def diagramsx(step):
forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily, dlgy)
Fx1 = -forces[0][0]
Fx2 = -(forces[1][0] + forces[2][0])
# input data
Vx = []
Mx = []
# step = 0.01
z0 = 0.0
z1 = L - Lf1 - Lf2
z2 = L - Lf1
z3 = L + step
int1, int2, int3 = 0.0, 0.0, 0.0
# working out the shear and moments in the three intervals
int1 = np.arange(z0, z1, step)
vlocal = np.ones(len(int1)) * Sx
mlocal = Sx * (2.8 + int1)
Vx = np.append(Vx, vlocal)
Mx = np.append(Mx, mlocal)
int2 = np.arange(z1, z2, step)
vlocal = np.ones(len(int2)) * (Sx + Fx2)
mlocal = Sx * (2.8 + int2) + Fx2 * (int2 - z1)
Vx = np.append(Vx, vlocal)
Mx = np.append(Mx, mlocal)
int3 = np.arange(z2, 30.00005, step)
vlocal = np.ones(len(int3)) * (Sx + Fx2 + Fx1)
mlocal = Sx * (2.8 + int3) + Fx2 * (int3 - z1) + Fx1 * (int3 - z2)
Vx = np.append(Vx, vlocal)
Mx = np.append(Mx, mlocal)
# finding the max values and their location on the z axis:
Vxmax = np.amax(abs(Vx))
Vxpos = (np.argmax(abs(Vx))) * step
Mxmax = np.amax(abs(Mx))
Mxpos = (np.argmax(abs(Mx))) * step
print "Vxmax =", Vxmax, "N", "at z =", Vxpos, "m"
print "Mxmax =", Mxmax, "N*m", "at z =", Mxpos, "m"
# plotting the diagrams
x = np.arange(0, z3, step)
y1 = Vx
y2 = Mx
if __name__ == "__main__":
plt.plot(x, y1, label="shear")
plt.plot(x, y2, label="moment")
plt.legend()
plt.show()
# return output
return Vx, Mx, Vxmax, Vxpos, Mxmax, Mxpos
def diagramsx(step):
forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily, dlgy)
Fx1 = -forces[0][0]
Fx2 = -(forces[1][0] + forces[2][0])
#input data
Vx = []
Mx = []
# step = 0.01
z0 = 0.
z1 = L-Lf1-Lf2
z2 = L-Lf1
z3 = L + step
int1, int2, int3 = 0.,0.,0.
# working out the shear and moments in the three intervals
int1 = np.arange(z0,z1,step)
vlocal = np.ones(len(int1))*Sx
mlocal = Sx*(2.8+int1)
Vx = np.append(Vx,vlocal)
Mx = np.append(Mx,mlocal)
int2 = np.arange(z1,z2,step)
vlocal = np.ones(len(int2))*(Sx + Fx2)
mlocal = Sx*(2.8+int2) + Fx2*(int2-z1)
Vx = np.append(Vx,vlocal)
Mx = np.append(Mx,mlocal)
int3 = np.arange(z2,30.00005,step)
vlocal = np.ones(len(int3))*(Sx + Fx2 + Fx1)
mlocal = Sx*(2.8+int3) + Fx2*(int3-z1) + Fx1*(int3-z2)
Vx = np.append(Vx,vlocal)
Mx = np.append(Mx,mlocal)
# finding the max values and their location on the z axis:
Vxmax = np.amax(abs(Vx))
Vxpos = (np.argmax(abs(Vx)))*step
Mxmax = np.amax(abs(Mx))
Mxpos = (np.argmax(abs(Mx)))*step
print "Vxmax =",Vxmax,"N", "at z =",Vxpos,"m"
print "Mxmax =",Mxmax,"N*m", "at z =",Mxpos,"m"
# plotting the diagrams
x = np.arange(0,z3,step)
y1 = Vx
y2 = Mx
if __name__=="__main__":
plt.plot(x,y1,label='shear')
plt.plot(x,y2,label='moment')
plt.legend()
plt.show()
# return output
return Vx, Mx, Vxmax, Vxpos, Mxmax, Mxpos
def diagramsy(step):
forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily,
dlgy)
Fy1 = forces[0][1]
Fy2 = forces[1][1] + forces[2][1]
#input data
Vy = []
My = []
# step = 0.01
z0 = 0.
z1 = L - Lf1 - Lf2
z2 = L - Lf1
z3 = L + step
int1, int2, int3 = 0., 0., 0.
