The following problem depicts a plane truss having 13 members (the numbered lines) connected by 8...
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The following problem depicts a plane truss having 13 members (the numbered lines) connected by 8 joints (the numbered circles). The indicated loads, in tons, are applied at joints 2, 5, and 6, and we wish to determine the resulting force in each member of the truss. 8 4 5 12 3 7 11 9 2 5 6 2 6 10 13 10 15 20 For the truss to be in static equilibrium, there must be no force, horizontally or vertically, at any joint. Thus, we can determine the member forces by equating the horizontal forces to the left and right at each joint, and similarly equating the vertical forces upward and downward at each joint. For the eight joints, this would give 16 equations, which is more than 13 unknown forces to be determined. For the truss to be statically determinate, that is, for there to be a unique solution, we assume that joint 1 is rigidly fixed both horizontally and vertically, and that joint 8 is fixed vertically. Resolving the member forces into horizontal and vertical components and defining = 2/2, we obtain the following system of equations for the member forces fi. Joint 2: f2=f6 f3 = 10 af = f4 + afs afi+fs+afs = 0 Joint 3: f4 = f8 Joint 4: f7=0 Joint 5: afs+f6af9 + f10 afs+ft+afg = 15 f10=f13 Joint 6: f11 = 20 f8+ afg = af12 Joint 7: af9f11af12 = 0 Joint 8f13+ af12 = 0 a) Solve this system of linear equations for the vector f by built-in functions in MATLAB. b) Construct in MATLAB the following subroutines. Compare your code results with the ones you obtain by using built-in commands in MATLAB and report your findings. i) Inner product of vectors b and f. ii) Multiplication of matrix A and vector f. iii) 2-norm computation of vector f. The following problem depicts a plane truss having 13 members (the numbered lines) connected by 8 joints (the numbered circles). The indicated loads, in tons, are applied at joints 2, 5, and 6, and we wish to determine the resulting force in each member of the truss. 8 4 5 12 3 7 11 9 2 5 6 2 6 10 13 10 15 20 For the truss to be in static equilibrium, there must be no force, horizontally or vertically, at any joint. Thus, we can determine the member forces by equating the horizontal forces to the left and right at each joint, and similarly equating the vertical forces upward and downward at each joint. For the eight joints, this would give 16 equations, which is more than 13 unknown forces to be determined. For the truss to be statically determinate, that is, for there to be a unique solution, we assume that joint 1 is rigidly fixed both horizontally and vertically, and that joint 8 is fixed vertically. Resolving the member forces into horizontal and vertical components and defining = 2/2, we obtain the following system of equations for the member forces fi. Joint 2: f2=f6 f3 = 10 af = f4 + afs afi+fs+afs = 0 Joint 3: f4 = f8 Joint 4: f7=0 Joint 5: afs+f6af9 + f10 afs+ft+afg = 15 f10=f13 Joint 6: f11 = 20 f8+ afg = af12 Joint 7: af9f11af12 = 0 Joint 8f13+ af12 = 0 a) Solve this system of linear equations for the vector f by built-in functions in MATLAB. b) Construct in MATLAB the following subroutines. Compare your code results with the ones you obtain by using built-in commands in MATLAB and report your findings. i) Inner product of vectors b and f. ii) Multiplication of matrix A and vector f. iii) 2-norm computation of vector f.
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