def design_rc_frame(fb, hz, design_drift=0.02, **kwargs):
"""
Displacement-based design of a reinforced concrete frame building.
:param fb: sfsimodels.FrameBuilding
:param hz:
:param design_drift:
:param kwargs:
:return:
"""
df = em.DesignedRCFrame(fb, hz)
df.design_drift = design_drift
verbose = kwargs.get('verbose', df.verbose)
for i in range(100):
mu_reduction_factor = 1.0 - float(i) / 100
theta_c = df.design_drift * mu_reduction_factor
displacements = dt.displacement_profile_frame(theta_c, df.heights,
df.hm_factor)
df.delta_d, df.mass_eff, df.height_eff = dt.equivalent_sdof(
df.storey_mass_p_frame, displacements, df.heights)
df.theta_y = dt.conc_frame_yield_drift(df.fye, df.concrete.e_mod_steel,
df.av_bay, df.av_beam)
delta_y = dt.yield_displacement(df.theta_y, df.height_eff)
df.mu = dt.ductility(df.delta_d, delta_y)
df.xi = dt.equivalent_viscous_damping(df.mu,
mtype="concrete",
btype="frame")
df.eta = dt.reduction_factor(df.xi)
df.t_eff = dt.effective_period(df.delta_d, df.eta, df.hz.corner_disp,
df.hz.corner_period)
if verbose > 1:
print('Delta_D: ', df.delta_d)
print('Effective mass: ', df.mass_eff)
print('Effective height: ', df.height_eff)
print('Mu: ', df.mu)
print('theta yield', df.theta_y)
print('xi: ', df.xi)
print('Reduction Factor: ', df.eta)
print('t_eff', df.t_eff)
if df.t_eff > 0:
break
else:
if verbose > 1:
print("drift %.2f is not compatible" % theta_c)
k_eff = dt.effective_stiffness(df.mass_eff, df.t_eff)
df.v_base = dt.design_base_shear(k_eff, df.delta_d)
df.storey_forces = dt.calculate_storey_forces(df.storey_mass_p_frame,
displacements,
df.v_base,
btype='frame')
return df
def design_rc_frame_w_sfsi_via_millen_et_al_2020(fb,
hz,
sl,
fd,
design_drift=0.02,
found_rot=0.00001,
found_rot_tol=0.02,
found_rot_iterations=20,
**kwargs):
import geofound as gf
df = em.DesignedSFSIRCFrame(fb, hz, sl, fd)
df.design_drift = design_drift
verbose = kwargs.get('verbose', df.verbose)
df.static_values()
psi = 0.75 * np.tan(df.sl.phi_r)
# add foundation to heights and masses
heights, storey_masses = dt.add_foundation(df.heights, df.storey_masses,
df.fd.height, df.fd.mass)
df.storey_mass_p_frame = storey_masses / df.n_seismic_frames
# initial estimate of foundation shear
# for iteration in range(found_rot_iterations): # iterate the foundation rotation
# df.delta_fshear = 0
disp_compatible = False
fd_compatible = False
for i in range(100):
fd_compatible = False
mu_reduction_factor = 1.0 - float(i) / 100
theta_c = df.design_drift * mu_reduction_factor
temp_found_rot = found_rot
temp_delta_fshear = 0
for iteration in range(
found_rot_iterations): # iterate the foundation rotation
displacements = dt.displacement_profile_frame(
theta_c,
heights,
df.hm_factor,
foundation=True,
fd_height=df.fd.height,
theta_f=temp_found_rot)
df.delta_d, df.mass_eff, df.height_eff = dt.equivalent_sdof(
