def mnCurve(self,xRatio=[0.16,0.2,0.3,0.4,0.5,0.8,0.9,1,1E99],n_layers=100,epsU=-0.0035,reverseMoment=False):
F=[]
M=[]
xRatio=[i*self.h for i in xRatio]
f_tot,m_tot,f_s,f_con,eps_s,sigma_s=self.calcX0(eps0=self.reinf.epsilon_u,x_NA=1E99, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
for i in xRatio:
#print(i)
f_tot,m_tot,f_s,f_con,eps_s,sigma_s=self.calcX0(eps0=epsU,x_NA=i, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
#for i in xRatio[:-1]:
for i in xRatio[-2::-1]:
#print(-i)
f_tot,m_tot,f_s,f_con,eps_s,sigma_s=self.calcXH(epsH=epsU,x_NA=i, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
f_tot,m_tot,f_s,f_con,eps_s,sigma_s=self.calcX0(eps0=self.reinf.epsilon_u,x_NA=1E99, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
mnInteraction = pd.DataFrame(np.array([F,M]).T,columns=['F','M'])#.sort_values(by=['x'])
if reverseMoment:
mnInteraction['M']=-mnInteraction['M']
fig,ax = utils.plotBase()
ax.plot(mnInteraction['M'],mnInteraction['F'],'-o', linewidth=2, markersize=5)
ax.set_title('M-N interaction diagram')
ax.set_xlabel('Moment [kNm]')
ax.set_ylabel('Axial load [kN]')
plt.show()
return mnInteraction
def plotStress(self,
curve,
title="",
lbl="",
xlim=(None, None),
ylim=(None, None),
plotting=True,
legend=True):
if plotting:
fig, ax = utils.plotBase()
ax.plot(curve['strain'],
curve['stress'],
'-',
linewidth=2,
markersize=5,
label=lbl)
if legend:
ax.legend(loc='lower right')
ax.set_title(title)
ax.set_xlabel('Strain [ε]')
ax.set_ylabel('Stress [MPa]')
ax.set_xlim(xlim)
ax.set_ylim(ylim)
plt.show()
return curve['strain'], curve['stress']
def plotStress(curve,title="",xlim=(None,None),ylim=(None,None)):
fig,ax = utils.plotBase()
ax.plot(curve[0],curve[1],'-', linewidth=2, markersize=5)
ax.set_title(title)
ax.set_xlabel('Strain [ε]')
ax.set_ylabel('Stress [MPa]')
ax.set_xlim(xlim)
ax.set_ylim(ylim)
plt.show()
def plot_deformed(self,
disp_magn=10,
title='deformed shape',
markersize=10,
grid=True,
figsize=(6, 4)):
displacements = self.nodes.copy()
for i in range(len(self.nodes)):
displacements.at[
i, 'x'] = self.nodes['x'][i] + self.disp[i * 2] * disp_magn
displacements.at[
i, 'y'] = self.nodes['y'][i] + self.disp[i * 2 + 1] * disp_magn
fig, ax = utils.plotBase(grid=grid, figsize=figsize)
for i in range(len(self.elements)):
x1, x2, y1, y2 = elmCoord(self.elements, self.nodes, i)
ax.plot([x1, x2], [y1, y2],
'-',
linewidth=2,
markersize=5,
color='b')
for i in range(len(self.elements)):
x1, x2, y1, y2 = elmCoord(self.elements, displacements, i)
ax.plot([x1, x2], [y1, y2],
'-',
linewidth=2,
markersize=5,
color='r')
for i in range(len(self.restraints)):
x = utils.df_value(self.nodes, self.restraints['node'][i], 'name',
'x')
y = utils.df_value(self.nodes, self.restraints['node'][i], 'name',
'y')
if self.restraints['x'][i] == 1 and self.restraints['y'][i] == 1:
ax.plot(x,
y,
's',
linewidth=2,
markersize=markersize,
color='k')
if self.restraints['x'][i] == 1 and self.restraints['y'][i] == 0:
ax.plot(x,
y,
'>',
linewidth=2,
markersize=markersize,
color='k')
if self.restraints['x'][i] == 0 and self.restraints['y'][i] == 1:
ax.plot(x,
y,
'^',
linewidth=2,
markersize=markersize,
color='k')
ax.set_title(title)
plt.axis('equal')
plt.show()
def epsilonBuildEps(self,epsH,eps0,plotting=False):
if plotting:
fig,ax = utils.plotBase()
ax.plot([0,self.h],[eps0,epsH],'-', linewidth=2, markersize=5)
ax.plot([0,self.h],[0,0],'-', linewidth=2, markersize=5,color='black')
ax.set_title('Strain distribution within section')
ax.set_xlabel('Distance [mm]')
ax.set_ylabel('Strain []')
ax.set_xlim(0,self.h)
ax.set_ylim(None,None)
plt.show()
return np.array([[0,self.h],[eps0,epsH]])
def plotStress(self,
curve,
title="",
lbl="",
xlim=(None, None),
ylim=(None, None),
plotting=True):
if plotting:
fig, ax = utils.plotBase()
ax.plot(curve['strain'],
curve['stress'],
'-',
linewidth=2,
markersize=5,
label=lbl)
ax.legend(loc='lower right')
ax.set_title(title)
ax.set_xlabel('Strain')
ax.set_ylabel('Stress [MPa]')
ax.set_xlim(xlim)
ax.set_ylim(ylim)
plt.show()
return curve['strain'], curve['stress']
if plotting:
fig, ax = utils.plotBase()
ax.plot([0, h], [eps0, epsH], '-', linewidth=2, markersize=5)
ax.plot([0, h], [0, 0],
'-',
linewidth=2,
markersize=5,
color='black')
ax.set_title('Strain distribution within section')
ax.set_xlabel('Distance [mm]')
ax.set_ylabel('Strain []')
ax.set_xlim(0, h)
ax.set_ylim(None, None)
plt.show()
return np.array([[0, h], [eps0, epsH]])
def mnCurve(self,xRatio=[0.16,0.2,0.3,0.4,0.5,0.8,0.9,1,1E99],n_layers=100,epsU=-0.0035,reverseMoment=False,points=None,r2kPath=None,legend=False,labels=None,title='M-N interaction diagram'):
F=[]
M=[]
xRatio=[i*self.h for i in xRatio]
f_tot,m_tot=self.calcX0(eps0=self.reinf.epsilon_u,x_NA=1E99, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
for i in xRatio:
#print(i)
f_tot,m_tot=self.calcX0(eps0=epsU,x_NA=i, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
# pure compression
# f_tot,m_tot,f_s,f_con,eps_s,sigma_s=self.calc(eps0=epsc1,epsH=epsc1, plotting=False,n_layers=n_layers)
# F.append(int(f_tot/1E3))
# M.append(int(m_tot/1E6))
for i in xRatio[-2::-1]:
#print(-i)
f_tot,m_tot=self.calcXH(epsH=epsU,x_NA=i, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
f_tot,m_tot=self.calcX0(eps0=self.reinf.epsilon_u,x_NA=1E99, plotting=False, n_layers=n_layers)
F.append(int(f_tot/1E3))
M.append(int(m_tot/1E6))
mnInteraction = pd.DataFrame(np.array([F,M]).T,columns=['F','M'])#.sort_values(by=['x'])
if reverseMoment:
mnInteraction['M']=-mnInteraction['M']
fig,ax = utils.plotBase()
if labels!=None: ax.plot(mnInteraction['M'],mnInteraction['F'],'-o', linewidth=2, markersize=5,label=labels[0])
else: ax.plot(mnInteraction['M'],mnInteraction['F'],'-o', linewidth=2, markersize=5,label='MN curve')
if r2kPath != None:
response2k = pd.read_csv(r2kPath)
response2k=np.array(response2k).T
if labels!=None: ax.plot(response2k[0],response2k[1],'-', linewidth=2, markersize=5,label=labels[1])
else: ax.plot(response2k[0],response2k[1],'-', linewidth=2, markersize=5,label='Response2k')
if points != None:
for i in range(len(points)):
M_Ed,F_Ed=points[i][0],points[i][1]
if labels!=None: ax.plot(M_Ed,F_Ed,marker='+', color=utils.colours[i+3],mew=3, markersize=10,label=labels[i+2])
else: ax.plot(M_Ed,F_Ed,'r+', mew=3, markersize=10,label='Design load')
if legend:
ax.legend()
ax.set_title(title)
ax.set_xlabel('Moment [kNm]')
ax.set_ylabel('Axial load [kN]')
plt.show()
return mnInteraction
def plot_var(self,
var,
disp_magn=10,
title='variable',
markersize=10,
grid=True,
scale=1,
figsize=(6, 4)):
fig, ax = utils.plotBase(grid=grid, figsize=figsize)
var = np.array(getattr(self, var)) * scale
norm = plt.Normalize(np.min(var), np.max(var))
cmap = plt.get_cmap('seismic')
c = cmap(norm(var))
for i in range(len(self.elements)):
x1, x2, y1, y2 = elmCoord(self.elements, self.nodes, i)
ax.plot([x1, x2], [y1, y2], '-', linewidth=2, markersize=5, c=c[i])
for i in range(len(self.restraints)):
x = utils.df_value(self.nodes, self.restraints['node'][i], 'name',
'x')
y = utils.df_value(self.nodes, self.restraints['node'][i], 'name',
'y')
if self.restraints['x'][i] == 1 and self.restraints['y'][i] == 1:
ax.plot(x,
y,
's',
linewidth=2,
markersize=markersize,
color='k')
if self.restraints['x'][i] == 1 and self.restraints['y'][i] == 0:
ax.plot(x,
y,
'>',
linewidth=2,
markersize=markersize,
color='k')
if self.restraints['x'][i] == 0 and self.restraints['y'][i] == 1:
ax.plot(x,
y,
'^',
linewidth=2,
markersize=markersize,
color='k')
fig.colorbar(cm.ScalarMappable(norm=norm, cmap=cmap), ax=ax, ticks=var)
plt.axis('equal')
ax.set_title(title)
plt.show()
def plot(self,
strain,
retn='stress',
title='con1',
lineType='-',
legend=True,
lbl='stmdl2',
xlim=(None, None),
ylim=(None, None),
ylabel='Stress [MPa]',
xlabel='Strain',
pseto='',
crkso=''):
# strain=np.arange(-np.absolute(self.strnc1),np.absolute(self.strnt1),0.0001)
fig, ax = utils.plotBase()
stress, etan = [], []
for j, i in enumerate(strain):
if crkso != '': self.crks = crkso
if pseto != '': self.pset = pseto
self.stress(i)
stress.append(self.stres)
etan.append(self.etan)
# if j>2:
# X=strain[-3:-1]
# Y=stress[-3:-1]
# print('step: {0}, etan: {1}, slope_intercept: {2}'.format(j,self.etan,self.slope_intercept(X,Y)[0]))
stress = np.array(stress)
etan = np.array(etan)
strain = strain.reshape(len(strain), 1)
stress = stress.reshape(len(stress), 1)
etan = etan.reshape(len(etan), 1)
self.df = pd.DataFrame(np.hstack((stress, strain, etan)),
columns=['stress', 'strain', 'etan'])
if 'etan' in retn:
if retn == 'etan' or retn == 'etan1':
ax.plot(self.df['strain'],
self.df['etan'],
lineType,
linewidth=2,
markersize=5,
label=lbl)
if retn == 'etan' or retn == 'etan2':
slope = self.slope_intercept(strain, stress)
ax.plot(strain[:-1],
slope,
lineType,
linewidth=2,
markersize=5,
label='slope')
else:
ax.plot(self.df['strain'],
self.df['stress'],
lineType,
linewidth=2,
markersize=5,
label=lbl)
if legend: ax.legend()
ax.set_title(title)
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.set_xlim(xlim)
ax.set_ylim(ylim)
plt.show()
def calc(self, eps0, epsH, plotting=False, n_layers=100):
epsilon = self.epsilonBuildEps(eps0=eps0, epsH=epsH, plotting=plotting)
#strain_conLim=.0035
h_i = self.h / n_layers
# Steel
f_s = []
m_s = 0
sigma_s = []
eps_s = []
x_s = np.array(self.section.reinf_sect).T[2]
for i in self.section.reinf_sect:
eps = self.epsilonFunc(i[2], epsilon)
eps_s.append(eps)
sigma = findPointZero(self.reinf.np, eps)
sigma_s.append(sigma)
A = np.pi * i[1]**2 / 4 * i[0]
f_s_i = sigma * A
f_s.append(f_s_i)
m_s += f_s_i * i[2]
# Steel stress distribution
sigma_sEnv = []
x_sEnv = []
for i in range(n_layers):
x_i = i * h_i
x_sEnv.append(x_i)
b_i = self.section.width(x_i)
e = self.epsilonFunc(x_i, epsilon)
s = findPointZero(self.reinf.np, e)
sigma_sEnv.append(s)
if plotting:
fig, ax = utils.plotBase()
ax.bar(x_s, sigma_s, width=5)
ax.plot(x_sEnv, sigma_sEnv, '--', linewidth=2, markersize=5)
ax.plot([0, self.h], [0, 0],
'-',
linewidth=2,
markersize=5,
color='black')
ax.set_title('Steel stress distribution within section')
ax.set_xlabel('Distance [mm]')
ax.set_ylabel('Stress [MPa]')
ax.set_xlim(0, self.h)
ax.set_ylim(None, None)
plt.show()
# Concrete
sigma_con = []
x_con = []
f_con = []
m_con = 0
for i in range(n_layers):
x_i = i * h_i
x_con.append(x_i)
b_i = self.section.width(x_i)
e = self.epsilonFunc(x_i, epsilon)
s = findPointZero(self.concr.np, e)
sigma_con.append(s)
f_con_i = s * b_i * h_i
f_con.append(f_con_i)
m_con += f_con_i * x_i
#print('e: {0}, s: {1}'.format(e,s))
if plotting:
fig, ax = utils.plotBase()
ax.plot(x_con, sigma_con, '-', linewidth=2, markersize=5)
ax.plot([0, self.h], [0, 0],
'-',
linewidth=2,
markersize=5,
color='black')
ax.set_title('Concrete stress distribution within section')
ax.set_xlabel('Distance [mm]')
ax.set_ylabel('Stress [MPa]')
ax.set_xlim(0, self.h)
ax.set_ylim(None, None)
plt.show()
f_tot = sum(f_con) + sum(f_s)
m_tot = m_con + m_s - 0.5 * f_tot * self.h
if plotting:
print('Total axial force: {} kN'.format(int(f_tot / 1E3)))
print('Total moment: {} kNm'.format(int(m_tot / 1E6)))
return f_tot, m_tot #,f_s,f_con,eps_s,sigma_s
