Definizione dati

Ecls=37*(10^6); 
R=133.33;
Arco=279.31;
Ppa=-400;
ptt=-540;
Iximp=43;
Ixarco=26;
Aimp=30;
Aarc=32;
Kbm=2*10^5;
Kcn=6*10^5;
Kdo=20*10^5;
Kep=67*10^5
Eia=Ecls*Ixarco;
Eit=Ecls*Iximp;
Ea=Ecls*Aimp;
Pt=Ppa*Cos[Pi/6];
Pn=Ppa*Sin[Pi/6];

θ0=Pi/6;
θ1=Pi/4;
θ2=Pi/3;
θ3=Pi*5/12;
θ4=Pi/2;
θ5=Pi*7/12;
θ6=Pi*2/3;
θ7=Pi*3/4;
θ8=Pi*5/6;
La=0;
Lb=93.67;
Lc=Lb+58.04;
Ld=Lc+42.49;
Le=Ld+36.8;
Lf=Le+36.8;
Lg=Lf+42.49;
Lh=Lg+58.04;
Li=Lh+93.67;

Forza sulle aste

feb=Kbm*(v1[Lb]*Sin[θ1]-u1[Lb]*Cos[θ1]-v9[θ1*R]);


fec=Kcn*(v2[Lc]*Sin[θ2]-u2[Lc]*Cos[θ2]-v10[θ2*R]);


fed=Kdo*(v3[Ld]*Sin[θ3]-u3[Ld]*Cos[θ3]-v11[θ3*R]);


fee=Kep*(v4[Le]-v12[θ4*R]);

fef=Kdo*(v5[Lf]*Sin[Pi-θ5]+u5[Lf]*Cos[Pi-θ5]-v13[θ5*R]);

feg=Kcn*(v6[Lg]*Sin[Pi-θ6]+u6[Lg]*Cos[Pi-θ6]-v14[θ6*R]);

feh=Kbm*(v7[Lh]*Sin[Pi-θ7]+u7[Lh]*Cos[Pi-θ7]-v15[θ7*R]);

Equazioni di campo e derivate

u1[x_]=C[49]+x C[50];
u2[x_]=C[51]+x C[52];
u3[x_]=C[53]+x C[54];
u4[x_]=C[55]+x C[56];
u5[x_]=C[57]+x C[58];
u6[x_]=C[59]+x C[60];
u7[x_]=C[61]+x C[62];
u8[x_]=C[63]+x C[64];

v1[x_]=C[65]+C[66] x+C[67] (x^2)+C[68] (x^3)+((ptt *(x^4))/(24 Eit));
v2[x_]=C[69]+C[70] x+C[71] (x^2)+C[72] (x^3)+((ptt* (x^4))/(24 Eit));
v3[x_]=C[73]+C[74] x+C[75] (x^2)+C[76] (x^3)+((ptt *(x^4))/(24 Eit));
v4[x_]=C[77]+C[78] x+C[79] (x^2)+C[80] (x^3)+((ptt *(x^4))/(24 Eit));
v5[x_]=C[81]+C[82] x+C[83] (x^2)+C[84] (x^3)+((ptt* (x^4))/(24 Eit));
v6[x_]=C[85]+C[86] x+C[87] (x^2)+C[88] (x^3)+((ptt *(x^4))/(24 Eit));
v7[x_]=C[89]+C[90] x+C[91] (x^2)+C[92] (x^3)+((ptt *(x^4))/(24 Eit));
v8[x_]=C[93]+C[94] x+C[95] (x^2)+C[96] (x^3)+((ptt* (x^4))/(24 Eit));

u9[s_]=C[5]+s C[6]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[1]+s C[2]+2 R C[4])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[2]-2 Eia C[3]-2 Eia s C[4]) Sin[(s/R)]);

u10[s_]=C[11]+s C[12]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[7]+s C[8]+2 R C[10])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[8]-2 Eia C[9]-2 Eia s C[10]) Sin[(s/R)]);

u11[s_]=C[17]+s C[18]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[13]+s C[14]+2 R C[16])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[14]-2 Eia C[15]-2 Eia s C[16]) Sin[(s/R)]);

u12[s_]=C[23]+s C[24]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[19]+s C[20]+2 R C[22])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[20]-2 Eia C[21]-2 Eia s C[22]) Sin[(s/R)]);

u13[s_]=C[29]+s C[30]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[25]+s C[26]+2 R C[28])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[26]-2 Eia C[27]-2 Eia s C[28]) Sin[(s/R)]);u14[s_]=C[35]+s C[36]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[31]+s C[32]+2 R C[34])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[32]-2 Eia C[33]-2 Eia s C[34]) Sin[(s/R)]);

u15[s_]=C[41]+s C[42]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[37]+s C[38]+2 R C[40])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[38]-2 Eia C[39]-2 Eia s C[40]) Sin[(s/R)]);

u16[s_]=C[47]+s C[48]+(1/(8 Eia))(R^2) (-(Ppa (-25 (R^2)+2 (s^2))+8 Eia (C[43]+s C[44]+2 R C[46])) Cos[(s/R)]+4 (3 Ppa R s+4 Eia R C[44]-2 Eia C[45]-2 Eia s C[46]) Sin[(s/R)]);

v9[s_]=-R u9'[s];
v10[s_]=-R u10'[s];
v11[s_]=-R u11'[s];
v12[s_]=-R u12'[s];
v13[s_]=-R u13'[s];
v14[s_]=-R u14'[s];
v15[s_]=-R u15'[s];
v16[s_]=-R u16'[s];

φ1[x_]=v1'[x];
φ2[x_]=v2'[x];
φ3[x_]=v3'[x];
φ4[x_]=v4'[x];
φ5[x_]=v5'[x];
φ6[x_]=v6'[x];
φ7[x_]=v7'[x];
φ8[x_]=v8'[x];

