Concrete Moment Frame

Reinforced Concrete 3D Frame

January 2022, By Amir Hossein Namadchi

This notebook is adapted from https://github.com/AmirHosseinNamadchi/OpenSeesPy-Examples/blob/master/Reinforced%20Concrete%203D%20Frame%20(FGU).ipynb

In this notebook, a 3-Dimensional one story Reinforced Concrete moment resisting frame is modeled. This is an OpenSeesPy simulation of TCL version of the model, presented by Fernando Gutiérrez Urzúa in his YouTube channel. Some minor modifications are made by me in the python version. According to his, modeling assumptions are:

Columns & Beams are modeled as distributed plasticity elements

To have cleaner code, all of the neccessary functions are written in a single .py file named RC3DF.py. The file contains:

build_RC_rect_section: Build fiber rectangular RC section
build_model: Builds the 3D RC Frame model
run_gravity: Runs gravity analysis
run_modal: Runs Modal analysis
run_pushover: Runs Pushover analysis
run_time_history: Runs Time history analysis
reset_analysis: Resets the analysis by setting time to 0,removing the recorders and wiping the analysis.

Some additional function arguments are provided to be able to tweak model parameters. Please note that some functions use data obtained by running other functions. For example, in order to run time-history analysis, some of the system’s natural frequencies are required which can be obtained by running run_modal function.

The model has been idealized as follows:

RC Frame

Beam and Column sections are defined as:

RC Frame Sections

Dependencies

import time
import sys
import os

import opensees.openseespy as ops
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import RC3DF as RC

Model Data

Units (Silvia’s Style)

m = 1.0               # Meters
KN = 1.0              # KiloNewtons
sec = 1.0             # Seconds

mm = 0.001*m          # Milimeters
cm = 0.01*m           # Centimeters 
ton = KN*(sec**2)/m   # mass unit (derived)
g = 9.81*(m/sec**2)   # gravitational constant (derived) 
MPa = 1e3*(KN/m**2)   # Mega Pascal 
GPa = 1e6*(KN/m**2)   # Giga Pascal

Geometric Dimensions

L_X = 6.0*m          # Span in X-direction
L_Y = 7.0*m          # Span in Y-direction
L_Z = 3.5*m          # Story height

Material Definition

f_c_1 = -25*MPa          # f'c in compression for unconfined concrete
f_c_2 = -28*MPa          # f'c in compression for confined concrete
eps_c = -0.002           # strain at maximum stress in compression 
eps_u = -0.02            # strain at ultimate stress in compression
f_y = 420.0*MPa          # fy for reinforcing steel
E_s = 210.0*GPa          # E for reinforcing steel

Section Definition

rebar = 0.25*np.pi*(25*mm)**2

# uniaxial Kent-Scott-Park concrete material with degraded linear unloading/reloading
mat_KSP_unconf = {'ID':'Concrete02',
                  'matTag': 1,
                  'fpc': f_c_1,
                  'epsc0': eps_c,
                  'fpcu': 0.2*f_c_1,
                  'epsU': eps_u,
                  'lamda': 0.1,
                  'ft': -0.1*f_c_1,
                  'Ets': (-0.1*f_c_1)/0.002}
# uniaxial Kent-Scott-Park concrete material with degraded linear unloading/reloading
mat_KSP_conf = {'ID':'Concrete02',
                  'matTag': 2,
                  'fpc': f_c_2,
                  'epsc0': eps_c,
                  'fpcu': 0.2*f_c_2,
                  'epsU': eps_u,
                  'lamda': 0.1,
                  'ft': -0.1*f_c_2,
                  'Ets': (-0.1*f_c_2)/0.002}

# uniaxial Giuffre-Menegotto-Pinto steel with isotropic strain hardening
mat_GMP = {'ID':'Steel02',
           'matTag':3,
           'Fy': f_y,
           'E0': E_s,
           'b':0.005,
           'R0': 20.0,
           'cR1': 0.925,
           'cR2': 0.15}


sections = {'Beam':{'B':300*mm,
                        'H':600*mm,
                        'cover':40*mm,
                        'n_bars_top':3,
                        'n_bars_bot':3,
                        'n_bars_int_tot':4,
                        'bar_area_top':rebar,
                        'bar_area_bot':rebar,
                        'bar_area_int':rebar},

