Tham khảo tài liệu 'fundamentals of structural analysis episode 1 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Beam and Frame Analysis Force Method Part I by S. T. Mau Improper internal connections. Statical determinacy. A stable beam or frame is statically indeterminate if the number of force unknowns is greater than the number of equilibrium equations. The difference between the two numbers is the degree of indeterminacy. The number of force unknowns is the sum of the number of reaction forces and the number of internal member force unknowns. For reaction forces a roller has one reaction a hinge has two reactions and a clamp has three reactions as shown below. -u. 1 5 Reaction forces for different supports. To count internal member force unknowns first we need to count how many members are in a frame. A frame member is defined by two end nodes. At any section of a member there are three internal unknown forces T V and M. The state of force in the member is completely defined by the six nodal forces three at each end node because the three internal forces at any section can be determined from the three equilibrium equations taken from a FBD cutting through the section as shown below if the nodal forces are known. Internal section forces are functions of the nodal forces of a member. Thus each member has six nodal forces as unknowns. Denoting the number of members by M and the number of reaction forces at each support as R the total number of force unknowns in a frame is then 6M SR. 95 Beam and Frame Analysis Force Method Part I by S. T. Mau On the other hand each member generates three equilibrium equations and each node also generates three equilibrium equations. Denoting the number o f nodes by N The total number of equilibrium equations is 3M 3N. Nodal Equilibrium Member Equilibrium Member Equilibrium FBDs of a node and two members. Because the number of members M appears both in the count for unknowns and the count for equations we can simplify the expression for counting unknowns as shown below. Number of unknowns 6M SR Number of equations 3M 3N Number of unknowns 3M
