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Tham khảo tài liệu 'fundamentals of structural analysis episode 1 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Truss Analysis Force Method Part I by S. T. Mau Problem 2. Solve for the force in the marked members in each truss shown. 1-a 1-b 2 3 4-a 4-b 4m 4m 4m 4m Problem 2. 55 Truss Analysis Force Method Part I by S. T. Mau 4. Matrix Method of Joint The development of the method of joint and the method of section pre-dates the advent of electronic computer. Although both methods are easy to apply it is not practical for trusses with many members or nodes especially when all member forces are needed. It is however easy to develop a matrix formulation of the method of joint. Instead of manually establishing all the equilibrium equations from each joint or from the whole structure and then put the resulting equations in a matrix form there is an automated way of assembling the equilibrium equations as shown herein. Assuming there are N nodes and M member force unknowns and R reaction force unknowns and 2N M R for a given truss we know there will be 2N equilibrium equations two from each joint. We shall number the joints or nodes from one to N. At each joint there are two equilibrium equations. We shall define a global x-y coordinate system that is common to all joints. We note however it is not necessary for every node to have the same coordinate system but it is convenient to do so. The first equilibrium equation at a node will be the equilibrium of forces in the x-direction and the second will be for the y-direction. These equations are numbered from one to 2N in such a way that the x-direction equilibrium equation from the ith node will be the 2i-1 th equation and the y-direction equilibrium equation from the same node will be the 2z th equation. In each equation there will be terms coming from the contribution of member forces externally applied forces or reaction forces. We shall discuss each of these forces and develop an automated way of establishing the terms in each equilibrium equation. Contribution from member forces. A typical member k having a starting node i and
