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LAPORAN TUGAS BESAR SI-3222 ANSTRUK II

Program Analisis Struktur Truss Diajukan untuk memenuhi syarat kelulusan mata kuliah SI-3212 Struktur Baja

Dosen : Erwin Lim, Ph.D.

Asisten : Kevin Daffa Arrahman

15015111

Gelasius Galvindy

15015116

Disusun Oleh : Luis Valerius Pasasa

15016141

PROGRAM STUDI TEKNIK SIPIL FAKULTAS TEKNIK SIPIL DAN LINGKUNGAN INSTITUT TEKNOLOGI BANDUNG 2019

KATA PENGANTAR Puji dan syukur Puji dan syukur penulis ucapkan atas kehadirat Tuhan Yang Maha Esa karena berkat rahmat-Nya penulis dapat menyelesaikan tugas besar ini dengan sebaikbaiknya. Laporan Tugas Besar ini dibuat sebagai syarat kelulusan Mata Kuliah SI-3221 Analisis Struktur II Penyelesaian laporan tugas besar ini tidak terlepas dari berbagai pihak yang senantiasa membantu, mendukung, serta memberikan kritik dan saran dalam berbagai bentuk. Penulis menyadari bahwa dalam pengerjaan laporan tugas besar ini masih terdapat banyak kekurangan, baik dalam redaksi maupun penyajian laporan. Penulis berharap terdapat kritik dan saran yang membangun pembaca sehingga terdapat bahan pembelajaran untuk perbaikan di masa depan. Bandung, Maret 2019

Penulis

DAFTAR ISI

KATA PENGANTAR........................................................................................................... 3 DAFTAR ISI.......................................................................................................................... 4 BAB I ...................................................................................................................................... 5 PENDAHULUAN ................................................................................................................. 5 1.1

Latar Belakang ....................................................................................................... 5

1.2

Tujuan ..................................................................................................................... 5

BAB II .................................................................................................................................... 6 PROGRAM ........................................................................................................................... 6 BAB III ................................................................................................................................. 18 PENYELESAIAN SOAL ................................................................................................... 18 3.1 Soal 1 .......................................................................................................................... 18 3.2 Soal 2 .......................................................................................................................... 22 3.3 Soal 3 ......................................................................................................................... 25 BAB IV ................................................................................................................................. 30 PENUTUP ............................................................................................................................ 30 4.1 Kesimpulan ................................................................................................................ 30 4.2 Saran .......................................................................................................................... 30

BAB I PENDAHULUAN

1.1

Latar Belakang Dalam melakukan konstruksi suatu gedung, dibutuhkan analisis struktur, perhitungan, dan pendesainan material-material yang dibutuhkan. Ketika melakukan analisis

struktur

dibutuhkan

bantuan

komputasi

perhitungan

agar

dapat

menyelesaikan perhitungan struktur yang lebih kompleks secara lebih efektif dan efisien. Hal inilah yang melatarbelakangi pembuatan tugas program analisis struktur rangka batang.

1.2

Tujuan Tujuan dari tugas besar ini adalah sebagai berikut: 1. Mendesain program untuk menghitung gaya-gaya pada rangka batang 2. Menyelesaikan soal-soal yang diberikan menggunakan program yang sudah dibuat.

BAB II PROGRAM

%Tugas Besar I Anstrik %Luis Valerius Pasasa | 15016141 clear clc filename = 'soal_1 rev.txt'; Input = csvread(filename); %Variable Counting Temp=1; %Reading and Storing Joint Data NJ = Input(Temp,1) for i=1:1:NJ COORD(i,1) = Input(i+Temp,1); COORD(i,2) = Input(i+Temp,2); end %Reading and Storing Support Data a=i; Temp=a+2; NS = Input(Temp,1) NCJT = 3; for i=1:1:NS for j=1:1:NCJT MSUP(i,j) = Input(i+Temp,j); end end %Reading and Storing Material Property Data a=i; Temp=Temp+a+1; NMP = Input(Temp,1) for i=1:1:NMP EM(i) = Input(i+Temp);

