# Comparative Assessment of Shear Demand for RC Beam-Column Joints under Earthquake Loading
## 4 Results and Discussion
### Evaluated Shear Strength  
Shear strengths evaluated according to building codes reviewed in Section 2.2 are graphically presented in Figure 17. The numerical values are given in Table 4. For the sake of synthesis, both the Figure and the Table include also the shear demand which is discussed subsequently.  
Shear strength has been evaluated considering the beam-column joints as being three dimensional without stirrups. The definition of joint type, at each flexural plane, according to Figure 5 applies only for ASCE41-17 and NZSEE2017. No distinction is given for EC8. A reduction of 30% has been applied to the strength values of NZSEE2017, complying with the provision for the bi-axial condition. The axial load for the column is considered at the seismic combination. Only tensile failure (e.g., Equation (6)) is reported because it has been recognized as dominant with respect to the compressive. Moreover, a constant value of 0.4 for the coefficient \(k_{j}\) (defined at Figure 4) in Equation (8) has been assumed according to the evidence of reduced ductility demand for the beam.  
Differences between predicted values of shear strength, using different building codes, are recognized. NZSE2017 gives generally the lowest prediction with respect to EC8 and ASCE41-17. The latter prevails for knee joints. Figure 18 shows the ratio between the evaluated shear demand via NLTH (assumed as the most accurate with respect to NLSA and MRSA) with respect to predicted shear strength (demand-to-strength) as a function of the different joint type. Demand-to-strength ratio is expected to be less than one according to the experimental absence of joint shear failure. Values larger than one are recognized mostly for exterior joint type. This condition can be explained as an excess of safety margins for corner joints if the plane exterior joint type is attributed to both the flexural planes.  
Figure 16: Bi-axial shear demand of beam–column joint obtained with NLTH (Case of +x and +y excitation). The reader is referred to the color version of this figure.  
Probably, a larger strength should be expected as the result of the confinement offered by the beams in both directions as claimed by [PERSON] [52] discussing experimental evidence.  
Figure 17: Evaluated joint shear demand and strength for beam–column joints of SPEAR frame. The reader is referred to the color version of this figure.  
Figure 18: NLTH Demand-to-strength ratios for the beam–column joints of SPEAR frame. The reader is referred to the color version of this figure. (Note. NLTH demands are evaluated using extreme absolute values.)  
\begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l} \hline \hline  & & & & \multicolumn{6}{c}{**Shear Strength**} & \multicolumn{6}{c}{**Shear Demand**} \\ \hline  & & & & \multicolumn{6}{c}{_mini(\(\theta_{j,a}\))_} & \multicolumn{6}{c}{_mini(\(\theta_{j,a}\))_} & \multicolumn{6}{c}{_max(\(\theta_{j,a}\))_} & \multicolumn{6}{c}{_max(\(\theta_{j,a}\))_} \\ \hline  & & & & \multicolumn{6}{c}{_All the Values Are Expressed in MPa_ _0.5_} & \multicolumn{6}{c}{_max(\(\theta_{j,a}\))_} \\ \hline
**COL** & **FL** & **T-XZ** & **T-YZ** & **\(\
u\)** & **ECS** & **ASCE41-17** & **NZSE2017** & **MRSA** & **NLSA** & **NLTH** \\
**(a)** & **FL** & **T-XZ** & **(a)** & **\(\
u\)** & **\(\
u_{i,x-y}\)** & **\  
To summarize, beam-column joints of the SPEAR frame showed significant strength differences. Two major aspects impacted the most, i.e.: (i) the definition of the joint type in each flexural plane; and (ii) the use of a different building code. For the latter, a discussion on the strength accuracy (e.g., [4]) cannot be sustained conclusively because the compared shear demands represent a condition far from failure, as it was observed experimentally.