1 2 Page 1 Lecture M4 Example of Use of Free Body Diagram 10 ft. flag pole (massless) in a wall with a weight (flag) at end Idealize as 2-D structure Replace supports by reactions which model them in the ideal case. FBDPage 2Page 3 Example 2 Bar with roller leaning against wall. friction = µ(find critical value) Draw FBDPage 4 Before proceeding to apply equilibrium to analyze for the support reactions it is important to identify the potential categories of problem that may exist: Three Problem Categories 1.) Dynamic: Number of rigid body degrees of freedom (DOF) > number of reactions ⇒ Body Moves Example FBD 2 reactions 3 DoF two components of translation, one axis of rotation ∴ Dynamic (Note, in 3-D there would be 6 degrees of freedom - 3 components of translation, 3 axes of rotation)Page 5 2. Statically Determinate Number of rigid body number of reactionsDegrees of Freedom = 3 D of F as before, but now 3 reactions Implication Can determine reactions and internal forces purely from Equilibrium considerations 3. Statically Indeterminate Number of rigid body Degrees of freedom < Number of reactions 4 Reactions, 3 D o F (as before) Implication Cannot determine reactions and internal forces from equilibrium but also need to include deformation of the structure - constitutive relations. ⇒Material does make a difference for internal and external reactions. (see block
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