df.storey_mass_p_frame, displacements, heights)
df.theta_y = dt.conc_frame_yield_drift(df.fye,
df.concrete.e_mod_steel,
df.av_bay, df.av_beam)
delta_y = dt.yield_displacement(df.theta_y,
df.height_eff - df.fd.height)
df.delta_frot = df.theta_f * df.height_eff
df.delta_f = df.delta_frot + temp_delta_fshear
df.delta_ss = df.delta_d - df.delta_f
df.mu = dt.ductility(df.delta_ss, delta_y)
if df.mu < 0:
raise DesignError('foundation rotation to large, Mu < 0.0')
eta_fshear = nf.foundation_shear_reduction_factor()
xi_ss = dt.equivalent_viscous_damping(df.mu)
eta_ss = dt.reduction_factor(xi_ss)
norm_rot = temp_found_rot / df.theta_pseudo_up
bhr = (df.fd.width / df.height_eff)
cor_norm_rot = nf.calculate_corrected_normalised_rotation(
norm_rot, bhr)
eta_frot = nf.foundation_rotation_reduction_factor(cor_norm_rot)
if verbose >= 1:
print("mu: ", df.mu)
print('DRF_ss: ', eta_ss)
print('DRF_frot: ', eta_frot)
eta_sys = nf.system_reduction_factor(df.delta_ss, df.delta_frot,
temp_delta_fshear, eta_ss,
eta_frot, eta_fshear)
df.eta = eta_sys
df.xi = dt.damping_from_reduction_factor(eta_sys)
df.t_eff = dt.effective_period(df.delta_d, df.eta,
df.hz.corner_disp,
df.hz.corner_period)
if verbose > 1:
print('Delta_D: ', df.delta_d)
print('Effective mass: ', df.mass_eff)
print('Effective height: ', df.height_eff)
print('Mu: ', df.mu)
print('theta yield', df.theta_y)
print('xi: ', df.xi)
print('Reduction Factor: ', df.eta)
print('t_eff', df.t_eff)
if df.t_eff > 0:
disp_compatible = True
k_eff = dt.effective_stiffness(df.mass_eff, df.t_eff)
v_base_dynamic = dt.design_base_shear(k_eff, df.delta_d)
v_base_p_delta = dt.p_delta_base_shear(df.mass_eff, df.delta_d,
df.height_eff,
v_base_dynamic)
df.v_base = v_base_dynamic + v_base_p_delta
prev_delta_fshear = temp_delta_fshear
temp_delta_fshear = df.v_base / (0.5 * df.k_f0_shear)
df.storey_forces = dt.calculate_storey_forces(
df.storey_mass_p_frame,
displacements,
df.v_base,
btype='frame')
n_ult = df.fd_bearing_capacity
moment_f = df.v_base * df.height_eff
hf = df.height_eff
prev_found_rot = temp_found_rot
temp_found_rot = calc_fd_rot_via_millen_et_al_2020(
df.k_f_0, df.fd.length, df.total_weight, n_ult, psi,
moment_f, df.height_eff)
if abs(prev_delta_fshear -
temp_delta_fshear) / df.delta_d < 0.01 and abs(
prev_found_rot -
temp_found_rot) * hf / df.delta_d < 0.01:
fd_compatible = True
break
else:
fd_compatible = False
else:
break
if disp_compatible:
break
if not fd_compatible:
print(i, iteration)
raise DesignError(
f'Foundation displacements not compatible in design (prev: {prev_found_rot}, last: {found_rot})'
)
if not disp_compatible:
raise DesignError('System displacements not compatible in design')
found_rot = temp_found_rot
df.theta_f = temp_found_rot
df.delta_fshear = temp_delta_fshear
df.theta_f = found_rot
if fd.type == 'pad_foundation':
