440:221 Intro to Engineering Mechanics: Statics Instructor: Alberto Cuitino TA: Pam Carabetta and Jingru Zhang Lt 13Lecture 13 Fall 2009 1 Based on Textbook Material: Engineering Mechanics Statics, 12 th Edition, R.C. Hibbeler, Pearson 2010. 440:221 Lectures Equilibrium of a RIGID BODY A School of Engineering, Fall 2009 2 440:221 Lectures Topics to be covered to be covered ? What are the equations of equilibrium in 2D for a rigid body? ? What is a two- and three-force member? ? How do we solve equilibrium problems? School of Engineering, Fall 2009 3 440:221 Lectures Conceptual Question 1 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) 2 forces and 1 couple moment B) 3 forces and 1 couple moment C) 3 forces C) 3 forces School of Engineering, Fall 2009 D) 4 forces 440:221 Lectures Conceptual Question 2 2 If the directions of the force and the couple moments. If the force couple moments are both reversed, what will happen to the beam? A) The beam will lift from A. B) The beam will lift at B. C) The beam will be restrained. D) The beam will break. A) Lift from A School of Engineering, Fall 2009 440:221 Lectures Let?s work on this problem on this Draw a FBD of the crane boom, which is supported by a pin at A and cable BC The load of 1250 lb is suspended at B and the boom weighs School of Engineering, Fall 2009 BC. The 650 lb. 440:221 Lectures Let?s work on this problem on this School of Engineering, Fall 2009 440:221 Lectures Solution FBD School of Engineering, Fall 2009 440:221 Lectures Another one ? Draw a FBD of member ABC, which is supported by a smooth collar at A, roller at B, and link CD. School of Engineering, Fall 2009 440:221 Lectures Another one ? School of Engineering, Fall 2009 440:221 Lectures Solution FBD School of Engineering, Fall 2009 440:221 Lectures Attention Quiz 1. Internal forces are not shown on a free-body diagram because the internal forces are (Choose the most appropriate internal _____. (Choose the answer.) A) Equal to zero B) Equal and opposite and they do not )q )q pp affect the calculations C) Negligibly small D) Not important B) 2. How many unknown support reactions are there in this problem? A) 2f d2 l t2 forces an coup e momen s B) 1 force and 2 couple moments School of Engineering, Fall 2009 C) 3 forces D) 3 forces and 1 couple moment D) 440:221 Lectures Equations of Equilibrium (rigid body 2D) of Equilibrium ? A body is subjected to a system of forces that lie in the x-y plane. When in equilibrium, the net force and net moment acting on the body are zero. This 2-D condition can be represented by the three scalar equations: ? F x = 0 ? F y = 0 ? M O = 0 where point O is any arbitrary point. Please note that these equations are the ones most commonly used for solving 2-D equilibrium problems. There are two other sets of equilibrium equations that are rarely used. For your reference, they School of Engineering, Fall 2009 are described in the textbook. 440:221 Lectures Equations of Equilibrium (rigid body 2D) ? F x = 0 ? F y = 0 ? M O = 0 hitOi bitit of Equilibrium ? where poin s any arbitrary po n . School of Engineering, Fall 2009 440:221 Lectures Two and three force members The solution to some equilibrium problems can be simplified if we recognize members that are subjected to forces at only two points - - members that subjected to forces at two (e.g., at points A and B). If we apply the equations of equilibrium to such a member, we can quickly determine that the resultant forces at A and B must be equal in magnitude and act in the opposite directions along the line joining School of Engineering, Fall 2009 in the directions joining points A and B. 440:221 Lectures Example of a two force member two- member In the cases above members AB can be considered as two force cases , members AB can - members, provided that their weight is neglected. This fact simplifies the equilibrium analysis of the of some rigid bodies since the directions of the resultant forces at A and B are thus known (along the line joining points A and B). School of Engineering, Fall 2009 (g 440:221 Lectures Take home message- message ? Be organized ?Draw FBD ? Check for two- and three-force members School of Engineering, Fall 2009 17 amc Microsoft PowerPoint - Lecture 13