cven214- lecture 2 strain -dr. wael alnahhal

7/25/2019 CVEN214- Lecture 2 Strain -Dr. Wael Alnahhal

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COLLEGE OF ENGINEERING

DEPARTMENT OF CIVIL & ARCHITECTURAL ENGINEERING

CVEN 214: STRENGTH OF MATERIALS

WAEL I. ALNAHHAL, Ph. D., P. Eng

Spring, 2015

Chapter 2: STRAIN


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Introduction

Applied

External Load

Internal

Loading DeformationsInternal

Stresses

Stability and Deformationsof a body depend on the intensity of

the external forces applied on the body as well as the load

carrying capacity of the body

Determine Using

Equilibrium

Equations

Strain


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Strain (deformation) terms

Deformationof the material is the change in

geometry when stress is applied

Deformation is expressed by the displacement

field of the material

Strainis the deformation per unit length

Deflectionis a term to describe the magnitudeto which a structural element bends under a

load


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Deformation

When a force is applied to a body, the internally

generated stress will change the bodys shape and size.

These changes are deformation.

Note the before and after

positions of 3 line segments

where the material is

subjected to tension.


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Strain

1. Normal Strain

The elongation / contraction of a line segment per unit of length is

referred to as normal strain.

Average normal strain is defined as

If the normal strain is known, then the approximate final length is

s

ssavg

='

( ) ss + 1'

+line elongate-line contracts

Units

Normal strain is a dimensionless quantitysince it is a ratio of two lengths


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Normal Strain

normalstress

normal strain

P

A

L

= =

= =

2

2

P P

A A

L

= =

=

2

2

P

A

L L

=

= =

Normal Strain tends to change the volume, Length or Sizeof a material


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Shear Strain

Change in angle between 2 line segmentsthat were perpendicular to one another

refers to shear strain.

'lim2

alongalong

tACnAB

nt

=

90-shear strain


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Shear Strain

Cubic element subjected to a shear stress will deform into a rhomboid. The

corresponding shearstrain is quantified in terms of the change in angle between

the sides

A

B

Note: Normal Strain tends to change the volume or Sizeof a material

While Shear Strain tends to change the Shapeof a material


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EXAMPLE 2.2


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EXAMPLE 2.2 (CONTINUED)


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EXAMPLE 2.2 (CONTINUED)


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Example 2.3The plate is deformed into the dashed shape. If, in this deformed shape, horizontal lines on

the plate remain horizontal and do not change their length, determine (a) the averagenormal strain along the sideAB, and (b) the average shear strain in the plate relative to the

x and y axes.


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Part (a)

LineAB, coincident with the y axis, becomes line after deformation, thus the length ofthis line is

The average normal strain forAB is therefore

The negative sign indicates the strain causes a contraction ofAB.

Solution:

( ) mm018.24832250' 22 =+=AB

( ) ( ) (Ans)mm/mm1093.7250

250018.248' 3=

=

=AB

ABABavgAB


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Part (b)

As noted, the once 90angle BAC between the sides of the plate, referenced from thex, y axes, changes to due to the displacement of B to B.

Since then is the angle shown in the figure. Thus,

Solution:

'2 =

xy xy

(Ans)rad0121.02250

3tan 1 =

= xy


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Example 2.4


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Solution Example 2.4


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CONCEPT QUIZ

1) The rectangular membrane has anunstretched length L1 and width L2. If the

sides are increased by small amounts L1

and L2, determine the normal strain along

the diagonal AB.

( )( )2221

2

2

2

1

21

21

2

2

2

1

2

2

2

1

2

2

1

1

D)C)

B)A)

LL

LL

LL

LL

LL

LL

L

L

L

L

+

+

+

+

+

++


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CONCEPT QUIZ (cont)

2) The rectangular plate is subjected to thedeformation shown by the dashed line.

Determine the average shear strain xyof the

plate.

( )22

200150

3D)

200

150C)

1200

17B)

150

3A)

+

cven214- lecture 2 strain -dr. wael alnahhal

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