φ9[s_]=-R u9''[s]-((u9[s])/R) ;
φ10[s_]=-R u10''[s]-((u10[s])/R);
φ11[s_]=-R u11''[s]-((u11[s])/R);
φ12[s_]=-R u12''[s]-((u12[s])/R);
φ13[s_]=-R u13''[s]-((u13[s])/R);
φ14[s_]=-R u14''[s]-((u14[s])/R);
φ15[s_]=-R u15''[s]-((u15[s])/R);
φ16[s_]=-R u16''[s]-((u16[s])/R);

M1[x_]=Eit*v1''[x];
M2[x_]=Eit*v2''[x];
M3[x_]=Eit*v3''[x];
M4[x_]=Eit*v4''[x];
M5[x_]=Eit*v5''[x];
M6[x_]=Eit*v6''[x];
M7[x_]=Eit*v7''[x];
M8[x_]=Eit*v8''[x];

M9[s_]=-Eia (R u9'''[s]+((u9'[s])/R));
M10[s_]=-Eia (R u10'''[s]+((u10'[s])/R));
M11[s_]=-Eia (R u11'''[s]+((u11'[s])/R));
M12[s_]=-Eia (R u12'''[s]+((u12'[s])/R));
M13[s_]=-Eia (R u13'''[s]+((u13'[s])/R));
M14[s_]=-Eia (R u14'''[s]+((u14'[s])/R));
M15[s_]=-Eia (R u15'''[s]+((u15'[s])/R));
M16[s_]=-Eia (R u16'''[s]+((u16'[s])/R));

T1[x_]=-Eit*v1'''[x];
T2[x_]=-Eit*v2'''[x];
T3[x_]=-Eit*v3'''[x];
T4[x_]=-Eit*v4'''[x];
T5[x_]=-Eit*v5'''[x];
T6[x_]=-Eit*v6'''[x];
T7[x_]=-Eit*v7'''[x];
T8[x_]=-Eit*v8'''[x];

T9[s_]=Eia (+R u9''''[s]+((u9''[s])/R));
T10[s_]=Eia (+R u10''''[s]+((u10''[s])/R));
T11[s_]=Eia (+R u11''''[s]+((u11''[s])/R));
T12[s_]=Eia (+R u12''''[s]+((u12''[s])/R));
T13[s_]=Eia (+R u13''''[s]+((u13''[s])/R));
T14[s_]=Eia (+R u14''''[s]+((u14''[s])/R));
T15[s_]=Eia (+R u15''''[s]+((u15''[s])/R));
T16[s_]=Eia (+R u16''''[s]+((u16''[s])/R));

N1[x_]=Ea u1'[x];
N2[x_]=Ea u2'[x];
N3[x_]=Ea u3'[x];
N4[x_]=Ea u4'[x];
N5[x_]=Ea u5'[x];
N6[x_]=Ea u6'[x];
N7[x_]=Ea u7'[x];
N8[x_]=Ea u8'[x];

N9[s_]=R Eia (+R u9'''''[s]+((u9'''[s])/R) )+Ppa R Sin[s/R];
N10[s_]=R Eia (+R u10'''''[s]+((u10'''[s])/R) )+Ppa R Sin[s/R];
N11[s_]=R Eia (+R u11'''''[s]+((u11'''[s])/R) )+Ppa R Sin[s/R];
N12[s_]=R Eia (+R u12'''''[s]+((u12'''[s])/R) )+Ppa R Sin[s/R];
N13[s_]=R Eia (+R u13'''''[s]+((u13'''[s])/R) )+Ppa R Sin[s/R];
N14[s_]=R Eia (+R u14'''''[s]+((u14'''[s])/R) )+Ppa R Sin[s/R];
N15[s_]=R Eia (+R u15'''''[s]+((u15'''[s])/R) )+Ppa R Sin[s/R];
N16[s_]=R Eia (+R u16'''''[s]+((u16'''[s])/R) )+Ppa R Sin[s/R];

