Application of ILDs for critical load analysis

Application of ILDs for static/ moving loads beyond single unit concentrated load

         ILD are drawn for a single unit concentrated load travelling on the span/ structure. In the following video, I tried to explain the application of concept of ILD to the analysis of static/moving loads other than unit load, other than concentrated loads, and for multiple loads.

ILD for trusses in which panel points are not vertically in line with loaded panel points

 


       In the following video, I tried to explain the procedure for drawing ILDs for member forces in trusses in which the top and bottom panel points are not vertically in line. In such trusses, a small correction needs to be done in the ILD. There should not be an abrupt change in the ILD at the point or section where the loading does not appear directly. So, that abrupt change at non-loading panel points needs to be smoothened.

ILD s for Simply supported Bridge Trusses

The following video is for the students of II year B. Tech (civil Engineering) Programme. The video details the procedure for drawing ILDs of simply supported trusses

Unit Load method for deflections of rigid frames

The following video is for II year under graduate students of Civil Engineering Programme

Strain energy method for slopes and Deflection of beams

The following video is made for students of II year of Bachelor's programme in Civil Engineering

PLotting truss structures using MATLAB code

Objective: The following article explains the MATLAB code to plot a figure of truss structure to scale

MATLAB Functions used: line( ), min( ), max( ), length( ), viscircles( ), patch( ), etc

Other features: THe supports and loading are also depicted in the plots. The load values and directions are clearly indicated in color

MATLAB Code:

function drawtruss2D(NODE,ELEM,L_BC)
    figure;line([NODE(ELEM(:,1),1) NODE(ELEM(:,2),1)]',[NODE(ELEM(:,1),2) ...
        NODE(ELEM(:,2),2)]','Color','b','LineWidth',2,'Marker','o',...
        'MArkerSize',8,'MarkerFacecolor','w');hold on;
    minX=min(NODE(:,1));maxX=max(NODE(:,1));minY=min(NODE(:,2));maxY=max(NODE(:,2));
    rangeX=maxX-minX;rangeY=maxY-minY;
    xlim([minX-0.2*rangeX maxX+0.2*rangeX]);ylim([minY-0.2*rangeY maxY+0.2*rangeY]);
    axis equal
    if nargin==3
        nl=rangeX*0.10;nb=rangeY*0.05;
        for o=1:length(L_BC)
           OType= L_BC{o}{1};
           switch OType
               case 'F'
                   X=[0;-nl*0.30;-nl*0.20;-nl;-nl;-nl*0.20;-nl*0.30;0];
                   Y=[0;nb;nb*0.2;nb*0.2;-nb*0.2;-nb*0.2;-nb;0]*0.7;
                   if length(L_BC{o})>4;X=X+nl;end
                   F=L_BC{o}{2};rot=L_BC{o}{3};
                   theta=rot/180*pi;
                   R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
                   Trans=[X Y]*R;Xt=Trans(:,1);Yt=Trans(:,2);
                   Xf=NODE(F,1);Yf=NODE(F,2);
                   patch(Xt+Xf,Yt+Yf,[1 0 0]);
                   Xa=[nl*0.25 nb*0.25]*R;
                   if length(L_BC{o})>4;text(Xt(1)+Xf+Xa(1),Yt(1)+Yf+Xa(2),L_BC{o}{4},'FontSize',18);
                   else text(Xt(4)+Xf+Xa(1),Yt(4)+Yf+Xa(2),L_BC{o}{4},'FontSize',18);end
               case 'H'
                   X=[0;-nl/4;-nl/2;-nl/2;nl/2;nl/2;nl/4;0];
                   Y=[0;-nb*0.8;-nb*0.8;-nb;-nb;-nb*0.8;-nb*0.8;0]*1.2;
                   F=L_BC{o}{2};rot=L_BC{o}{3};
                   theta=rot/180*pi;
                   R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
                   Trans=[X Y]*R;Xt=Trans(:,1);Yt=Trans(:,2);
                   Xf=NODE(F,1);Yf=NODE(F,2);
                   patch(Xt+Xf,Yt+Yf,[0.5 1 0.5]);
               case 'R'
                   X=[-nl/2;-nl/2;nl/2;nl/2];
                   Y=[-nb*0.4;-nb;-nb;-nb*0.4]*1.2;
                   F=L_BC{o}{2};rot=L_BC{o}{3};
                   theta=rot/180*pi;
                   R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
                   Trans=[X Y]*R;Xt=Trans(:,1);Yt=Trans(:,2);
                   Xf=NODE(F,1);Yf=NODE(F,2);
                   patch(Xt+Xf,Yt+Yf,[1 1 0.5]);
                   viscircles([0 0]*R+[Xf Yf],nb*0.4,'LineWidth',5,'EdgeColor','y');
                   viscircles([0 0]*R+[Xf Yf],nb*0.6,'EdgeColor','k');
           end                     
                   
        end
    end
return

Typical input Files:

%Truss data for various problems
FlagNo=12;
switch FlagNo
    case 1  % Single Braced Truss %Page 693 Vazirani and Ratwani
        NODET=[0 0;8 0];NODE=[];for i=1:5;NODE=[NODE;NODET+[[0;0] 6*[i-1;i-1]]];end
        ELEMT=[1 3;1 4; 3 4 ;2 4];ELEM=[];for i=1:4;ELEM=[ELEM;ELEMT+(i-1)*2];end
  drawtruss2D(NODE,ELEM,{{'F',3,0,'30 kN',1},{'F',4,180,'30 kN'},{'R',2,0,'30 kN'},{'H',1,0,'30 kN'}});
    case 2  %
        NODET=[3 0;3 4;6 0;6 8];NODE=[0 0;0 8];n=4;
        for i=1:n
            NODE=[NODE;NODET+[6*(i-1)*ones(4,1) zeros(4,1)]];            
        end
        ELEMT=[1 3;1 4; 2 4;3 5;4 5;2 6;5 6];ELEM=[1 2];
        ELEMT1=[1 3;1 4; 3 5;4 5;4 6;2 6;5 6];
        for i=1:n
            if i<=n/2
                ELEM=[ELEM;ELEMT+4*(i-1)]; 
            else
                ELEM=[ELEM;ELEMT1+4*(i-1)]; 
            end
        end
        drawtruss2D(NODE,ELEM);
    case 3 %Page 11 Vazirani
        NODE=[0 0;0 4;4 2;4 6;8 4;8 8;12 4;12 8;16 0;16 4;20 -4;20 0];
        ELEM=[1 2;1 3;2 3;2 4;3 4; 3 5; 4 5; 4 6; 5 6;5 7;6 8;7 8;7 9;7 10;8 10;9 10;9 11;9 12;10 12;11 12];
        drawtruss2D(NODE,ELEM,{{'F',4,90,'30 kN'},{'H',1,0,'30 kN'},{'H',11,0,'30 kN'}});
    case 4 %PAge 51, Negi and Jangid
        NODE=[0 0;4 0; 8 0;8 -4;4 -2];
        ELEM=[1 2;1 5;2 5;2 3;5 3; 5 4;3 4];
        drawtruss2D(NODE,ELEM,{{'F',1,90,'P'},{'F',2,90,'P'},{'F',3,90,'P'},{'R',1,30,'  '},{'H',4,0,' '}});
   case 5 %PAge 51b, Negi and Jangid
        NODE=[0 0;3 3; 3 0;6 6;6 0;9 9;9 0;12 6;12 0;15 3;15 0;18 0];
      ELEM=[1 2;1 3;2 3;2 4;2 5; 3 5;5 4;4 6;4 7;5 7;7 6;6 8;7 8;7 9;9 8;8 10;9 10;9 11;11 10;10 12;11 12];
drawtruss2D(NODE,ELEM,{{'F',7,90,'P',1},{'R',12,0,'  '},{'H',1,0,' '}});
  case 6 
        NODE=[0 0;3 3*sqrt(3); 6 0;2.25 2.25;3.75 2.25;3 3*tand(15)];
        ELEM=[1 2;2 3;3 1;1 4;2 5;3 6;4 5;5 6;6 4];
        drawtruss2D(NODE,ELEM,{{'F',6,90,'P',1},{'R',3,0,'  '},{'H',1,0,' '}});
  case 7 
        NODE=[0 0;3 0;6 3;6 6;3  3;0 3];
        ELEM=[1 2;2 3;3 4;4 5;5 6;6 1;1 5;5 2;5 3];
        drawtruss2D(NODE,ELEM,{{'F',4,0,'H',1},{'F',4,270,'W',1},{'R',6,90,'  '},{'H',1,90,' '}});  
  case 8 
        NODE=[0 0;8 0;4 3;4 0];
        ELEM=[1 3;1 4;3 4;3 2;4 2];
        drawtruss2D(NODE,ELEM,{{'F',4,90,'15 kN',1},{'R',2,0,'  '},{'H',1,0,' '}}); 
 case 9 
        NODE=[0 0;0 4;4 4;4 0];
        ELEM=[1 2;1 3;1 4;2 3;3 4];
        drawtruss2D(NODE,ELEM,{{'F',2,0,'P'},{'R',4,0,'  '},{'H',1,0,' '}}); 
 case 10 
        NODE=[0 0;3 1;5 1;3 3];
        ELEM=[1 2;1 4;2 4;2 3;3 4];
        drawtruss2D(NODE,ELEM,{{'F',2,90,'40 kN',1},{'R',3,0,'  '},{'H',1,0,' '}}); 
 case 11 
        NODE=[0 0;0.5 -sind(60);1.5 -sind(60);2 0;1.5 sind(60);1 0];
        ELEM=[1 2;2 3;3 4;4 5;5 6;1 6;2 6;3 6;4 6;];
        drawtruss2D(NODE,ELEM,{{'F',5,0,'100 kN',1},{'R',3,0,'  '},{'H',1,90,' '}}); 
case 12 
        NODE=[0 0;0 3;0 6;4 0;4 3;4 6];
        ELEM=[1 2;2 3;1 4;2 4;2 5;3 5;3 6;4 5;5 6];
        drawtruss2D(NODE,ELEM,{{'F',6,0,'100 kN',1},{'R',4,0,'  '},{'H',1,0,' '}}); 

end

Output plots: