ENGI 1313 Mechanics I

1. ENGI 1313 Mechanics I Lecture 22: Equivalent Force Systems and Distributed Loading

2. Lecture 22 Objective • to demonstrate by example equivalent force systems • to determine an equivalent force for a distributed load

3. Example 22-01 • Handle forces F1 and F2 are applied to the drill. Replace this system by an equivalent resultant force and couple moment acting at point O. Express the results in Cartesian vector form.

4. Equivalent Distributed Loads • Reduce to Single Equivalent Load • Magnitude and position • Applications • Environment • Wind • Fluid • Dead load • Weight • Snow, sand • Objects

5. Distributed Loads • Load Intensity • Pressure (Pa) • Force per unit area • N/m2 or lb/ft2 • Infinite # parallel vertical loads • Reduce from Area to Line Load

6. Distributed Loads (cont.) • Consider Element Length (dx) • Element force (dF) acts on element length (dx) • The line load w(x) represents force per unit length

7. Distributed Loads (cont.) • Magnitude Net Force (FR) • Summation of all element forces • Area under line load curve

8. Distributed Loads (cont.) • Resultant Moment (MRo) • Element force moment • Total moment • Equivalent force

9. Distributed Loads (cont.) • Centroid • Geometric center of area • Resultant force line of action

10. L/2 Example 22-02 • Determine equivalent resultant force and location for the following distributed load.

11. L/3 Example 22-03 • Determine equivalent resultant force and location for the following distributed load.

12. Comprehension Quiz 22-01 • What is the location of FR or distance d? • A) 2 m • B) 3 m • C) 4 m • D) 5 m • E) 6 m • Answer: D d FR 3 m 3 m

13. Example 22-04 • The beam is subjected to the distributed loading. Determine the length b of the uniform load and its position a on the beam such that the resultant force and couple moment acting on the beam are zero.

14. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1