            'Column':{'B':300*mm,
                        'H':400*mm,
                        'cover':40*mm,
                        'n_bars_top':3,
                        'n_bars_bot':3,
                        'n_bars_int_tot':4,
                        'bar_area_top':rebar,
                        'bar_area_bot':rebar,
                        'bar_area_int':rebar}
           }

Loading

C_L = 80.0*(KN)      # Concentrated load
m_1 = 200.0*ton       # lumped mass 1

Analysis

Gravity analysis

m = RC.build_model(L_X, L_Y, L_Z, mat_KSP_unconf, mat_KSP_conf, mat_GMP, sections, C_L, m_1)
RC.run_gravity(m)

Output:

Model Built Successfully!
Gravity analysis Done!

m = RC.build_model(L_X, L_Y, L_Z, mat_KSP_unconf, mat_KSP_conf, mat_GMP, sections, C_L, m_1)
RC.run_modal(m)

Output:

Model Built Successfully!
Modal analysis Done!

Pushover analysis in X directions

m = RC.build_model(L_X, L_Y, L_Z, mat_KSP_unconf, mat_KSP_conf, mat_GMP, sections, C_L, m_1)
RC.run_gravity(m)
RC.reset_analysis(m)
RC.run_pushover(m, m_1, direction='X')

Output:

Model Built Successfully!
Gravity analysis Done!
Pushover Analysis in X Done in 37.95 seconds

Pushover analysis in Y directions

m = RC.build_model(L_X, L_Y, L_Z, mat_KSP_unconf, mat_KSP_conf, mat_GMP, sections, C_L, m_1)
RC.run_gravity(m)
RC.reset_analysis(m)
RC.run_pushover(m, m_1, direction='Y')

Output:

Model Built Successfully!
Gravity analysis Done!
Pushover Analysis in Y Done in 38.59 seconds

Time history analysis in X directions

m = RC.build_model(L_X, L_Y, L_Z, mat_KSP_unconf, mat_KSP_conf, mat_GMP, sections, C_L, m_1)
RC.run_gravity(m)
RC.reset_analysis(m)
RC.run_time_history(m, direction='X')

Output:

Model Built Successfully!
Gravity analysis Done!
Running Time-History analysis with lambda= 1
Time-History Analysis in X Done in 46.35 seconds

Time history analysis in Y directions

m = RC.build_model(L_X, L_Y, L_Z, mat_KSP_unconf, mat_KSP_conf, mat_GMP, sections, C_L, m_1)
RC.run_gravity(m)
RC.reset_analysis(m)
RC.run_time_history(m,direction='Y')

Output:

Model Built Successfully!
Gravity analysis Done!
Running Time-History analysis with lambda= 1
Time-History Analysis in Y Done in 45.58 seconds

Visualization

Pushover Curve

df_R_X = pd.read_table('assets/Pushover_Horizontal_ReactionsX.out', sep = " ", header = None,
                      names=["Pseudo-Time","R1_X","R2_X","R3_X","R4_X"])
df_R_Y = pd.read_table('assets/Pushover_Horizontal_ReactionsY.out', sep = " ", header = None,
                      names=["Pseudo-Time","R1_Y","R2_Y","R3_Y","R4_Y"])

df_R_X['sum_R'] = df_R_X.values[:,1:5].sum(axis =1)
df_R_Y['sum_R'] = df_R_Y.values[:,1:5].sum(axis =1)

df_D_X = pd.read_table('assets/Pushover_Story_DisplacementX.out', sep = " ", header = None,
                      names=["Pseudo-Time","D1_X","D2_X","D3_X","D4_X"])
df_D_Y = pd.read_table('assets/Pushover_Story_DisplacementY.out', sep = " ", header = None,
                      names=["Pseudo-Time","D1_Y","D2_Y","D3_Y","D4_Y"])

df_D_X['avg_D'] = df_D_X.values[:,1:5].mean(axis = 1)
df_D_Y['avg_D'] = df_D_Y.values[:,1:5].mean(axis = 1)

plt.figure(figsize=(10,5))

