Mechanical Engineering Department

WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT

STRESS ANALYSIS ES-2502, C’2012

Lecture 04: Stress

19 January 2012

Mechanical Engineering Department

Instructor: Cosme Furlong HL-151

(508) 831-5126 cfurlong@wpi.edu

http://www.wpi.edu/~cfurlong/es2502.html

General information

Teaching Assistants: Morteza Khaleghi HL-150

(508) 831-5125 mkhaleghi@wpi.edu

Tatiana Popova

tpopova@wpi.edu

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Stress: Definition: intensity of internal force: acting on a

specific plane passing through a point

Equivalent

force and

moment at

the section

FFR

oRoMM

O

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Stress: Definition: intensity of internal force: acting on a

specific plane passing through a point

Finite force F acting on

a finite area A

Definition

Normal stress:

A

Fz

Az

0lim

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Stress: Definition: intensity of internal force: acting on a

specific plane passing through a point

Finite force F acting

on a finite area A Definitions

Shear stresses:

A

Fx

Azx

0lim

A

Fy

Azy

0lim

A

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Stress: Definition: intensity of internal force: acting on a

specific plane passing through a point

Finite force F acting on

a finite area A

Normal and shear

stresses on plane x

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General state of stresses

Further sectioning leads

to a “stress cube”

State of stresses of

a finite size cube

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State of stresses: normal stress equilibrium (1D)

Finite size cube:

stress cube

One-dimensional

normal stress

)(')( AA

;0F

Therefore,

'

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State of stresses: shear stress equilibrium

Finite size cube:

stress cube

Forces:

)(')( yxyx zyzy

;0yF

Therefore, zyzy '

Moments:

yzxzyx yzzy )()(

;0xM

Therefore, yzzy

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P

P

Average normal stress in an axially loaded bar

Tensile test

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Average normal stress in an axially loaded bar

Tensile test

Necking

Typical results

Ductile

material

Brittle

material

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Average normal stress in an axially loaded bar

Bar subjected to

axial load

Internal distribution

of forces

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Average normal stress in an axially loaded bar

Internal distribution

of forces zRz FF

A

dAdF

AP

Average normal stress:

A

P

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Average normal stress in an axially loaded bar

Tensile average

normal stress

Compressive

average normal

stress

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Average normal stress in an axially loaded bar

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Average direct shear stress

Bar subjected to

shear load

ABCD section

A

B

C

D

A

B

C

D

AV

AV

(Area under

shear)

(Internal

loading)

V

avgA

V

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Average normal stress: example A

The casting shown is made of steel having a specific weight of st=490 lbf /ft3.

Determine the average compressive stress acting at points A and B.

Approach:

1) Define free-body

diagrams

2) Determine

internal loadings

3) Compute average

stresses

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Average normal stress: example A

The casting shown is made of steel having a specific weight of st=490 lbf /ft3.

Determine the average compressive stress acting at points A and B.

Free-body diagram

(FBD)

Compute internal

loading

&

Average

compressive

stresses z

(Stress cube)

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Average shear stress: example B

Wood joints 150 mm deep (perpendicular to the plane) are loaded as shown.

Determine the average shear stress developed along planes a-a and b-b.

Approach:

1) Define free-body

diagrams

2) Determine

internal loadings

3) Compute average

stresses

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Average shear stress: example B

Wood joints 150 mm deep (perpendicular to the plane) are loaded as shown.

Determine the average shear stress developed along planes a-a and b-b.

Free-body diagram

(FBD)

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Average shear stress: example B

Wood joints 150 mm deep (perpendicular to the plane) are loaded as shown.

Determine the average shear stress developed along planes a-a and b-b.

Compute internal

loading

&

Average shear

stresses (Stress

cube)

(Stress cube)

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Reading assignment

• Chapter 1 of textbook

• Review notes and text: ES2001, ES2501

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Homework assignment

• As indicated on webpage of our course