2. An important problem in structural engineering is that of finding the forces in a statically...

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2. An important problem in structural engineering is that of finding the forces in a statically determinate truss (see figure). This type of structure can be described as a system of coupled linear algebraic equations derived from force balances. The sum of the forces in both horizontal and vertical directions must be zero at each node, because the system is at rest. Therefore, for node 1: FH = -F COS 30 + F3 COs 60 = 0 Fv = -F sin 30-F3 sin 60 +F,, = 0 for node 2: F = F + F cos 30 + H = 0 F = F sin 30 + V = 0 for node 3: F = -F2 F3 COS 60 = 0 2000 N 90 F F3 H, 2 30 60% 3 F2 tv. Fy = F3 sin 60 + 3 = 0 where Fi,, is the external vertical force applied to node i (where a positive force is upward). Express this set of linear algebraic equations in matrix form and then use MATLAB to solve for the unknowns. 2. An important problem in structural engineering is that of finding the forces in a statically determinate truss (see figure). This type of structure can be described as a system of coupled linear algebraic equations derived from force balances. The sum of the forces in both horizontal and vertical directions must be zero at each node, because the system is at rest. Therefore, for node 1: FH = -F COS 30 + F3 COs 60 = 0 Fv = -F sin 30-F3 sin 60 +F,, = 0 for node 2: F = F + F cos 30 + H = 0 F = F sin 30 + V = 0 for node 3: F = -F2 F3 COS 60 = 0 2000 N 90 F F3 H, 2 30 60% 3 F2 tv. Fy = F3 sin 60 + 3 = 0 where Fi,, is the external vertical force applied to node i (where a positive force is upward). Express this set of linear algebraic equations in matrix form and then use MATLAB to solve for the unknowns.