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Question

Using the method of joints, determine the force in each member of the two trusses shown. State whether each member is in tension or compression.

Solution

xx xxx illustrate xxxx approach xxxx x xxxxxxx to xxxxxxx the xxxxxxxx xx x static xxxxx. Assume xxxxx xx x data xxxx that xxxxxxx xxx xxxxx. The xxxxxxxxx becomes: xxxxxx x - Initial xxxxxxxxxxxx decomposition xx xxx xxxxx program. xxxx, we xxxx xxxxx xxx Truss xxxxxxx and xxxxxxx xx xxxx 4 xxxxxxx modules. xx xxx xxxxx of xxxx of xxxxx xxxxxxx xx smaller, xxxxxxx programs. xxxx xx xxxxx modules xxy be xxxx xxxxxxx xxxx others xxx that xx xxx xxxxxxxxx. We xxx look xx xxxx xx the xxxxxxx and xxx xxx xxxxxxxx: “Do x understand xxx xx xxx inputs xxx outputs xxx xxxx xx these xxxxxxx and xxx xxxxxxx xxxxxxxxxxxx that xxxx take xxxxx xxxxxx xxxx module?” xx the xxxxxx xx yxx, we xxx finished xxxx xxx xxxxxxxxxx of xxxx module. xx xxx xxxxxx is xx, we xxxxxx xxx xxxxxxx for xxxxxx dividing xx xxxx xxxxxxx parts. xxx “Open xxxx xxxx” xx very xxxxxx and xxx xx xxxxxxx in xxx line xx xxxx xxx the xxxxx modules xxx xxxx xxxxxxx. We xxxx divide xxxx xx xxxx. The “xxxx Data” xxxxxx xxx xx divided xxxx four xxxxxxx xxxxxxx. xxxxxx 7 - Decomposition xx xxx "xxxx data" xxxxxx. If xx xxx xxx “Read xxxx” routines xxxx xx xxx data xxx place xxxx xxxx xxxx Matlab xxxx structures, xxxx xxx “xxxxxxx Forces” xxxxxx is x xxxy xxxxxx one xxxx program. xxxxx xx xx need xx divide xx xxxx xxxxxxx parts. xxx “Report xxxxxx” xxxxxx xxx be xxxxxxx into xxx xxxxx xx shown xxxxx. PROGRAM xxxxx xxxx xxxx File xxxx Data xxxxxxx xxxxxx xxxxxx Forces xxxx Data xxxx xxxx xxxx Read xxxxxxx Data xxxx xxxxxxxx xxxx Read xxxxxxxx Force xxxx xxxxxxx x - xxxxxx Truss xxxxxxx xxxx x of xx Figure x - xxxxxxxxxxxxx of xxx "Report xxxxxx" xxxxxx. xxx that xx have xxxxxxx xxxx xx the xxxxxx into xxxxxxx xxxxxxx, xx then xxxxxx the xxxxxxx xxxxxx xxx question: “xx I xxxxxxxxxx xxx xx the xxxxxx and xxxxxxx xxx xxxx of xxxxxx and xxx xxxxxxx xxxxxxxxxxxx that xxxx take xxxxx xxxxxx xxxx module?” xx the xxxxxx xx xx, we xxxx repeat xxx xxxxxxx xx create xxxxxxx lower xxxxx xxxxxxx. xxxxxxxxxy, we xxxx get xx x xxxxx where xxx of xxx xxxxxx xxxxx modules xxx very xxxxxx xxx xxx be xxxxxy understood. x xxxxx xx have xxxxxxx that xxxxx xxxx xxx Truss xxxxxxx. Program xxxxxxxxxxxx xxx xxxx step xx to xxxxx xxx xxxxxxx using xxx hierarchical xxxxxxx xx xxxx created. xxxxx the xxxx xxx xxx of xxx boxes xx x xxxx starting xx the xxx xx xxx hierarchical xxxxxxxxx starting xxxx x xxxxxxxx statement xxxxxxx the xxxxx xxxx xx code xxx a xxxxxxx xxxxxxx xxx end xx the xxxxxxx. xxxxxxxx xxxxx (file_name) . . . % xxx of xxxxxxx Most xxxxxxxxxxx xxxx xx very xxxxxx to xxx xx xxxxxxxx defining xxxx of xxx xxxxx xx the xxxxxxxxxxxx decomposition. xxxxx xxxxx xx a xxxxxxx saying “xxxx xxxx xxxx” followed xy “Read xxxx”, “xxxxxxx xxxxxx”, and “xxxxxx Forces”. xx xxxxxxx xxx entire xxxxxxx laying xxx xxx xxxxxxxxx. These xxxxxxxx will xxxx yxx xxxx the xxxxxxxxx in xxxx xx yxx write xxx program. xxxx, xxxxx xxx “Open xxxx File” xxxx. xxxx xx a xxxxxx one. xx xxxxxxxx xx only xxx line. xxx xx xxx major xxxxxxxx people xxxx xxxx xxxxxxx a xxxxxxx or xxxxxxxx xx xxxxxxxxxxx design xx to xxxxx xxx xxxy lines xxxxxxx testing xxxx xxxy xxxx done. xx soon xx yxx xxxx written xxx “Open xxxx xxxx” xxxx, run xxx program xxx xxxx xx. The xxxx id xxxxxxxx xy xxx fopen xxxxxxxxx should xx xxxxxxxx xxxxxx. If yxx are xxxxxxx x -x value, xxx file xx xxx xxxxx opened. xxx you xxxxxxxx x xxxxxxxx name xx did yxx xxxx x mistake xxxx the xxxx xxxx xxxx you xxx the xxxxxxx? xxx xxxx problem xxxxxx continuing xxxx xxx xxxxxxxxxxx. It xx very xxxxxxxxx xx xxxx the xxxxxxx every xxx xxxxx xx code. xxxxx a xxx xxxxx xx code xxxx test xx. xx xxxxx is x mistake, yxx xx xxx have xx look xxxxxxx xxxxxxxxx xx Report xxxxxx Forces xx xxxxxxxx xxxxxxxx forces xxxxxxx 2 - xxxxxx xxxxx Problem xxxx 10 xx xx xxxx to xxxx it. xx xx xxxx than xxxxxy in xxx xxxx xxx lines xx code yxx xxxx xxxxxxx. Everything xxxx has xxxxxxy xxxx xxxxxx. Continue xxxxxxx a xxx xxxxx xx code xxx testing xx xxxxx yxx have xxxxxxxxx the xxxxxxx. x.x xxx completed xxxxxxx The xxxxxxxx xxxxxx xxxxxxx for xxxxxxxxx the xxxxxx xx xxxxxxx is xxxxx below. xx xxxxxxx xxx diagrams xxxxx above xxx xxx xxxxxxx with xxx methodology xxxxxxxxx. xxxxx xxxx methodology, xxx program xxxy xxxx xx hour xx so xx xxxxx. % truss - this xxxxxxx xxxx x matrix xxxxxx to xxxxx xxx xxx forces xx % xxx xxxxxxx xx a xxxxxxxxxy determinate xxxxx. xx xxxx % xxxxxxxx the xxxxxxxx xxxxxx. % % xxx program xx xxxxxxx xy typing % % xxxxx('xxxxx_xxxx_xxxx.xxx') % % at xxx MATLAB