end EM=EM'; %Reading and Storing Cross-sectional Property Data a=i; Temp=Temp+a+1; NCP = Input(Temp,1) for i=1:1:NCP CP(i) = Input(i+Temp); end CP=CP'; %Reading and Storing Member Data a=i; Temp=Temp+a+1; NM = Input(Temp,1); for i=1:1:NM MPRP(i,1)= Input(i+Temp,1); MPRP(i,2)= Input(i+Temp,2); MPRP(i,3)= Input(i+Temp,3); MPRP(i,4)= Input(i+Temp,4); end %Reading and Storing Load Data a=i; Temp=Temp+a+1; NJL = Input(Temp,1); for i=1:1:NJL JP(i) = Input(i+Temp); end for i=1:1:NJL for j=1:1:NCJT PJ(i,1) = Input(i+Temp,2); PJ(i,2) = Input(i+Temp,3); end end JP=JP'; %Determining Number of Degrees of Freedom NR=0 NCJT=2;

for i=1:1:NS for j=2:1:(NCJT+1) if MSUP(i,j)==1 NR=NR+1; else j=j+1; end end end NDOF=NCJT*NJ-NR; %Generating Structure Coordinate Number I=1; J=0; K=NDOF; for a=I:1:NJ ICOUNT=0; I1=1; for b=I1:1:NS if MSUP (b,1)==a ICOUNT=1; I2=1; for c=I2:1:NCJT I3=(a-1)*NCJT+c; if MSUP(b,c+1)==1 K=K+1; NSC(I3)=K; else J=J+1; NSC(I3)=J; end end end end if ICOUNT==0 I2=1; for d=I2:1:NCJT I3=(a-1)*NCJT+d; J=J+1 NSC(I3)=J;

end end end NSC=NSC'; %Generating Structure Stiffness Matrix for Plane Trusses S = zeros (NDOF,NDOF); for i=1:1:NDOF for j=1:1:NDOF S(i,j)=0; end end for IM=1:1:NM JB=MPRP(IM,1); JE=MPRP(IM,2); I=MPRP(IM,3); E=EM(I); I=MPRP(IM,4); A=CP(I); XB=COORD(JB,1); YB=COORD(JB,2); XE=COORD(JE,1); YE=COORD(JE,2); BL=((XE-XB)^2+(YE-YB)^2)^(0.5) CX=(XE-XB)/BL; CY=(YE-YB)/BL; GK = MSTIFFG(E,A,BL,CX,CY, NDOF, NCJT); S = S + STORES(JB, JE, NCJT, NDOF, NSC, GK); end %Forming Joint Load Factor for i=1:1:NDOF P(i)=0; end for i=1:1:NJL I1=JP(i); I2=(I1-1)*NCJT; for j=1:1:NCJT

I2=I2+1; N=NSC(I2); if N<=NDOF P(N)=P(N)+PJ(i,j); end end end %Calculating Joint Displacement by Gauss-Jordan Method for i=1:1:NDOF Z1=S(i,i); for j=1:1:NDOF S(i,j)=S(i,j)/Z1 end P(i)=P(i)/Z1; for K=1:1:NDOF if K ~=i Z=S(K,i); for M=1:1:NDOF S(K,M)=S(K,M)-S(i,M)*Z; end P(K)=P(K)-P(i)*Z; end end end %Determination of Member Forces and Support Reactions for Plane Trusses for I=1:1:NR R(I)=0; end Axial_Forces=zeros(NM,1); R=zeros(NR,1) for IM=1:1:NM JB = MPRP(IM,1); JE = MPRP(IM,2); I = MPRP(IM,3); E = EM(I); I = MPRP(IM,4); A = CP(I); XB = COORD(JB,1); YB = COORD(JB,2); XE = COORD(JE,1); YE = COORD(JE,2);

