<Text-field style="Heading 1" layout="Heading 1"><Font family="Trebuchet MS" foreground="[153,153,153]">Introduction</Font></Text-field>

<Text-field style="Heading 1" layout="Heading 1"><Font family="Trebuchet MS">3. Calculation</Font><Equation executable="false" style="2D Math" input-equation="" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2I1EhRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2I1EhRic=</Equation></Text-field>

If you have chosen "introduce the data manually", write "true" on the items you want to be displayed during calculation, and write "false" to hide them.

You can also place a "true" in 'Do not display anything' or in 'Display all': then it wouldn't be necessary to change ww[i], anim[j] or dibuj[k].

Calculation will be faster without animations (anim[1]:="false", and anim[2]:="false").

To change the scale of the accumulated diagrams use the following two variables:

dia_scale_factor:=1e-2: #scale factor of the accumulated beam diagrams def_scale_factor:=3e11: #scale factor of the accumulated deformed shape printlevel:=0:

------------------------------------------------------------------- 'restart' IF -------------------------------------------------------------------

if rstrt=1 then #only if restart is needed printf("\134n"); error "please, press 'Go up' and execute blocks 1 and 2 before Calculation"; else if conmap[2]="true" then

################################### MANUAL DATA INTRODUCTION #################################

qq[1]:="false": #Do not display anything \134 qq[2]:="false": #Display all | Displaying options qq[3]:="true": #Select data or graphics (then select some of the followings:)/ #------------------------------------------------------------------------------- ww[1]:="true": #Initial structure to be calculated in each step \134 ww[2]:="true": #Beam diagrams on each step \134 ww[3]:="true": #Deformed shape on each step \134 ww[4]:="true": #Accumulated beam diagrams (if "true", then select anim[1]) \134 anim[1]:="false": #Animated beam diagrams \134 ww[5]:="true": #Accumulated deformed shape (if "true", then select anim[2]) \134 anim[2]:="true": #Animated deformed shape | Graphics dibuj[1]:="true": #Bars \134 / dibuj[2]:="true": #Numbers \134 / dibuj[3]:="false": #Coordinate system | Items to be displayed in / dibuj[4]:="true": #Supports | graphics / dibuj[5]:="false": #Loads / / dibuj[6]:="false": #Forces / / ww[6]:="true": #Current and previous value of det(KA) \134 ww[7]:="true": #Initial, final and maximum values of beam diagrams in all bars \134 ww[8]:="true": #Maximum value of (Bending moment)/(Plastic moment) | Data ww[9]:="true": #Forces/reaction in nodes / ww[10]:="true": #Node displacements /

################################### end of manual data introduction #################################

errcalc(qq,ww,anim,dibuj); #error handling in manual data introduction else calcerror:=0: maplcalc(); #data introduction by maplets end if: rstrt:=1:

Before 'repeat' and 'calculation' loops, values are inicializated:

repe:=1: #variable to repeat the calculation, displaying the results hng:=1: #variable to control if any interelemental hinge has been formed yy:=10: #precision in the search of the maximum of M/Mp (it'll search from L/yy to L*(yy-1)/yy ): #that's because in the extremes, sometimes beam diagrams functions take a singular value printlevel:=0: otra_defo_acum:=NULL: #inicialization of variables used in graphs otro_diag_esf:=NULL: intload:=0: maxgraph(); if calcerror=0 then printf("\134n\134t\134t>> Begin of calculation");print();printf("\134t\134t\134t\134t."); end if:

-----------------------------------------------BEGINNING OF RESTART LOOP-----------------------------------------------

This loop repeats the calculation with the new data if an interelemental hinge has been created

for reiniciar do if calcerror=1 then break: end if: if repe=1 then esca_dia:=0.0: esca_def:=0.0: #autoscale else esca_dia:=escaladiag: esca_def:=escaladef: end if; a_lambda:=0: paso:=0: #inicialization esca_beam:=0.0: esca_ds:=0.0: dnd_0:=array(1..nnd,1..13): dbr_0:=array(1..nbr,1..13): for i from 1 to nnd do for j from 1 to 13 do dnd_0[i,j]:=dnd[i,j];od:od: #initial value of dnd is stored, for i from 1 to nbr do for j from 1 to 13 do dbr_0[i,j]:=dbr[i,j];od:od: #to inicializate it before each step if repe=2 and intload=1 then if qq[1]="false" then for kk from 1 to 1 do for kkk from 1 to 1 do printlevel:=5: od:od: printf("\134n\134t\134t\134t\134tNew structure data (after placing nodes where hinges will be formed): \134n\134t\134t\134t\134t\134tNumber of nodes: %d\134n\134t\134t\134t\134t\134tNumber of bars: %d\134n\134t\134t\134t\134t\134tNumber of interelemental loads: %d\134n\134t\134t\134t\134t\134tNumber of materials: %d\134n\134t\134t\134t\134t\134tNumber of sections: %d\134n",nnd,nbr,nbc,nmt,nsc); printf("\134n\134t\134t\134t\134tMaterial data for each section:");evalm(dmt); printf("\134n\134t\134t\134t\134tSection data:"); evalm(dsc); printf("\134n\134t\134t\134t\134tInterelemental loads data:"); evalm(dbc); printf("\134n\134t\134t\134t\134tNodal data:"); evalm(dnd); printf("\134n\134t\134t\134t\134tComplete element data:"); evalm(dbr); for k from 1 to 1 do printlevel:=0: od: end if:end if:

Ar:=array(1..2): #array to store the current and the previous value of det(KA)

----------------------------------------------BEGINNING OF CALCULATION LOOP-----------------------------------------------

This loop will be iterating until KA matrix became singular.

for paso from 1 do rotint:=0: #in principle, it will be supposed that no interelemental hinge has been formed if repe=1 then print();printf("\134t\134t\134t\134t."); end if: if qq[1]="false" then if repe=2 then printf("\134n\134n<<<<<<< Step %d >>>>>>>\134n",paso); end if:end if;

#dnd is inicializated as a matrix with unknowns to be calculated in each step. for i from 1 to nnd do for j from 1 to 10 do dnd[i,j]:=dnd_0[i,j];od;od; #initial matrices are stored, to re-inicializate them in a later step dnd_in:=array(1..nnd, 1..13): dmt_in:=array(1..nmt, 1..2): dsc_in:=array(1..nsc, 1..4): nbc_in:=array(1..nbc, 1..8): for ind from 1 to nnd do for j from 1 to 13 do dnd_in[ind,j]:=dnd[ind,j]:od:od: for imt from 1 to nmt do for j from 1 to 2 do dmt_in[imt,j]:=dmt[imt,j]:od:od: for isc from 1 to nsc do for j from 1 to 4 do dsc_in[isc,j]:=dsc[isc,j]:od:od: for ibc from 1 to nbc do for j from 1 to 8 do dbc_in[ibc,j]:=dbc[ibc,j]:od:od:

esc_g:=autoscala(dnd,nnd,1); dib_b:=dibuja_barras(dnd,dbr,dsc,nbr,esc_g): #bars dib_n:=dibuja_numeros(dnd,dbr,nbr,esc_g,color=orange): #numbers of bars sico1:=sico_p(0,0,0,esc_g,['Xg','Yg'],color=magenta): #coordinate system dib_a:=dibuja_apoyos(dnd,nnd,esc_g,color=black,thickness=3): #supports dib_c:=dibuja_cargas(dnd,nnd,esc_g,color=red,thickness=3): #loads dib_f:=dibuja_fuerzas(dbc,dnd,dbr,nbc,esc_g,color=red,thickness=3): #forces zz:=NULL: if dibuj[1]="true" or qq[1]="true" then zz:=zz,dib_b: end if: if dibuj[2]="true" or qq[1]="true" then zz:=zz,dib_n: end if: if dibuj[4]="true" or qq[1]="true" then zz:=zz,dib_a: end if: if dibuj[3]="true" then zz:=zz,sico1: end if: if dibuj[5]="true" then zz:=zz,dib_c: end if: if dibuj[6]="true" then zz:=zz,dib_f: end if: if qq[1]="false" then if repe=2 then if ww[1]="true" or qq[2]="true" then ss:=NULL: ss:=ss,dib_b,dib_n,dib_a,dib_c,dib_f; for k from 1 to 1 do for kk from 1 to 1 do printlevel:=7: od:od: display(ss,'title'='Structure_to_be_solved'); #draw the structure for k from 1 to 1 do printlevel:=0: od: end if;end if;end if;

Direct Stiffness Method Analysis

matrizK(nbr,dmt,dbr,dsc,nnd,dnd): #calculates stiffness matrix

gdldesp(nnd,dnd): #calculates d.o.f. and displacements

empo(nbr,nbc,dbc,dbr,dmt,dsc): #calculates beam end forces

dbraux:=array(1..nbr,1..13): #original dbr is stored, to put bar numbers after fuerzas function for i from 1 to nbr do for j from 1 to 13 do dbraux[i,j]:=dbr[i,j]:od:od: dbr:=fuerzas(nbr,nbc,dbc,dbr,dmt,dsc,fep): #calculates forces and updates dbr matrix for i from 1 to nbr do for j from 1 to 12 do dbraux[i,j]:=dbr[i,j]:od:od: dbr:=array(1..nbr,1..13): for i from 1 to nbr do for j from 1 to 13 do dbr[i,j]:=dbraux[i,j]:od:od:

---------------------------------------------- 'finishing' IF----------------------------------------------

This 'if' marks when finishing the loop, basing on the value of det(KA)

rotint:=0; if paso=1 then #if the beginning structure is a mechanism, it's not calculated Ar[2]:=abs(det(KA)); det1(); if det(KA)=0 then printf("\134nThe determinant of KA is Null. It's a mechanism\134n"); rotint:=0:repe:=0: break; end if: #in the following steps, a mechanism will have been formed if enough hinges else #have been created, so the value of det(KA) will be 'little' or Null Ar[1]:=Ar[2]; Ar[2]:=abs(det(KA)); det2(); if evalf(abs((Ar[1]-Ar[2])/Ar[1]))>0.99999999 then det3(); break; else det4(); end if: end if;

---------------------------------------------- end of 'finishing' IF----------------------------------------------

sol:=linsolve(KA,bA): #if the structure is not a mechanism, it is solved

#dnd is stored. After 'fuerzas' function, the number of nodes will be added dndaux:=array(1..nnd,1..13): for i from 1 to nnd do for j from 1 to 13 do dndaux[i,j]:=dnd[i,j]:od:od: dnd:=despreac(nnd,ncoco,gdl,dnd,sol,kest,bf): #calculates displacements, reactions and the unknowns of dnd for i from 1 to nnd do for j from 1 to 12 do dndaux[i,j]:=dnd[i,j]:od:od: dnd:=array(1..nnd,1..13): for i from 1 to nnd do for j from 1 to 13 do dnd[i,j]:=dndaux[i,j]:od:od:

esfu(nnd,dnd,nbr,dbr,dmt,dsc,nbc,dbc): #calculates the stress

RESULTS

BEAM DIAGRAMS

printbmdiag();

These are the diagrams of the current step, not accumulated diagrams. Autoscale

if esca_beam=0. then esca_beam:=0.02/autoscala(dnd,nnd,2)/2: end if:

Inicialization of the vector that will store stress equations.

for ibr from 1 to nbr do NVM[ibr]:=[0,0,0]:od:

Laws due to interelemental loads

for ibc from 1 to nbc do if (dbc[ibc,2]='pun') then NVM_:=NVM_pun(dbc[ibc,4],dbc[ibc,5],dbc[ibc,6],dbc[ibc,3],dbr[dbc[ibc,1],5]): end if: if (dbc[ibc,2]='dis') then NVM_:=NVM_dis(dbc[ibc,5],dbc[ibc,6],dbc[ibc,7],dbc[ibc,8],dbc[ibc,3],dbc[ibc,4],dbr[dbc[ibc,1],5]): end if: if (dbc[ibc,2]='ter') then NVM_:=NVM_ter(dmt[dbr[dbc[ibc,1],3],1],dsc[dbr[dbc[ibc,1],4],1], dsc[dbr[dbc[ibc,1],4],2],dbr[dbc[ibc,1],5],dmt[dbr[dbc[ibc,1],3],2], dbc[ibc,3],dbc[ibc,4],dsc[dbr[dbc[ibc,1],4],3]): end if: if (dbc[ibc,2]='def') then NVM_:=NVM_def(dmt[dbr[dbc[ibc,1],3],1],dsc[dbr[dbc[ibc,1],4],1], dsc[dbr[dbc[ibc,1],4],2],dbr[dbc[ibc,1],5],dbc[ibc,3],dbc[ibc,4],dbc[ibc,5]): end if: NVM[dbc[ibc,1]]:=evalm(NVM[dbc[ibc,1]]+NVM_): od:

Adding the laws of displacements in the extremes.

for ibr from 1 to nbr do NVM[ibr]:=evalm(NVM[ibr]+[-esf[ibr][1]+fep[ibr][1],-esf[ibr][2]+fep[ibr][2],-esf[ibr][3]+esf[ibr][2]*x+fep[ibr][3]-fep[ibr][2]*x]): od:

if qq[1]="false" then if repe=2 then if ww[2]="true" or qq[2]="true" then pNVM:=array(1..nbr): for ibr from 1 to nbr do pp:=plot([NVM[ibr][1],NVM[ibr][2],NVM[ibr][3]],x=0..dbr[ibr,5],color=[yellow,cyan,magenta],legend=["Axial force", "Shear force","Bending Moment"],thickness=2): pNVM[ibr]:=translate(rotate(scale(pp,1,esca_beam),dbr[ibr,6]),dnd[dbr[ibr,1],1],dnd[dbr[ibr,1],2]); od:

dNVM:=NULL: for ibr from 1 to nbr do dNVM:=dNVM,pNVM[ibr]: od:

for ki from 1 to 1 do for k from 1 to 1 do for kkk from 1 to 1 do printlevel:=7: od:od:od: display(zz,dNVM,title=`Beam_diagrams`); for k from 1 to 1 do printlevel:=0: od: end if:end if:end if:

strsearch(); #search for the maximum of beam diagrams calcerror:=compr(Mmax): #check if bending moment is not null in all bars if calcerror=1 then break: end if: rotint:=maxsearch(Nmax,Vmax,Mmax); #search for the maximum of M/Mp

----------------------- 'IF' SENTENCE TO DISTINGUISH IF THERE IS INTERELEMENTAL HINGE OR NOT-----------------------

If there is an interelemental hinge, data are changed to place a node where the new hinge is going to appear. Then calculation is re-started: the hinge will be formed in the new node.

if rotint=0 then ########## without interelemental hinge ######### if qq[1]="false" then if repe=2 then if ww[8]="true" or qq[2]="true" then printf("\134nThe maximum accumulated value of (Bending moment)/(Plastic moment) is %g, and it's reached in bar %d, extreme %d\134n", MPmax[1],MPmax[2],MPmax[3]); end if:end if:end if:

Numeric evaluations of the maximum value of (Bending moment)/(Plastic moment).

