# Section 5.1-5.2 - Gordon State College

EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Todays Objectives: Students will be able to: In-Class Activities: a) Identify support reactions, and, Check Homework b) Draw a free-body diagram. Reading Quiz Applications Support Reactions Free-Body Diagrams Concept Quiz

Group Problem Solving Attention Quiz Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. READING QUIZ 1. If a support prevents translation of a body, then the support exerts a ___________ on the body. A) Couple moment B) Force C) Both A and B. D) None of the above 2. Internal forces are _________ shown on the free body diagram of a whole body.

A) Always B) Often C) Rarely D) Never Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. APPLICATIONS The truck ramps have a weight of 400 lb each. Each ramp is pinned to the body of the truck and held in the position by a cable. How can we determine the cable tension and support reactions? How are the idealized model and the free body diagram used to do this?

Which diagram above is the idealized model? Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. APPLICATIONS (continued) Two smooth pipes, each having a mass of 300 kg, are supported by the tines of the loaders fork attachment. How can we determine all the reactive forces? Again, how can we make use of an idealized model and a free body diagram to answer this question? Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc.

All rights reserved. CONDITIONS FOR RIGID-BODY EQUILIBRIUM (Section 5.1) Forces on a particle In contrast to the forces on a particle, the forces on a rigid-body are not usually concurrent and may cause rotation of the body (due to moments created by the forces). For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be equal to zero. F = 0 (no translation)

Forces on a rigid body Statics, Fourteenth Edition R.C. Hibbeler and MO = 0 (no rotation) Copyright 2016 by Pearson Education, Inc. All rights reserved. THE PROCESS OF SOLVING RIGID BODY EQUILIBRIUM PROBLEMS For analyzing an actual physical system, first we need to create an idealized model (above right). Then we need to draw a free-body diagram (FBD) showing all the external (active and reactive) forces. Finally, we need to apply the equations of equilibrium to solve for any unknowns.

Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. FREE-BODY DIAGRAMS (Section 5.2) Idealized model Free-body diagram (FBD) 1. Draw an outlined shape. Imagine the body to be isolated or cut free from its constraints and draw its outlined shape. 2. Show all the external forces and couple moments. These typically include: a) applied loads, b) support reactions, and, c) the weight of the body.

Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. FREE-BODY DIAGRAMS (continued) Idealized model Free-body diagram 3. Label loads and dimensions on the FBD: All known forces and couple moments should be labeled with their magnitudes and directions. For the unknown forces and couple moments, use letters like Ax, Ay, MA. Indicate any necessary dimensions. Statics, Fourteenth Edition

R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. SUPPORT REACTIONS IN 2-D A few example sets of diagrams s are shown above. Other support reactions are given in your textbook (Table 5-1). As a general rule, if a support prevents translation of a body in a given direction, then a force is developed on the body in the opposite direction. Similarly, if rotation is prevented, a couple moment is exerted on the body in the opposite direction. Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc.

All rights reserved. EXAMPLE I Given: The operator applies a vertical force to the pedal so that the spring is stretched 1.5 in. and the force in the short link at B is 20 lb. Draw: An idealized model and freebody diagram of the foot pedal. The idealized model Statics, Fourteenth Edition R.C. Hibbeler The free-body diagram Copyright 2016 by Pearson Education, Inc. All rights reserved.

EXAMPLE II Given: The unloaded platform is suspended off the edge of the oil rig. The platform has a mass of 200 kg. Draw: An idealized model and free-body diagram of the platform. The idealized model of the platform is considered in two dimensions because the loading and the dimensions are all symmetrical about a vertical plane passing through its center. Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. EXAMPLE II (continued)

The connection at A is treated as a pin, and the cable supports the platform at B. Note the assumed directions of the forces! The point G is the center of gravity of the platform. The idealized model Statics, Fourteenth Edition R.C. Hibbeler The free-body diagram Copyright 2016 by Pearson Education, Inc. All rights reserved. CONCEPT QUIZ 1. The beam and the cable (with a frictionless pulley at D) support an 80 kg load at C. In a FBD of only the beam, there are how many unknowns? A) Two forces and one couple moment

B) Three forces and one couple moment C) Three forces D) Four forces Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. CONCEPT QUIZ (continued) 2. If the directions of the force and the couple moments are both reversed, what will happen to the beam? A) B) C) D)

The beam will lift from A. The beam will lift at B. The beam will be restrained. The beam will break. Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. GROUP PROBLEM SOLVING I Given: Draw: A FBD of the smooth pipe which rests against the

opening at the points of contact A, B, and C. Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. GROUP PROBLEM SOLVING I (continued) NA The idealized model 30 NB 300 N

30 0.5m NC 0.5m 0.26m 0.15m The free body diagram Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc.

All rights reserved. GROUP PROBLEM SOLVING II Given: Draw: Draw a FBD of the bent rod supported by a smooth surface at B and by a collar at A, which is fixed to the rod and is free to slide over the fixed inclined rod. Statics, Fourteenth Edition R.C. Hibbeler Copyright 2016 by Pearson Education, Inc. All rights reserved. GROUP PROBLEM SOLVING II (continued)

The idealized model RA 4 3 5 The free body diagram Statics, Fourteenth Edition R.C. Hibbeler RB Copyright 2016 by Pearson Education, Inc. All rights reserved. 12

ATTENTION QUIZ 1. Internal forces are not shown on a free-body diagram because the internal forces are _____. (Choose the most appropriate answer.) A) Equal to zero B) Equal and opposite and they do not affect the calculations C) Negligibly small D) Not important 2. How many unknown support reactions are there in this problem? A) Two forces and two couple moments B) One force and two couple moments C) Three forces D)