assert isinstance(fd, sm.PadFoundation)
ip_axis = 'length'
mom_ratio = 0.6
moment_beams_cl, moment_column_bases, axial_seismic = moment_equilibrium.assess(
df, df.storey_forces, mom_ratio)
# TODO: need to account for minimum column base moment which shifts mom_ratio
h_eff = df.interstorey_heights[0] * mom_ratio + fd.height
pad = df.fd.pad
pad.n_ult = df.soil_q * pad.area
col_loads = df.get_column_vert_loads()
ext_nloads = max(col_loads[0])
int_nloads = np.max(col_loads[1:-1])
m_foot_int = np.max(
moment_column_bases[1:-1]) * h_eff / df.interstorey_heights[0]
pad.n_load = int_nloads
tie_beams = getattr(fd, f'tie_beam_in_{ip_axis}_dir')
tb_length = (fd.length -
(fd.pad_length * fd.n_pads_l)) / (fd.n_pads_l - 1)
tie_beams = None
if hasattr(fd, f'tie_beam_in_{ip_axis}_dir'):
tie_beams = getattr(fd, f'tie_beam_in_{ip_axis}_dir')
if tie_beams is not None:
tb_sect = getattr(fd, f'tie_beam_in_{ip_axis}_dir').s[0]
assert isinstance(tb_sect, sm.sections.RCBeamSection)
# See supporting_docs/tie-beam-stiffness-calcs.pdf
k_ties = (6 * tb_sect.i_rot_ww_cracked *
tb_sect.mat.e_mod_conc) / tb_length
else:
k_ties = 0
l_in = getattr(pad, ip_axis)
k_f_0_pad = gf.stiffness.calc_rotational_via_gazetas_1991(
sl, pad, ip_axis=ip_axis)
rot_ipad = calc_fd_rot_via_millen_et_al_2020_w_tie_beams(
k_f_0_pad, l_in, int_nloads, pad.n_ult, psi, m_foot_int, h_eff,
2 * k_ties)
# Exterior footings
if rot_ipad is None: # First try moment ratio of 0.5
# m_cap = pad.n_load * getattr(pad, ip_axis) / 2 * (1 - pad.n_load / pad.n_ult)
m_cap = calc_moment_capacity_via_millen_et_al_2020(
l_in, pad.n_load, pad.n_ult, psi, h_eff)
raise DesignError(
f"Design failed - interior footing moment demand ({m_foot_int/1e3:.3g})"
f" kNm exceeds capacity (~{m_cap/1e3:.3g} kNm)")
m_foot_ext = np.max(moment_column_bases[np.array(
[0, -1])]) * h_eff / df.interstorey_heights[0]
pad.n_load = ext_nloads
# rot_epad = check_local_footing_rotations(sl, pad, m_foot_ext, h_eff, ip_axis=ip_axis, k_ties=k_ties)
rot_epad = calc_fd_rot_via_millen_et_al_2020_w_tie_beams(
k_f_0_pad, l_in, ext_nloads, pad.n_ult, psi, m_foot_ext, h_eff,
k_ties)
if rot_epad is None:
m_cap = pad.n_load * getattr(
pad, ip_axis) / 2 * (1 - pad.n_load / pad.n_ult)
raise DesignError(
f"Design failed - interior footing moment demand ({m_foot_ext/1e3:.3g})"
f" kNm exceeds capacity (~{m_cap/1e3:.3g} kNm)")
if max([rot_ipad, rot_epad]) - found_rot > theta_c - df.theta_y:
# footing should be increased or design drift increased
pad_rot = max([rot_ipad, rot_epad])
plastic_rot = theta_c - df.theta_y
raise DesignError(
f"Design failed - footing rotation ({pad_rot:.3g}) "
f"exceeds plastic rotation (~{plastic_rot:.3g})")
return df
def design_rc_wall_via_millen_et_al_2020(wb,
hz,
sl,
fd,
design_drift=0.025,
**kwargs):
"""
Displacement-based design of a concrete wall.
