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### Check out-of-plane
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# Copyright ©VIIA 2025
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### 1. Import modules
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# General imports
import math
import json
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### 2. Function to check for out-of-plane behaviour walls
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[docs]def viia_check_out_of_plane(
wall_type: float, wall_height: float, total_height: float, wall_thickness: float, wall_weight: float,
overburden_load: float, inclination_angle: float, peak_ground_acceleration: float, fundamental_period: float):
"""
Function to find the seismic out-of plane resistance and seismic demand of masonry walls
Input:
- wall_type (float): Type of the wall studied, either vertically spanning, i.e. type 1 or cantilever wall,
i.e. type 2.
- wall_height (float): Height of the wall considered, in [m].
- total_height (float): Total height of the building considered, in [m].
- wall_thickness (float): The thickness of the wall considered, in [m].
- wall_weight (float): Self weight of the masonry wall, in [kg/m3].
- overburden_load (float): The overburden load on the wall, in [kN/m].
- inclination_angle (float): The rotation angle of the wall, in [deg].
- peak_ground_acceleration (float): Maximum ground acceleration at the location of the building, in [m/s2].
- fundamental_period (float): Fundamental period of vibration of the building, in [s].
Output:
- Returns the seismic out-of-plane resistance and seismic demand of masonry walls is calculated.
"""
hw = wall_height
ht = total_height
tw = wall_thickness
w = wall_weight
fnt = overburden_load
psi = inclination_angle
agd = peak_ground_acceleration
t1 = fundamental_period
tnom = tw / (0.975 - 0.025 * fnt / w)
g = 9.81 # ground acceleration in m/s2
# finding eccentricities according to the boundary conditions
if wall_type == 1:
eb, ep, e0, et, beta = _boundary_one(tw)
elif wall_type == 2:
eb, ep, beta = boundary_two(tw)
# finding the weight distribution, assuming uniform thickness of walls
if wall_type == 1:
wb, wt, yb, yt = weight_distribution_one(w, hw)
elif wall_type == 2:
y = weight_distribution_two(hw)
# calculating the seismic resistance
if wall_type == 1:
ar = seismic_resistance_one(wb, wt, yb, yt, hw, fnt, eb, et, e0, ep, psi, w, tnom, g, beta)
ar = round(ar, 2)
elif wall_type == 2:
ar = seismic_resistance_two(w, hw, y, fnt, eb, ep, g, tnom, beta)
ar = round(ar, 2)
# Calculating the seismic demand
sad = determine_s_ad(wall_type, hw, ht, fnt, w, agd, t1)
sad = round(sad, 2)
results = {
'ratio': 'Fnt/W=' + str(fnt / w),
'wall thickness': str(tw * 1000) + 'mm',
'values': [{'height': hw, 'resistance': ar, 'demand': sad}]}
# Saving to a json file
with open('results.json', 'w') as file:
json.dump(results, file, indent=4)
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### 3. Helper functions
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def _boundary_one(tw):
""" This function finds the eccentricities eb, ep, e0, et, and beta for vertically spanning walls."""
eb = 0
ep = 0
e0 = 0.5 * tw
et = 0.5 * tw
beta = 4.07
return eb, ep, e0, et, beta
[docs]def boundary_two(tw):
""" This function finds the eccentricities eb, ep, and beta for cantilever walls."""
eb = 0.5 * tw
ep = 0
beta = 3.1
return eb, ep, beta
[docs]def weight_distribution_one(w, hw):
"""
This function finds the weight for the lower half of the wall, the weight of the upper half of the wall and the y
distances where these weights act for vertically spanning walls
Input:
- w : masonry wall weight
- hw: height of the wall considered
Output:
- wb: weight of the lower half of the wall
- wt: weight of the upper half of the wall
- yb: distance y where the weight of the lower wall acts
- yt: distance y where the weight of the upper wall acts
"""
wb = 0.5 * w
wt = 0.5 * w
yb = 0.25 * hw
yt = 0.25 * hw
return wb, wt, yb, yt
[docs]def weight_distribution_two(hw):
""" This function finds the y distance where the weight acts for cantilever walls."""
y = 0.5 * hw
return y
[docs]def seismic_resistance_one(wb, wt, yb, yt, hw, fnt, eb, et, e0, ep, psi, w, tnom, g, beta):
""" This function calculates the seismic out-of-plane resistance of vertically spanning masonry walls."""
# virtual work calculation
a = wb * yb + wt * (hw - yt) + fnt * hw
b = wb * eb + wt * (e0 + eb + et) + fnt * (e0 + eb + et + ep) - psi * (wb * yb + wt * yt)
# angle = b / a
# maximum deflection
delta_i = b * hw / (2 * a)
delta_m = 0.6 * delta_i
# mass moment of inertia j, of the total kinematic wall system, gets canceled in the main formula for resistance
j = (1 / 12) * (w / g) * (tnom ** 2 + (hw / 2) ** 2) + (
wb * (eb ** 2 + yb ** 2) + wt * ((e0 + eb + et) ** 2 + yt ** 2)
+ fnt * (e0 + eb + et + ep) ** 2) / g
# mass participation factor
gamma = w * hw ** 2 / (8 * j * g)
# period
tp = beta * (j / a) ** 0.5
# seismic resistance; vertically spanning wall
ar = ((2 * math.pi) / tp) ** 2 * (delta_m / (gamma * g))
return ar
[docs]def seismic_resistance_two(w, hw, y, fnt, eb, ep, g, tnom, beta):
""" This function calculates the seismic out-of-plane resistance of cantilever masonry walls."""
# Virtual work
a = w * y + fnt * hw
b = w * eb + fnt * (eb + ep)
# angle = b / a
# maximum deflection
delta_i = b * hw / a
delta_m = 0.3 * delta_i
# mass moment of inertia j, of the total kinematic wall system, gets canceled in the main formula for resistance
j = (1 / 12) * (w / g) * (tnom ** 2 + hw ** 2) + (
w * (eb ** 2 + y ** 2) + fnt * (hw ** 2 + (eb + ep) ** 2)) / g
# mass participation factor
gamma = w * hw ** 2 / (2 * j * g)
# period
tp = beta * (j / a) ** 0.5
# seismic resistence; cantiliver wall
ar = ((2 * math.pi) / tp) ** 2 * (delta_m / (gamma * g))
return ar
[docs]def determine_s_ad(wall_type, hw, ht, fnt, w, agd, t1):
""" This function calculates the seismic demand Sad (in g) according to the wall type, i.e. type 1 for vertically
spanning and type 2 for cantilever walls."""
if wall_type == 1:
qa = 2
else:
qa = 1
ta = ((0.28 * hw) / (1 + (2 * fnt / w))) ** 0.5
z = 0.5 * hw
sad = (agd / qa) * (3 * (1 + z / ht) / (1 + (1 - ta / t1) ** 2) - 0.5)
if sad >= agd / qa:
return sad
else:
sad = agd / qa
return sad
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### 4. End of script
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