Condizioni al contorno

cc[1]=u1[La]==0;
cc[2]=v1[La]==0;
cc[3]=M1[La]==0;
(* condizioni in B *)
cc[4]=u1[Lb]-u2[Lb]==0;
cc[5]=v1[Lb]-v2[Lb]==0;
cc[6]=φ1[Lb]-φ2[Lb]==0;
cc[7]=-N1[Lb]+N2[Lb]+feb*Cos[θ1]==0;
cc[8]=-T1[Lb]+T2[Lb]-feb*Sin[θ1]==0;
cc[9]=M1[Lb]-M2[Lb]==0;
(* condizioni in C *)
cc[10]=u2[Lc]-u3[Lc]==0;
cc[11]=v2[Lc]-v3[Lc]==0;
cc[12]=φ2[Lc]-φ3[Lc]==0;
cc[13]=-N2[Lc]+N3[Lc]+fec*Cos[θ2]==0;
cc[14]=-T2[Lc]+T3[Lc]-fec*Sin[θ2]==0;
cc[15]=M2[Lc]-M3[Lc]==0;
(* condizioni in D *)
cc[16]=u3[Ld]-u4[Ld]==0;
cc[17]=v3[Ld]-v4[Ld]==0;
cc[18]=φ3[Ld]-φ4[Ld]==0;
cc[19]=-N3[Ld]+N4[Ld]+fed*Cos[θ3]==0;
cc[20]=-T3[Ld]+T4[Ld]-fed*Sin[θ3]==0;
cc[21]=M3[Ld]-M4[Ld]==0;
(* condizioni in E *)
cc[22]=u4[Le]-u5[Le]==0;
cc[23]=v4[Le]-v5[Le]==0;
cc[24]=φ4[Le]-φ5[Le]==0;
cc[25]=-N4[Le]+N5[Le]==0;
cc[26]=-T4[Le]+T5[Le]-fee==0;
cc[27]=-M4[Le]+M5[Le]==0;
(* condizioni in F *)
cc[28]=u5[Lf]-u6[Lf]==0;
cc[29]=v5[Lf]-v6[Lf]==0;
cc[30]=φ5[Lf]-φ6[Lf]==0;
cc[31]=-N5[Lf]+N6[Lf]-fef*Cos[Pi-θ5]==0;
cc[32]=-T5[Lf]+T6[Lf]-fef*Sin[Pi-θ5]==0;
cc[33]=-M5[Lf]+M6[Lf]==0;
(* condizioni in G *)
cc[34]=u6[Lg]-u7[Lg]==0;
cc[35]=v6[Lg]-v7[Lg]==0;
cc[36]=φ6[Lg]-φ7[Lg]==0;
cc[37]=-N6[Lg]+N7[Lg]-feg*Cos[Pi-θ6]==0;
cc[38]=-T6[Lg]+T7[Lg]-feg*Sin[Pi-θ6]==0;
cc[39]=-M6[Lg]+M7[Lg]==0;
(* condizioni in H*)
cc[40]=u7[Lh]-u8[Lh]==0;
cc[41]=v7[Lh]-v8[Lh]==0;
cc[42]=φ7[Lh]-φ8[Lh]==0;
cc[43]=-N7[Lh]+N8[Lh]-feh*Cos[Pi-θ7]==0;
cc[44]=-T7[Lh]+T8[Lh]-feh*Sin[Pi-θ7]==0;
cc[45]=-M7[Lh]+M8[Lh]==0;
(* condizioni in I*)
cc[46]=u8[Li]==0;
cc[47]=v8[Li]==0;
cc[48]=M8[Li]==0;
cc[49]=u9[θ0 R]==0;
cc[50]=v9[θ0 R]==0;
cc[51]=φ9[θ0 R]==0;

(* condizioni in M*)

cc[52]=u9[θ1 R]-u10[θ1 R]==0;
cc[53]=v9[θ1 R]-v10[θ1 R]==0;
cc[54]=φ9[θ1 R]-φ10[θ1 R]==0;
cc[55]=-N9[θ1 R]+N10[θ1 R]==0;
cc[56]=-T9[θ1 R]+T10[θ1 R]+feb==0;
cc[57]=-M9[θ1 R]+M10[θ1 R]==0;
(* condizioni in N*)
cc[58]=u10[θ2 R]-u11[θ2 R]==0;
cc[59]=v10[θ2 R]-v11[θ2 R]==0;
cc[60]=φ10[θ2 R]-φ11[θ2 R]==0;
cc[61]=-N10[θ2 R]+N11[θ2 R]==0;
cc[62]=-T10[θ2 R]+T11[θ2 R]+fec==0;
cc[63]=-M10[θ2 R]+M11[θ2 R]==0;

(* condizioni in O*)

cc[64]=u11[θ3 R]-u12[θ3 R]==0;
cc[65]=v11[θ3 R]-v12[θ3 R]==0;
cc[66]=φ11[θ3 R]-φ12[θ3 R]==0;
cc[67]=-N11[θ3 R]+N12[θ3 R]==0;
cc[68]=-T11[θ3 R]+T12[θ3 R]+fed==0;
cc[69]=-M11[θ3 R]+M12[θ3 R]==0;

(* condizioni in P*)
cc[70]=u12[θ4 R]-u13[θ4 R]==0;
cc[71]=v12[θ4 R]-v13[θ4 R]==0;
cc[72]=φ12[θ4 R]-φ13[θ4 R]==0;
cc[73]=-N12[θ4 R]+N13[θ4 R]==0;
cc[74]=-T12[θ4 R]+T13[θ4 R]+fee==0;
cc[75]=-M12[θ4 R]+M13[θ4 R]==0;
(* condizioni in Q*)
cc[76]=u13[θ5 R]-u14[θ5 R]==0;
cc[77]=v13[θ5 R]-v14[θ5 R]==0;
cc[78]=φ13[θ5 R]-φ14[θ5 R]==0;
cc[79]=-N13[θ5 R]+N14[θ5 R]==0;
cc[80]=-T13[θ5 R]+T14[θ5 R]+fef==0;
cc[81]=-M13[θ5 R]+M14[θ5 R]==0;
(* condizioni in R*)

cc[82]=u14[θ6 R]-u15[θ6 R]==0;
cc[83]=v14[θ6 R]-v15[θ6 R]==0;
cc[84]=φ14[θ6 R]-φ15[θ6 R]==0;
cc[85]=-N14[θ6 R]+N15[θ6 R]==0;
cc[86]=-T14[θ6 R]+T15[θ6 R]+feg==0;
cc[87]=-M14[θ6 R]+M15[θ6 R]==0;

