ES220 Statics

1. ES220 Statics Exam II Review Notes

2. Equilibrium of Rigid Bodies Chapter 4

3. Recall: Rigid Body Motion Translation Caused by Force(s): Rotation Caused by Moment(s): A Force acting at a distance from a Point Several applied Moments: Determine magnitude and direction of single resultant moment, which determines direction of impending rotation.

4. Static Equilibrium of Rigid Bodies A body at rest remains at rest A body in motion continues to move in a straight line at constant velocity Conditions for equilibrium: is a vector pointing from point A to the point where acts

5. Moment of a Force about a Point Moment Vector: Magnitude: Position Vector: Perpendicular distance = d Moment vector is perpendicular to both r and F.

6. Forces Principal of Transmissibility: Can slide a force along its line of action Very useful in summing moments!

7. Determining Moments in 2D

8. Determining Moments in 2D Right Hand Rule:

9. Moment Vector Position Vector: Determining Moments in 3D

10. Calculating a Vector Cross Product

11. Rigid Bodies A 2D or 3D bodies with dimensions (Contrast with a point, which is infinitely small) Systems of rigid bodies and supports Externally applied forces or moments Contact with other things: Other rigid bodies Supports, cables, etc. Contact cause reaction forces or moments

12. Rigid Bodies in 2D 3 Equilibrium equations Therefore, can solve for 3 unknowns Examples: Three support reactions Unknown magnitudes of 3 forces, of known directions Unknown magnitude of 1 force with known direction; unknown magnitude and direction of 1 force

14. Free Body Diagrams Choose body, detach from the ground, supports, connections, other bodies Draw body and all external forces acting ON body. Where body contacts ground, supports, connections, or other bodies, draw the appropriate reaction forces Include weight of body, acting down through the center of gravity Label the magnitude & direction of known forces Identify unknown forces/reactions Show the line of action, if known Include dimensions, which are required in order to sum moments, SM = 0.

15. Hints for Free Body Diagrams Assume unknown forces act in positive direction If answer is negative, you assumed the wrong direction, and force is in negative direction Assume forces in cables and rods are tensile If answer is negative, your assumption was wrong, and the rod is in compression Note that cables can never be in compression!! For summing moments: Resolve forces into x and y components Find perpendicular distance from force to the point about which you are summing the moment.

19. Two-Force Members Pinned at both ends (joints), with no applied loads between joints Line of action of forces is directed along a line drawn between the two joints

20. Three Force Members Three forces are either Concurrent (all 3 forces pass through a single point) (See next slide) Parallel

21. Three Force Members: Concurrent Lines of action of the 3 concurrent forces intersect to form a triangle Draw known lines of action of 2 forces to intersect at a point Draw 3rd line of action: from point where 3rd force acts to intersection point Use this triangle to find ?, the direction of the 3rd force Knowing ?, use law of sines to find magnitudes of three forces

23. Rigid Bodies in 3D 6 Equilibrium equations Therefore, can solve for up to 6 unknowns We often had fewer than 6 unknowns

28. Centroids and Centers of Gravity Chapter 5

29. 2D: Composite Plates Break plate up into common shapes, for which centroid coordinates are known Determine centroid of composite plate using:

33. 2D: Composite Wires Break wire up into line segments, for which centroid coordinates are known Determine centroid of composite wire using:

35. 3D: Composite Bodies Break body up into common volumes, for which centroid coordinates are known Determine centroid of composite body using:

40. 3D: Composite Plates/Sheets Break plate/sheet up into common shapes, for which centroid coordinates are known Determine centroid of composite plate/sheet using:

41. 3D: Composite Wires Break wire up into line segments, for which centroid coordinates are known Determine centroid of composite wire using: