T AB The Concurrent System The Free Body Diagram

Concept of Free Body Diagrams Particle System Rigid Body Systems Concept of Equilibrant Graphical Determination of Equilibrant Applied and Reaction Forces in Beams Types of Beam Supports Free Body diagram of Rigid Bodies

Free Body Diagrams Essential step in solving Equilibrium problems Complex Structural systems reduced into concise FORCE systems WHAT IS A FREE BODY DIAGRAM? A FBD is a simplified representation of a PARTICLE or RIGID BODY that is isolated from its surroundings and on which all applied forces and reactions are shown. All forces acting on a particle original body must be considered, and equally important any force not directly applied on the body must be excluded.

W A B C W BC BA Free Body Diagram

Draw the Free Body Diagrams

REAL LIFE CONCURRENT SYSTEMS Equilibrium of a Particle

1. Two cables support the traffic light weighing 250 pounds. Determine the tension in the cables AB and BC. Solution: Resolving T 1 along x and y directions: Resolving T 2 along x and y directions:. A B 200lb AC B T1T1 T2T2 T1T1 T2T2 T 1Y T 2Y T 1X T 2X T 3 =200lb 1

Substituting equation 1 in the above equation, we get.342T T 2 = T 1 =200 T 1 =226lb From equation 1 we get T 2 =1.085*226 T 2 = lb Answers: Tension in cable AB = 226lb Tension in cable BC = lb

Q=800# P=? Force in Boom= 4000# ? A B C Problem

W=100# A C D E B 4 3 BA=? BC=? CD=? CE=? Problem Change

400# F1 F2 300N 450N F1 X Y X X X Y Y Y F 3 kN 7 kN 4.5 kN 7.5 kN 2.25 kN F P P P P

CONCEPT OF THE EQUIBILIRIANT Resultant R E Equilibrant

Line of action of CB Line of action of CA X Y CB CA W=200# RESULTANT EQUILIBRIANT TIP-TO-TAIL METHOD AB C Measure CB and CA 200 #

PARALLELOGRAM METHOD RESULTANT EQUILIBRIANT A B C CB CA Measure CB and CA 200 #

ASimple Supported Beam A Cantilever Beam RIGID BODY SYSTEMS

A Propped Cantilever with Three Concentrated Load A Simply Supported Beam with Three concentrated Loads

APPLIED AND REACTION FORCES IN BEAMS In the Chapter on Force Systems, we discussed the concept of APPLIED FORCES, REACTION FORCES and INTERNAL FORCES Here we well discuss the relevance and importance of APPLIED FORCES and REACTION FORCES in the case of Beams. Before we proceed further please study the animated visuals on the next slide

APPLIED FORCES AND REACTION FORCES ON RIGID BODY SYSTEMS A Foundation resting on Soil, with APPLIED FORCES and REACTION FORCES A Simple Supported Beams with APPLIED FORCES and REACTION FORCES A Cantilever Beam with APPLIED FORCES and REACTION FORCES

A Beam is an example of Rigid Body. Generally loads are applied on the beams. And the beams develop reactions. We named the loads hat are applied on the beams like Dead Load, Live Load, Wind Load. Earthquake Loads as APPLIED FORCES, and the consequent reactions that are simultaneously developed as REACTION FORCES. These REACTION FORCES generally develop at the supports. We use the same color code as described earlier for clarity. The reactions develop as a direct consequence of Newton’s Third Law,. Which states that for every action there is an equal and opposite reaction. In the three examples presented, if we separate the rigid body for its supports we can see equal and opposite forces acting at the supports..

From the above we can describe the concept of the FREE BODY DIAGRAM of a Rigid Body as folows. It is representing the rigid body with all the Forces- the APPLIED FORCES and REACTION FORCES acting on it It is axiomatic that the Rigid Body must be in equilibrium under the action of the APPLIED FORCES and the REACTION FORCES. Hence the FREE BODY DIAGRAMS can also be called as EQUILIBRIUM DIAGRAMS, even though the former name is more popular. Finding the REACTION of beams for various types of APPLIED LOADS is a basic requirement in STATICS

The above diagrams, which show the complete system of applied and reactive forces acting on a body, are called free body diagrams. The whole system of applied and reactive forces acting on a body must be in a state of equilibrium. Free-body diagrams are, consequently,often called equilibrium diagrams. Drawing equilibrium diagrams and finding reactions for loaded structural members is a common first step in a complete structural analysis

Roller, Hinge and Fixed Supports Hinge supports Roller Supports Fixed Supports

ROLLER SUPPORT Applied Force Reactive Forces The Reactive Force must always be perpendicular to the surface for a ROLLER

Roller Support Roller Support allows horizontal movement It allows the beam to bend

Rocker Support A Rocker Support is similar to the Roller Support

A variation of Roller Support

PIN or HINGE SUPPORT Applied Force Reactive Force The Reactive Force can be in any direction

Pin or Hinge Support Pin support does no allow any movement It allows the beam to bend

FIXED SUPPORT No movement No Rotation

Half the strength of the Bridge is lost by not allowing the Bridge to expand due to the Temperature Rise Why Roller Support is Important? 500 ft. 2.34” T= 100 deg T= 40 deg

Why Hinge Support is Important ?

Why Fixed Support is Important? A Cantilever has to be fixed to support a load Hinge

REAL LIFE HINGES A Steel Hinge A Concrete Hinge A Neoprene Pad Hinge The shear deformation of the Neoprene pad mimics the horizontal movement of a Roller The close confinement of the steel rods will not allow moment transfer, but only Vertical & Horizontal Forces Top part Bottom part Pin The rotation of the top part about the pin allows a Hinge action

Question 1. What is the difference between a Rigid Body and a Particle Question 2: Explain the Difference between a Roller Support, Hinge Support and Fixed Support

FREE BODY DIAGRAMS OF RIGID SYSTEMS

Free Body Diagrams 1.Try to draw the free body diagram for a axle of a bicycle wheel as shown below: 2.Draw the free body diagram for a propped cantilever shown below: 3.Does a Neoprene pad bearing function like a Hinge or a Roller. 4.Attempt to draw the Free body diagram for the circled part of the building P Axle

5. Draw the Free Body Diagram for the following Dam: Water