WORCESTER POLYTECHNIC INSTITUTE

Transcription

1 WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT STRESS ANALYSIS ES-2502, C 2012 Lecture 02: Internal Forces 13 January 2012

2 General information Instructor: Cosme Furlong HL-151 (508) Teaching Assistants: Morteza Khaleghi HL-150 (508) Tatiana Popova

3 Force analysis. Free-body diagrams Static equilibrium: forces Arbitrary component under load Static equilibrium condition (vectorial representation) : m F 0

4 Force analysis. Free-body diagrams Static equilibrium: forces Forces acting on a particle or body (vectorial representation): F 0 Fx i Fy j Fz k Null vector!! Individual orthogonal components (scalar representation): F x 0 F y 0 F z 0 Null - Scalar!!

5 Force analysis. Free-body diagrams Static equilibrium: moments m M x o Static equilibrium condition (vectorial representation): M 0 o Orthogonal components: i M j M k 0i 0j 0k y o z o Moments Vectorial evaluation: r i f i r i F i 0

6 Force analysis. Free-body diagrams Static equilibrium: moments C A B A B sin( ) u c Vector Scalar Unit vector

7 Moment of a force: about z-axis Magnitude of moment: ( M ) F d o z x y

8 Moment of a force: about x-axis Magnitude of moment: ( M ) F d o x z y

9 Moment of a force: null effect Magnitude of moment with respect to point O: M o 0

10 Force analysis: example The 50 lb force acts on the gear in the direction shown. Determine the moment of this force about the y-axis. F Z Approach: F Y 1) Determine x-y-z components of applied force 2) Compute moment about y-axis F X

11 Equivalent systems: are they really? Force translated along its line of application: F F F F - F Example: F F Idealization: similar effects at the support??

12 Equivalent systems: are they really? Equivalent force and couple/moment system: Example: d F F M F d Idealization: similar effects at the support??

13 Equilibrium of rigid bodies: equivalent systems Two-force member Two-force member

14 Distributed loads: equivalent systems Original 3D problem 2D projection Equivalent system

15 Free-body diagrams Operator applies 20-lb to pedal stretching spring by 1.5 in. Schematic representation: Free-body diagram: Actual mechanism

16 Force analysis. Free-body diagrams Number of unknowns? Equilib. Equations? Is this a statically indetermined case? Overall FBD

17 Force analysis. Free-body diagrams

18 Force analysis. Free-body diagrams 3D Number of unknowns? Equilib. Equations? 2D Overall FBD Individual FBD s

19 Internal resultant loading Arbitrary component under load Component is in equilibrium Internal forces maintaining equilibrium Virtual section

20 Internal resultant loading Internal forces maintaining equilibrium Equivalent force and moment at the section

21 Internal resultant loading Components of the equivalent force and moment

22 Internal resultant loading Equivalent forces and moments at the section Component is in equilibrium

23 Internal resultant loading: example Determine resultant internal loading acting on the cross section at C of the cantilever shown: Approach: 1) Define free-body diagrams 2) Apply equilibrium equations

24 Internal resultant loading: example Free-body diagrams (FBDs): Section to the right of C Section to the left of C Use either section to determine internal loadings

25 Reading assignment Chapter 1 of textbook Review notes and text: ES2001, ES2501

26 Homework assignment As indicated on webpage of our course