:param wb: WallBuilding object
:param hz: Hazard Object
:param design_drift: Design drift
:param kwargs:
:return: DesignedWall object
"""
dw = em.DesignedSFSIRCWall(wb, hz, sl, fd)
dw.design_drift = design_drift
verbose = kwargs.get('verbose', dw.verbose)
dw.static_dbd_values()
print("udw: ", dw.sl.unit_dry_weight)
dw.static_values()
# add foundation to heights and masses
heights, storey_masses = dt.add_foundation(dw.heights, dw.storey_masses,
dw.fd.height, dw.fd.mass)
dw.storey_mass_p_wall = storey_masses / dw.n_walls
# k = min(0.2 * (fu / fye - 1), 0.08) # Eq 4.31b
k = min(0.15 * (dw.fu / dw.fye - 1), 0.06) # Eq 6.5a from DDBD code
l_c = dw.max_height
long_db = dw.preferred_bar_diameter
l_sp = 0.022 * dw.fye * long_db / 1.0e6 # Eq 4.30
l_p = max(k * l_c + l_sp + 0.1 * dw.wall_depth, 2 * l_sp)
phi_y = dt.yield_curvature(dw.epsilon_y, dw.wall_depth, btype="wall")
delta_y = dt.yield_displacement_wall(phi_y, heights, dw.max_height)
phi_p = dw.phi_material - phi_y
# determine whether code limit or material strain governs
theta_ss_code = design_drift
dw.theta_y = dw.epsilon_y * dw.max_height / dw.wall_depth
theta_p_code = (theta_ss_code - dw.theta_y)
theta_p = min(theta_p_code, phi_p * l_p)
# Assume no torsional effects
increments = theta_p + dw.theta_y
for i in range(20):
reduced_theta_p = theta_p - increments * float(i) / 20
if reduced_theta_p > 0.0:
non_linear = 1
delta_p = reduced_theta_p * (dw.heights - (0.5 * l_p - l_sp))
delta_p = np.insert(delta_p, 0,
0) # no plastic deformation at foundation
if verbose > 2:
print('reduced_theta_p: ', reduced_theta_p)
print('delta_p: ', delta_p)
delta_st = delta_y + delta_p
else:
raise DesignError('can not handle linear design, resize footing')
dw.design_drift = reduced_theta_p + dw.theta_y
delta_ls = delta_st
displacements = delta_ls * dw.hm_factor
dw.delta_d, dw.mass_eff, dw.height_eff = dt.equivalent_sdof(
dw.storey_mass_p_wall, displacements, heights)
delta_y = dt.yield_displacement_wall(phi_y, dw.height_eff,
dw.max_height)
dw.mu = dt.ductility(dw.delta_d, delta_y)
dw.xi = dt.equivalent_viscous_damping(dw.mu,
mtype="concrete",
btype="wall")
dw.eta = dt.reduction_factor(dw.xi)
dw.t_eff = dt.effective_period(dw.delta_d, dw.eta, dw.hz.corner_disp,
dw.hz.corner_period)
if verbose > 1:
print('Delta_D: ', dw.delta_d)
print('Effective mass: ', dw.mass_eff)
print('Effective height: ', dw.height_eff)
print('Mu: ', dw.mu)
print('theta yield', dw.theta_y)
print('xi: ', dw.xi)
print('Reduction Factor: ', dw.eta)
print('t_eff', dw.t_eff)
if dw.t_eff > 0:
break
else:
if verbose > 1:
print("drift %.2f is not compatible" % reduced_theta_p)
k_eff = dt.effective_stiffness(dw.mass_eff, dw.t_eff)
dw.v_base = dt.design_base_shear(k_eff, dw.delta_d)
moment_f = dw.v_base * dw.height_eff
psi = 0.75 * np.tan(dw.sl.phi_r)
theta_f = calc_fd_rot_via_millen_et_al_2020(dw.k_f_0, dw.fd.length,
dw.total_weight,
dw.bearing_capacity, psi,
moment_f, dw.height_eff)
print("theta_f: ", theta_f)
# TODO: ADD calculation of rotation
dw.storey_forces = dt.calculate_storey_forces(dw.storey_mass_p_wall,
displacements,
dw.v_base,
btype='wall')
return dw
def design_rc_wall(wb, hz, design_drift=0.025, **kwargs):
"""
Displacement-based design of a reinforced concrete wall.
