[Solved]Consider Truss Bridge Diagrammed Bridge Composed Trusses Steel Beams Connected Joints Nod Q37300182
Please answer a-c using MATLAB coding! Thanks.
Consider the truss bridge diagrammed below. The bridge is composed of trusses (steel beams) that are connected at joints or nodes. Each truss exerts a force, F,, on the nodes that it touches. When the bridge is at rest, these forces balance. A positive force means that the beam is in tension: it is being pulled apart by the nodes. A negative force means that the beam is being pushed inwards and is in compression. 4 V3/2 Fi 12 Fo 13 10 5 1.5 0 0.5 2.5 3.5 Figure 1: A truss bridge Cars and trucks will pass over this bridge, and we would like to figure out what forces will act on the bridge as its load changes. Let Ws, W7, Ws be the weights, measured in Newtons, of vehicles on the bridge located at nodes 6,7,8, respectively We can find equations for the unknown forces with Newton’s second and third laws of motion. ·x-and y-forces sum to zero on node (2) . x and y-forces sum to zero on node (3) F2+ F3 12_ . r and y-forces sum to zero on node (4) ·x-forces sum to zero on node (5) . r and y-forces sum to zero on node (6) ー 12 ·x and y-forces sum to zero on node (7) (10) Write this linear system as a matrix equation Ax-b where x is a vector of the forces: Fi F2 F13 (a) Use the backslash command to solve for x, the vector of forces on the bridge, when the weights of the vehicles are WO = 10000, W7-11500, and WS-15000. Save z in A1.dat. (b) Find the largest force (in absolute value) of the vector z. Save its absolute value in A3.dsti You nmay s A2.dat. You may find some of the commands max, abs, or norm useful. (c) Now suppose that we add weight to the truck at position 6 in increments of 100 New- tons until the bridge collapses. Each bridge member can withstand 30000 Newtons of compression or tension (i.e., positive or negative forces.) Therefore, the bridge will collapse when the absolute value of the largest force is larger than 30000. Find the smallest weight of the truck at position 6 for which the bridge collapses. Save your answer as A3.dat. Find which force is the one that exceeded 30000. If the force is F, save the value of j in A4.dat Show transcribed image text Consider the truss bridge diagrammed below. The bridge is composed of trusses (steel beams) that are connected at joints or nodes. Each truss exerts a force, F,, on the nodes that it touches. When the bridge is at rest, these forces balance. A positive force means that the beam is in tension: it is being pulled apart by the nodes. A negative force means that the beam is being pushed inwards and is in compression. 4 V3/2 Fi 12 Fo 13 10 5 1.5 0 0.5 2.5 3.5 Figure 1: A truss bridge Cars and trucks will pass over this bridge, and we would like to figure out what forces will act on the bridge as its load changes. Let Ws, W7, Ws be the weights, measured in Newtons, of vehicles on the bridge located at nodes 6,7,8, respectively
We can find equations for the unknown forces with Newton’s second and third laws of motion. ·x-and y-forces sum to zero on node (2) . x and y-forces sum to zero on node (3) F2+ F3 12_ . r and y-forces sum to zero on node (4) ·x-forces sum to zero on node (5) . r and y-forces sum to zero on node (6) ー 12 ·x and y-forces sum to zero on node (7) (10)
Write this linear system as a matrix equation Ax-b where x is a vector of the forces: Fi F2 F13 (a) Use the backslash command to solve for x, the vector of forces on the bridge, when the weights of the vehicles are WO = 10000, W7-11500, and WS-15000. Save z in A1.dat. (b) Find the largest force (in absolute value) of the vector z. Save its absolute value in A3.dsti You nmay s A2.dat. You may find some of the commands max, abs, or norm useful. (c) Now suppose that we add weight to the truck at position 6 in increments of 100 New- tons until the bridge collapses. Each bridge member can withstand 30000 Newtons of compression or tension (i.e., positive or negative forces.) Therefore, the bridge will collapse when the absolute value of the largest force is larger than 30000. Find the smallest weight of the truck at position 6 for which the bridge collapses. Save your answer as A3.dat. Find which force is the one that exceeded 30000. If the force is F, save the value of j in A4.dat
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Answer to Consider the truss bridge diagrammed below. The bridge is composed of trusses (steel beams) that are connected at joints… . . .
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