HES1125 Lecture - 2008 - Wk 3 - Chpt 04 - 6 slides per page

# HES1125 Lecture - 2008 - Wk 3 - Chpt 04 - 6 slides per page...

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8/7/2008 1 Engineering Mechanics: Statics Chapter 4: Equilibrium of a Rigid Body Chapter Four Outline 4. Equilibrium of a Rigid Body 4.1 Conditions for Rigid Equilibrium 42 Free Body Diagrams 4.2 Free-Body Diagrams 4.3 Equations of Equilibrium 4.4 Two and Three-Force Members 4.5 Equilibrium in Three Dimensions 4.6 Equations of Equilibrium 4.7 Friction 4.1 Conditions for Rigid-Body Equilibrium z Equations of Equilibrium for Rigid Body F =0 = 0 M O = 0 A rigid body will remain in equilibrium provided the sum of all the external forces acting on the body = 0 and sum of moments of the external forces about a point = 0 4.2 Free-Body Diagrams z A Free Body Diagram (FBD) is the best method to represent all the known and unknown forces in a system A FBD is a sketch of the outlined shape of the body z A FBD is a sketch of the outlined shape of the body, which represents it being isolated from its surroundings z It is necessary to show all the forces and couple moments that the surroundings exert on the body so that these effects can be accounted for when equations of equilibrium are applied 4.2 Free-Body Diagrams Support Reactions z If the support prevents the translation of a body in a given direction, then a force is developed on the body in that direction z If rotation is prevented, a couple moment is exerted on the body 4.2 Free-Body Diagrams Support Reactions – Roller or Cylinder connection z Prevents the beam from translating in the vertical direction. Thus, a roller can only exerts a force on the beam in the vertical direction. Concrete Girder rests on the ledge that is assumed to act as a smooth surface (ie a roller).

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8/7/2008 2 4.2 Free-Body Diagrams Support Reactions – Roller or Cylinder connection Rocker support for this bridge girder allows horizontal movements so that the bridge is free to expand and contract due to temperature changes. Ie. Very similar to a Roller. 4.2 Free-Body Diagrams Support Reactions Pin Connection z The pin passes through a hold in the beam and two leaves that are fixed to the ground. Thus, a pin connection prevents translation of the beam in any direction Φ z The pin exerts a force F on the beam in this direction 4.2 Free-Body Diagrams Support Reactions - Pin Connection Utility building is pin supported at the top of the column 4.2 Free-Body Diagrams Support Reactions - Pin Connection Cable exerts a force on the bracket (ie a pin type connection) 4.2 Free-Body Diagrams Support Reactions - Fixed Support This support prevents both translation and rotation of the beam. Floor beams of this building are welded together and thus form fixed connections 4.2 Free-Body Diagrams
8/7/2008 3 4.2 Free-Body Diagrams 4.2 Free-Body Diagrams 4.2 Free-Body Diagrams External and Internal Forces z A rigid body is a composition of particles, both external and internal forces may act on it.

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## HES1125 Lecture - 2008 - Wk 3 - Chpt 04 - 6 slides per page...

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