Seismic strengthening and rehabilitation of RC frame structures with weak beam-column joints by installing wing walls

Abstract

A substantial number of reinforced concrete (RC) buildings with seismically substandard beam-column joints have suffered severe damage in past earthquakes. This paper focuses on the installation of RC wing walls to upgrade weak beam-column joints and to rehabilitate those moderately damaged by earthquakes. Cyclic load tests were conducted using four specimens representing an exterior 1.5-story frame with a beam-column joint. The first specimen was for a benchmark specimen, the second and third were strengthened by installing wing walls to the interior or exterior of the columns, and the fourth was rehabilitated after the existing frame was moderately damaged. Consequently, the benchmark specimen suffered severe damage to the beam-column joint. The two strengthened specimens showed different damage behaviour: the second one was ductile with beam yielding, and the third one prevented the column-sway mechanism. For the rehabilitated specimen, the beam yielded and the maximum strength was nearly equivalent to that of the second specimen in which wing walls were installed to the interior side of the columns, but damage to the joint was more severe. The test results indicated that the developed wing wall installation method is practical not only for strengthening poorly detailed beam-column joints but also for rehabilitating such joints moderately damaged by earthquakes.

Appendix A

Popular design codes and literatures proposed evaluation methods for joint shear strength. Their applicability to unreinforced joints was also examined as follows. The tested material properties in Tables 2 and 3 were used in calculation.

1.1 ACI 352R-02 (Joint ACI-ASCE Committee 352 2002)

Shear strength of beam-column joints was given as Eq. (23).

$$V_{n} = 0.083\gamma \sqrt {f_{c}^{\prime } } b_{j} h_{c}$$

(23)

$$b_{j} = \hbox{min} \left( {\frac{{b_{b} + b_{c} }}{2},b_{b} + \sum {\frac{{mh_{c} }}{2}} ,b_{c} } \right)$$

(24)

where V_n is joint shear strength; γ is a factor dependent on shape of beam-column joint and seismic zone or non-seismic zone, giving 12 for exterior joints without transverse beams in seismic zone; f ^′ _c is concrete compressive strength (MPa); b_j is the effective joint width as defined in Eq. (24); h_c is column depth; b_b is beam width; b_c is column width; and m is a factor dependent on eccentricity between the centers of beam and column: 0.3 for cases exceeding b_c/8 and 0.5 for other cases.

1.2 ASCE/SEI 41-17 (American Society of Civil Engineers 2017)

ASCE/SEI 41-17 (American Society of Civil Engineers 2017) proposed to calculate the shear strength of beam-column joint as follows,

$$V_{n} = 0.083\lambda \gamma \sqrt {f_{c}^{\prime } } A_{{j^{\prime } }}$$

(25)

$$A_{{j^{\prime } }} = b_{{j^{\prime } }} \times h_{c}$$

(26)

$$b_{{j^{\prime } }} = \hbox{min} \left( {b_{c} ,b_{b} + h_{c} ,2b_{1} } \right)$$

(27)

where λ = 0.75 for lightweight aggregate concrete and 1.0 for nominal weight aggregate concrete; γ is a factor dependent on joint shape, existence of transverse beams, and amount of confinement reinforcement in the joint, giving 6 for unreinforced exterior joints without transverse beams. A_j′ is effective horizontal joint area as defined by Eq. (26); b_j′ is the effective joint width as defined in Eq. (27); and b₁ is the smaller perpendicular distance from the longitudinal axis of the beam to the column side. Other symbols represent the same meaning as those in Eqs. (23) and (24).

The joint shear strength was calculated similarly to ACI 352R-02 (Joint ACI-ASCE Committee 352 2002) with differences in the definitions of γ and effective joint width (b_j or b_j′). In particular, ASCE/SEI 41-17 (American Society of Civil Engineers 2017) considered the amount of confinement reinforcement in the joint.

1.3 NZS 3101 (New Zealand Standards 2017)

Shear strength of beam-column joints was given as:

$$V_{jh} = \hbox{min} \left( {0.20f_{c}^{\prime } b_{j} h_{c} ,\,10b_{j} h_{c} } \right)$$

(28)

where b_j is the effective joint width, which shall be taken as:

if b_c ≥ b_w:

$$b_{j} = \hbox{min} \left( {b_{c} ,b_{w} + 0.5h_{c} } \right)$$

(29a)

if b_c < b_w:

$$b_{j} = \hbox{min} \left( {b_{w} ,b_{c} + 0.5h_{c} } \right)$$

(29b)

where b_w is width of web (beam). Other symbols represent the same as the above.

1.4 Park method (Park and Mosalam 2013)

$$V_{n} = k\left[ {\gamma_{ext} \sqrt {f_{c}^{\prime } } b_{j} h_{c} \frac{\cos \theta }{{\cos \left( {\pi /4} \right)}}} \right]$$

(30)

$$k = 0.4 + 0.6\left[ {\frac{{SI_{j} - X_{1} }}{{X_{2} - X_{1} }}} \right] \le 1.0$$

(31)

$$SI_{j} = \frac{{A_{s} f_{y} }}{{b_{j} h_{c} \sqrt {f_{c}^{\prime } } }}\left( {1 - 0.85\frac{{h_{b} }}{H}} \right)$$

(32)

$$X_{1} = \gamma_{ST1} \frac{\cos \theta }{\cos (\pi /4)}\;{\text{and}}\;X_{2} = \gamma_{ext} \frac{\cos \theta }{\cos (\pi /4)}$$

(33)

where k is a strength factor defined in Eq. (31); γ_ext is equal to 1.0 MPa^0.5, which corresponds to the upper limit of the normalized joint shear strength for the joint aspect ratio h_b/h_c= 1.0; θ = tan⁻¹(h_b/h_c), is angle of joint diagonal; SI_j is a joint shear index dependent on the tensile stress of the beam longitudinal reinforcement, which is derived from Eq. (32), assuming its yielding; A_s/f_y is area and yield stress of the beam tensile reinforcement; h_b is total height of beam cross section; γ_ST1 is equal to 0.33 in MPa; and H is height between upper and lower column inflection points. According to the experimental setup in Fig. 9, shear force on the beam will also be applied to the first-story column. Hence, the axial force to the first-story column should be fluctuating, while the axial force to the second-story column was consistent. Consequently, the flexural strengths of the first-story column were different in the positive and negative loading directions, causing different locations of its inflection point (1.18 m and 1.09 m at the positive and negative loading directions, respectively, by assuming that flexural hinges were formed at the beam end and the bottom of the first-story column).

The calculated shear strengths of the beam-column joint in the benchmark specimen, J3, are presented in Table 7 where the beam bending strength, column bending strength, joint shear strength by AIJ method, and joint moment capacity by Shiohara method in Table 5 are also shown for clear comparisons.

Table 7 Calculated Joint shear strengths compared with the values in Table 5

As compared in Table 7, the minimum value of joint shear strength was 67 kN (conversion into M_j was 12 kN m and 13 kN m in the positive and negative loading directions, respectively, as underlined in the table), which was calculated using ASCE method. However, it was approximately 14% higher than the joint moment capacity of 11 kN m calculated by Shiohara method. Comparing with the bending strengths of the beam and columns, and the joint shear strengths, the moment capacity of the joint was the lowest, as double underlined in Table 7. These results justified the strength validation previously illustrated in Sect. 5.4.