def solve_x_Asp_known(α1, fc, b, h0, N, e, fy_, As_, as_):
'''已知受压钢筋面积As_求x'''
_a = α1 * fc * b / 2
_b = -α1 * fc * b * h0
_c = N * e - fy_ * As_ * (h0 - as_)
d = _b**2 - 4 * _a * _c
if d > 0:
valids = []
d = sqrt(d)
x1 = (-_b + d) / 2 / _a
if x1 > 0:
valids.append(x1)
x2 = (-_b - d) / 2 / _a
if x2 > 0:
valids.append(x2)
n = len(valids)
if n < 1:
raise numeric.NumericError('No proper solution.')
elif n == 1:
return valids[0]
else:
return min(valids)
else:
raise numeric.NumericError('No solution.')
def solve_x_As_known(cls, N, e, α1, fc, b, x, h0, fy_, as_, Es, εcu, β1,
As):
'''已知受拉钢筋面积As求x'''
x0 = x
x1 = cls.f_x_As_known(N, e, α1, fc, b, x0, h0, fy_, as_, Es, εcu, β1,
As)
count = 0
while abs(x1 - x0) > 1E-6 and count < 100:
x0 = x1
x1 = cls.f_x_As_known(N, e, α1, fc, b, x0, h0, fy_, as_, Es, εcu,
β1, As)
count += 1
if count > 99:
raise numeric.NumericError('No real solution.')
return x1
def active_earth_pressure_live(cls, φ, α, B, γ, H, G, δ=None):
δ = δ or φ / 2
ω = α + δ + φ
tmp = (1 / tan(φ) + tan(ω)) * (tan(ω) - tan(α))
if tmp < 0:
raise numeric.NumericError(
'公式(4.2.3-7)tanθ=-tan(ω)+sqrt((1/tan(φ)+tan(ω))*(tan(ω)-tan(α)))\
计算时根号中出现负值，请检查角度输入是否合理')
tanθ = -tan(ω) + sqrt(tmp) # (4.2.3-7)
l0 = H * (tan(α) + tanθ)
h = G / B / l0 / γ # (4.3.4-1)
β = 0
μ = cls.fμ(φ, α, β, δ)
E = 1 / 2 * B * μ * γ * H * (H + 2 * h) # (4.2.3-6)
C = H / 3 * (H + 3 * h) / (H + 2 * h)
return (l0, h, E, C)
def solve_M(cls, α1, fc, fy, r, rs, A, As, N):
"""
求解alpha和M,已知N和As
"""
def f(α, α1, fc, fy, r, rs, A, As, N):
# 式(E.0.4-1)两边取等号求解α，由于方程非线性，构造牛顿迭代法表达式
if α < 0.625:
return (N + α1 * fc * A * sin(2 * pi * α) / 2 / pi +
1.25 * fy * As) / (α1 * fc * A + 3 * fy * As)
return (N + α1 * fc * A * sin(2 * pi * α) / 2 / pi) / (
α1 * fc * A + fy * As)
# 牛顿迭代法
α = None
try:
α = numeric.iteration_method_solve(f,
0.2,
α1=α1,
fc=fc,
fy=fy,
r=r,
rs=rs,
A=A,
As=As,
N=N)
except:
try:
α = numeric.iteration_method_solve(f,
0.65,
α1=α1,
fc=fc,
fy=fy,
r=r,
rs=rs,
A=A,
As=As,
N=N)
except:
pass
if α != None:
Mu = cls.f_M(α, α1, fc, fy, r, rs, A, As)
return (α, Mu)
raise numeric.NumericError('No real solution')
def solve_As(α1, fc, fy, r, rs, A, N, M):
"""
求解alpha和As,已知N和M
"""
def _fMeq(α, α1, fc, fy, r, rs, A, N, M):
# 由方程（E.0.4-1)得到As的表达式，代入（E.0.4-2)，得到关于α的方程
if α < 0.625:
αt = 1.25 - 2 * α
else:
αt = 0
C1 = 2 / 3 * sin(pi * α)**3 / pi
C2 = (sin(pi * α) + sin(pi * αt)) / pi
fyAs = (N - α1 * fc * A *
(α - sin(2 * pi * α) / 2 / pi)) / (α - αt)
return α1 * fc * A * r * C1 + fyAs * rs * C2 - M
# 以1.25/3为界查找有值区间
x0 = 0
x1 = 1.25 / 3 * 0.999
f0 = _fMeq(x0, α1, fc, fy, r, rs, A, N, M)
f1 = _fMeq(x1, α1, fc, fy, r, rs, A, N, M)
if f0 * f1 > 0:
x0 = 1.25 / 3 * 1.001
x1 = 1
f0 = _fMeq(x0, α1, fc, fy, r, rs, A, N, M)
f1 = _fMeq(x1, α1, fc, fy, r, rs, A, N, M)
if f0 * f1 > 0:
raise numeric.NumericError('No real solution.')
α = numeric.binary_search_solve(_fMeq,
x0,
x1,
α1=α1,
fc=fc,
fy=fy,
r=r,
rs=rs,
A=A,
N=N,
M=M)
As = fc_round.f_As(α, α1, fc, fy, A, N)
return (α, As)
def solve_As(cls, α1, fc, fy, r1, r2, rs, A, N, M):
"""
求解α和As,已知N和M
"""
def _fMeq(α, α1, fc, fy, r1, r2, rs, A, N, M):
# 由方程（E.0.3-1)得到As的表达式，代入（E.0.3-2)，得到关于α的方程
if α < 0.625:
αt = 1.25 - 2 * α
else:
αt = 0
fyAs = (N - α * α1 * fc * A) / (α - αt)
return α1 * fc * A * (r1 + r2) * sin(
pi * α) / 2 / pi + fyAs * rs * (
(sin(pi * α) + sin(pi * αt)) / pi) - M
# 以1.25/3为界查找有值区间
x0 = 0
x1 = 1.25 / 3 * 0.999
f0 = _fMeq(x0, α1, fc, fy, r1, r2, rs, A, N, M)
f1 = _fMeq(x1, α1, fc, fy, r1, r2, rs, A, N, M)
if f0 * f1 > 0:
x0 = 1.25 / 3 * 1.001
x1 = 1
f0 = _fMeq(x0, α1, fc, fy, r1, r2, rs, A, N, M)
f1 = _fMeq(x1, α1, fc, fy, r1, r2, rs, A, N, M)
if f0 * f1 > 0:
raise numeric.NumericError('No real solution.')
α = numeric.binary_search_solve(_fMeq,
x0,
x1,
α1=α1,
fc=fc,
fy=fy,
r1=r1,
r2=r2,
rs=rs,
A=A,
N=N,
M=M)
As = cls.f_As(α, α1, fc, fy, A, N)
return (α, As)