinforcing details. ACI, Structural Journal, 97(1), 11–25.Google Scholar
- International Federation for Structural Concrete (fib). (2010). Fib model code for concrete structures, 1.Google Scholar
- Li, B., Lam, E. S. S., Wu, B., & Wang, Y. (2015). Effect of high axial load on seismic behavior of reinforced concrete beam-column joints with and without strengthening. ACI, Structural Journal, 112(6), 713–723.View ArticleGoogle Scholar
- Masi, A., Santarsiero, G., Mossucca, A., & Nigro, D. (2014). Influence of axial load on the seismic behavior of RC beam-column joints with wide. Applied Mechanics and Materials, 508, 208–214.View ArticleGoogle Scholar
- Masi, A., Santarsiero, G., & Nigro, D. (2013). Cyclic tests on external RC beam-column joints: role of seismic design level and axial load value on the ultimate capacity. Journal of Earthquake Engineering, 17(1), 110–136.View ArticleGoogle Scholar
- Pantelides, C. P., Clyde, C., & Reaveley, D. L. (2002). performance-based evaluation of exterior reinforced concrete building joints for seismic excitation. Earthquake Spectra, 18(3), 449–480.View ArticleGoogle Scholar
- Pantelides, C., Okahashi, Y., & Reaveley, L. (2008). Seismic rehabilitation of reinforced concrete frame interior beam-column joints with FRP composites. ASCE, Journal of Composites for Construction, 12(4), 435–445.View ArticleGoogle Scholar
- Sarsam, K. F., & Phillips, M. E. (1985). The shear design of in situ reinforced beam-column joints subjected to monotonic loading. Magazine of Concrete Research, 37(130), 16–28.View ArticleGoogle Scholar
- Tran, M. T. (2016). Influence factors for the shear strength of exterior and interior reinforced concrete beam-column joints. Sustainable Development of Civil, Urban and Transportation Engineering Conference, Procedia Engineering, 142, 63–70.Google Scholar
- Vollum, R. L., & Newman, J. B. (1999). The design of external, reinforced concrete beam column joints. The Structural Engineer, 77(23–24), 21–27.Google Scholar
- Wong, H.F. (2005). Shear strength and seismic performance of non-seismically designed reinforced concrete beam-column joints. PhD Dissertation, Department of Civil Engineering, the Hong Kong University of Science and Technology.Google Scholar