br:=MPmax[2]: #Bar extr:=MPmax[3]: #Extreme N_V_M:=3: #Considered stress: bending MOMENT #(dbr[ibr,5] is the lenght of the bar) if (paso=1) then MMax_Mp:=abs(evalf(subs(x=(extr-1)*dbr[br,5],NVM[br][N_V_M]))/dsc[dbr[br,4],4]); else MMax_Mp:=abs(evalf(subs(x=(extr-1)*dbr[br,5],NVM[br][N_V_M]/(dsc[dbr[br,4],4]-abs(a_NVM[br][N_V_M]))))); end if:

Only bending moments in the extremes of bars are considered, because there is a node in all the places where a hinge will be formed. The next plastic hinge will appear in the extreme ('extr') (1 or 2) of the bar ('br') where MMax/Mp were greater.

Factor d_lambda is defined:

d_lambda:=abs(1/MMax_Mp); rotula:=1: if paso=1 then dlam:=array(1..1,1..1,[[d_lambda]]); #in the first step, the array is created else dlamaux:=extend(dlam,1,0); #in next steps, a row is added where the new value is stored dlamaux[paso,1]:=d_lambda; dlam:=dlamaux; end if;

#reactions in nodes if qq[1]="false" then if repe=2 then if ww[9]="true" or qq[2]="true" then fest2:=array(1..3*nnd): printf("\134nForces in nodes:\134n Fx Fy Mz"); n:=0: for i from 1 to 3*nnd do for j from 1 by 3 to 3*nnd do if i=j then n:=n+1:printf("\134n Node %d ",n); end if; od: if evalf(10^(Digits-4)*abs(fest[i]))<1 then fest2[i]:=0.: else fest2[i]:=fest[i]: end if: printf("%+.4e ",fest2[i]); od; end if;end if;end if;

INCREMENTAL DEFORMED SHAPE

Autoscale

if esca_ds=0 then esca_ds:=0.005/autoscala(dnd,nnd,3): end if;

The Principle of Virtual Forces method is used (not considering shear force). The deformed shape is calculated taking into account thermic loads, or previous deformations.

def:=array(1..nbr): for ibr from 1 to nbr do delt_u[ibr]:=int(NVM[ibr][1]/dsc[dbr[ibr,4],1]/dmt[dbr[ibr,3],1],x=0..d): delt_v[ibr]:=uloc[ibr][3]*d+int(NVM[ibr][3]*(d-x)/dsc[dbr[ibr,4],2]/dmt[dbr[ibr,3],1],x=0..d): if nbc>0 then for ibc from 1 to nbc do if dbc[ibc,1]=ibr then if (dbc[ibc,2]='ter') then delt_u[ibr]:=delt_u[ibr]+dmt[dbr[ibr,3],2]*d*(dbc[ibc,3]+dbc[ibc,4])/2: delt_v[ibr]:=delt_v[ibr]-dmt[dbr[ibr,3],2]*d^2*(dbc[ibc,3]-dbc[ibc,4])/2/dsc[dbr[ibr,4],3]: end if: if (dbc[ibc,2]='def') then delt_u[ibr]:=delt_u[ibr]+dbc[ibc,3]: delt_v[ibr]:=delt_v[ibr]+dbc[ibc,4]: end if: end if: od: end if: if qq[1]="false" then if repe=2 then ppp:=plot([d+delt_u[ibr]*esca_ds,delt_v[ibr]*esca_ds,d=0..dbr[ibr,5]],color=black,thickness=3): def[ibr]:=translate(rotate(ppp,dbr[ibr,6]),dnd[dbr[ibr,1],1]+dnd[dbr[ibr,1],6]*esca_ds,dnd[dbr[ibr,1],2]+dnd[dbr[ibr,1],7]*esca_ds); end if;end if; od: if qq[1]="false" then if repe=2 then if ww[3]="true" or qq[2]="true" then defo:=NULL: for ibr from 1 to nbr do defo:=defo,def[ibr]: od: #the diagrams of all deformed shapes are stored in the same drawing for k from 1 to 1 do for kk from 1 to 1 do printlevel:=8: od:od: display(zz,defo,title=`Deformed_shape`); for k from 1 to 1 do printlevel:=0: od: end if;end if;end if:

#node displacements if qq[1]="false" then if repe=2 then if ww[10]="true" or qq[2]="true" then printf("\134n\134nNode displacements:\134n ux uy theta"); for ind from 1 to nnd do printf("\134n Node %d ", ind); for i from 6 to 8 do printf(" %+.4e ", dnd[ind,i]); od; od; end if:end if:end if:

ACCUMULATE

Beam diagrams, nodal displacements and deformed shapes are accumulated

for ibr from 1 to nbr do if (paso = 1) then #if it's the first step, variables are created a_NVM[ibr]:=evalm(d_lambda*NVM[ibr]): a_uloc[ibr]:=evalm(d_lambda*uloc[ibr]): a_delt_u[ibr]:=d_lambda*delt_u[ibr]: a_delt_v[ibr]:=d_lambda*delt_v[ibr]: x_a[ibr]:=dnd[dbr[ibr,1],6]*esca_def*d_lambda: y_a[ibr]:=dnd[dbr[ibr,1],7]*esca_def*d_lambda: else #if it's not the first step, its values are accumulated a_NVM[ibr]:=evalm(a_NVM[ibr]+d_lambda*NVM[ibr]): a_uloc[ibr]:=evalm(a_uloc[ibr]+d_lambda*uloc[ibr]): a_delt_u[ibr]:=a_delt_u[ibr]+d_lambda*delt_u[ibr]: a_delt_v[ibr]:=a_delt_v[ibr]+d_lambda*delt_v[ibr]: x_a[ibr]:=x_a[ibr]+dnd[dbr[ibr,1],6]*esca_def*d_lambda: y_a[ibr]:=y_a[ibr]+dnd[dbr[ibr,1],7]*esca_def*d_lambda: end if: od:

a_lambda:=a_lambda+d_lambda: #the value of a_lambda is updated if paso=1 then alam:=array(1..1,1..1,[[a_lambda]]): #in the first step, the array is created else alamaux:=extend(alam,1,0); #in next steps, a row is added, where the new value is stored alamaux[paso,1]:=a_lambda; alam:=alamaux; end if: if paso=1 then Mpas:=array(1..1,1..nbr): #in the first step, the array is created for ibr from 1 to nbr do Mpas[1,ibr]:=evalm(a_NVM[ibr][3]): od: else Mpasaux:=extend(Mpas,1,0); #in next steps, a row is added, where the new value is stored for ibr from 1 to nbr do Mpasaux[paso,ibr]:=evalm(a_NVM[ibr][3]): od: Mpas:=Mpasaux: end if:

Scales for the diagrams:

if repe=1 then escaladiag:=dia_scale_factor/autoscala2(): escaladef:=def_scale_factor/autoscala3(): end if:

ACCUMULATED BEAM DIAGRAMS

if qq[1]="false" then if repe=2 then if ww[4]="true" or qq[2]="true" then if paso=2 then printlevel:=8: end if: abd(a_NVM[brult][3]); #all beam diagrams for all bars for all steps for k from 1 to 1 do printlevel:=8: od: display(aya,title=`Accumulated_beam_diagrams`); for k from 1 to 1 do printlevel:=0: od: end if:end if: else anim[1]:="false": abd(a_NVM[brult][3]); end if:

ACCUMULATED DEFORMED SHAPE

if qq[1]="false" then if repe=2 then if ww[5]="true" or qq[2]="true" then ads(); #all deformed shapes for all bars for all steps for k from 1 to 1 do printlevel:=8: od: display(ayay,title=`Accumulated_deformed_shape`); for k from 1 to 1 do printlevel:=0: od: end if:end if: else anim[2]:="false"; ads(); end if:

In the 3D-matrix 'desplaza', all nodal displacements will be stored, so all the data concerning to displacements and rotations of all nodes of the structure will be available at the end of the loop.

if paso=1 then #in the first step, the array is created desplaza:=array(1..1,1..nbr,1..6); for ibr from 1 to nbr do for inn from 1 to 6 do desplaza[1,ibr,inn]:=a_uloc[ibr][inn]; od;od; else #in next steps, a row is added. 'extend' doesn't work in 3D-arrays for ipa from 1 to paso-1 do for ibr from 1 to nbr do for inn from 1 to 6 do desplazaAux[ipa,ibr,inn]:=desplaza[ipa,ibr,inn]; #copies all to an auxiliary array od;od;od; desplaza:=array(1..paso,1..nbr,1..6); #creates a new array with an additional row for ipa from 1 to paso-1 do for ibr from 1 to nbr do for inn from 1 to 6 do desplaza[ipa,ibr,inn]:=desplazaAux[ipa,ibr,inn]; #copies all, but the bottom row is empty od;od;od; for ibr from 1 to nbr do for inn from 1 to 6 do #fills the bottom row desplaza[paso,ibr,inn]:=a_uloc[ibr][inn]; od;od; end if;

Before the next step, dbr matrix must be updated with the new hinge (erc)

if rotula=1 then dbr[br,6+extr]:=1: end if; #this loop stores the number of the node, bar and extreme where the new hinge has been formed if paso=1 then brextr:=array(1..1,1..3,[[dbr[br,extr],br,extr]]); #in the first step, the array is created else brextraux:=extend(brextr,1,0); #in next steps, a row is added, where the new value of the node is stored brextraux[paso,1]:=dbr[br,extr]; brextraux[paso,2]:=br; brextraux[paso,3]:=extr: brextr:=brextraux; end if; #this loop puts '1' (hinge) if any bar converging to the node has a hinge for ibr from 1 to nbr do nodoA:=0:nodoB:=0: for i from 1 to nbr do if dbr[ibr,1]=dbr[i,1] and dbr[i,7]=1 then nodoA:=1: end if; if dbr[ibr,1]=dbr[i,2] and dbr[i,8]=1 then nodoA:=1: end if; if dbr[ibr,2]=dbr[i,1] and dbr[i,7]=1 then nodoB:=1: end if; if dbr[ibr,2]=dbr[i,2] and dbr[i,8]=1 then nodoB:=1: end if; od: dbr[ibr,11]:=nodoA: dbr[ibr,12]:=nodoB: od: esc_g:=autoscala(dnd,nnd,1): dib_b:=dibuja_barras(dnd,dbr,dsc,nbr,esc_g): dib_n:=dibuja_numeros(dnd,dbr,nbr,esc_g,color=orange): sico1:=sico_p(0,0,0,esc_g,['Xg','Yg'],color=magenta): dib_a:=dibuja_apoyos(dnd,nnd,esc_g,color=black,thickness=3): dib_c:=dibuja_cargas(dnd,nnd,esc_g,color=red,thickness=3): dib_f:=dibuja_fuerzas(dbc,dnd,dbr,nbc,esc_g,color=red,thickness=3): else ####### with interelemental hinge ####### if hng=1 then printf("\134n\134n\134t\134t\134t>There will be an interelemental hinge. Initial data are being changed to place a node there."); hng:=2: else printf("\134n\134n\134t\134t\134t>There will be another interelemental hinge. Initial data are being changed to place a node there."); end if; break; end if;

------------------------------ end of 'if' sentece to distinguish if there is interelemental hinge or not --------------------------------

end do;

---------------------------------------------- end of calculation loop ----------------------------------------------

if rotint=0 then #if rotint=0, that means that calculation block is finished, and no interelemental hinge has appeared if repe=1 then #Now, the loop is repeated, but calculating, printing and displaying all the desired data/graphics #sets the scale for displaying the diagrams esca_dia:=escaladiag: esca_def:=escaladef: #restores the initial data to do the final loop, displaying graphics and other results. for ibr from 1 to nbr do for j from 1 to 13 do dbr[ibr,j]:=dbr_0[ibr,j]: od:od: for ind from 1 to nnd do for j from 1 to 13 do dnd[ind,j]:=dnd_in[ind,j]: od:od: for imt from 1 to nmt do for j from 1 to 2 do dmt[imt,j]:=dmt_in[imt,j]: od:od: for isc from 1 to nsc do for j from 1 to 4 do dsc[isc,j]:=dsc_in[isc,j]: od:od: for ibc from 1 to nbc do for j from 1 to 8 do dbc[ibc,j]:=dbc_in[ibc,j]: od:od: repe:=repe+1: if qq[1]="true" then break; end if; #if no displays are required, calculation finishes here else break: end if: end if; #Here, data are changed if there has been an interelemental hinge, and calculation will be re-started.

if repe=1 then #this 'if' changes the data, if an interelemental hinge has been formed #it's not necessary in the final loop (displaying graphics and more). dndz:=array(1..nnd,1..13): dbrz:=array(1..nbr,1..13): dbcz:=array(1..nbc,1..13): for ind from 1 to nnd do for j from 1 to 13 do dndz[ind,j]:=dnd[ind,j];od:od: for ibr from 1 to nbr do for j from 1 to 13 do dbrz[ibr,j]:=dbr[ibr,j];od:od: if nbc>0 then for ibc from 1 to nbc do for j from 1 to 8 do dbcz[ibc,j]:=dbc[ibc,j]; od:od: else dbrz:=0: end if: #function to introduce the new node and bar, change its numbers, divide distributed loads, change the interelemental #punctual load for a load in the new node, etc. aara:=interel(nnd,nbr,nsc,nbc,nmt,dndz,dbrz,dsc,dbcz,dmt,1); nbr:=aara[1]; nnd:=aara[2]; nbc:=aara[3]; dbr:=aara[4]; dnd:=aara[5]; dbc:=aara[6]; intload:=1:

Now, length, angles and hinges of each bar will be completed, after changing the data

Lenghts

for ibr from 1 to nbr do dbr[ibr,5]:=evalf(sqrt((dndN[dbr[ibr,2],1]-dndN[dbr[ibr,1],1])^2+(dndN[dbr[ibr,2],2]-dndN[dbr[ibr,1],2])^2)): od:

Angles

#angles for ibr from 1 to nbr do dbr[ibr,6]:=arctan(dndN[dbr[ibr,2],2]-dndN[dbr[ibr,1],2],dndN[dbr[ibr,2],1]-dndN[dbr[ibr,1],1]): od:

Hinges

for ibr from 1 to nbr do #there will be a hinge if any bar converging to the node has a hinge nodoA:=0: #first, it is considered a rigid joint nodoB:=0: #if it has a hinge, a 1 will be placed in the following loop for i from 1 to nbr do if dbr[ibr,1]=dbr[i,1] and dbr[i,7]=1 then nodoA:=1: end if; if dbr[ibr,1]=dbr[i,2] and dbr[i,8]=1 then nodoA:=1: end if; if dbr[ibr,2]=dbr[i,1] and dbr[i,7]=1 then nodoB:=1: end if; if dbr[ibr,2]=dbr[i,2] and dbr[i,8]=1 then nodoB:=1: end if; od: dbr[ibr,11]:=nodoA: dbr[ibr,12]:=nodoB: od: end if: #end of 'repe' if brult:=br: extrult:=extr:

end do;

------------------------------------------------ end of repeat loop -------------------------------------------------

prnt(calcerror); #final summary printlevel:=0: end if; #end of 'restart' if

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