Contoh Rangka Gambar : Pemograman Finite Element Method Pada Element Truss Dengan Menggunakan Matlab

BAB IV APLIKASI PADA TRUSS ELEMENT

Dalam bab ini akan diberikan suatu contoh perhitungan rangka truss 2 dimensi seperti pada Gambar 4.1, dengan 8 titik simpul dan 13 elemen, hasil yang diperoleh dari program dengan menggunakan matlab dibandingkan dengan perhitungan dengan mikrosoft excel 2003 Adapun data-data yang akan dipergunakan dalam analisa tersebut adalah : 4.1 Contoh Rangka Gambar 4.1 : 1. Panjang bentangL = 3 m = 300 cm 2. Tinggi bangunan kolomH= 5 m = 500 cm 3. Beban Vertikal P1= 5000 kg P2=7500 kg 4. Ukuran penampang A1 ; B x H = 20x30 cm 2 A2 ; B x H = 20x15 cm 2 A3; B x H = 20x40 cm 2 7. Modulus Elastisitas beton E = 2.09 x 10 6 kgcm 2 8. Perletakan sendi-roll Gambar 4.1. Struktur rangka

4. 2. Pemrograman Matlab

Sebagai data masukan pada Matlab, dibuat M-file baru kemudian ketik material properti, informasi koordinat, informasi element, dan kondisi tumpuan. Untuk model soal pada gambar 4.1 diatas, data masukan untuk elemen truss 8 titik buhul dengan 13 elemen adalah sebagai berikut : 1. Fungsi Assembly, dengan program sebagai berikut : function[A]=assembly; load scratch_file.txt; tA=scratch_file; clear scratch_file; m=maxtA:,2; A=zerosm,m; B=zerossizetA B=A;C=A; for i=1:lengthtA; C=A; BtAi,2,tAi,3=tAi,1; AtAi,2,tAi,3=BtAi,2,tAi,3+CtAi,2,tAi,3; end; delete scratch_file.txt;

2. Fungsi Exact, dengan program sebagai berikut :

function[Aex,Bex,Cex]=extractK,index m=sizeK,1; ind=zerosm,m;Aex=zerosmm,1;Bex=Aex;Cex=Aex; for i=1:m; indi,:=index; end; for i=1:m; for j=1:m; im=j+mi-1; Aexim=Ki,j; Bexim=indj,i; Cexim=indi,j; end; end; y=[Aex Bex Cex]; fid=fopenscratch_file.txt,a+; for i=1:mm; fprintffid,12.8f 6.2f 6.2f\n,yi,:; end; clear K index; fclosefid;

3. Fungsi ldata, dengan program sebagai berikut :

function[IR,IF,Support]=ldataSupport,dof; Menentukan besar ukuran matriks [id,jd]=sizedof; Support=sortrowsSupport,1; Restraint=zerosid,jd; Restraint:,1=dof:,1; Check titik sebagai tumpuan atau tidak i=ismemberRestraint:,1,Support:,1; Menentukan indeks jika titik adalah suatu tumpuan ii=findi==1; Pakai dof dari titik sebagai perletakan Restraintii,2:jd=Support:,2:jd; ubah ke vektor iR=reshapeRestraint:,2:jd,1,jd-1id; iD=reshapedof:,2:jd,1,jd-1id; Bentuk matriks vektor IF dan IR iR0=findiR==0; iR1=findiR==1; IF=sortiDiR0; IR=sortiDiR1; 4. Fungsi Sdata, dengan program sebagai berikut : function[dof,index,coord,element]=... sdataprop,element,coord,type Menyiapkan data untuk masukan coord=sortrowscoord,1; element=sortrowselement,1; m=sizeelement,1; n=sizecoord,1; switch type; case{t2d,T2D}; nd=2; untuk rangka 2D end; dof=zerosn,nd+1; index=zerosm,nd2; switch type; case{t2d,T2D}; for ii=1:n; i=coordii,1; J J1 J2 J3 dofii,:=[i 2i-1 2i]; end; for ii=1:m; J J1 J2 J3 K K1 K2 K3 indexii,:=[dofelementii,2,2:3... dofelementii,3,2:3]; end; end

