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Get Full Access to Virginia Tech - ESM 3704 - Class Notes - Week 7
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# What does positive strain mean? Description

##### Description: strain, Hooke's Law, Poisson's Ratio, factor of safety
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Basic Principles of Structures : Week 7

## What positive strain means? Strain - measure of deformation

strain= change in length

original length ALL inches, feet Lot inches, feet

dimensionless

Shudy Sou

normal strain :

fr

Exongitudinal - All

F

AW

--

Elatitudinal -

AW

latitudinal

nal =

* positive strain means it got longer,

## What is elastic and plastic behaviour? negative strain means it got shorter

Example 59 find the strain in the cable

12"

KI

Elong

at We also discuss several other topics like What is the meaning of ethnocentrism in anthropology?

L = 1122+12 = 12.04 L = 24.08 Lo- 24' AL= 0.08

Eling Element Ew7,0033

Example 5.7 calculate the strain developed

## How is poisson's ratio calculated? p=100 kip ISI SF.036" ?

long

shortened, so it is

5045)

d=6"

negative

Evorga 20.036" Enoga -.003

IZ

shear strain:

tito

-Intel Don't forget about the age old question of What is the meaning of conditional proofs?
We also discuss several other topics like What is the meaning of performance production measures in measuring motor performance?

8( gamma) = shear strain 8 is measured in radians -

1 circle = 2th radians

radians = degrees & ZT

- 360

to

original angle = 90° = Il

Example:

determine the average normal strain along AC and the shear strain at E relative to the x, y axes

Ac

Ac = 150 +1502 = 212.132 mm

150

MM

150 mm

150mm zum

150 mm We also discuss several other topics like Where was martin luther king's childhood home?

mo - AC

Ac' = J150271523 = 213.551 mm

150

mm

152 mm

E = AL = 213.551- 212.132

To 212.132 E = .0067 (normal strain) shear strain:

tan' a 150

75 mm 8= 45.379°

O'= 20 o'= 90.7599

76mm

mm

152 mm

radians - degrees x 270

360

90.759 x 270 = 1.584 rad

360

8= 7 - o

8 = 1-1.584 Don't forget about the age old question of Why is oxygen so important to most animals?

18=

-.0132

Ssans

ultimate

Stress -strain curve

yield strength plastic behavior elastic behavior plastic behavior

o breaking

linear

stress will tensile strength strength

eventually decrease elastic behavior

elastic region

as strain increases

Strain

permanent

region will cause deformation permanerit deformation A: “strongesť - can withstand the most stress B: brittle has little to no plastic region Don't forget about the age old question of What is optimistic time in pert?

C: ductile - ex steel strain

stress

Hooke's Law

: relationship between stress and strain

* only in the elastic region where there is a LINEAR

relationship between stress and strain

o-EE

strain

stress

elastic modulusia constant for any given material

Example :

axial load (normal force) = 4 Kip (kilopounds) yield stress = 51.5 ksi (kilopounds per square inch) determine the cross-sectional area.

If the member is 3 feet long and elongates by 0.02 inches, what load was applied ? E-14*10% ksi

ve

Å

57.5=4

A- .07 in

Lo= 3 ft = 36 in

keep units

E = AL = .025 555*104 (strain) Lo 36

AL = .02 in Keren en

sistent

o=EE

0 =(14*103)(5.55*10-4)= 7.78 ksi

o

7.18-

P=.545 kip]

Example:

If the wire has a diameter of 0.2 inches, determine how much it stretches when the distributed load acts

on the strut.

AL=?

200 16 let

wire has an elastic modulus of 29x109 ksi

q ft

find force acting through AB :

R=900#

KAB 1 300

resultant force from distibuted load: R- Ź(9)(200) = 900 #

point of application : 2 / L = 2 (9)

= 6 ft

from small end

q ft

Ozm = -900-3 + (ABsin30). 9-0

AB= 600 #

find AL:

P= 600 # A= r2 = π(0.2) = .03 in

0=600 - 20000 psi o

= 20 ksi

:03

OE€ E= AL

20 = ( 29x10°) E= 6.9x104

cos30-23

АР.

L 30°

JB

e necin 29 ft

AB = 10.39 ft

9 ft Bar 6.9x10-4=AL IAL= .007 ft

10.39 ft

Poisson's Ratio

force

force

7 ore I ho

-

to

-

The

Two types of strain Elongitudinal - AL

same direction as the force

Elatitudinal =

ah

In the elastic region the ratio

{lat will be constant

Elong

This ratio is

Poisson's Ratio

M =

Elat

(mu)

Elong

- negative because one of the two values will be getting smaller

Poisson's Ratio will always be between 0 and 0.5

300N

+ 15mm

Example:

determine the change in the length and diameter of the rod if an axial load of 300 N is applied. E= 2.70 GPa v=0.4

belastic 100 spoissons ratio modulus

. * Pascal = N/m2 –

OI >300 N .

should convert

mm tom 200 mm

o= 300 = 1.698x10° N/m2 or Pa

776.0075) ds 15 mm r= 7.5 mm

= .0075 m O E Elomp 1.699 *10* = ( 2.70x409) Eling Elang = 6.294104

= AU

Evega 4L

6.29~104 =

DL= 1.26*10*mor

Z

m

126 mm

0.42 - {cat

als will al

Elat

-2.5*10-4

Poisson's Ratio

6.29x1054

mm

-2.5 x 10

=

.

Este and

Ad = –.0377 mm]

15 mm

Factor of Safety =

failure stress Allowed stress

If Ophil - 1000 Pa and diameter = 15 mm, what force can be applied?

oh

1000+

P

P

-.177 N]

76.0075)

Use factor of safety of 2 :

2=

O fail

Fallow = 500 Pa

O allow

z= 1000 Pa

Tallow 500 Pa = p

(.0075)

och

P=.028 N

Axial Forces

o-E Elong P = E.AL

alt

AL - PL

AE

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