MEM202 Engineering Mechanics Statics - Personal Websites - Office

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MEM202 Engineering Mechanics - Statics MEM

MEM202 Engineering MechanicsStatics

Course Web site: www.pages.drexel.edu/~cac542

COURSE DESCRIPTIONThis course covers intermediate static mechanics, an extension of the fundamental concepts and methods of static mechanics introduced in the freshmen course tDEC 111, and tDEC 113. Topics include problem formulation and solution methods; two- and three-dimensional vector representations of forces, moments, and couples; static equilibrium of particles, rigid bodies, and engineering structures; analysis of external and internal forces in structures via the methods of free-body diagrams; and properties of cross-sectional areas.

PREREQUISITE(S)Sophomore standing; tDEC 111, tDEC 113.

Lectures are based on the textbook “Engineering Mechanics – STATICS,” 2nd ed., by William F. Riley and Leroy D. Sturges, John Wiley & Sons, Inc. 1996.

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MEM202 Engineering Mechanics - Statics MEMCOURSE OBJECTIVESThis course is aimed at providing the starting engineering students in their sophomore year a smooth transition from science-based mechanics problems to engineering-based mechanics problems, i.e. from equilibrium of relatively simple force systems to force systems in structures with connected members and with complex geometry. Conduct of the course emphasizes the correct and efficient free-body representation of the members in the structural system, along with formatted but logical solution techniques for the problems. The specific course objectives are:

• Efficient use of trigonometric functions to decompose forces in selected coordinate directions;

• Proficiency in computing moments by forces about a selected point; • Confidence in representing correctly a free-body diagram for a member in a loaded

structure; • Confidence in setting up and the solution to the free-body diagram on hand; • Understand the physical nature of the internal force and moments in a structural

member; • Confidence in handling the properties of a given cross-sectional area of any shape; • Familiar with the unique characteristics of tension, compression, shearing, bending,

and torsion in structural members.

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COURSE REQUIREMENTSClass attendance (CA): Class attendance is mandatory, and is counted as 10% of your final term grade. A sign-up sheet will be circulated during each lecture and recitation to record the attendance. Please inform instructor/TA prior to the lecture/recitation that you can not attend.Homework assignments (HW): HW assignments and their due dates are listed in Course Outline. HW will be collected, recorded, but not checked. A grade will be given to each HW based on number of problems that have been completed and submitted. HW grade for the entire term will be counted as 10% of your final term grade. No late submissions of HW will be accepted as the solutions will be posted on the day they are collected.Mid-term Examinations (MT): There will be two 50-minute mid-term examinations; the date and material covered in each mid-term are listed in Course Outline. Each mid-term is counted as 25% of your final term grade.Final Examination (FL): Final examination will be a comprehensive examination, coveringthe material taught in the entire term. It will be counted as 30% of your final term grade.Term Grade: Term grade will be calculated based on 10% for CA, 10% for HW, 25% for each MT, and 30% for FL. Final letter grade will be assigned based on 100% ≥ A ≥ 90% > B ≥ 80% > C ≥ 70% > D ≥ 60% > F. There will be no grade curving. However, a student who earns a grade 90% or higher in his/her final examination will automatically receive an A grade for the course.

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Chapter 1General Principles

aara:Vector

a:ScalarhandBy Book

secsecondssecondTTimelbpoundNNewtonFForceftfeetmmeterLLength

slugkgkilogramMMassU.S.SI

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Method of Problem Solving

1. Read the problem carefully.2. Identify the result requested.3. Identify the principles to be used to obtain the result.4. Prepare a scaled sketch (e.g., a free-body diagram)

and tabulate the information provided.5. Apply the appropriate principles and equations.6. Report the answer with the appropriate number of

significant figures and the appropriate units.7. Study the answer and determine if it is reasonable.

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Good Bad

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Chapter 2Concurrent Force Systems

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2.1 Introduction

A physical body subjected to a pair of loads

The body is simplified to a particle – particle

mechanicsThe body deforms, may fail eventually

The Body does not deform – rigid body mechanics

tDEC 111 Physics MEM230 Mechanics of Materials MEM202 Statics

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2.2 Forces and Their CharacteristicsA force is a vector; it has (1) magnitude, (2) direction, and (3) a point of application

A free vector A sliding vector A bound vector

In Statics forces are treated as sliding vectors

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2.2 Forces and Their CharacteristicsPrinciple of Transmissibility

The external effect of a force on a rigid body is the same for all points of application of the force along its line of action.

Principle of Transmissibility is applicable to rigid-body mechanics. Therefore, in Statics forces are treated as sliding vectors.

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2.2 Forces and Their CharacteristicsClassification of Forces

1Fr

Oy

x

z

2FrL

nFr

5. General Forces1. Concurrent Forces

2. Coplaner Forces

3. Parallel Forces

4. Collinear Forces⎩⎨⎧

⇒⇒

=∑ DynamicsmaStatics

Fi

0r

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2.3 Resultant of Two Concurrent Forces(Parallelograms and Laws of Sines and Cosines)

1Fr

2Fr

Rr

φβ

γφ

1Fr

2Fr

Principle of Transmissibility

⇒

21 and between Angle : FFrr

φ

α

1221 FFFFRrrrrr

+=+=

1 and between Angle : FRrr

β

γβπβφαφπγ −−=−=−= ;

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2.3 Resultant of Two Concurrent Forces(Parallelograms and Laws of Sines and Cosines)

1Fr

2Fr

Rr

φβ

γφ

βγ α

ab

c

γβα sinsinsin :Sines ofLaw cba

==

γcos2 :Cosines ofLaw 222 abbac −+=

( )R

FR

FR

FFRR

φβφπγββγ

sinsinsinsinsinsinsin

of direction thedetermine toSines of Law Use

2222 =⇒−

==⇒=

r

( )φ

φπγ

cos2cos2cos2

of magnitude thedetermine toCosines of Law Use

212

22

12

212

22

1212

22

12

FFFFRFFFFFFFFR

R

++=⇒

−−+=−+=

r

φπγ −=γβπβφα −−=−=

α

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2.3 Resultant of Two Concurrent Forces(Parallelograms and Laws of Sines and Cosines - Examples)

56º

lb 5001 =Fr

lb 8002 =Fr

x

y

Rr

β

ooo 12456180 =−=φ

φ( )( ) ( ) 32221

22

21

2

106.442124cos8005002800500cos2

×=++=

++=o

φFFFFR

lb 3.665=Ro

o

5.853.665124sin800sinsinsin 121 =⎟⎟

⎠

⎞⎜⎜⎝

⎛ ×=⎟

⎠⎞

⎜⎝⎛= −−

RF φβ

35ºN 9001 =F

rN 6002 =Fr

x

y

Rr

40º

o40=φ

( )( ) ( ) 32221

22

21

2

10997.140cos6009002600900cos2

×=++=

++=o

φFFFFR

N 413,1=Ro

o

8.151413

40sin600sinsinsin 121 =⎟⎟⎠

⎞⎜⎜⎝

⎛ ×=⎟

⎠⎞

⎜⎝⎛= −−

RF φβ

Homework: Problems 2-3, 2-11, 2-16

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2.4 Resultant of Three or More Concurrent Forces(Parallelograms and Laws of Sines and Cosines)

1Fr

2Fr

3Fr

123Rr

2112 FFRrrr

+=

321

213

123

312123

FFF

FR

FR

FRR

rrr

rr

rr

rrr

++=

+=

+=

+=

3223 FFRrrr

+=

3113 FFRrrr

+=

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2.4 Resultant of Three or More Concurrent Forces(Parallelograms and Laws of Sines and Cosines - Example)

312 :2 Step FRRrrr

+=Determine the resultant of F1, F2, and F3forces

2112 :1 Step FFRrrr

+=

lb 954cos2 121

22

2112

=

++= φFFFFR

o0.27sinsin12

1111 =⎟⎟

⎠

⎞⎜⎜⎝

⎛= −

RF φβ

ooo 6030301 =+=φ ooo 6740272 =+=φ

lb 386,1cos2 23122

3212 =++= φFRFRR

o3.39sinsin 21212 =⎟

⎠⎞

⎜⎝⎛= −

RR φβ

ooo 3.59203.39 =+=θ

Homework: Problems 2-19, 2-24, 2-28

MEM202 Engineering Mechanics Statics - Personal Websites - Office

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