5. Fungsi Input Data Elemen truss 2D, dengan program sebagi berikut :

clear all,clc Data Umum type=t2d property i E A prop=[1 2.09e6 600 2 2.09e6 300 3 2.09e6 800 Koordinat x y coord =[ 1 0 0 2 600 0 3 600 500 4 1200 0 5 1200 500 6 1800 0 7 1800 500 8 2400 0] EL J1 J2 Prop element=[ 1 1 2 3 2 1 3 2 3 2 3 2 4 2 4 3 5 3 4 2 6 3 5 1 7 4 5 2 8 4 6 3 9 4 7 2 10 5 7 1 11 6 7 2 12 6 8 3 13 7 8 2] Perletakan Support=[1 1 1 8 0 1]; Gaya P yang bekerja J X Y JL= [2 0 10000 3 0 5000 4 0 10000 5 0 7500 6 0 10000 7 0 5000] Beban Merata AML=[0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0] Memanggil Fungsi [dof,index,coord,element]=sdataprop,element,coord,type; [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=... t2d_stiffprop,element,coord,index; [IR,IF,Support]=ldataSupport,dof; [DF,AR,AM]=analysis_resultelement,dof,index,IF,IR,... S,SmS,JL,AML,RT,Support,type [joint_disp,support_reaction,beam_endforces]=... print_resultdof,Support,element,IF,IR,DF,AR,AM,type;

6. Fungsi t2f_stiff, dengan program sebagi berikut :

function[S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=... t2d_stiffprop,element,coord,index; E=propelement:,4,2; Modulus elastisitas A=propelement:,4,2; Luas penampang Joint=coord:,1; m=sizeelement,1; Bentuk matriks Xi Xj dan Yi Yj Xj=zeros1,m; Xk=Xj; Yj=Xj; Yk=Xj; for i=1:m; ij=findJoint==elementi,2; ik=findJoint==elementi,3; Xji=coordij,2; Xki=coordik,2; Yji=coordij,3; Yki=coordik,3; end; Menghitung panjang elemen L=sqrtXk-Xj.2+Yk-Yj.2; Cx=Xk-Xj.L; Cy=Yk-Yj.L; Bentuk matriks kekakuan 16x16 SmS=zeros4,4,m; Sm=SmS; RT=SmS; for i=1:m; R=[Cxi Cyi; -Cyi Cxi ]; RT:,:,i=[R zeros2,2; zeros2,2 R]; Matriks rotasi SmS:,:,i=EiAiLi[1 0 -1 0;0 0 0 0;... -1 0 1 0;0 0 0 0] Sm:,:,i=RT:,:,i.SmS:,:,iRT:,:,i; [Aex,Bex,Cex]=extractSm:,:,i,indexi,:; end; dispBentuk matriks kekakuan; S=assembly;

7. Fungsi Analisa Struktur analysis_result , dengan program sebagai berikut :

function[DF,AR,AM]=analysis_resultelement,dof,index,... IF,IR,S,SmS,JL,AML,RT,Support,type clear Sff Srf; ndof=length[IF IR]; mencari jumlah derajat kebebasan Membentuk matriks Sff Sff=SIF,IF; Membentuk matriks Srf Srf=SIR,IF; Membentuk matriks beban titik AJ i=1:sizeJL,1; AJ=zeros1,ndof; switch type; case{t2d,T2D}; AJdofJLi,2=JLi,2; AJdofJLi,3=JLi,3; end; Membentuk matriks beban titik ekivalen AE [mi,ni]=sizeindex; transpose ke..xm matriks m=jumlah elemen AMLT=AML; AE=zerosndof,1; for i=1:sizeelement,1; Ji=indexi,:; switch type; case {t2d,T2D}; AMLi=[AMLT1,i;AMLT2,i;AMLT3,i;AMLT4,i]; end; AEJi=AEJi-RT:,:,iAMLi; end; AE=AE; Menghitung Reaksi perletakan AR dan perpindahan titik DF AC=AJ+AE; AFC=ACIF; ARC=ACIR; DF=Sff\AFC; AR=-ARC+SrfDF; Menghitung Gaya batang Dj=zeros1,ndof; AM=zerosni,mi; DjIF=DF; for i=1:sizeelement,1; DM=RT:,:,iDjindexi,:; AM:,i=AMLi,:+SmS:,:,iDM; end; AM=AM.;

8. Fungsi Menampilkan Hasil Analisa print_result, dengan program sebagai berikut:

function[joint_disp,support_reaction,beam_endforces]=... print_resultdof,Support,element,IF,IR,DF,AR,AM,type Print hail keluaran Print Reaksi Perletakan [id,jd]=sizedof; [iS,jS]=sizeSupport; reaction=zerosid,jd; support_reaction=zerosiS,jd; reaction:,1=dof:,1; for i=1:sizeAR,1; [ii,jj]=finddof:,2:jd==IRi; reactionii,jj+1=ARi; end; for i=1:sizeSupport,1; ii=findreaction:,1==Supporti,1; support_reactioni,:=reactionii,:; end; Print perpindahan titik untuk semua dof joint_disp=zerossizedof; joint_disp:,1=dof:,1; bb=ismember dof,IF; ii=findbb==1; for i=1:sizeDF,1; [ii,jj]=finddof:,2:jd==IFi; joint_dispii,jj+1=DFi; end; switch type; case {t2d,T2D}; disp ; dispTABEL PERPINDAHAN TITIK; dispTitik Dx Dy; fprintf5.0f 12.4f 12.4f\n, joint_disp.; Print Reaksi perletakan disp ; dispTABEL REAKSI PERLETAKAN; dispTitik Rx Ry ; fprintf5.0f 12.4f 12.4f\n,support_reaction.; Print Gaya Batang beam_endforces=[element:,1 AM]; disp ; dispTABEL GAYA BATANG; dispBatang Fx1 Fy1 Fx2 Fy2 ; fprintf5.0f 12.4f 12.4f 12.4f 12.4f\n,beam_endforces.; case {p2d,P2D}; disp ; dispTABEL PERPINDAHAN TITIK; dispTitik Dx Dy Rz; fprintf5.0f 12.4f 12.4f\n, joint_disp.; Print Reaksi perletakan disp ; dispTABEL REAKSI PERLETAKAN; dispTitik Rx Ry Mz; fprintf5.0f 12.4f 12.4f\n,support_reaction.; Print Gaya Batang beam_endforces=[element:,1 AM]; disp ; dispTABEL GAYA BATANG; dispBatang Fx1 Fy1 Mz1 Fx2 Fy2 Mz2; fprintf5.0f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f\n,beam_endforces.; case {t3d,T3D}; disp ; dispTABEL PERPINDAHAN TITIK; dispTitik Dx Dy Dz; fprintf5.0f 12.4f 12.4f\n, joint_disp.; Print Reaksi perletakan disp ; dispTABEL REAKSI PERLETAKAN; dispTitik Rx Ry Rz; fprintf5.0f 12.4f 12.4f 12.4f\n,support_reaction.; Print Gaya Batang beam_endforces=[element:,1 AM]; disp ; dispTABEL GAYA BATANG; dispBatang Fx1 Fy1 Fz1 Fx2 Fy2 Fz2; fprintf5.0f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f\n,beam_endforces.; case {p3d,P3D}; disp ; dispTABEL PERPINDAHAN TITIK; dispTitik Dx Dy Dz Rx Ry Rz; fprintf5.0f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f\n, joint_disp.; Print Reaksi perletakan disp ; dispTABEL REAKSI PERLETAKAN; dispTitik Rx Ry Rz Mx My Mz; fprintf5.0f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f\n,support_reaction.; Print Gaya Batang beam_endforces=[element:,1 AM]; disp ; dispTABEL GAYA BATANG; dispBatang Fx1 Fy1 Fz1 Mx1 My1 Mz1 Fx2 Fy2 Fz2 Mx2 My2 Mz2 fprintf5.0f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f 12.4f\n,beam_endforces.; end; Setelah semua fungsi-fungsi diatas dibuat pada M-File dan di simpan, sesuai dengan eksistensinya, maka Program dapat dijalankan, dengan membuka File Input Data Elemen truss 2D, dan dieksekusi run maka akan tampil hasil keluaran Matlab sebagai Out put program. Tampilan Output program pada command window sebagai berikut : type = t2d prop = 1 2100000 600 2 2100000 300 3 2100000 800 coord = 1 0 0 2 600 500 3 600 0 4 1200 500 5 1200 0 6 1800 0 7 1800 500 8 2400 0 element = 1 1 2 3 2 1 3 2 3 2 3 2 4 2 4 3 5 3 4 2 6 3 5 1 7 4 5 2 8 4 6 3 9 4 7 2 10 5 7 1 11 6 7 2 12 6 8 3 13 7 8 2 JL = 2 0 10000 3 0 5000 4 0 10000 5 0 7500 6 0 10000 7 0 5000 AML = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,3 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,4 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,5 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,6 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,7 