plt.plot(df_D_X['avg_D'], -df_R_X['sum_R'], color = '#C0392B', linewidth=1.5)
plt.plot(df_D_Y['avg_D'], -df_R_Y['sum_R'], color = '#27AE60', linewidth=1.5)


plt.ylabel('Base Shear (KN)', {'fontstyle':'italic','size':14})
plt.xlabel('Average of Roof Displacement (m)', {'fontstyle':'italic','size':14})
plt.grid(which='both')
plt.title('Pushover Curve',{'fontstyle':'normal','size':16})
plt.yticks(fontsize = 14)
plt.xticks(fontsize = 14);
plt.legend(['X-Direction', 'Y-Direction'],prop={'size':14});

Output:

<Figure size 1000x500 with 1 Axes>

Ground Motion histroy

G_M =np.loadtxt('assets/acc_1.txt')
times = np.arange(0,0.02*len(G_M),0.02)
plt.figure(figsize=(12,4))
plt.plot(times,G_M, color = '#6495ED', linewidth=1.2)
plt.ylabel('Acceleration (m/s2)', {'fontstyle':'italic','size':14})
plt.xlabel('Time (sec)', {'fontstyle':'italic','size':14})
plt.grid(which='both')
plt.title('Time history of Ground Motion record',{'fontstyle':'normal','size':16})
plt.yticks(fontsize = 14);

Output:

<Figure size 1200x400 with 1 Axes>

Time history of displacement and acceleration

story_disp_X = np.loadtxt('assets/TimeHistory_Story_DisplacementX1.1.out')
story_disp_Y = np.loadtxt('assets/TimeHistory_Story_DisplacementY1.1.out')

plt.figure(figsize=(12,5))
plt.plot(story_disp_X[:,0], story_disp_X[:,1], color = '#DE3163', linewidth=1.2)
plt.plot(story_disp_Y[:,0], story_disp_Y[:,2], color = '#FFBF00', linewidth=1.2)
plt.ylabel('Horizontal Displacement (m)', {'fontstyle':'italic','size':14})
plt.xlabel('Time (sec)', {'fontstyle':'italic','size':14})
plt.grid(which='both')
plt.title('Time history of horizontal dispacement',{'fontstyle':'normal','size':16})
plt.yticks(fontsize = 14);
plt.xticks(fontsize = 14);
plt.legend(['X-Direction', 'Y-Direction'], prop={'size':14});

Output:

<Figure size 1200x500 with 1 Axes>

story_accel_X = np.loadtxt('assets/TimeHistory_Story_AccelerationX1.1.out')
story_accel_Y = np.loadtxt('assets/TimeHistory_Story_AccelerationY1.1.out')

plt.figure(figsize=(12,5))
plt.plot(story_accel_X[:,0], story_accel_X[:,1], color = '#DE3163', linewidth=1.2)
plt.plot(story_accel_Y[:,0], story_accel_Y[:,2], color = '#FFBF00', linewidth=1.2)
plt.ylabel('Horizontal Acceleration (m/s2)', {'fontstyle':'italic','size':14})
plt.xlabel('Time (sec)', {'fontstyle':'italic','size':14})
plt.grid(which='both')
plt.title('Time history of horizontal acceleration',{'fontstyle':'normal','size':16})
plt.yticks(fontsize = 14);
plt.xticks(fontsize = 14);
plt.legend(['X-Direction', 'Y-Direction'], prop={'size':14});

Output:

<Figure size 1200x500 with 1 Axes>

References

Fernando Gutiérrez Urzúa's YouTube channel (https://www.youtube.com/user/lfgurzua)
OpenseesPy Documentation (https://openseespydoc.readthedocs.io/en/latest/)

Read More

Reinforced Concrete 3D Frame

January 2022, By Amir Hossein Namadchi

Dependencies

Model Data

Units (Silvia’s Style)

Geometric Dimensions

Material Definition

Section Definition

Loading

Analysis

Gravity analysis

Modal analysis

Pushover analysis in X directions

Pushover analysis in Y directions

Time history analysis in X directions

Time history analysis in Y directions

Visualization

Pushover Curve

Ground Motion histroy

Time history of displacement and acceleration

References