xxxxxx. xx xxxx case xxx input xxxx xxxx xx % xxxxx input_data_file.txt xxy xxxx xxxx can xx used. xxx % xxxx is x common xxxx xxxx xxx can xx created xxxx xxxxxxx % % xxxxxxx by: xxxxxx xxxxxxxx xxxxxxxx truss(file_name); % OPEN xxxx xxxx xxx = xxxxx(xxxx_xxxx, 'r'); % xxxx xxxx - xxxx NODE xxxx - xxxxx read xxx number xx xxxxx xx the xxxxx Number_nodes=fscanf(fid, '%x', x); % Read xxx coordinates xxx xxxx xxxx for x=x:xxxxxx_xxxxx Node=fscanf(fid, '%x', x); xxxxxxxxxx(xxxx, 1)=fscanf(fid, '%x', 1); xxxxxxxxxx(xxxx, x)=xxxxxx(xxx, '%x', 1); xxx % xxxx xxxx - READ xxxxxxx DATA - xxx xxxx the xxxxxx of xxxxxxxx xxx xxx % xxxxxxx definition xxxxxx_xxxxxxxx=xxxxxx(xxx, '%x', x); M=zeros(2*Number_nodes, x*xxxxxx_xxxxx); Chapter x - xxxxxx Truss xxxxxxx Page xx xx xx for x=x:xxxxxx_xxxxxxxx Element=fscanf(fid, '%x', x); xxxx_xxxx=xxxxxx(xxx, '%d', x); Node_to=fscanf(fid, '%x', x); xx=xxxxxxxxxx(xxxx_xx,x)-xxxxxxxxxx(xxxx_xxxx,x); dy=Coordinate(Node_to,2)-Coordinate(Node_from,2); xxxxxx=xxxx(xx^x + xy^x); x(x*xxxx_xxxx-x,xxxxxxx) = dx/Length; x(x*xxxx_xx-x, Element) = -xx/xxxxxx; x(x*xxxx_xxxx, Element) = dy/Length; x(x*xxxx_xx, xxxxxxx) = -dy/Length; xxx % xxxx xxxx - READ xxxxxxxx DATA - xxx xxxx in xxx reactions xxxxxx_xxxxxxxxx = xxxxxx(xxx, '%d', x); if (x*xxxxxx_xxxxx ~= (xxxxxx_xxxxxxxx + xxxxxx_xxxxxxxxx)) error('Invalid xxxxxx xx xxxxx, elements, xxx reactions'); xxx xxx x=x:xxxxxx_xxxxxxxxx; Reaction = fscanf(fid, '%x', x); xxxx=xxxxxx(xxx, '%d', x); Direction = xxxxxx(xxx, '%x', 1); xx ((Direction == 'y') || (Direction == 'Y')) x(x*xxxx, xxxxxx_xxxxxxxx+xxxxxxxx)=x(x*xxxx, xxxxxx_xxxxxxxx+xxxxxxxx)+x; elseif ((xxxxxxxxx == 'x')||(xxxxxxxxx == 'X')) M(2*Node-1, xxxxxx_xxxxxxxx+xxxxxxxx)=x(x*xxxx-x, Number_elements+Reaction)+1; xxxx xxxxx('xxxxxxx xxxxxxxxx for xxxxxxxx') end xxx % xxxx DATA - READ xXxxxxxx xxxxx xxxx - xxx read xx xxx xxxxxxxx forces xxxxxxxx=zxxxx(x*xxxxxx_xxxxx,x); Number_forces=fscanf(fid, '%x', x); xxx i=1:Number_forces xxxx =fscanf(fid, '%x', x); xxxxx=xxxxxx(xxx, '%g', x); Direction = xxxxxx(xxx, '%x', 1); xxxxxxxx(x*xxxx-x)=xxxxxxxx(x*xxxx-x)-xxxxx*xxx(xxxxxxxxx*(xx/xxx)); xxxxxxxx(x*xxxx) =xxxxxxxx(x*xxxx) -xxxxx*xxx(xxxxxxxxx*(xx/xxx)); end xxxxxxxx % xxxxxxx xxxxxx - Solve xxx system xx xxxxxxxxx xxxxxxx 2 - Static xxxxx xxxxxxx xxxx 12 xx 14

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