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,4 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,5 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,6 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,7 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,5 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,6 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,7 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,6 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,7 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,7 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,9 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,9 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,10 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,9 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,10 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,11 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,9 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,10 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,11 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,12 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,9 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,10 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,11 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,12 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,13 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SmS:,:,1 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,2 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,3 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,4 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,5 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,6 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,7 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,8 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,9 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 SmS:,:,10 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 SmS:,:,11 = 1.0e+009 8.8200 0 -8.8200 0 0 0 0 0 -8.8200 0 8.8200 0 0 0 0 0 SmS:,:,12 = 1.0e+009 7.3500 0 -7.3500 0 0 0 0 0 -7.3500 0 7.3500 0 0 0 0 0 0 0 0 0 SmS:,:,13 = 1.0e+009 5.6464 0 -5.6464 0 0 0 0 0 -5.6464 0 5.6464 0 0 0 0 0 Bentuk matriks kekakuan DF = 1.0e-004 -0.2471 0.3991 -0.0388 0.4147 -0.2083 0.6560 -0.0918 0.6277 -0.4228 0.5012 -0.1165 0.5168 -0.4616 AR = 1.0e+004 -0.0000 -2.3750 -2.3750 AM = 1.0e+004 -3.7099 0 3.7099 0 2.8500 0 -2.8500 0 1.3750 0 -1.3750 0 -2.8500 0 2.8500 0 -1.3668 0 1.3668 0 3.9000 0 -3.9000 0 -2.5000 0 2.5000 0 3.7099 0 -3.7099 0 -6.7500 0 6.7500 0 5.0767 0 -5.0767 0 -1.3750 0 1.3750 0 2.8500 0 -2.8500 0 -3.7099 0 3.7099 0 TABEL PERPINDAHAN TITIK Titik Dx Dy 1 0.0000 0.0000 2 -0.0000 0.0000 3 -0.0000 0.0000 4 -0.0000 0.0001 5 -0.0000 0.0001 6 -0.0000 0.0001 7 -0.0000 0.0001 8 -0.0000 0.0000 TABEL REAKSI PERLETAKAN Titik Rx Ry 1 -0.0000 -23750.0000 8 0.0000 -23750.0000 TABEL GAYA BATANG Batang Fx1 Fy1 Fx2 Fy2 1 -37098.6860 0.0000 37098.6860 0.0000 2 28500.0000 0.0000 -28500.0000 0.0000 3 13750.0000 0.0000 -13750.0000 0.0000 4 -28500.0000 0.0000 28500.0000 0.0000 5 -13667.9369 0.0000 13667.9369 0.0000 6 39000.0000 0.0000 -39000.0000 0.0000 7 -25000.0000 0.0000 25000.0000 0.0000 8 37098.6860 0.0000 -37098.6860 0.0000 9 -67500.0000 0.0000 67500.0000 0.0000 10 50766.6229 0.0000 -50766.6229 0.0000 11 -13750.0000 0.0000 13750.0000 0.0000 12 28500.0000 0.0000 -28500.0000 0.0000 13 -37098.6860 0.0000 37098.6860 0.0000

4.3. Verifikasi Program