Static Analysis Fundamentals: Forces & Safety Factor

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: • Select “Slide Show” with the menu: Slide Show|View Show (F5 key), and hit “Enter” • 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” • 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”.

2. Introduction to Static Analysis – Part 2 EGR 1301 – Lecture 5 Prof. Dick Campbell Speaking

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”.

4. y x 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.

5. y x 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 1st Law) • Solve two equations, two unknowns • Find tension force in cable • Calculate safety factor

6. Force Vectors and Static Analysis • Consider the foot bridge • Loaded by six persons (approx. 1000 lbs) • Loaded at the center of the bridge • Simplifying assumption: • Neglect the weight of the bridge

7. Static Analysis of the Bridge Cable • Resolve the three forces into i,j components. • Our unknowns are F1 and F2. • Since the i,j directions are independent, we can solve these two equations for the unknowns

8. Static Analysis of the Bridge Cable (cont.) substituting: Safety Factor (Cable Strength - 16,000 lbs):

9. What happens to the Safety Factor if we increase the sag? Let Then: What happens to the Safety Factor if we include the weight of the bridge? Let Then: Static Analysis of the Bridge Cable (cont.)

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

11. Homework Assignment #1Problem #2 Given Determine the required forces (magnitudes) in cables 1 & 2 so that the system will remain in static equilibrium.

12. This Concludes Lecture 5