BL = ((XE-XB)^2+(YE-YB)^2)^0.5; CX = (XE-XB)/BL; CY = (YE-YB)/BL; V = MDISPG(JB, JE, NCJT, NDOF, NSC, P); T = MTRANS(CX, CY, NCJT); U = MDISPL(NCJT, V, T); BK = MSTIFFL(E, A, BL, NCJT); Q = MFORCEL(NCJT, BK, U); F = MFORCEG(NCJT, T, Q); F=F' R = R + STORER(JB, JE, NCJT, NDOF, NSC, F, NR, N); Axial_Forces(IM,1)=Q(3); end P=P' %Display untuk Joint Displacement JD=zeros (NJ,3); J=1; K=1; for I=1:1:NJ; JD(I,1)=I; if J<=NS && I==MSUP(J,1) if MSUP (J,2):1 JD(I,2)=0; else JD(I,2)=P(K,1); K=K+1; end if MSUP (J,3):1 JD (I,3)=0; else JD(I,3)=P(K,1); K=K+1; end J=J+1; else JD(I,2)=P(K,1); K=K+1; JD(I,3)=P(K,1); K=K+1;

end end Joint_No=zeros(NJ,1); X_Translation=zeros(NJ,1); Y_Translation=zeros(NJ,1); for i=1:NJ Joint_No(i,1)=JD(i,1); X_Translation(i,1)=JD(i,2); Y_Translation(i,1)=JD(i,3); end %Output Support Reaction SR=zeros(NS,1); X_Reaction=zeros(NS,1); Y_Reaction=zeros(NS,1); Joint_NO=zeros(NS,1); for i=1:1:NS Joint_NO(i,1)=MSUP(i,1); end for i=1:1:NS if MSUP (i,2)==1 X_Reaction(i,1)=R(i); else X_Reaction(i,1)=0; end if MSUP (i,3)==1 Y_Reaction(i,1)=R(i+1); else Y_Reaction(i,1)=0; end end %Output Member Axial Forces Member=zeros(NM,1); for I=1:1:NM Member(I,1)=I; if Axial_Forces(I,1)<0 Qaf(I,1)="C"; else Qaf(I,1)="T";

end end disp('***********************************************') disp('* Results of Analysis *') disp('***********************************************') disp('') disp(' ===================') disp(' Join Displacements') disp(' ===================') disp('') JD=table(Joint_No, X_Translation, Y_Translation); disp(JD); disp(' ===================') disp(' Member Axial Forces') disp(' ===================') disp('') MAF=table(Member, Axial_Forces, Qaf); disp(MAF); disp(' =================') disp(' Support Reactions') disp(' =================') disp('') Support_Reaction=table(Joint_NO, X_Reaction, Y_Reaction); disp(Support_Reaction); disp('') disp('***************End of Analysis***************') %Flowchart for Subroutine MSTIFFG for Determining Member Global Stiffness %Matrix for Plane Trusse function GK = MSTIFFG(E, A, BL, CX, CY,NDOF, NCJT) GK=zeros(2*NCJT,2*NCJT); Z=E*A/BL; Z1=Z*(CX^2); Z2=Z*(CY^2); Z3=Z*CX*CY; GK(1,1)=Z1; GK(3,1)=-Z1;

GK(1,2)=Z3; GK(3,2)=-Z3; GK(1,3)=-Z1; GK(3,3)=Z1; GK(1,4)=-Z3; GK(3,4)=Z3; GK(2,1)=Z3; GK(4,1)=-Z3; GK(2,2)=Z2; GK(4,2)=-Z2; GK(2,3)=-Z3; GK(4,3)=Z3; GK(2,4)=-Z2; GK(4,4)=Z2; %Storing Member Global Stiffness Matris in Structure Stiffness Matrix function S = STORES(JB, JE, NCJT, NDOF, NSC, GK) Y=zeros(NDOF,NDOF); for i=1:1:(2*NCJT) if i<=NCJT I1=(JB-1)*NCJT+i; else I1=(JE-1)*NCJT+(i-NCJT); end N1=NSC(I1); if N1<=NDOF for j=1:1:(2*NCJT) if j<=NCJT I1=(JB-1)*NCJT+j; else I1=(JE-1)*NCJT+(j-NCJT); end N2=NSC(I1); if N2<=NDOF Y(N1,N2) = Y(N1,N2)+ GK(i,j); end end

