01-Review - Introduction Civ E 270 Khattak N Mechanics of...

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Introduction Civ E 270 Khattak, N 1 Mechanics of Deformable Bodies Mechanics : Used to describe and predict the behaviour of particles and bodies under the action of forces. Based on the nature of particles or bodies we can break down mechanics as: Mechanics Solid Mechanics Fluid Mechanics Rigid Body Mechanics (Deformations are not considered to influence the behaviour) Deformable Body Mechanics (Deformations are taken into account and influence the behaviour) Statics Dynamics Mechanics of materials Strength of materials
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Introduction Civ E 270 Khattak, N 2 Typical structural supports Name Symbol Description Number of Reactions Fixed Translation prevented Rotation prevented Pin or Hinge (External, Internal) Translation prevented Rotation free Roller Translation perpendicular to the roller prevented Translation in the direction of the roller free Rotation free Free Free to translate Free to rotate
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Introduction Civ E 270 Khattak, N 3 Rigid Body Mechanics Deformable Body Mechanics P P/2 P/2 If the structure is statically indeterminate, we need to go a step further and consider deflections within the structure as well. Use geometric compatibility and deformation criteria to start solving for unknown reactions. (Civ E 270) Use statics to solve for remaining unknown reactions. Deformable Body Mechanics is used to solve statically indeterminate structures Equilibrium equations ° F x = 0 ° F y = 0 ° M = 0 are used to determine all the unknown reactions. Number of unknowns < Number of available equilibrium equations Statically ________________structure Number of unknowns > Number of available equilibrium equations Statically ________________structure If the structure is statically determinate, simple statics can be used to solve it. (EngG 130) P Δ
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Introduction Civ E 270 Khattak, N 4 Forces on a structure Externally applied forces on a structure create internal force effects. External forces: _________ Internal force effects: _________ _________ _________ Sign Convention Two types of sign convention are used, one for the external forces and the other for internal forces External Forces The external sign convention is generally used in writing the equations of equilibrium Internal Forces, i.e. P (Axial), V (Shear), M (Moment) The internal sign convention is generally used to plot the axial force, shear force and bending moment diagrams. (a) Axial Force (P): A force that is directed along or parallel to the member (b) Shear Force (V): A force that is directed perpendicular to the member (c) Bending Moment (M): A moment that causes the beam to bend in a plane ( + ) Tension (+) Compression (-) Positive Shear Clockwise rotation Positive Moment Negative Moment Upward acting forces are positive Forces acting to the right are positive Counter clockwise moments are positive Negative Shear Counterclockwise rotation
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Introduction Civ E 270 Khattak, N 5 Free Body Diagrams and the use of Statics to find Reactions A free body diagram is a carefully prepared drawing that illustrates the body of interest to be separated from its surroundings (supports), and shows all applied forces on the body (both known and unknown). The word “free” in the name, “free body diagram” indicates that all
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