:param wb: WallBuilding object
:param hz: Hazard Object
:param design_drift: Design drift
:param kwargs:
:return: DesignedWall object
"""
dw = em.DesignedRCWall(wb, hz)
dw.design_drift = design_drift
verbose = kwargs.get('verbose', dw.verbose)
dw.static_dbd_values()
# k = min(0.2 * (fu / fye - 1), 0.08) # Eq 4.31b
k = min(0.15 * (dw.fu / dw.fye - 1), 0.06) # Eq 6.5a from DDBD code
l_c = dw.max_height
long_db = dw.preferred_bar_diameter
l_sp = 0.022 * dw.fye * long_db / 1.0e6 # Eq 4.30
l_p = max(k * l_c + l_sp + 0.1 * dw.wall_depth, 2 * l_sp)
phi_y = dt.yield_curvature(dw.epsilon_y, dw.wall_depth, btype="wall")
delta_y = dt.yield_displacement_wall(phi_y, dw.heights, dw.max_height)
phi_p = dw.phi_material - phi_y
# determine whether code limit or material strain governs
theta_ss_code = design_drift
dw.theta_y = dw.epsilon_y * dw.max_height / dw.wall_depth
theta_p_code = (theta_ss_code - dw.theta_y)
theta_p = min(theta_p_code, phi_p * l_p)
# Assume no torsional effects
increments = theta_p + dw.theta_y
for i in range(20):
reduced_theta_p = theta_p - increments * float(i) / 20
if reduced_theta_p > 0.0:
non_linear = 1
delta_p = reduced_theta_p * (dw.heights - (0.5 * l_p - l_sp))
if verbose > 2:
print('reduced_theta_p: ', reduced_theta_p)
print('delta_p: ', delta_p)
delta_st = delta_y + delta_p
else:
raise DesignError('can not handle linear design, resize footing')
dw.design_drift = reduced_theta_p + dw.theta_y
delta_ls = delta_st
displacements = delta_ls * dw.hm_factor
dw.delta_d, dw.mass_eff, dw.height_eff = dt.equivalent_sdof(
dw.storey_mass_p_wall, displacements, dw.heights)
delta_y = dt.yield_displacement_wall(phi_y, dw.height_eff,
dw.max_height)
dw.mu = dt.ductility(dw.delta_d, delta_y)
dw.xi = dt.equivalent_viscous_damping(dw.mu,
mtype="concrete",
btype="wall")
dw.eta = dt.reduction_factor(dw.xi)
dw.t_eff = dt.effective_period(dw.delta_d, dw.eta, dw.hz.corner_disp,
dw.hz.corner_period)
if verbose > 1:
print('Delta_D: ', dw.delta_d)
print('Effective mass: ', dw.mass_eff)
print('Effective height: ', dw.height_eff)
print('Mu: ', dw.mu)
print('theta yield', dw.theta_y)
print('xi: ', dw.xi)
print('Reduction Factor: ', dw.eta)
print('t_eff', dw.t_eff)
if dw.t_eff > 0:
break
else:
if verbose > 1:
print("drift %.2f is not compatible" % reduced_theta_p)
k_eff = dt.effective_stiffness(dw.mass_eff, dw.t_eff)
dw.v_base = dt.design_base_shear(k_eff, dw.delta_d)
dw.storey_forces = dt.calculate_storey_forces(dw.storey_mass_p_wall,
displacements,
dw.v_base,
btype='wall')
return dw
def design_rc_frame_w_sfsi_via_millen_et_al_2018(fb,
hz,
sl,
fd,
design_drift=0.02,
found_rot=0.00001,
found_rot_tol=0.02,
found_rot_iterations=20,
**kwargs):
df = em.DesignedSFSIRCFrame(fb, hz, sl, fd)
df.design_drift = design_drift
df.theta_f = found_rot
verbose = kwargs.get('verbose', df.verbose)
df.static_values()
# add foundation to heights and masses
heights, storey_masses = dt.add_foundation(df.heights, df.storey_masses,
df.fd.height, df.fd.mass)
df.storey_mass_p_frame = storey_masses / df.n_seismic_frames
# initial estimate of foundation shear
for iteration in range(
found_rot_iterations): # iterate the foundation rotation
df.delta_fshear = 0
for i in range(100):