(* condizioni in S*)
cc[88]=u15[θ7 R]-u16[θ7 R]==0;
cc[89]=v15[θ7 R]-v16[θ7 R]==0;
cc[90]=φ15[θ7 R]-φ16[θ7 R]==0;
cc[91]=-N15[θ7 R]+N16[θ7 R]==0;
cc[92]=-T15[θ7 R]+T16[θ7 R]+feh==0;
cc[93]=-M15[θ7 R]+M16[θ7 R]==0;
(* condizioni in T*)
cc[94]=u16[θ8 R]==0;
cc[95]=v16[θ8 R]==0;
cc[96]=φ16[θ8 R]==0;

sistema=Table[cc[i],{i,1,96}]//Simplify;
c=Table[C[i],{i,1,96}];
Cost=NSolve[sistema,c, WorkingPrecision->200]

u1[x_]=u1[x]/.Cost[[1]];

u2[x_]=u2[x]/.Cost[[1]];

u3[x_]=u3[x]/.Cost[[1]];

u4[x_]=u4[x]/.Cost[[1]];

u5[x_]=u5[x]/.Cost[[1]];

u6[x_]=u6[x]/.Cost[[1]];

u7[x_]=u7[x]/.Cost[[1]];

u8[x_]=u8[x]/.Cost[[1]];

u9[x_]=u9[x]/.Cost[[1]];

u10[x_]=u10[x]/.Cost[[1]];

u11[x_]=u11[x]/.Cost[[1]];

u12[x_]=u12[x]/.Cost[[1]];

u13[x_]=u13[x]/.Cost[[1]];

u14[x_]=u14[x]/.Cost[[1]];

u15[x_]=u15[x]/.Cost[[1]];

u16[x_]=u16[x]/.Cost[[1]];

v1[x_]=v1[x]/.Cost[[1]];

v2[x_]=v2[x]/.Cost[[1]];

v3[x_]=v3[x]/.Cost[[1]];

v4[x_]=v4[x]/.Cost[[1]];

v5[x_]=v5[x]/.Cost[[1]];

v6[x_]=v6[x]/.Cost[[1]];

v7[x_]=v7[x]/.Cost[[1]];

v8[x_]=v8[x]/.Cost[[1]];

v9[x_]=v9[x]/.Cost[[1]];

v10[x_]=v10[x]/.Cost[[1]];

v11[x_]=v11[x]/.Cost[[1]];

v12[x_]=v12[x]/.Cost[[1]];

v13[x_]=v13[x]/.Cost[[1]];

v14[x_]=v14[x]/.Cost[[1]];

v15[x_]=v15[x]/.Cost[[1]];

v16[x_]=v16[x]/.Cost[[1]];

Plottaggi Impalcato

Spostamento di asta dell’ impalcato

GrafT=Show[{Plot[U1[x],{x,0,Lb}]},{(Plot[U2[x],{x,Lb,Lc}])},{(Plot[U3[x],{x,Lc,Ld}])},{(Plot[U4[x],{x,Ld,Le}])},{(Plot[U5[x],{x,Le,Lf}])},{(Plot[U6[x],{x,Lf,Lg}])},{(Plot[U7[x],{x,Lg,Lh}])},{(Plot[U8[x],{x,Lh,Li}])},PlotRange->All]

Spostamento  verticale dell’ impalcato

V1[x_]=v1[x]/.Cost[[1]];

V2[x_]=v2[x]/.Cost[[1]];

V3[x_]=v3[x]/.Cost[[1]];

V4[x_]=v4[x]/.Cost[[1]];

V5[x_]=v5[x]/.Cost[[1]];

V6[x_]=v6[x]/.Cost[[1]];

V7[x_]=v7[x]/.Cost[[1]];

V8[x_]=v8[x]/.Cost[[1]];

GrafT=Show[{Plot[V1[x],{x,0,Lb}]},{(Plot[V2[x],{x,Lb,Lc}])},{(Plot[V3[x],{x,Lc,Ld}])},{(Plot[V4[x],{x,Ld,Le}])},{(Plot[V5[x],{x,Le,Lf}])},{(Plot[V6[x],{x,Lf,Lg}])},{(Plot[V7[x],{x,Lg,Lh}])},{(Plot[V8[x],{x,Lh,Li}])},PlotRange->All]

Andamento delle rotazioni dell’ impalcato

R1[x_]=φ1[x]/.Cost[[1]];
R2[x_]=φ2[x]/.Cost[[1]];
R3[x_]=φ3[x]/.Cost[[1]];
R4[x_]=φ4[x]/.Cost[[1]];
R5[x_]=φ5[x]/.Cost[[1]];
R6[x_]=φ6[x]/.Cost[[1]];
R7[x_]=φ7[x]/.Cost[[1]];
R8[x_]=φ8[x]/.Cost[[1]];

GrafT=Show[{Plot[R1[x],{x,0,Lb},AxesOrigin->Automatic]},{(Plot[R2[x],{x,Lb,Lc},AxesOrigin->Automatic])},{(Plot[R3[x],{x,Lc,Ld},AxesOrigin->Automatic])},{(Plot[R4[x],{x,Ld,Le},AxesOrigin->Automatic])},{(Plot[R5[x],{x,Le,Lf}])},{(Plot[R6[x],{x,Lf,Lg},AxesOrigin->Automatic])},{(Plot[R7[x],{x,Lg,Lh},AxesOrigin->Automatic])},{(Plot[R8[x],{x,Lh,Li},AxesOrigin->Automatic])},PlotRange->All]

Sforzo normale dell’ impalcato

SN1[x_]=N1[x]/.Cost[[1]];

SN2[x_]=N2[x]/.Cost[[1]];

SN3[x_]=N3[x]/.Cost[[1]];

SN4[x_]=N4[x]/.Cost[[1]];

SN5[x_]=N5[x]/.Cost[[1]];

SN6[x_]=N6[x]/.Cost[[1]];

SN7[x_]=N7[x]/.Cost[[1]];

SN8[x_]=N8[x]/.Cost[[1]];

GrafT=Show[{Plot[SN1[x],{x,0,Lb},Filling->Axis]},{(Plot[SN2[x],{x,Lb,Lc},Filling->Axis])},{(Plot[SN3[x],{x,Lc,Ld},Filling->Axis])},{(Plot[SN4[x],{x,Ld,Le},Filling->Axis])},{(Plot[SN5[x],{x,Le,Lf},Filling->Axis])},{(Plot[SN6[x],{x,Lf,Lg},Filling->Axis])},{(Plot[SN7[x],{x,Lg,Lh},Filling->Axis])},{(Plot[SN8[x],{x,Lh,Li},Filling->Axis])},PlotRange->All]

Andamento del taglio dell’ impalcato

TA1[x_]=T1[x]/.Cost[[1]];

TA2[x_]=T2[x]/.Cost[[1]];

TA3[x_]=T3[x]/.Cost[[1]];

TA4[x_]=T4[x]/.Cost[[1]];

TA5[x_]=T5[x]/.Cost[[1]];

TA6[x_]=T6[x]/.Cost[[1]];

TA7[x_]=T7[x]/.Cost[[1]];

TA8[x_]=T8[x]/.Cost[[1]];

GrafT=Show[{Plot[TA1[x],{x,0,Lb},Filling->Axis]},{(Plot[TA2[x],{x,Lb,Lc},Filling->Axis])},{(Plot[TA3[x],{x,Lc,Ld},Filling->Axis])},{(Plot[TA4[x],{x,Ld,Le},Filling->Axis])},{(Plot[TA5[x],{x,Le,Lf},Filling->Axis])},{(Plot[TA6[x],{x,Lf,Lg},Filling->Axis])},{(Plot[TA7[x],{x,Lg,Lh},Filling->Axis])},{(Plot[TA8[x],{x,Lh,Li},Filling->Axis])},PlotRange->All]

Andamento del momento flettente dell’ impalcato

MO1[x_]=-M1[x]/.Cost[[1]];

MO2[x_]=-M2[x]/.Cost[[1]];

MO3[x_]=-M3[x]/.Cost[[1]];

MO4[x_]=-M4[x]/.Cost[[1]];

MO5[x_]=-M5[x]/.Cost[[1]];

MO6[x_]=-M6[x]/.Cost[[1]];

MO7[x_]=-M7[x]/.Cost[[1]];

MO8[x_]=-M8[x]/.Cost[[1]];

GrafT=Show[{Plot[MO1[x],{x,0,Lb}]},{(Plot[MO2[x],{x,Lb,Lc}])},{(Plot[MO3[x],{x,Lc,Ld}])},{(Plot[MO4[x],{x,Ld,Le}])},{(Plot[MO5[x],{x,Le,Lf}])},{(Plot[MO6[x],{x,Lf,Lg}])},{(Plot[MO7[x],{x,Lg,Lh}])},{(Plot[MO8[x],{x,Lh,Li}])},PlotRange->All]

Plottaggi Arco

Andamento dello spostamento tangente dell’arco

(* SPOSTAMENTO TANGENTE *)

U9[s_]=u9[s]/.Cost[[1]];

U10[s_]=u10[s]/.Cost[[1]];

U11[s_]=u11[s]/.Cost[[1]];

U12[s_]=u12[s]/.Cost[[1]];

U13[s_]=u13[s]/.Cost[[1]];

U14[s_]=u14[s]/.Cost[[1]];

U15[s_]=u15[s]/.Cost[[1]];

U16[s_]=u16[s]/.Cost[[1]];

g1=Plot[U9[s],{s,θ0 R,θ1 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g2=Plot[U10[s],{s,θ1 R,θ2 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g3=Plot[U11[s],{s,θ2 R,θ3 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g4=Plot[U12[s],{s,θ3 R,θ4 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g5=Plot[U13[s],{s,θ4 R, θ5 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g6=Plot[U14[s],{s,θ5 R, θ6 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g7=Plot[U15[s],{s,θ6 R,θ7 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g8=Plot[U16[s],{s,θ7 R,θ8 R },AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,g5,g6,g7,g8,AxesOrigin->{0,0},PlotRange->All]

Andamento dello spostamento normale dell’arco

V9[s_]=v9[s]/.Cost[[1]];

V10[s_]=v10[s]/.Cost[[1]];

V11[s_]=v11[s]/.Cost[[1]];

V12[s_]=v12[s]/.Cost[[1]];

V13[s_]=v13[s]/.Cost[[1]];

V14[s_]=v14[s]/.Cost[[1]];

V15[s_]=v15[s]/.Cost[[1]];

V16[s_]=v16[s]/.Cost[[1]];

g1=Plot[V9[s],{s,θ0 R,θ1 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g2=Plot[V10[s],{s,θ1 R,θ2 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g3=Plot[V11[s],{s,θ2 R,θ3 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g4=Plot[V12[s],{s,θ3 R,θ4 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g5=Plot[V13[s],{s,θ4 R, θ5 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g6=Plot[V14[s],{s,θ5 R, θ6 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g7=Plot[V15[s],{s,θ6 R,θ7 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g8=Plot[V16[s],{s,θ7 R,θ8 R },AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,g5,g6,g7,g8,AxesOrigin->{0,0},PlotRange->All]

Andamento della rotazione  dell’arco

(* ROTAZIONE *)

R9[s_]=φ9[s]/.Cost[[1]];

R10[s_]=φ10[s]/.Cost[[1]];

R11[s_]=φ11[s]/.Cost[[1]];

R12[s_]=φ12[s]/.Cost[[1]];

R13[s_]=φ13[s]/.Cost[[1]];

R14[s_]=φ14[s]/.Cost[[1]];

R15[s_]=φ15[s]/.Cost[[1]];

R16[s_]=φ16[s]/.Cost[[1]];

g1=Plot[R9[s],{s,θ0 R,θ1 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g2=Plot[R10[s],{s,θ1 R,θ2 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g3=Plot[R11[s],{s,θ2 R,θ3 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g4=Plot[R12[s],{s,θ3 R,θ4 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g5=Plot[R13[s],{s,θ4 R, θ5 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g6=Plot[R14[s],{s,θ5 R, θ6 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g7=Plot[R15[s],{s,θ6 R,θ7 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g8=Plot[R16[s],{s,θ7 R,θ8 R },AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,g5,g6,g7,g8,AxesOrigin->{0,0},PlotRange->All]