end end S=Y; %Determining Member Global Displacement Vector function V = MDISPG(JB, JE, NCJT, NDOF, NSC, P) for I=1:1:2*NCJT V(I)=0; end J = (JB-1)*NCJT; for I=1:1:NCJT J = J+1; N = NSC(J); if N<=NDOF V(I)=P(N); end end J = (JE-1)*NCJT; I=NCJT+1; for I=NCJT+1:1:2*NCJT J=J+1; N=NSC(J); if N<=NDOF V(I)=P(N); end end %Determining Member Transformation Matrix for Plane Trusses function T = MTRANS(CX, CY, NCJT) for I=1:1:2*NCJT for J=1:1:2*NCJT T(I,J)=0; end end T(1,1)=CX; T(2,1)=-CY;

T(1,2)=CY; T(2,2)=CX; T(3,3)=CX; T(4,3)=-CY; T(3,4)=CY; T(4,4)=CX; %Determining Member Local Displacement Vector function U=MDISPL(NCJT, V, T) for I=1:1:2*NCJT U(I)=0; end for I=1:1:2*NCJT for J=1:1:2*NCJT U(I)=U(I)+T(I,J)*V(J); end end %Determining Member Local Stiffness Matrix for Plane Trusses function BK = MSTIFFL(E, A, BL, NCJT) for I=1:1:2*NCJT for J=1:1:2*NCJT BK(I,J)=0; end end Z=E*A/BL; BK(1,1)= Z; BK(1,3)=-Z BK(3,1)=-Z; BK(3,3)=Z; %Determining Member Local Force Vector function Q = MFORCEL(NCJT, BK, U) for I=1:1:2*NCJT

Q(I)=0; end; for I=1:1:2*NCJT for J=1:1:2*NCJT Q(I)=Q(I)+BK(I,J)*U(J); end end %Determining Member Global Force Vector function F = MFORCEG(NCJT, T, Q) for I=1:1:2*NCJT F(I)=0; end for I=1:1:2*NCJT for J=1:1:2*NCJT F(I)=F(I)+T(J,I)*Q(J); end end %Storing Member Global Forces in Support Reaction Vector function R = STORER(JB, JE, NCJT, NDOF, NSC, F, NR,N) R=zeros(NR,1); for I=1:1:2*NCJT if I<=NCJT I1=((JB-1)*NCJT)+I; else I1=((JE-1)*NCJT)+(I-NCJT); end N=NSC(I1); if N>NDOF R(N-NDOF)= R(N-NDOF) + F(I); end end end

BAB III PENYELESAIAN SOAL

3.1 Soal 1

𝑩𝒂𝒕𝒂𝒔 𝒏𝒊𝒍𝒂𝒊 𝑭 = 𝛔𝐲 𝐱 𝐀 𝑭𝒊𝒛𝒊𝒏 = 𝟑𝟔𝟓 𝒌𝑵

𝑩𝒆𝒓𝒅𝒂𝒔𝒓𝒌𝒂𝒏 𝒏𝒊𝒍𝒂𝒊 𝑭 𝒎𝒆𝒎𝒃𝒆𝒓 𝟏 𝒅𝒊𝒅𝒂𝒑𝒂𝒕 𝑷 𝒚𝒂𝒏𝒈 𝒔𝒆𝒔𝒖𝒂𝒊 𝒂𝒅𝒂𝒍𝒂𝒉 𝟏𝟒𝟎𝟎𝒌𝑵

3.2 Soal 2

PENGECEKAN SOAL 2

3.3 Soal 3

BAB IV PENUTUP

4.1 Kesimpulan 1. Program yang sudah dibuat dapat dilihat pada BAB II 2. Jawaban dan pengecekan jawaban dapat dilihat pada BAB III

4.2 Saran Dalam melakukan pembuatan programming dapat diperjelas setiap variable yang digunakan itu apa, lalu dibuat pemodelan struktur langsung dari MATLABnya.

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