7/28/2019 Performance on Mechanics of Materials – MAE 243 (Section 002)

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Mechanics of Materials – MAE 243 (Section 002)

Spring 2008

Dr. Konstantinos A. Sierros

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General info

• M, W, F 8:00-8:50 A.M. at Room G-83 ESB

• Office: Room G-19 ESB

• E-mail: kostas.sierros@mail.wvu.edu

• Tel: 304-293-3111 ext.2310

•Course notes: http://www.mae.wvu.edu/~cairns/teaching.html

USER NAME: cairns PASSWORD: materials

•

Facebook : Konstantinos Sierros (using courses: Mechanics of Materials)

• Office hours: M, W 9:00-10:30 A.M. or by appointment

7/28/2019 Performance on Mechanics of Materials – MAE 243 (Section 002)

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Course textbook 

Mechanics of Materials, 6th edition,

James M. Gere, Thomson,

Brooks/Cole, 2006

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Why do we study Mechanics of Materials?

Anyone concerned with the strength and physical performance of 

natural/man-made structures should study Mechanics of Materials

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Why do we study Mechanics of Materials?

SAFETY and COST !!

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Structural integrity of materials is important… 

7/28/2019 Performance on Mechanics of Materials – MAE 243 (Section 002)

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1.1: Introduction to Mechanics of Materials

Definition: Mechanics of materials is a branch of applied

mechanics that deals with the behaviour of solid bodiessubjected to various types of loading 

Compression Tension (stretched) Bending Torsion (twisted) Shearing  

7/28/2019 Performance on Mechanics of Materials – MAE 243 (Section 002)

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1.1: Introduction to Mechanics of Materials

Fundamental concepts

• stress and strain

• deformation and

displacement

• elasticity and

inelasticity

• load-carrying

capacity

Design and analysis of mechanical

and structural systems

7/28/2019 Performance on Mechanics of Materials – MAE 243 (Section 002)

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1.1: Introduction to Mechanics of Materials

•

Examination of stressesand strains inside real

 bodies of finite dimensions

that deform under loads

•In order to determine

stresses and strains we use:

1. Physical properties of 

materials

2. Theoretical laws and

concepts

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Problem solving

•Draw the free-body diagram

• Check your diagram

• Calculate the unknowns

•

Check your working• Compute the problem

• Check your working

• Write the solution

• Check your working

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Free body diagrams I

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Free body diagrams II

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Statics example

200kN A steel beam with a tensile strength of 

700 MPA is loaded as shown.

 Assuming that the beam is made from

hollow square tubing with thedimensions shown will the loading in

the x direction exceed the failure

stress?

3

4

2m

0.02m

0.01m

7/28/2019 Performance on Mechanics of Materials – MAE 243 (Section 002)

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200kN

3

4

2m

160kN

120kN

120N

160kN

240kN.m

Step 1: Free body diagram

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Step 2: Calculate moment of inertia

0.02m0.02m

0.01m

I=1/12 x (0.024)- 1/12 x (0.014) m4 

=1.25 x 10-8 m4 

 A=0.022-0.012 m2

=0.0003 m2

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Step 3: Shear and moment diagrams

200kN

3

4

2mV

x

120

M

x

-240

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• Stress due to axial loading

• Stress due to bending

ANS: Total stress greater than failure stresstherefore failure will occur

 MPakPa

 A

 F axial 

33.533

0003.0

160  

 MPakPa

 I 

 Mcbend 

1920

1025.1

01.0240

8

  

Step 4: Calculation of maximum tensile stress

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Key to success

Ask questions and seek help if you feel like it!!!