Andamento dello sforzo normale  dell’arco

SN9[s_]=N9[s]/.Cost[[1]];

SN10[s_]=N10[s]/.Cost[[1]];

SN11[s_]=N11[s]/.Cost[[1]];

SN12[s_]=N12[s]/.Cost[[1]];

SN13[s_]=N13[s]/.Cost[[1]];

SN14[s_]=N14[s]/.Cost[[1]];

SN15[s_]=N15[s]/.Cost[[1]];

SN16[s_]=N16[s]/.Cost[[1]];

g1=Plot[SN9[s],{s,θ0 R,θ1 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g2=Plot[SN10[s],{s,θ1 R,θ2 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g3=Plot[SN11[s],{s,θ2 R,θ3 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g4=Plot[SN12[s],{s,θ3 R,θ4 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g5=Plot[SN13[s],{s,θ4 R, θ5 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g6=Plot[SN14[s],{s,θ5 R, θ6 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g7=Plot[SN15[s],{s,θ6 R,θ7 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g8=Plot[SN16[s],{s,θ7 R,θ8 R },AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,g5,g6,g7,g8,AxesOrigin->{0,0},PlotRange->All]

Andamento del taglio  dell’arco

TA9[s_]=T9[s]/.Cost[[1]];

TA10[s_]=T10[s]/.Cost[[1]];

TA11[s_]=T11[s]/.Cost[[1]];

TA12[s_]=T12[s]/.Cost[[1]];

TA13[s_]=T13[s]/.Cost[[1]];

TA14[s_]=T14[s]/.Cost[[1]];

TA15[s_]=T15[s]/.Cost[[1]];

TA16[s_]=T16[s]/.Cost[[1]];

g1=Plot[TA9[s],{s,θ0 R,θ1 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g2=Plot[TA10[s],{s,θ1 R,θ2 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g3=Plot[TA11[s],{s,θ2 R,θ3 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g4=Plot[TA12[s],{s,θ3 R,θ4 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g5=Plot[TA13[s],{s,θ4 R, θ5 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g6=Plot[TA14[s],{s,θ5 R, θ6 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g7=Plot[TA15[s],{s,θ6 R,θ7 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g8=Plot[TA16[s],{s,θ7 R,θ8 R },AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,g5,g6,g7,g8,AxesOrigin->{0,0},PlotRange->All]

Andamento del momento flettente dell’arco

MO9[s_]=-M9[s]/.Cost[[1]];

MO10[s_]=-M10[s]/.Cost[[1]];

MO11[s_]=-M11[s]/.Cost[[1]];

MO12[s_]=-M12[s]/.Cost[[1]];

MO13[s_]=-M13[s]/.Cost[[1]];

MO14[s_]=-M14[s]/.Cost[[1]];

MO15[s_]=-M15[s]/.Cost[[1]];

MO16[s_]=-M16[s]/.Cost[[1]];

g1=Plot[-MO9[s],{s,θ0 R,θ1 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g2=Plot[-MO10[s],{s,θ1 R,θ2 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g3=Plot[-MO11[s],{s,θ2 R,θ3 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g4=Plot[-MO12[s],{s,θ3 R,θ4 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g5=Plot[-MO13[s],{s,θ4 R, θ5 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g6=Plot[-MO14[s],{s,θ5 R, θ6 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g7=Plot[-MO15[s],{s,θ6 R,θ7 R},AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];
g8=Plot[-MO16[s],{s,θ7 R,θ8 R },AxesOrigin->{0,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,g5,g6,g7,g8,AxesOrigin->{0,0},PlotRange->All]

Plottaggi Parametrici Arco

Andamento dello spostamento tangente in forma parametrica

GrafA1=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+ 500 U9[s]) Cos[(s/R)],(R+ U9[s]) Sin[(s/R)]}},{s,R θ0,R θ1},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA2=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500  U10[s]) Cos[(s/R)],(R+ U10[s]) Sin[(s/R)]}},{s,R θ1,R θ2},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA3=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500  U11[s]) Cos[(s/R)],(R+ U11[s]) Sin[(s/R)]}},{s,R θ2,R θ3},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA4=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500 U12[s]) Cos[(s/R)],(R+ U12[s]) Sin[(s/R)]}},{s,R θ3,R θ4},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA5=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500  U13[s]) Cos[(s/R)],(R+ U13[s]) Sin[(s/R)]}},{s,R θ4,R θ5},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA6=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500  U14[s]) Cos[(s/R)],(R+ U14[s]) Sin[(s/R)]}},{s,R θ5,R θ6},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA7=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500  U15[s]) Cos[(s/R)],(R+ U15[s]) Sin[(s/R)]}},{s,R θ6,R θ7},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA8=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+500  U16[s]) Cos[(s/R)],(R+ U16[s]) Sin[(s/R)]}},{s,R θ7,R θ8},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA=Show[GrafA1,GrafA2,GrafA3,GrafA4,GrafA5,GrafA6,GrafA7,GrafA8,PlotRange->All]

Andamento dello spostamento normale in forma parametrica

GrafA1=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+ 100 V9[s]) Cos[(s/R)],(R+ V9[s]) Sin[(s/R)]}},{s,R θ0,R θ1},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA2=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100  V10[s]) Cos[(s/R)],(R+ V10[s]) Sin[(s/R)]}},{s,R θ1,R θ2},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA3=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100  V11[s]) Cos[(s/R)],(R+ V11[s]) Sin[(s/R)]}},{s,R θ2,R θ3},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA4=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100 V12[s]) Cos[(s/R)],(R+ V12[s]) Sin[(s/R)]}},{s,R θ3,R θ4},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA5=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100  V13[s]) Cos[(s/R)],(R+ V13[s]) Sin[(s/R)]}},{s,R θ4,R θ5},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA6=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100  V14[s]) Cos[(s/R)],(R+ V14[s]) Sin[(s/R)]}},{s,R θ5,R θ6},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA7=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100  V15[s]) Cos[(s/R)],(R+V15[s]) Sin[(s/R)]}},{s,R θ6,R θ7},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA8=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+100  V16[s]) Cos[(s/R)],(R+ V16[s]) Sin[(s/R)]}},{s,R θ7,R θ8},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA=Show[GrafA1,GrafA2,GrafA3,GrafA4,GrafA5,GrafA6,GrafA7,GrafA8,PlotRange->All]

Andamento della rotazione in forma parametrica

GrafA1=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+ 1500 R9[s]) Cos[(s/R)],(R+ R9[s]) Sin[(s/R)]}},{s,R θ0,R θ1},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];;
GrafA2=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500  R10[s]) Cos[(s/R)],(R+ R10[s]) Sin[(s/R)]}},{s,R θ1,R θ2},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA3=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500   R11[s]) Cos[(s/R)],(R+ R11[s]) Sin[(s/R)]}},{s,R θ2,R θ3},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA4=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500  R12[s]) Cos[(s/R)],(R+ R12[s]) Sin[(s/R)]}},{s,R θ3,R θ4},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA5=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500   R13[s]) Cos[(s/R)],(R+ R13[s]) Sin[(s/R)]}},{s,R θ4,R θ5},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA6=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500   R14[s]) Cos[(s/R)],(R+ R14[s]) Sin[(s/R)]}},{s,R θ5,R θ6},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA7=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500   R15[s]) Cos[(s/R)],(R+R15[s]) Sin[(s/R)]}},{s,R θ6,R θ7},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA8=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+1500   R16[s]) Cos[(s/R)],(R+ R16[s]) Sin[(s/R)]}},{s,R θ7,R θ8},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA=Show[GrafA1,GrafA2,GrafA3,GrafA4,GrafA5,GrafA6,GrafA7,GrafA8,PlotRange->All]

Andamento del taglio in forma parametrica

GrafA1=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005  TA9[s]) Cos[(s/R)],(R+0.0002  TA9[s]) Sin[(s/R)]}},{s,R θ0,R θ1},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA2=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005  TA10[s]) Cos[(s/R)],(R+0.0002 TA10[s]) Sin[(s/R)]}},{s,R θ1,R θ2},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA3=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005    TA11[s]) Cos[(s/R)],(R+0.0002  TA11[s]) Sin[(s/R)]}},{s,R θ2,R θ3},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA4=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005 TA12[s]) Cos[(s/R)],(R+0.0002  TA12[s]) Sin[(s/R)]}},{s,R θ3,R θ4},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA5=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005    TA13[s]) Cos[(s/R)],(R+0.0002  TA13[s]) Sin[(s/R)]}},{s,R θ4,R θ5},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA6=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005  TA14[s]) Cos[(s/R)],(R+0.0002  TA14[s]) Sin[(s/R)]}},{s,R θ5,R θ6},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA7=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005  TA15[s]) Cos[(s/R)],(R+0.0002 TA15[s]) Sin[(s/R)]}},{s,R θ6,R θ7},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA8=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0005  TA16[s]) Cos[(s/R)],(R+0.0002 TA16[s]) Sin[(s/R)]}},{s,R θ7,R θ8},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA=Show[GrafA1,GrafA2,GrafA3,GrafA4,GrafA5,GrafA6,GrafA7,GrafA8,PlotRange->All]

Andamento del momento flettente in forma parametrica

GrafA1=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006  MO9[s]) Cos[(s/R)],(R+0.00006  MO9[s]) Sin[(s/R)]}},{s,R θ0,R θ1},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA2=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006  MO10[s]) Cos[(s/R)],(R+0.00006 MO10[s]) Sin[(s/R)]}},{s,R θ1,R θ2},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA3=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006   MO11[s]) Cos[(s/R)],(R+0.00006  MO11[s]) Sin[(s/R)]}},{s,R θ2,R θ3},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA4=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006 MO12[s]) Cos[(s/R)],(R+0.00006  MO12[s]) Sin[(s/R)]}},{s,R θ3,R θ4},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA5=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006    MO13[s]) Cos[(s/R)],(R+0.00006  MO13[s]) Sin[(s/R)]}},{s,R θ4,R θ5},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA6=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006  MO14[s]) Cos[(s/R)],(R+0.00006  MO14[s]) Sin[(s/R)]}},{s,R θ5,R θ6},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA7=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006  MO15[s]) Cos[(s/R)],(R+0.00006 MO15[s]) Sin[(s/R)]}},{s,R θ6,R θ7},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA8=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.00006  MO16[s]) Cos[(s/R)],(R+0.00006 MO16[s]) Sin[(s/R)]}},{s,R θ7,R θ8},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA=Show[GrafA1,GrafA2,GrafA3,GrafA4,GrafA5,GrafA6,GrafA7,GrafA8,PlotRange->All]