# working out the shear and moments in the three intervals
int1 = np.arange(z0, z1, step)
vlocal = -q * int1
mlocal = -q * int1 * int1 / 2.
Vy = np.append(Vy, vlocal)
My = np.append(My, mlocal)
int2 = np.arange(z1, z2, step)
vlocal = -q * int2 + Fy2
mlocal = -q * int2 * int2 / 2. + Fy2 * (int2 - z1)
Vy = np.append(Vy, vlocal)
My = np.append(My, mlocal)
int3 = np.arange(z2, 30.000009, step)
vlocal = -q * int3 + Fy2 + Fy1
mlocal = -q * int3 * int3 / 2. + Fy2 * (int3 - z1) + Fy1 * (int3 - z2)
Vy = np.append(Vy, vlocal)
My = np.append(My, mlocal)
# finding the max values and their location on the z axis:
Vymax = np.amax(abs(Vy))
Vypos = (np.argmax(abs(Vy))) * step
Mymax = np.amax(abs(My))
Mypos = (np.argmax(abs(My))) * step
print "Vymax =", Vymax, "N", "at z =", Vypos, "m"
print "Mymax =", Mymax, "N*m", "at z =", Mypos, "m"
# plotting the diagrams
x = np.arange(0, z3, step)
y1 = Vy
y2 = My
if __name__ == "__main__":
plt.plot(x, y1, label='shear')
plt.plot(x, y2, label='moment')
plt.legend()
plt.show()
# return output
return Vy, My, Vymax, Vypos, Mymax, Mypos
def diagramsy(step):
forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily, dlgy)
Fy1 = forces[0][1]
Fy2 = forces[1][1] + forces[2][1]
#input data
Vy = []
My = []
# step = 0.01
z0 = 0.
z1 = L-Lf1-Lf2
z2 = L-Lf1
z3 = L + step
int1, int2, int3 = 0.,0.,0.
# working out the shear and moments in the three intervals
int1 = np.arange(z0,z1,step)
vlocal = -q*int1
mlocal = -q*int1*int1/2.
Vy = np.append(Vy,vlocal)
My = np.append(My,mlocal)
int2 = np.arange(z1,z2,step)
vlocal = -q*int2 + Fy2
mlocal = -q*int2*int2/2. + Fy2*(int2-z1)
Vy = np.append(Vy,vlocal)
My = np.append(My,mlocal)
int3 = np.arange(z2,30.000009,step)
vlocal = -q*int3 + Fy2 + Fy1
mlocal = -q*int3*int3/2. + Fy2*(int3-z1) + Fy1*(int3-z2)
Vy = np.append(Vy,vlocal)
My = np.append(My,mlocal)
# finding the max values and their location on the z axis:
Vymax = np.amax(abs(Vy))
Vypos = (np.argmax(abs(Vy)))*step
Mymax = np.amax(abs(My))
Mypos = (np.argmax(abs(My)))*step
print "Vymax =",Vymax,"N", "at z =",Vypos,"m"
print "Mymax =",Mymax,"N*m", "at z =",Mypos,"m"
# plotting the diagrams
x = np.arange(0,z3,step)
y1 = Vy
y2 = My
if __name__=="__main__":
plt.plot(x,y1,label='shear')
plt.plot(x,y2,label='moment')
plt.legend()
plt.show()
# return output
return Vy,My, Vymax, Vypos, Mymax, Mypos
dlgy = 1.8 L = 30. Lf1 = 4.0 Lf2 = 12.5 Lf3 = 5.2 W = 65000.0 Sx = 170000.0 dtailz = 2.8 dtaily = 5.0 # moments of inertia Ixx = np.pi*R*R*R*ts Iyy = Ixx Ixy = 0. forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily, dlgy) Fx1 = forces[0][0] Fx2 = forces[1][0] + forces[2][0] Fy1 = forces[0][1] Fy2 = forces[1][1] + forces[2][1] # solving the equations interval = np.linspace(0.,2*np.pi,n) part11 = - Fx1/Ixx*ts*(R*R*np.sin(interval)) part21 = - Fy1/Iyy*ts*(R*R*np.cos(interval)) part12 = - Fx2/Ixx*ts*(R*R*np.sin(interval)) part22 = - Fy2/Iyy*ts*(R*R*np.cos(interval)) qb1 = part11 + part21 q01 = Fx1*(R+dlgy)/(2*A)
dlgy = 1.8 L = 30.0 Lf1 = 4.0 Lf2 = 12.5 Lf3 = 5.2 W = 65000.0 Sx = 170000.0 dtailz = 2.8 dtaily = 5.0 # moments of inertia Ixx = np.pi * R * R * R * ts Iyy = Ixx Ixy = 0.0 forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily, dlgy) Fx1 = forces[0][0] Fx2 = forces[1][0] + forces[2][0] Fy1 = forces[0][1] Fy2 = forces[1][1] + forces[2][1] # solving the equations interval = np.linspace(0.0, 2 * np.pi, n) part11 = -Fx1 / Ixx * ts * (R * R * np.sin(interval)) part21 = -Fy1 / Iyy * ts * (R * R * np.cos(interval)) part12 = -Fx2 / Ixx * ts * (R * R * np.sin(interval)) part22 = -Fy2 / Iyy * ts * (R * R * np.cos(interval)) qb1 = part11 + part21 q01 = Fx1 * (R + dlgy) / (2 * A)
def shearstressT():
#### geom calculations
Iyy = mn.realMomentOfInertia('y', R, ts, fh, tf, hst, wst, tst)
Sfic = 20.
d = 0.2
step = 100.
a = np.sqrt(R*R-d*d)
alpha = np.arcsin(0.2/R)
###################### SHEAR CENTER CALCULATION FOR REAL STRUCTURE
########## CELL 1
int12 = np.linspace(0,2*a,step)
qb12 = -(Sfic/Iyy)*tf*0.5*int12*int12
int21 = np.linspace(0,np.pi+2*alpha,step)
qb21 = qb12[-1] - (Sfic/Iyy)*ts*R*R*np.sin(int21)
# qs0 = -int(qb*ds)/int(ds)
term1 = (Sfic/Iyy)*(tf/2.)*((2*a)*(2*a)*(2*a)/3.) - qb12[-1]*R*(np.pi+2*alpha)
term2 = (Sfic/Iyy)*ts*R*R*R*0.5*(-np.cos(3*np.pi+2*alpha)+np.cos(np.pi))
qs0 = (term1 + term2)/(2*a + (np.pi+2*alpha)*R)
q112 = qb12 + qs0
q121 = qb21 + qs0
############ CELL 2
int12 = np.linspace(0,np.pi-2*alpha,step)
qb12 = - (Sfic/Iyy)*ts*R*R*np.sin(int12)
int21 = np.linspace(0,2*a,step)
qb21 = qb12[-1] -(Sfic/Iyy)*tf*0.5*int12*int12
# qs0 = -int(qb*ds)/int(ds)
term1 = -(Sfic/Iyy)*(ts*R*R*R*0.5)*(np.cos(-np.pi+4*alpha)-np.cos(np.pi))
term2 = -qb12[-1]*2*a - (Sfic/Iyy)*tf*0.5*((2*a)*(2*a)*(2*a)/3.)
qs0 = (term1 + term2)/(2*a + (np.pi-2*alpha)*R)
q212 = qb12 + qs0
q221 = qb21 + qs0
########### STRUCTURE
q1 = q112
q2 = q212
qfl = q121 - q221[::-1]
########### MOMENT EQUIVALENCE AROUND CENTER
sc_y = (R*sum(q1) + R*sum(q2) + d*sum(qfl))/Sfic
#print sc_y
##############################################################
############ TORQUE CALCULATION AROUND Z
'''
T = Sx*(dlgy+dtailz-dy) torque at z=0 around shear center
T2 = FyL*dx - FyR*dx - Fx2*dy
T1 = Fx1*dy
T - T1 - T2 = 0
'''
forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily, dlgy)
Fx1 = forces[0][0]
Fx2 = forces[1][0] + forces[2][0]
FyR = forces[2][1]
FyL = forces[1][1]
a = np.array([[1,1,Sx],[0,1,-Fx2],[1,0,-Fx1]])
b = np.array([Sx*(dlgy+dtailz), FyL*Lf3*0.5 - FyR*Lf3*0.5,0])
x = np.linalg.solve(a, b)
T1 = x[0]
T2 = x[1]
dy = x[2]
T = Sx*(dlgy+dtailz-dy)
step = 0.01
z = np.arange(0,30+step,step)
y1 = np.ones((13.5+step)/step)*(T)
y2 = np.ones(12.5/step)*(T-T2)
y3 = np.ones(4.0/step)*(T-T2-T1)
y = np.append(y1,y2)
y = np.append(y,y3)
if __name__=="__main__":
plt.plot(z,y)
plt.show()
shearT = []
torques = (T, T-T2, T-T2-T1)
for i in range(3):
T = Sx*(dlgy+dtailz-dy)
if i==1:
T = T - T2
if i==2:
T = T - T2 - T1
# geometrical parameters of the strucutre
alpha = np.arccos((R-fh)/R)
A2 = alpha*R*R - np.cos(alpha)*np.sin(alpha)*R*R
A1 = np.pi*R*R - A2
#print 'A1',A1,'A2',A2
# lengths calculations
s1 = 2*np.pi*R - 2*alpha*R
s2 = 2*np.pi*R - s1
s12 = 2*np.sin(alpha)*R
# using equality of rates of twist and simplifying:
term1 = s1/(A1*ts) + s12/(A1*tf) + s12/(A2*tf)
term2 = s2/(A2*ts) + s12/(A2*tf) + s12/(A1*tf)
# solving for q1 and q2
a = np.array([[term1,-term2], [2*A1,2*A2]])
b = np.array([0,T])
x = np.linalg.solve(a, b)
q1 = x[0]
q2 = x[1]
tau1 = q1/ts
tau2 = q2/ts
tau12 = (q1-q2)/tf
shearT.append((tau1,tau2,tau12))
return shearT, torques
def shearstressT():
#### geom calculations
Iyy = mn.realMomentOfInertia('y', R, ts, fh, tf, hst, wst, tst)
Sfic = 20.
d = 0.2
step = 100.
a = np.sqrt(R * R - d * d)
alpha = np.arcsin(0.2 / R)
###################### SHEAR CENTER CALCULATION FOR REAL STRUCTURE
########## CELL 1
int12 = np.linspace(0, 2 * a, step)
qb12 = -(Sfic / Iyy) * tf * 0.5 * int12 * int12
int21 = np.linspace(0, np.pi + 2 * alpha, step)
qb21 = qb12[-1] - (Sfic / Iyy) * ts * R * R * np.sin(int21)
# qs0 = -int(qb*ds)/int(ds)
term1 = (Sfic / Iyy) * (tf / 2.) * (
(2 * a) * (2 * a) * (2 * a) / 3.) - qb12[-1] * R * (np.pi + 2 * alpha)
term2 = (Sfic / Iyy) * ts * R * R * R * 0.5 * (
-np.cos(3 * np.pi + 2 * alpha) + np.cos(np.pi))
qs0 = (term1 + term2) / (2 * a + (np.pi + 2 * alpha) * R)
q112 = qb12 + qs0
q121 = qb21 + qs0
############ CELL 2
int12 = np.linspace(0, np.pi - 2 * alpha, step)
qb12 = -(Sfic / Iyy) * ts * R * R * np.sin(int12)
int21 = np.linspace(0, 2 * a, step)
qb21 = qb12[-1] - (Sfic / Iyy) * tf * 0.5 * int12 * int12
# qs0 = -int(qb*ds)/int(ds)
term1 = -(Sfic / Iyy) * (ts * R * R * R * 0.5) * (
np.cos(-np.pi + 4 * alpha) - np.cos(np.pi))
term2 = -qb12[-1] * 2 * a - (Sfic / Iyy) * tf * 0.5 * ((2 * a) * (2 * a) *
(2 * a) / 3.)
