5.7.1. Objectives and Methods
FEM parametric analysis of RC beam-column joints using high strength mate- rials was performed with the parameters of concrete strength and joint lateral reinforcement. From the analytical results, verification of the guideline equa- tion and the previous design equation of ultimate joint shear strength was discussed. The effects of concrete strength and joint lateral reinforcement on the joint shear strength were also investigated.
A two-dimensional nonlinear FEM program with the constitutive laws of high strength materials was used for the analysis. The Ihzuka's equation
(Ref. 5.26) was used for the compressive strength reduction factor of concrete.
The Fafitis and Shah's Model represented the linear property of the ascending curves of high strength concrete. The modified Kent-Park's Model was used for the confinement effects of lateral reinforcement on the core concrete (Refs. 5.32 and 5.33). The bond link elements composed of two orthogonal springs were used to represent bond between longitudinal bars and concrete. The bond stress-bond slip relationships were determined from the test results. One half of the specimen was analyzed considering the symmetry around a point. After a constant axial loading was applied at the top of the column, lateral displace- ment control was used.
In order to verify the analytical model, the AT series beam-column joint specimens tested by Takezaki and Noguchi (Ref. 5.36) were analyzed and com- pared with the test results. The analytical story shear force-story displacement relationships gave reasonable agreement with the test results, for four speci- mens of AT series including two failure modes, i.e. joint failure and beam flexural yielding.
5.7.2. Comparison between Test and Analytical Results
Specimens in the AT series are shown in Table 5.4. As for the material pro- perties, the yielding strength of beam main bars was 556 MPa, the yielding strength of joint lateral reinforcement was 804 MPa and concrete compressive strength was 80.5 MPa.
Analytical results of the story shear force-story drift curves are shown with the test results in Fig. 5.24. The analytical initial stiffness, crack propagation, and the stiffness degradation by the yielding of beam main bars gave good agreement with the test results. But after the beam yielding, the displacement increased without strength decay under monotonic loading in the analysis.
It was different from the test results where the strength decay was observed after the peak under reversed cyclic loading. The maximum strength and the associated story drift were a little larger than the test results.
5.7.3. Results of Parametric Analysis
Beam-column joints were parametrically analyzed for the shear reinforcement ratios, pw = 0, 0.09, 0.18, 0.36, 0.54, 0.9, 1.2, 2.4 percent and concrete strength
Table 5.4. Specimens.
Specimen
Beam
Main bar Stirrup
Joint lateral reinforcement Joint shear stress at beam
yielding, r py (MPa)
AT-2 6-D13 D 2-D10® 150
Pw = 0.47%
AT-3 8-D13 D 2-D10® 100
Pw = 0.71%
AT-4 AT-5
10-D13
• 2-D10® 80 Pw = 0.89%
• 4-D6 x 3® 50 Pw = 0.47%
8.92
= 0.15 Fc
11.9
= 0.20 Fc
D 2-D6 x 2@ 60 Pw = 0.18%
14.9
= 0.25 Fc
300 p"
1
1 ~~
Analytical Experimental
i
1
i^l.
*
[
• • • '
- A T - 2
4t i t 10 9 20 Story Drift (mm)
Fig. 5.24. Story shear-relative displacement relationships.
300
5 200
; 1 0 0 -
Fig. 5.25. Story shear force-story drift relationships.
aB = 21, 36, 51, 65, 80, 100, 120 MPa, by Noguchi and Takezaki using their original FEM program. The basic specimen was the specimen AT-4. Effects of joint shear reinforcement ratios and concrete compressive strength were studied.
In the parametric analysis, the amount of beam main bars was deliberately increased to avoid beam flexural yielding prior to the joint shear failure. The analytical story shear force-story drift relationships for different shear rein- forcement ratios are shown in Fig. 5.25. Although the initial stiffness was almost the same, the maximum strength was reached earlier when the shear reinforcement ratio was lower. Subsequent strength decay also became larger.
- O —
0. 5 I. 0 1. 5 2. 0
Lateral reinforcement rations (%)
Fig. 5.26. Joint shear stress-lateral reinforcement ratio relationships.
300
Constant ratio of beam main bare ( A T - 4 )
'^
Unit: MPa
Fc=20.6 Fc=35.3 Fc=53.9 Fc=78.4 Fc=98.1 Fc=118 20 30 40
Story drift (mm)
SO
Fig. 5.27. Story shear force-story drift relationships.
The analytical joint shear strength-joint shear reinforcement ratio relation- ships are shown in Fig. 5.26. The joint shear strength increased remarkably from pw = 0 to 0.36 percent and nearly reached the maximum strength at pw — 0.54 percent. Even when the shear reinforcement ratio was very large like pw = 2.4 percent, the strength remained almost the same.
The analytical story shear force-story drift relationships for different con- crete strength are shown in Figs. 5.27 and 5.28. The beam main bar ratio was kept constant in Fig. 5.27. On the other hand, the beam main bar ratio was increased in Fig. 5.28 for ultrahigh strength concrete such as 100 MPa or 120 MPa in order to maintain the joint shear failure mode. It is seen the initial stiffness tends to increase as the concrete strength increases.
In the case of the constant beam main bar ratio, the increase of joint shear strength was remarkable up to 80 MPa of concrete strength, but afterward the
Story drift (mm)
Fig. 5.28. Story shear force-story drift relationships.
Fig. 5.29. Joint shear stress-concrete strength relationships.
strength came to a peak owing to the change of failure mode from joint shear failure to the beam flexural yielding. In the case of the joint shear failure type by increasing beam main bars ratio, the strength increase did not stop even in ultrahigh strength concrete like 100 MPa and 120 MPa.
The analytical joint maximum shear stress-concrete strength relationships are shown in Fig. 5.29 comparing with test results. The analytical joint maxi- mum shear stress did not increase in proportion to concrete compressive strength, erg, but it increased in proportion to the square root of as- Most of test results of specimens failing in joint shear failure were distributed just above the curve of 1.9 x (the square root of as) as shown in Fig. 5.29.
5.7.4. Conclusions
The analytical joint shear strength increased remarkably from pw = 0 to 0.36 percent and nearly reached the maximum strength at pw = 0.54 percent.
Even for higher shear reinforcement ratio such as pw = 2.4 percent, no strength increase was observed.
The analytical joint maximum shear stress did not increase in proportion to concrete compressive strength, CTB, but increased in proportion of the square root or two-thirds power of <JB-