Andamento dello sforzo normale in forma parametrica

GrafA1=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002  SN9[s]) Cos[(s/R)],(R+0.0002  SN9[s]) Sin[(s/R)]}},{s,R θ0,R θ1},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA2=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002  SN10[s]) Cos[(s/R)],(R+0.0002 SN10[s]) Sin[(s/R)]}},{s,R θ1,R θ2},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA3=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002    SN11[s]) Cos[(s/R)],(R+0.0002  SN11[s]) Sin[(s/R)]}},{s,R θ2,R θ3},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA4=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002 SN12[s]) Cos[(s/R)],(R+0.0002 SN12[s]) Sin[(s/R)]}},{s,R θ3,R θ4},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA5=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002    SN13[s]) Cos[(s/R)],(R+0.0002  SN13[s]) Sin[(s/R)]}},{s,R θ4,R θ5},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA6=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002  SN14[s]) Cos[(s/R)],(R+0.0002  SN14[s]) Sin[(s/R)]}},{s,R θ5,R θ6},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA7=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002  SN15[s]) Cos[(s/R)],(R+0.0002 SN15[s]) Sin[(s/R)]}},{s,R θ6,R θ7},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];
GrafA8=ParametricPlot[{{-R Cos[(s/R)],R Sin[(s/R)]},{-(R+0.0002  SN16[s]) Cos[(s/R)],(R+0.0002 SN16[s]) Sin[(s/R)]}},{s,R θ7,R θ8},AxesOrigin->{0,R Sin [θ0]},PlotStyle->{Red,Thickness[0.004]}];

GrafA=Show[GrafA1,GrafA2,GrafA3,GrafA4,GrafA5,GrafA6,GrafA7,GrafA8,PlotRange->All]

Spstamento totale in forma parametrica

p0=ParametricPlot[{R Cos[s/R],R Sin[s/R]},{s,θ0 R,(Pi-θ0) R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Green,Thickness[0.003]}];

p1=ParametricPlot[{(R*Cos[s/R]-200*U9[s]*Sin[s/R]+10*V9[s]*Cos[s/R]),(R*Sin[s/R]+10*U9[s]*Cos[s/R]+10*V9[s]*Sin[s/R])},{s,θ0 R,θ1 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p2=ParametricPlot[{(R*Cos[s/R]-200*U10[s]*Sin[s/R]+10*V10[s]*Cos[s/R]),(R*Sin[s/R]+10*U10[s]*Cos[s/R]+10*V10[s]*Sin[s/R])},{s,θ1 R,θ2 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p3=ParametricPlot[{(R*Cos[s/R]-200*U11[s]*Sin[s/R]+10*V11[s]*Cos[s/R]),(R*Sin[s/R]+10*U11[s]*Cos[s/R]+10*V11[s]*Sin[s/R])},{s,θ2 R,θ3 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p4=ParametricPlot[{(R*Cos[s/R]-200*U12[s]*Sin[s/R]+10*V12[s]*Cos[s/R]),(R*Sin[s/R]+10*U12[s]*Cos[s/R]+10*V12[s]*Sin[s/R])},{s,θ3 R,θ4 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p5=ParametricPlot[{(R*Cos[s/R]-200*U13[s]*Sin[s/R]+10*V13[s]*Cos[s/R]),(R*Sin[s/R]+10*U13[s]*Cos[s/R]+10*V13[s]*Sin[s/R])},{s,θ4 R,θ5 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p6=ParametricPlot[{(R*Cos[s/R]-200*U14[s]*Sin[s/R]+10*V14[s]*Cos[s/R]),(R*Sin[s/R]+10*U14[s]*Cos[s/R]+10*V14[s]*Sin[s/R])},{s,θ5 R,θ6 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p7=ParametricPlot[{(R*Cos[s/R]-200*U15[s]*Sin[s/R]+10*V15[s]*Cos[s/R]),(R*Sin[s/R]+10*U15[s]*Cos[s/R]+10*V15[s]*Sin[s/R])},{s,θ6 R,θ7 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

p8=ParametricPlot[{(R*Cos[s/R]-200*U16[s]*Sin[s/R]+10*V16[s]*Cos[s/R]),(R*Sin[s/R]+10*U16[s]*Cos[s/R]+10*V16[s]*Sin[s/R])},{s,θ7 R,θ8 R  },AxesOrigin->{0,R Sin[θ0]},PlotStyle->{Red,Thickness[0.004]}];

Show[p0,p1,p2,p3,p4,p5,p6,p7,p8,PlotRange->All]

Valori delle forza sulle aste

feb=Kbm*(v1[Lb]*Sin[θ1]-u1[Lb]*Cos[θ1]-v9[θ1*R])

fec=Kcn*(v2[Lc]*Sin[θ2]-u2[Lc]*Cos[θ2]-v10[θ2*R])

fed=Kdo*(v3[Ld]*Sin[θ3]-u3[Ld]*Cos[θ3]-v11[θ3*R])

fee=Kep*(v4[Le]-v12[θ4*R])

fef=Kdo*(v5[Lf]*Sin[Pi-θ5]+u5[Lf]*Cos[Pi-θ5]-v13[θ5*R])

feg=Kcn*(v6[Lg]*Sin[Pi-θ6]+u6[Lg]*Cos[Pi-θ6]-v14[θ6*R])

feh=Kbm*(v7[Lh]*Sin[Pi-θ7]+u7[Lh]*Cos[Pi-θ7]-v15[θ7*R])

Valori degli spostamenti sulle aste

δeb=(v1[Lb]*Sin[θ1]-u1[Lb]*Cos[θ1]-v9[θ1*R])

δec=(v2[Lc]*Sin[θ2]-u2[Lc]*Cos[θ2]-v10[θ2*R])

δed=(v3[Ld]*Sin[θ3]-u3[Ld]*Cos[θ3]-v11[θ3*R])

δee=(v4[Le]-v12[θ4*R])

δef=(v5[Lf]*Sin[Pi-θ5]+u5[Lf]*Cos[Pi-θ5]-v13[θ5*R])

δeg=(v6[Lg]*Sin[Pi-θ6]+u6[Lg]*Cos[Pi-θ6]-v14[θ6*R])

δeh=(v7[Lh]*Sin[Pi-θ7]+u7[Lh]*Cos[Pi-θ7]-v15[θ7*R])

Ing Alessandro Geniola