INTRODUCTION AND LITERATURE REVIEW
A- CWSLC; B-CWSMC; C-CWSSC
4.7 RESULTS AND DISCUSSIONS
Some of the typical finite element models of control as well as retrofitted beam-column joint specimens are shown in Fig. 4.11 - 4.16. The nonlinear analysis was carried out in ANSYS 6.0 for all the specimens with different deficiencies and sizes along with corresponding retrofitted models. Some of the representative results obtained from the analysis is presented in Fig. 4.17 - 4.23. Fig. 4.17 shows the appearance of first flexural crack, which occurs in the beam near the beam-column joint at a load of 13800 N and displacement of about 1.4 mm at the beam tip for BWFLC. Fig. 4.18 shows the ultimate cracks at failure, which occurs in the beam as well as in the joint at a load of 75600 N for BWFLC. Fig.4.19 shows the stress contour for the same specimen. As shown in the window, “TIME” stands for the failure tip load, “DMX” for maximum deflection and TH-951_06610408
Fig.4.11 Finite element model of BWFLC Fig.4.12 Finite element model of BWFLR
Fig.4.13 Finite element model of BWSLC Fig.4.14 Finite element model of BWSLR
Fig.4.15 Finite element model of CWSLC Fig.4.16 Finite element model of CWSLR
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“SMN” maximum bending stress at failure. The maximum deflection for the specimen BWFLC is 16.692 mm and maximum normal stress due to bending at failure is 19.947N/mm . 2
Fig.4.20 shows the first flexural crack for BWFLR, which occurs at a load of 15500 N.
Thus, due to retrofitting, the development of first crack occurred at a higher load level in comparison to that in the corresponding control specimen. Fig. 4.21 shows the ultimate cracks of BWFLR which occurs at the ultimate load of 82000 N. Fig. 4.22 shows the plot of stress contour for BWFLR.
A typical load-displacement curve involving both control and retrofitted specimens is shown in Fig. 4.23. It can be observed that for BWFLC at a load of 13800 N, the slope of the curve changes indicating the development of first crack. After the first crack, further increase in load leads to stiffness reduction due to the development of subsequent cracks.
A substantial stiffness reduction has been observed to have taken place after the load at beam tip exceeded the load corresponding to the yielding of steel. The beam tip deflection increases rapidly and the steel yielding occurs at a load of about 60000 N at a displacement of about 12.5 mm. The failure for the control specimen occurs at the load of 75600 N and at a displacement of 16.692 mm. Further, the load-displacement plot indicates that at a load of 15500 N, the slope of the curve changes indicating the development of first crack for retrofitted specimen BWFLR. The steel yielding occurs at a load of about 63000 N. The failure of the retrofitted specimen occurs at a load of 82000 N and at a displacement of 17.392 mm. Thus, it is clear that there is substantial gain in ultimate load carrying capacity due to retrofitting. The curves shown in Fig. 4.23 has been marked showing the first crack, yielding of steel and ultimate load. The failure load obtained from numerical analysis for both control and retrofitted specimens are shown in Table 4.3. In the same table, the result obtained by strength criteria is also presented for comparison. The beam-column joints with beam weak in flexure and beam weak in shear TH-951_06610408
Fig. 4.17 First crack in BWFLC
Fig. 4.18 Ultimate cracks for BWFLC
Fig. 4.19 Ultimate failure load and ultimate stresses for BWFLC TH-951_06610408
Fig. 4.20 First crack in BWFLR
Fig. 4.21 Ultimate cracks for BWFLR
Fig. 4.22 Ultimate failure load and ultimate stresses for BWFLR TH-951_06610408
were designed as strong column-weak beam. The beam was idealised as a cantilever beam for arriving at the failure tip load of the beam. However, the same assumption was not valid for column weak in shear specimens. Hence, the calculation of load carrying capacity for such specimens was not provided in the table. The calculation for ultimate load carrying capacity for control and retrofitted specimens with strength based criteria is presented in Appendix-B. From Table 4.3 it is clear that the ultimate capacities as obtained through numerical simulations are quite close to those obtained from strength based criteria, indicating the reliability of the simulated results. In addition, it can be noted from the table that the results obtained by numerical studies were slightly higher than those obtained by strength criteria. Further, it can also be noted that the percentage gain in strength obtained from analysis using ANSYS with respect to that obtained on the basis of strength criteria increases as the specimen size decreases in all the cases considered for the study. This reflects the existence of size effect on the result obtained from analysis using ANSYS.
0 10000 20000 30000 40000 50000 60000 70000 80000 90000
0 5 10 15 20
DISPLACEMENT(mm)
LOAD(kN)
FBWFR FBWFC
FIRST CRACK STEEL YEILDING
ULTIMATE LOAD
Fig. 4.23 Typical Load-Displacement Graph
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Table 4.3 Ultimate load of specimens
Control specimens Retrofitted specimens
Name of specimen
Ultimate load by
FE analysis
with ANSYS
(kN)
Ultimate load by strength criteria
(kN)
Gain in ultimate strength by
ANSYS w.r.t.
strength criteria (%)
Name of specimen
Ultimate load by
FE analysis
with ANSYS
(kN)
Ultimate load by strength criteria
(kN)
Gain in ultimate strength by
ANSYS w.r.t.
strength criteria (%) BWFLC 75.60 70.048 7.925994 BWFLR 82.00 82.19 -0.23117 BWFMC 35.84 31.115 15.1856 BWFMR 44.00 37.17 18.37503 BWFSC 9.45 8.045 17.46426 BWFSR 13.32 8.90 49.66292 BWSLC 73.20 66.360 10.30741 BWSLR 83.70 82.19 1.837206 BWSMC 35.84 29.630 20.95849 BWSMR 44.20 37.17 18.9131
BWSSC 9.10 7.3380 24.01199 BWSSR 13.20 8.90 48.31461 CWSLC 58.50 --- --- CWSLR 68.30 --- --- CWSMC 31.50 --- --- CWSMR 35.60 --- --- CWSSC 7.8 --- --- CWSSR 10.30 --- ---