Example #1
0
def boomAreas(Mx, My, booms, R, ts, floorHeight, tf, hst, wst, tst):
    Ixx = main.realMomentOfInertia("x", R, ts, floorHeight, tf, hst, wst, tst)
    Iyy = main.realMomentOfInertia("y", R, ts, floorHeight, tf, hst, wst, tst)
    stressBases = [0] * len(booms)
    floorDist1 = [0] * len(booms)
    floorDist2 = [0] * len(booms)

    floorAngle = np.arccos((R - floorHeight) / R)
    floorLength = R * np.sin(floorAngle)
    floorAttach1 = (floorLength, floorHeight - R)
    floorAttach2 = (-floorLength, floorHeight - R)

    Cx, Cy = main.realCentroid(R, ts, floorHeight, tf, hst, wst, tst)

    for i, (x, y) in enumerate(booms):
        #Calculate stress without terms that will vanish
        stressBases[i] = My / Iyy * (x - Cx) + Mx / Ixx * (y - Cy)
        #         if stressBases[i] == 0:
        #             print My, Iyy, Mx, Ixx, x, Cx, y, Cy
        #Check how close this boom is to the floor attachment
        floorDist1[i] = ((x - floorAttach1[0])**2 +
                         (y - floorAttach1[1])**2)**0.5
        floorDist2[i] = ((x - floorAttach2[0])**2 +
                         (y - floorAttach2[1])**2)**0.5

    #Check which booms the floor should be connected to
    attach1 = floorDist1.index(min(floorDist1))
    attach2 = floorDist2.index(min(floorDist2))

    attachments = connections(booms, (attach1, attach2))

    areas = []
    for n in range(len(booms)):
        A = 0.
        for m in attachments[n]:
            if (n == attach1 and m == attach2) or (n == attach2
                                                   and m == attach1):
                t_D = tf
            else:
                t_D = ts

            d = ((booms[n][0] - booms[m][0])**2 +
                 (booms[n][1] - booms[m][1])**2)**0.5
            if stressBases[n] == 0:
                A = 10**99  #To avoid nan
            else:
                A += t_D * d / 6. * (2 + stressBases[m] / stressBases[n])

        areas.append(A)
    return areas, (attach1, attach2)
Example #2
0
def boomAreas(Mx, My, booms, R, ts, floorHeight, tf, hst, wst, tst):
    Ixx = main.realMomentOfInertia("x", R, ts, floorHeight, tf, hst, wst, tst)
    Iyy = main.realMomentOfInertia("y", R, ts, floorHeight, tf, hst, wst, tst)
    stressBases = [0]*len(booms)
    floorDist1 = [0]*len(booms)
    floorDist2 = [0]*len(booms)
    
    floorAngle = np.arccos((R-floorHeight)/R)
    floorLength = R*np.sin(floorAngle)
    floorAttach1 = (floorLength, floorHeight - R)
    floorAttach2 = (-floorLength, floorHeight - R)
    
    Cx, Cy = main.realCentroid(R, ts, floorHeight, tf, hst, wst, tst)
    
    for i,(x,y) in enumerate(booms):
        #Calculate stress without terms that will vanish
        stressBases[i] = My/Iyy*(x-Cx)+Mx/Ixx*(y-Cy)
#         if stressBases[i] == 0:
#             print My, Iyy, Mx, Ixx, x, Cx, y, Cy
        #Check how close this boom is to the floor attachment
        floorDist1[i] = ((x-floorAttach1[0])**2+(y-floorAttach1[1])**2)**0.5
        floorDist2[i] = ((x-floorAttach2[0])**2+(y-floorAttach2[1])**2)**0.5
    
    #Check which booms the floor should be connected to
    attach1 = floorDist1.index(min(floorDist1))
    attach2 = floorDist2.index(min(floorDist2))
    
    attachments = connections(booms, (attach1, attach2))
    
    areas = []
    for n in range(len(booms)):
        A = 0.
        for m in attachments[n]:
            if (n==attach1 and m==attach2) or (n==attach2 and m==attach1):
                t_D = tf 
            else:
                t_D = ts
            
            d = ((booms[n][0]-booms[m][0])**2+(booms[n][1]-booms[m][1])**2)**0.5
            if stressBases[n]==0:
                A=10**99                #To avoid nan
            else:
                A+=t_D*d/6.*(2+stressBases[m]/stressBases[n])
            
        areas.append(A)
    return areas, (attach1, attach2)
Example #3
0
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
Example #4
0
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