def make_analytical(self):
if self.cantilever_side == 1:
if self.load_kind == 'Point':
self.analytical = ppbeam.cant_left_point(self.w1,self.a,self.span_length,self.backspan_length)
elif self.load_kind == 'Moment':
self.analytical = ppbeam.cant_left_point_moment(self.w1,self.a,self.span_length,self.backspan_length)
elif self.load_kind == 'UDL':
self.analytical = ppbeam.cant_left_udl(self.w1,self.a,self.b,self.span_length,self.backspan_length)
elif self.load_kind == 'TRAP':
self.analytical = ppbeam.cant_left_trap(self.w1, self.w2, self.a, self.b, self.span_length, self.backspan_length)
elif self.load_kind == 'SLOPE':
self.analytical = ppbeam.cant_left_nl(self.w1,self.span_length)
else:
self.analytical = ppbeam.no_load(0)
elif self.cantilever_side == 2:
if self.load_kind == 'Point':
self.analytical = ppbeam.cant_right_point(self.w1,self.a,self.span_length,self.backspan_length)
elif self.load_kind == 'Moment':
self.analytical = ppbeam.cant_right_point_moment(self.w1,self.a,self.span_length,self.backspan_length)
elif self.load_kind == 'UDL':
self.analytical = ppbeam.cant_right_udl(self.w1,self.a,self.b,self.span_length,self.backspan_length)
elif self.load_kind == 'TRAP':
self.analytical = ppbeam.cant_right_trap(self.w1, self.w2, self.a, self.b, self.span_length, self.backspan_length)
elif self.load_kind == 'SLOPE':
self.analytical = ppbeam.cant_right_nl(self.w1,self.span_length)
else:
self.analytical = ppbeam.no_load(0)
else:
if self.load_kind == 'Point':
self.analytical = ppbeam.pl(self.w1,self.a,self.span_length)
elif self.load_kind == 'Moment':
self.analytical = ppbeam.point_moment(self.w1,self.a,self.span_length)
elif self.load_kind == 'UDL':
self.analytical = ppbeam.udl(self.w1,self.a,self.b,self.span_length)
elif self.load_kind == 'TRAP':
self.analytical = ppbeam.trap(self.w1,self.w2,self.a,self.b,self.span_length)
elif self.load_kind == 'END_DELTA':
self.analytical = ppbeam.end_delta(self.w1,self.w2,self.span_length)
else:
self.analytical = ppbeam.no_load(0)
def applied_loads_left(self):
self.Loads = []
self.extra_station = []
for load in self.Load_List:
w1 = float(load[1])
w2 = float(load[2])
a = float(load[3])
b = float(load[4])
load_type = load[-2]
lc = self.Length
#['Point','Moment','UDL','TRAP','SLOPE']
if load_type == 'Point':
self.Loads.append(ppbeam.cant_left_point(w1, a, lc, 0))
b = min(lc, a + 0.01)
c = max(0, a - 0.01)
self.extra_station.extend([c, a, b])
elif load_type == 'Moment':
self.Loads.append(ppbeam.cant_left_point_moment(w1, a, lc, 0))
b = min(lc, a + 0.01)
c = max(0, a - 0.01)
self.extra_station.extend([c, a, b])
elif load_type == 'UDL':
self.Loads.append(ppbeam.cant_left_udl(w1, a, b, lc, 0))
self.extra_station.extend([a, b])
elif load_type == 'TRAP':
self.Loads.append(ppbeam.cant_left_trap(w1, w2, a, b, lc, 0))
self.extra_station.extend([a, b])
elif load_type == 'SLOPE':
self.Loads.append(ppbeam.cant_left_nl(w1, lc))
else:
pass
self.chart_stations.extend(self.extra_station)
self.chart_stations = list(set(self.chart_stations))
self.chart_stations.sort()
def __init__(self,beam_spans=[120.00], beam_momentofinertia=[120.00], cant='N', beam_loads_raw=[[1000.00,1000.00,60.00,60.00,'POINT',0]], E=29000000.00, iters=100, displace=[0,0]):
# Implementation of the Theory of Three Momements, https://en.wikipedia.org/wiki/Theorem_of_three_moments
# Inputs:
# beam_spans = a list of span lengths -- Expected Units: in -- Example: [120,120]
# beam_momentofinteria = a list of Moment of Inertias per span -- Expected Units: in^4 -- Example: [118,118]
# cant = cantilever designation as a string either 'L','R','B', or 'N'
# L = Left
# R = Right
# B = Both
# N = None
#
# beam_loads_raw = a list of loads (see examples of Loads below), for single applied load expects [[load per below]]
#
# Point Loads:
# [P,P,a,a,'POINT',span]
# P = Load -- Expected Units: lbs
# a = Load location from left support -- Expected Units: in
# 'POINT' = Loading type as string and in all caps options are: 'POINT', 'POINT_MOMENT', 'UDL', or 'TRAP'
# span = integer indicating what span the load is in -- 0 for first span
# P+
# ___a__|_____
# ^ ^
#
# Point Moments:
# [M,M,a,a,'POINT_MOMENT',span]
# M = Moment -- Expected Units: in-lbs
# a = Moment location from left support -- Expected Units: in
# 'POINT_MOMENT' = Loading type as string and in all caps options are: 'POINT', 'POINT_MOMENT', 'UDL', or 'TRAP'
# span = integer indicating what span the load is in -- 0 for first span
# --->M+
# ___a__|___|___
# ^ <--- ^
#
# Uniform loads:
# [w,w,a,b,'UDL',span]
# w = Load -- Expected Units: lbs per in
# a = Load start location from left support -- Expected Units: in
# b = Load end location from left support -- Expected Units: in
# 'UDL' = Loading type as string and in all caps options are: 'POINT', 'POINT_MOMENT', 'UDL', or 'TRAP'
# span = integer indicating what span the load is in -- 0 for first span
# ___w+__
# ___a_|_____|_____
# ^ | ^
# |----b-----|
#
# Trapezoidal Loads:
# [w1,w2,a,b,'TRAP',span]
# w1 = Start Load -- Expected Units: lbs per in
# w2 = End Load -- Expected Units: lbs per in
# a = Load start location from left support -- Expected Units: in
# b = Load end location from left support -- Expected Units: in
# 'TRAP' = Loading type as string and in all caps options are: 'POINT', 'POINT_MOMENT', 'UDL', or 'TRAP'
# span = integer indicating what span the load is in -- 0 for first span
# w1+
# | w2+
# ___a__|_____|___
# ^ | ^
# |------b----|
# E = modulus of elasticity assumed to be constant over all spans as a float -- Expected Units: psi
# iters = Integer number of stations to create per span
# displace = list of support displacements -- Expected Units: in -- Example: if you have N spans you should have N+1 displacement values inclusive of cantilever ends
# take care to make sure values are 0 for cantilever ends. 4 span total both cantilever list would be [0,1,0,0,0]
N = len(beam_spans) # number of spans
sumL = np.cumsum(beam_spans) # cumulative sum of beam lengths
sumL = sumL.tolist()
xs = np.zeros((iters+1, N))
j = 0
for j in range(0, N):
xs[0, j] = 0
xs[iters, j] = beam_spans[j]
i = 0
for i in range(1, iters):
xs[i, j] = xs[i-1, j] + beam_spans[j]/iters
v_diag = np.zeros((iters+1, N))
v_diag_cantL = np.zeros((iters+1, N))
v_diag_cantR = np.zeros((iters+1, N))
m_diag = np.zeros((iters+1, N))
m_diag_cantL = np.zeros((iters+1, N))
m_diag_cantR = np.zeros((iters+1, N))
s_diag = np.zeros((iters+1, N))
d_diag = np.zeros((iters+1, N))
r_span = np.zeros((2, N))
# Span as simple support Moment, Shears, and Reactions
j = 0
for j in range(0, N):
for loads in beam_loads_raw:
if loads[5] == j:
if loads[4] == "POINT":
load = ppbeam.pl(loads[0], loads[2], beam_spans[j])
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
r_span[0, j] = r_span[0, j]+load.rl
r_span[1, j] = r_span[1, j]+load.rr
elif loads[4] == "POINT_MOMENT":
load = ppbeam.point_moment(loads[0], loads[2], beam_spans[j])
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
r_span[0, j] = r_span[0, j]+load.rl
r_span[1, j] = r_span[1, j]+load.rr
elif loads[4] == "UDL":
load = ppbeam.udl(loads[0], loads[2], loads[3], beam_spans[j])
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
r_span[0, j] = r_span[0, j]+load.rl
r_span[1, j] = r_span[1, j]+load.rr
elif loads[4] == "TRAP":
load = ppbeam.trap(loads[0], loads[1], loads[2], loads[3], beam_spans[j])
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
r_span[0, j] = r_span[0, j]+load.rl
r_span[1, j] = r_span[1, j]+load.rr
elif loads[4] == "NL":
load = ppbeam.no_load()
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
r_span[0, j] = r_span[0, j]+load.rl
r_span[1, j] = r_span[1, j]+load.rr
else:
pass
else:
pass
# Horizontal center of moment region
j = 0
a_xl_xr = np.zeros((3, N))
m_xx = np.zeros((iters+1, N))
for j in range(0, N):
m_xx[:, j] = m_diag[:, j]*xs[:, j]
A = sci.integrate.simps(m_diag[:, j], xs[:, j])
a_xl_xr[0, j] = A
if A == 0:
a_xl_xr[1, j] = 0
a_xl_xr[2, j] = 0
else:
xl = (1/A)*sci.integrate.simps(m_xx[:, j], xs[:, j])
a_xl_xr[1, j] = xl
a_xl_xr[2, j] = beam_spans[j] - xl
# Cantilever Moments, Shears, and reactions
mr_cant = 0
ml_cant = 0
rr_cant = 0
rl_cant = 0
if cant[0] == 'L' or cant[0] == 'B':
v_diag[:, 0] = 0
m_diag[:, 0] = 0
s_diag[:, 0] = 0
d_diag[:, 0] = 0
for loads in beam_loads_raw:
if loads[5] == 0:
if loads[4] == "POINT":
load = ppbeam.cant_left_point(loads[0], loads[2], beam_spans[0], 0)
v = load.v(xs[:,0])
m = load.m(xs[:,0])
s = load.eis(xs[:,0]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,0]) / (beam_momentofinertia[j]*E)
v_diag[:, 0] = v_diag[:, 0]+v
m_diag[:, 0] = m_diag[:, 0]+m
s_diag[:, 0] = s_diag[:, 0]+s
d_diag[:, 0] = d_diag[:, 0]+d
rr_cant = rr_cant+load.rr
mr_cant = mr_cant+load.mr
if loads[4] == "POINT_MOMENT":
load = ppbeam.cant_left_point_moment(loads[0], loads[2], beam_spans[0], 0)
v = load.v(xs[:,0])
m = load.m(xs[:,0])
s = load.eis(xs[:,0]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,0]) / (beam_momentofinertia[j]*E)
v_diag[:, 0] = v_diag[:, 0]+v
m_diag[:, 0] = m_diag[:, 0]+m
s_diag[:, 0] = s_diag[:, 0]+s
d_diag[:, 0] = d_diag[:, 0]+d
rr_cant = rr_cant+load.rr
mr_cant = mr_cant+load.mr
elif loads[4] == "UDL":
load = ppbeam.cant_left_udl(loads[0], loads[2], loads[3], beam_spans[0], 0)
v = load.v(xs[:,0])
m = load.m(xs[:,0])
s = load.eis(xs[:,0]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,0]) / (beam_momentofinertia[j]*E)
v_diag[:, 0] = v_diag[:, 0]+v
m_diag[:, 0] = m_diag[:, 0]+m
s_diag[:, 0] = s_diag[:, 0]+s
d_diag[:, 0] = d_diag[:, 0]+d
rr_cant = rr_cant+load.rr
mr_cant = mr_cant+load.mr
elif loads[4] == "TRAP":
load = ppbeam.cant_left_trap(loads[0], loads[1], loads[2], loads[3], beam_spans[0], 0)
v = load.v(xs[:,0])
m = load.m(xs[:,0])
s = load.eis(xs[:,0]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,0]) / (beam_momentofinertia[j]*E)
v_diag[:, 0] = v_diag[:, 0]+v
m_diag[:, 0] = m_diag[:, 0]+m
s_diag[:, 0] = s_diag[:, 0]+s
d_diag[:, 0] = d_diag[:, 0]+d
rr_cant = rr_cant+load.rr
mr_cant = mr_cant+load.mr
elif loads[4] == "NL":
load = ppbeam.no_load()
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
rr_cant = 0
mr_cant = 0
else:
pass
else:
pass
if cant[0] == 'R' or cant[0] == 'B':
v_diag[:, N-1] = 0
m_diag[:, N-1] = 0
s_diag[:, N-1] = 0
d_diag[:, N-1] = 0
for loads in beam_loads_raw:
if loads[5] == N-1:
if loads[4] == "POINT":
load = ppbeam.cant_right_point(loads[0], loads[2], beam_spans[N-1], 0)
v = load.v(xs[:,N-1])
m = load.m(xs[:,N-1])
s = load.eis(xs[:,N-1]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,N-1]) / (beam_momentofinertia[j]*E)
v_diag[:, N-1] = v_diag[:, N-1]+v
m_diag[:, N-1] = m_diag[:, N-1]+m
s_diag[:, N-1] = s_diag[:, N-1]+s
d_diag[:, N-1] = d_diag[:, N-1]+d
rl_cant = rl_cant+load.rl
ml_cant = ml_cant+load.ml
if loads[4] == "POINT_MOMENT":
load = ppbeam.cant_right_point_moment(loads[0], loads[2], beam_spans[N-1], 0)
v = load.v(xs[:,N-1])
m = load.m(xs[:,N-1])
s = load.eis(xs[:,N-1]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,N-1]) / (beam_momentofinertia[j]*E)
v_diag[:, N-1] = v_diag[:, N-1]+v
m_diag[:, N-1] = m_diag[:, N-1]+m
s_diag[:, N-1] = s_diag[:, N-1]+s
d_diag[:, N-1] = d_diag[:, N-1]+d
rl_cant = rl_cant+load.rl
ml_cant = ml_cant+load.ml
elif loads[4] == "UDL":
load = ppbeam.cant_right_udl(loads[0], loads[2], loads[3], beam_spans[N-1], 0)
v = load.v(xs[:,N-1])
m = load.m(xs[:,N-1])
s = load.eis(xs[:,N-1]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,N-1]) / (beam_momentofinertia[j]*E)
v_diag[:, N-1] = v_diag[:, N-1]+v
m_diag[:, N-1] = m_diag[:, N-1]+m
s_diag[:, N-1] = s_diag[:, N-1]+s
d_diag[:, N-1] = d_diag[:, N-1]+d
rl_cant = rl_cant+load.rl
ml_cant = ml_cant+load.ml
elif loads[4] == "TRAP":
load = ppbeam.cant_right_trap(loads[0], loads[1], loads[2], loads[3], beam_spans[N-1], 0)
v = load.v(xs[:,N-1])
m = load.m(xs[:,N-1])
s = load.eis(xs[:,N-1]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,N-1]) / (beam_momentofinertia[j]*E)
v_diag[:, N-1] = v_diag[:, N-1]+v
m_diag[:, N-1] = m_diag[:, N-1]+m
s_diag[:, N-1] = s_diag[:, N-1]+s
d_diag[:, N-1] = d_diag[:, N-1]+d
rl_cant = rl_cant+load.rl
ml_cant = ml_cant+load.ml
elif loads[4] == "NL":
load = ppbeam.no_load()
v = load.v(xs[:,j])
m = load.m(xs[:,j])
s = load.eis(xs[:,j]) / (beam_momentofinertia[j]*E)
d = load.eid(xs[:,j]) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
rl_cant = 0
ml_cant = 0
else:
pass
else:
pass
self.F = np.zeros((N+1,N+1))
j=0
for j in range(1,N):
self.F[j,j-1] = beam_spans[j-1]/beam_momentofinertia[j-1]
self.F[j,j] = 2*((beam_spans[j-1]/beam_momentofinertia[j-1])+(beam_spans[j]/beam_momentofinertia[j]))
self.F[j,j+1] = beam_spans[j]/beam_momentofinertia[j]
if cant[0]=='L':
self.F[0,0] = 1
self.F[1,:] = 0
self.F[1,1] = 1
self.F[N,N] = 1
elif cant[0]=='R':
self.F[0,0] = 1
self.F[N,N] = 1
self.F[N-1,:] = 0
self.F[N-1,N-1] = 1
elif cant[0]=='B':
self.F[0,0] = 1
self.F[1,:] = 0
self.F[1,1] = 1
self.F[N,N] = 1
self.F[N-1,:] = 0
self.F[N-1,N-1] = 1
else:
self.F[0,0] = 1
self.F[N,N] = 1
self.delta = np.zeros((N+1,1))
j=0
for j in range(1,N):
l = j-1
r = j
#support settlement delta