mu_reduction_factor = 1.0 - float(i) / 100
theta_c = df.design_drift * mu_reduction_factor
displacements = dt.displacement_profile_frame(
theta_c,
heights,
df.hm_factor,
foundation=True,
fd_height=df.fd.height,
theta_f=df.theta_f)
df.delta_d, df.mass_eff, df.height_eff = dt.equivalent_sdof(
df.storey_mass_p_frame, displacements, heights)
df.theta_y = dt.conc_frame_yield_drift(df.fye,
df.concrete.e_mod_steel,
df.av_bay, df.av_beam)
delta_y = dt.yield_displacement(df.theta_y,
df.height_eff - df.fd.height)
df.delta_frot = df.theta_f * df.height_eff
df.delta_f = df.delta_frot + df.delta_fshear
df.delta_ss = df.delta_d - df.delta_f
df.mu = dt.ductility(df.delta_ss, delta_y)
if df.mu < 0:
raise DesignError('foundation rotation to large, Mu < 0.0')
eta_fshear = nf.foundation_shear_reduction_factor()
xi_ss = dt.equivalent_viscous_damping(df.mu)
eta_ss = dt.reduction_factor(xi_ss)
norm_rot = found_rot / df.theta_pseudo_up
bhr = (df.fd.width / df.height_eff)
cor_norm_rot = nf.calculate_corrected_normalised_rotation(
norm_rot, bhr)
eta_frot = nf.foundation_rotation_reduction_factor(cor_norm_rot)
if verbose >= 1:
print("mu: ", df.mu)
print('DRF_ss: ', eta_ss)
print('DRF_frot: ', eta_frot)
eta_sys = nf.system_reduction_factor(df.delta_ss, df.delta_frot,
df.delta_fshear, eta_ss,
eta_frot, eta_fshear)
df.eta = eta_sys
df.xi = dt.damping_from_reduction_factor(eta_sys)
df.t_eff = dt.effective_period(df.delta_d, df.eta,
df.hz.corner_disp,
df.hz.corner_period)
if verbose > 1:
print('Delta_D: ', df.delta_d)
print('Effective mass: ', df.mass_eff)
print('Effective height: ', df.height_eff)
print('Mu: ', df.mu)
print('theta yield', df.theta_y)
print('xi: ', df.xi)
print('Reduction Factor: ', df.eta)
print('t_eff', df.t_eff)
if df.t_eff > 0:
break
else:
if verbose > 1:
print("drift %.2f is not compatible" % theta_c)
k_eff = dt.effective_stiffness(df.mass_eff, df.t_eff)
v_base_dynamic = dt.design_base_shear(k_eff, df.delta_d)
v_base_p_delta = dt.p_delta_base_shear(df.mass_eff, df.delta_d,
df.height_eff, v_base_dynamic)
df.v_base = v_base_dynamic + v_base_p_delta
df.storey_forces = dt.calculate_storey_forces(df.storey_mass_p_frame,
displacements,
df.v_base,
btype='frame')
stiffness_ratio = nf.foundation_rotation_stiffness_ratio(cor_norm_rot)
k_f_eff = df.k_f_0 * stiffness_ratio
temp_found_rot = found_rot
moment_f = df.v_base * df.height_eff
found_rot = moment_f / k_f_eff
df.delta_fshear = df.v_base / (0.5 * df.k_f0_shear)
iteration_diff = (abs(temp_found_rot - found_rot) / found_rot)
if iteration_diff < found_rot_tol:
if verbose:
print('found_rot_i-1: ', temp_found_rot)
print('found_rot_i: ', found_rot)
print('n_iterations: ', iteration)
break
elif iteration == found_rot_iterations - 1:
print('found_rot_i-1: ', temp_found_rot)
print('found_rot_i: ', found_rot)
print('iteration difference: ', iteration_diff)
df.mu = -1
raise DesignError('Could not find convergence')
df.theta_f = found_rot
return df
def test_effective_stiffness():
assert isclose(dt.effective_stiffness(300, 2.0), 2959.76, rel_tol=0.0001)
assert isclose(dt.effective_stiffness(200, 1.0), 7892.7048, rel_tol=0.0001)
assert isclose(dt.effective_stiffness(100., 2.0), 986.588, rel_tol=0.0001), dt.effective_stiffness(100., 2.0)