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Learning Objectives
1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations of static equilibrium of the overall structure and each individual member. 2). To do an engineering estimate of these quantities.
Definitions
Two-Force Member : a structural member that is loaded only at two pin joints along the member. Multi-Force Member : a structural member that is loaded at more than two points along the member. Truss : a rigid framework of straight, lightweight two-force members that are joined together at their ends. Frame : an assembly of rigid members (of which at least one is a multi – force member ) intended to be a stationary structure for supporting a load. Machine : an assembly of rigid members designed to do mechanical work by transmitting a given set of input loading forces into another set of output forces.
Newton’s Third Law
Newton’s Third Law : For each action there is an action and
Frames and Machines Example 1
Given: The frame shown is loaded with a 600 N force and is supported by a pin support at joint A and a roller support at joint E.
Find: Assuming the weight of the members are negligible compared to the applied load, a) Sketch free body diagrams of the overall structure and of individual members ABC, BDE, and DCF. b) Determine the reactions at supports A and E. c) Determine the force at joint C acting on member ABC. Express this force in vector form. d) If the maximum rated load of pin C is 2,000N, will the frame fail?
Frames and Machines Example 2
Given: Frame ABCDEF is loaded as shown and is in static equilibrium.
Find: Five alternative free body diagrams for member CE are shown. Explain what (if anything) is erroneous in each diagram.