PSI - Issue 60

Anupoju Rajeev et al. / Procedia Structural Integrity 60 (2024) 222–232 Author name / StructuralIntegrity Procedia 00 (2019) 000–000

229

8

Effective cover Effective depth

43 mm 257 mm 100 mm

Spacing between stirrups

3. Results and discussions The sectional analysis of RC column under consideration resulted in the following values at yield and ultimate states as shown in Table 5. The ultimate strain in concrete is assumed as �,��� =0.015 [26]. Also, it is important to establish the achieved curvature ductility � and displacement ductility � for given reinforcement. � =1+ �� � (3) � = 1 + 254 � � −1� � �1− � 2 � (4) Table 5 Sectional properties of column

Parameter � (Moment at fixed end during yield) � (Moments at fixed end during ultimate) � (Curvature at fixed end during yield) � (Curvature at fixed end during ultimate) � (Load at mid span during yield) � (Load at mid span during ultimate) � (Deflection at free end during yield) � (Deflection at free end at during ultimate)

Value

2078 N-m 2213 N-m 0.1039 0.6250 3464 N 3702 N 31.2 mm

102.5 mm From Table 5, the value of curvature and displacement ductility can be obtained as � =6.01 � =3.287 Once establishing the ( − ) curve, we can calculate the equivalent stiffness of the material in elastic �� and elastic-plastic state �� . These stiffness values can be obtained using Equation 5 & 6. �� =1.11×10 � / (5) �� =3.15×10 � / (6) After yielding the stiffness of the material has been reduced by a significant amount which is expected. The effective mass both in elastic and plastic case are calculated by multiplying the load mass factors �� to the total mass of the system. Several solving techniques can be employed to solve the differential equation. In this study the Newmark-Beta algorithm has been used to solve for the displacement for delta increment of time. A value of time increment ∆ � =10 �� ( ) ensures the convergence of the solution for this study. Fig. 3 displays both the un-deformed specimen model and the deformed specimen model, showcasing the displacement contour. As stated earlier the profile of load is step pulse having a constant value P for a duration � . However, in such extreme events, a designer is not interested in the entire displacement time history and is only concerned with the maximum deflection. Varying the magnitude and duration one can achieve any of the three-loading combinations