self.delta[j] = ((-6*a_xl_xr[1,l]*a_xl_xr[0,l])/(beam_spans[l]*beam_momentofinertia[l])+(-6*a_xl_xr[2,r]*a_xl_xr[0,r])/(beam_spans[r]*beam_momentofinertia[r]))+(6*E*(((displace[l]-displace[r])/beam_spans[l])+((displace[r+1]-displace[r])/beam_spans[r])))
if cant[0]=='L':
self.delta[0] = 0
self.delta[1] = mr_cant
elif cant[0]=='R':
self.delta[N] = 0
self.delta[N-1] = ml_cant
elif cant[0]=='B':
self.delta[0] = 0
self.delta[1] = mr_cant
self.delta[N] = 0
self.delta[N-1] = ml_cant
else:
pass
#Moments @ Interior Supports
M = np.dot(inv(self.F),self.delta)
#Reactions @ interior Supports
R = np.zeros((N+1,1))
j=0
for j in range(0,N+1):
l = j-1
r = j
if j == 0:
R[j] = (r_span[0,r]) - (M[j]/beam_spans[r]) + (M[j+1]/beam_spans[r])
elif j == N:
R[j] = (r_span[1,l]) - (M[j]/beam_spans[l]) + (M[j-1]/beam_spans[l])
elif j > 0 and j < N:
R[j] = (r_span[0,r]+r_span[1,l]) - (M[j]/beam_spans[r]) - (M[j]/beam_spans[l]) + (M[j+1]/beam_spans[r]) + (M[j-1]/beam_spans[l])
else:
pass
#Support Moment response on spans
j=0
for j in range(0,N):
if j==0 and cant[0]=='L':
j+=1
elif j==0 and cant[0]=='B':
j+=1
elif j==N-1 and cant[0]=='R':
j+=1
elif j==N-1 and cant[0]=='B':
j+=1
else:
load1 = ppbeam.point_moment(M[j],0,beam_spans[j])
load2 = ppbeam.point_moment(-1.0*M[j+1],beam_spans[j],beam_spans[j])
v = load1.v(xs[:,j]) + load2.v(xs[:,j])
m = load1.m(xs[:,j]) + load2.m(xs[:,j])
s = (load1.eis(xs[:,j]) + load2.eis(xs[:,j])) / (beam_momentofinertia[j]*E)
d = (load1.eid(xs[:,j]) + load2.eid(xs[:,j])) / (beam_momentofinertia[j]*E)
v_diag[:, j] = v_diag[:, j]+v
m_diag[:, j] = m_diag[:, j]+m
s_diag[:, j] = s_diag[:, j]+s
d_diag[:, j] = d_diag[:, j]+d
#correct d for support displacement
for j in range(0,N):
span = beam_spans[j]
slope_i = math.atan(-1.0*(displace[j]-displace[j+1])/span)
s_diag[:,j] = s_diag[:,j] + slope_i
for i in range(0,len(xs[:,j])):
delt_i = displace[j] + (((displace[j+1]-displace[j])/span)*xs[i,j])
d_diag[i,j] = d_diag[i,j] + delt_i
#correct cantilever d for support displacement
if cant[0]=='L' or cant[0] =='B':
if displace[2] == 0 and displace[1] == 0:
pass
else:
d_diag[:,0] = d_diag[:,0]+displace[1]
if cant[0]=='R' or cant[0] =='B':
if displace[N-2] == 0 and displace[N-1] == 0:
pass
else:
d_diag[:,-1] = d_diag[:,-1]+displace[-2]
#correct cantilever slope and deflection for interior span end slopes
if cant[0]=='L' or cant[0]=='B':
cant_l_fix = ppbeam.cant_left_nl(s_diag[0,1], beam_spans[0])
s = cant_l_fix.eis(xs[:,0])
d = cant_l_fix.eid(xs[:,0])
s_diag[:, 0] = s_diag[:, 0]+s
d_diag[:, 0] = d_diag[:, 0]+d
else:
pass
if cant[0]=='R' or cant[0]=='B':
cant_r_fix = ppbeam.cant_right_nl(s_diag[-1,-2])
s = cant_r_fix.eis(xs[:,-1])
d = cant_r_fix.eid(xs[:,-1])
s_diag[:, -1] = s_diag[:, -1]+s
d_diag[:, -1] = d_diag[:, -1]+d
else:
pass
j=0
for j in range(1,N):
xs[:,j] = xs[:,j] + sumL[j-1] #converts lengths to global rather than local ie span 2 x[0] now = span 1 x[-1] or length in lieu of 0
xs = xs/12
for j in range(0,N):
v_diag[:,j] = v_diag[:,j]/1000 #assumes input of lbs and converts output to kips
m_diag[:,j] = m_diag[:,j]/(12*1000) #assumes input of in and lbs and converts output to ft-kips
self.xs = xs
self.v_diag = v_diag
self.m_diag = m_diag
self.s_diag = s_diag
self.d_diag = d_diag
self.R = R
self.M = M