Question

Q.1. A plane truss is loaded and while solving for internal forces in truss members we are able to formulate the ten equations given below: Ax +AD0; Ay +AB074+ BC+H(3/5) BD 0 BC +(3/5) CE-0 CD + (4/5) BD -0; Ax, Ay and Ey are support reactions, while the letters BC, CD etc. represent the internal forces in corresponding truss members. Solve for all unknown forces using -AB- (4/5) BD-0 -AD+DE-(3/5) BD-0 Ey + (4/5) CE-0 -24 CD-(4/5) CE -0 -DE -(3/5) CE0: MATLAB Hint: You have to re-arrange the equations with all the constants on RHS. All the unknowns must be on LHS of the equations

Answer 1

CODE

%formulating and solving ten liner eqautions Ax = b
%first create the coefficient matrix A i.e. LHS
%column/variables are in the following order:
%Ax|Ay|Ey|AD|AB|BC|BD|CE|CD|DE => 10 columns
A= [
1, 0, 0, 1, 0, 0, 0, 0, 0, 0;
0, 1, 0, 0, 1, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 1, 0.6, 0, 0, 0;
0, 0, 0, 0, -1, 0, -0.8, 0, 0, 0;
0, 0, 0, 0, 0, -1, 0, 0.6, 0, 0;
0, 0, 0, 0, 0, 0, 0, -0.8, -1, 0;
0, 0, 0, -1, 0, 0, -0.6, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0.8, 0, 1, 0;
0, 0, 0, 0, 0, 0, 0, -0.6, 0, -1;
0, 0, 1, 0, 0, 0, 0, 0.8, 0, 0;
]
% b is the RHS of constants
b = [0; 0; -74; 0; 0; 24; 0; 0; 0; 0]
% x is the solution corresoponding to the same order as colums in A
x = inv(A)*b
x

SCREENSHOTS

trusslinearSolve.m* ×1+ %formulating and solving ten liner eqaut ions Ax = b first create the coefficient matrix A i.e. LHS %column/variables are in the following order: %Ax l Ay | Ey I AD l AB IBC IBDİCE I CD I DE-> 10 columns 1, 0, 0, 1, 0, 0, 0, 0, 0, 0: 0, 1, 0, 0, 1, 0, 0, 0, 0, 0: 0, 0, 0, 0, 0, 1, 0.6, 0, 0, 0 0, 0, 0, 0, -1, 0, -0.8, 0, 0, 0: 0, 0, 0, 0, 0, -1, 0, 0.6, 0, 0 0, 0, 0, 0, 0, 0, 0, -0.8, -1, 0: 0, 0, 0, -1, 0, 0,-0.6, 0, 0, 1: 0, 0, 0, 0, 0, 0, 0.8, 0, 1, 0 0, 0, 0, 0, 0, 0, 0, -0.6, 0, -1 0, 0, 1, 0, 0, 0, 0, 0.8, 0, 0 10 12 13 14 15 16 17 % b is the RHS of constants b= [0; 0; -74; 0; 0; 24; 0; 0; 0; 0] % x is the 3 lution c rre30ponding to the same rder as colums in A x = inv (A) *b 19

OUTPUT

Command Window >>trusslinearSolve 1.0000 0 1.0000 0 1.0000 0 0 -1.0000 0 0 1.0000 0 0.6000 0 -0.8000 0 0 0 1.0000 0 -1.0000 0.6000 0 -0.8000-1.0000 0 -1.0000 0 -0.6000 0.8000 1.0000 1.0000 0 -1.0000 0 -0.6000 0.8000 1.0000 -74 2 4

-74.0000 -37.3333 61.3333 74.0000 37.3333 -46.0000 46.6667 76.6667 37.3333 46.0000

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