22. MEC 121: Statics

22.1 Philosophy

1. Even when problems seem impossible keep trying, it will help you learn to solve problems (This is like learning a new sport, except here you are building strength and coordination for problem solving). Solving problems is mainly a skill of recognizing patterns and then using techniques you have seen before.

2. If there is a topic you do not understand in a previous section, it will make it hard to solve problems in more advanced sections.

3. As you solve problems, you will find that you work faster.

4. Avoid shortcuts, they always take longer.

5. Try alternate ways of solving problems, this will strengthen your skills.

6. If you are really stuck on a problem leave it until the next day, then try again.

7. Solve problems with variables, and units, this will reduce errors, and makes errors easier to find and fix.

8. Solving problems is the only way to do well.

9. Always look at your answer to see if it makes sense, and find ways to check the results.

10. Always use Free Body Diagrams, and list assumptions, this will reduce assumption based mistakes in simple problems, and give you clues for solving complicated problems.

11. Carefully read any question before starting. If it is confusing, underlining or writing out the details in point form can help.

22.2 Resources

1. A tutorial disk is included with the text. It seems reasonable if you are having problems with a particular section of the text.

2. Books may be found in the library.

3. Books can be purchased, but read a few problems in any book you are considering to make sure they are to your liking before buying.

4. Read the textbook chapters as indicated, and try suggested problems.

Topic Section Page Practice Questions

Introduction 1.1-1.6 13 1,2,7,11,12,19

Newtons Laws 2.1-2.3 23 2,3,6,7,10,13,17,19,22,25

Vectors and Scalars 2.4 34 29,30,33,39,41,49,50

2.5-2.6 49 55,57,61,65,69

2.7-2.8 58 74,77,78,81,87,89,95

2.9 68 103,105,109,113

Particle Equilibrium 3.1-3.3 82 1,3,5,9,15,18,29

Free Body Diagrams 3.4 94 31,34,38,42

2 & 3 D Force Systems

Support Reactions

Moment of a Force 4.1-4.4 116 5,7,10,13,14,17,27,34

Scalar and Vector Forces 4.5 127 45,51,53,54,55

Cross Products 4.6 137 61,63,70,73,74,77

Principle of Transmissibility 4.7 155 82,85,95,106

Moments about an Axis

Rigid Body Equilibrium 5.1-5.2 187 2,3,6,10

2 & 3 Force Members 5.3-5.7 224 66,67,69,79,82,87

2 & 3 Dimensional Equilibrium

Structures 6.1-6.3 245 1,2,3,9,11,14,15.18,19

Forces in 2 Dimensions 6.4 255 21,23,26,30,34,37,39

Method of Joints

Method of Section

Frames 6.6 279 49,55,57,59,65,73,77,81,

Method of Members 85,87,91,98

Centre of Mass 9.1-9.2 413 9,11,14,21,29,31

Centroids of Lines/Areas/Volumes 9.3 424 35,47,50,55,63,71

Composite Bodies

Dry Friction 8.1-8.2 359 1,2,3,5,7,19,21,27,33,34,42

Friction Angle 46,47

Friction on Particles and Rigid Bodies 8.3 375 53,54,58,59,62,63

Wedges

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22.47 Bedford, A., Fowler, W., “Engineering Mechanics Statics”, Addison-Wesley Publishing Co., Inc., 1995.

22.48 Beer, F.P., Johnston, E.R., Statics & Mechanics of Materials, McGraw-Hill, 1992.

22.49 Hibbeler, R.C., Engineering Mechanics: Statics and Dynamics, 6th edition, MacMillan Publishing Co., New York, USA, 1992.

22.50 Pytel, A., Kiusalaas, J., Engineering Mechanics; Statics and Dynamics, Harper Collins, 1994.

22.3 Assignments

• The assignments are to be done individually from beginning to end. My experience shows that study groups are of great help, and will help a student get by many small problems quickly. But students who never do any problems individually (i.e., assignments) always do poorly when they must solve problems themselves on exams.

• Stassen’s Ten Commandments for Assigned Calculations: The following format requirements must be met before an assignment will be accepted or given credit.

1. The problem Assignment Sheet must be attached to the front of the report. The name of the author and the Section Number must be placed at the upper right-hand corner of the front page.

2. All calculations must be shown and a clear “heading” must be given with each step of the calculations.

3. All units must be attended to properly in balanced equations. Answers without units are not valid, except 0 or unitless values such as ratios.

4. Where applicable references must be given for all relationships obtained from textbooks.

5. Clear diagrams must be provided where necessary.

6. Do not use unnecessary terms like “I” or verbose terms such as “to find”, etc. It is expected that proper and concise statements are made where needed.

7. At the conclusion of each problem the final result must be clearly summarized and highlighted.

8. Where necessary a conclusion should be drawn or a final comment made. Sometimes a recommendation is necessary and should be included in the report.

9. Reports must be written on one side of letter size paper. Only in the case of graphic solutions can “odd” paper sizes be used, but these must be folded to size.

10. Calculations should progress in a logical and sequential manner to the final result.

NOTE: A good maxim for overall appearance is that the work should be ready for typing.

22.4 Bridge Building Competition

Objective: To use simple materials to construct a bridge with the highest strength to weight ratio.

Rules:

1. The materials that may be used are listed below. If there are any questions regarding acceptable materials the course instructor can be consulted. Any questions must be resolved before the judging. The total weight must be below 500g. Use,

- common toothpicks, such as the tapered wooden or round variety (< 1/16”).

- white glue, balsa glue, 5 minute epoxy, super-glue, or a similar adhesive is to be used only for joining the toothpicks or thread.

- common sewing thread that can be used on a common sewing machine or serger.

2. The bridge will be mounted between two flat surfaces 8” apart, assume the maximum length of the edges will be 24 inches or less.

3. The bridge will be loaded on the upper surface until failure. The loading area must be at least 8” by 8” square.

Evaluation:

1. The bridge will be weighed and checked for conformance to the rules.

2. A water vessel will be placed on top, and slowly filled with water until the bridge fails. Failure will be determined by the P.Eng. judges to be when the structure is no longer operating as originally anticipated, or 1cm below the original height of the load.

3. The water container, with water, will be measured to give the failure load.

4. A ratio of failure load to weight ratio of the bridge will be used to rank the performance.

Hints:

1. Heavy is not necessarily better (an ant would outperform a human with the characteristics used here)

2. Equilateral triangles form good supports in a solid structures.

3. Consider the Golden Gate Bridge in San Francisco for support structures.

4. Try building prototypes first to test the structure.