© 2006 Baylor University EGR 1301 Slide 1 Lecture 5 Introduction to Engineering Approximate Running Time - 15 minutes Distance Learning / Online Instructional Presentation Presented by Department of Mechanical Engineering Baylor University Procedures: 1.Select “Slide Show” with the menu: Slide Show|View Show (F5 key), and hit “Enter” 2.You will hear “CHIMES” at the completion of the audio portion of each slide; hit the “Enter” key, or the “Page Down” key, or “Left Click” 3.You may exit the slide show at any time with the “Esc” key; and you may select and replay any slide, by navigating with the “Page Up/Down” keys, and then hitting “Shift+F5”.

© 2006 Baylor University EGR 1301 Slide 2 Introduction to Static Analysis – Part 2 EGR 1301 – Lecture 5 Prof. Dick Campbell Speaking

© 2006 Baylor University EGR 1301 Slide 3 Learning Objectives Understand the concept of Force as a vector. Understand separating a vector into components. Apply this concept to analyzing sums of Forces. Determine the load in structural elements. Understand the concept of a “Factor of Safety”.

© 2006 Baylor University EGR 1301 Slide 4 Force as a Vector Forces –Have magnitude and direction –in an x-y coordinate system, the force may be broken down into “components” along the coordinate axes. The magnitude of a vector can be found by the magnitude of its components using Pythagorean theorem. x y

© 2006 Baylor University EGR 1301 Slide 5 Setting Up the Analysis Draw a sketch of the Forces Write each force in terms of i and j components (components perpendicular to each other can be treated separately) Sum of i and j components = zero (Newton’s 1 st Law) Solve two equations, two unknowns Find tension force in cable Calculate safety factor x y

© 2006 Baylor University EGR 1301 Slide 6 Force Vectors and Static Analysis Consider the foot bridge –Loaded by six persons (approx lbs) –Loaded at the center of the bridge Simplifying assumption: –Neglect the weight of the bridge

© 2006 Baylor University EGR 1301 Slide 7 Resolve the three forces into i,j components. Our unknowns are F 1 and F 2. Since the i,j directions are independent, we can solve these two equations for the unknowns Static Analysis of the Bridge Cable

© 2006 Baylor University EGR 1301 Slide 8 Static Analysis of the Bridge Cable (cont.) substituting: Safety Factor (Cable Strength - 16,000 lbs):

© 2006 Baylor University EGR 1301 Slide 9 Static Analysis of the Bridge Cable (cont.) Then: What happens to the Safety Factor if we increase the sag? Let What happens to the Safety Factor if we include the weight of the bridge? Let Then:

© 2006 Baylor University EGR 1301 Slide 10 Homework Assignment #1 Problem #1 Given a load of 500 N (Newtons) supported by two cables as shown, determine the force in each cable.

© 2006 Baylor University EGR 1301 Slide 11 Homework Assignment #1 Problem #2 Given Determine the required forces (magnitudes) in cables 1 & 2 so that the system will remain in static equilibrium.

© 2006 Baylor University EGR 1301 Slide 12 This Concludes Lecture 5