qs0 = (term1 + term2) / (2 * a + (np.pi - 2 * alpha) * R)
q212 = qb12 + qs0
q221 = qb21 + qs0
########### STRUCTURE
q1 = q112
q2 = q212
qfl = q121 - q221[::-1]
########### MOMENT EQUIVALENCE AROUND CENTER
sc_y = (R * sum(q1) + R * sum(q2) + d * sum(qfl)) / Sfic
#print sc_y
##############################################################
############ TORQUE CALCULATION AROUND Z
'''
T = Sx*(dlgy+dtailz-dy) torque at z=0 around shear center
T2 = FyL*dx - FyR*dx - Fx2*dy
T1 = Fx1*dy
T - T1 - T2 = 0
'''
forces = mn.reactionForces(Lf1, Lf2, Lf3, L, R, W, Sx, dtailz, dtaily,
dlgy)
Fx1 = forces[0][0]
Fx2 = forces[1][0] + forces[2][0]
FyR = forces[2][1]
FyL = forces[1][1]
a = np.array([[1, 1, Sx], [0, 1, -Fx2], [1, 0, -Fx1]])
b = np.array([Sx * (dlgy + dtailz), FyL * Lf3 * 0.5 - FyR * Lf3 * 0.5, 0])
x = np.linalg.solve(a, b)
T1 = x[0]
T2 = x[1]
dy = x[2]
T = Sx * (dlgy + dtailz - dy)
step = 0.01
z = np.arange(0, 30 + step, step)
y1 = np.ones((13.5 + step) / step) * (T)
y2 = np.ones(12.5 / step) * (T - T2)
y3 = np.ones(4.0 / step) * (T - T2 - T1)
y = np.append(y1, y2)
y = np.append(y, y3)
if __name__ == "__main__":
plt.plot(z, y)
plt.show()
shearT = []
torques = (T, T - T2, T - T2 - T1)
for i in range(3):
T = Sx * (dlgy + dtailz - dy)
if i == 1:
T = T - T2
if i == 2:
T = T - T2 - T1
# geometrical parameters of the strucutre
alpha = np.arccos((R - fh) / R)
A2 = alpha * R * R - np.cos(alpha) * np.sin(alpha) * R * R
A1 = np.pi * R * R - A2
#print 'A1',A1,'A2',A2
# lengths calculations
s1 = 2 * np.pi * R - 2 * alpha * R
s2 = 2 * np.pi * R - s1
s12 = 2 * np.sin(alpha) * R
# using equality of rates of twist and simplifying:
term1 = s1 / (A1 * ts) + s12 / (A1 * tf) + s12 / (A2 * tf)
term2 = s2 / (A2 * ts) + s12 / (A2 * tf) + s12 / (A1 * tf)
# solving for q1 and q2
a = np.array([[term1, -term2], [2 * A1, 2 * A2]])
b = np.array([0, T])
x = np.linalg.solve(a, b)
q1 = x[0]
q2 = x[1]
tau1 = q1 / ts
tau2 = q2 / ts
tau12 = (q1 - q2) / tf
shearT.append((tau1, tau2, tau12))
return shearT, torques
