86

84

description

ضض

Transcript of 86

Page 2: 86

٢جزوه آموزشی مقاومت مصالح

مھندس حامد حبیبی: مولف

( شماره تماس : 09124167740 )

Page 3: 86

���) ��� ��� �(

∑ ∑ ∫ =→=⇒=A

ii dAdAF 000 σσ

��� ���� ��� ���� ���� ���� �� ���� �� �!"#� $%� � . ���� '��( ��� ���� )�* +

σ+ ,-.� /�0 �� y ,�� ,-.� � ,12� .

∫−= ydAM )(σ

�3�� �� $%� ,-.� �""0 �4#� /�0 � �5 �6�( �� �0 �6 %7"8.

� ������ �� ����� �� ������ � �!:

�3� �� ��� ���� 9!� �� : 3 /1; <� �=� + /1; <� 9-� % ( ���� %� ��1> �=�� %6

�."; �(�."; �(�."; �(�."; �( ::::' �0 �6� �� 9 !�( �� �6�( �>�14� "�� @ @(�0 �3 �3�� �.

Page 4: 86

???tan yy uu −=⇒−= δθε

P

y

x

P

x

yx

yx

y

x

eLimLimLimLim

xxx

u

x

−=∆

−=∆

−=∆

−=

∆=

→∆→∆→∆→∆ 0000

tan θθε

P

y−=ε

�#� $%�&' (� )' �'�� *�� +���,:

yP

E

EP

y

E)(

−=⇒=

−⇒= σ

σσε

��0 �B�� ��%�:∫∫ =−⇒=AA

ydAP

EdA 0)(0σ

'2!# C8D� + E"F � �B�� ��%�∫ ∫ =→=−A

ydAydAP

E00

�."; �( 9�� # ��� �� �-��� C�� :0%�∑∑=

i

ii

A

yAy

Page 5: 86

{

I

MyI

yM

EI

M

PR

P

EIMdAy

P

EM

dAEyP

dAyP

EM

Aا����

−=⇒−=

==⇒=⇒=

−=−

=

∫ ∫

σσ

1

1)(

2

22

C : : : : ���0 # ���� �6�( <� �."; �( ���� %.0��* .I

Mc−=σ

).� ).� ).� ).�

H ,�� ���I �1#:0� /"( �����

cmkgmtwl

M

I

MC

.10125.3.125.38

51

8

522

max

max

×==×

==

−=σ

) 9 �K2� ���� ��%� ( ,�� ���� '��( ���� �."; �(.

Page 6: 86

∫ =A

ydA 0 ��";�(

252

50

2

10125.312

)50(30

12

4523

===

×===

hC

cmbh

I

222525

10125.3

2510125.3maxmax5

5

max cm

kg

cm

kg ±=→=⇒×

××= σσσ

<4� /"( % �2

1400cm

kg

a =�

22

2

900

9.8114008

8

××==⇒=⇒=

l

SwS

wlSM xa

xaxxa

εσσσ

m

ton

cm

kgw 573.73.5 ==

N( ?,1,1400 max2=== lw

m

ton

cm

kg

cmlw

SlS

wlSM xa

xaxa 30310

9.8114008.8.

8.

2

1

2

12

=⇒

××=

=→=⇒=σ

σσ

� (322

86.14214008

)400(10

8cmS

wlMS

S

Mx

aax

a =⇒×

===→=σσ

σ

3

3

161180

117160

cmINP

cmINP

@ (

Page 7: 86

⇒×

×

==⇒=5.014

2

40010

.

2max

vV th

wl

A

Vττ��%� /"(

).� ).� ).� ).�::::

� ).� ��. ���0 <4� /"( % �2

50cm

kg

a =σ ,�� . �36� %.0��*)L ( ���I �3��( ��

H���

wc

Il

eI

cWl

I

Mc aa

σσ

822

−=⇒−=−=

cmll 7072510

5010125.38max

5

=⇒×

×××=

).�).�).�).�::::

?=σ

Page 8: 86

mkgwl

M .1008

2200

8

22

max =×

==

cmA

yAyydA

i

ii

A

73.10353530

5.22)540(35.25300 =

×+×

×−×+×××==→=

∑∑

∫�.";�(

( ) 23

23

2 )73.905.22(35312

3535.273.10530

12

530?? −×+

×+−×+

×=+== ∫ ∑ ∑ dAIdAyI ioi

435737 cm=

202.30

35737

73.10100100cm

kgري��I

MC−=⇒

××−=

−= σσ

219.14

35737

)73.1040(100100cm

kgآ�� =⇒−−××

−= σσ

).�).�).�).�::::

=→=

==→=

=

34

34

2

1072.25

9.81573

2.18

cmScmI

C

IScmScmI

cmA

yyyy

xxxx

Q8�Q8�Q8�Q8�((((?max =σ

� �5��+ ���0 ��� ���

Page 9: 86

2

2

6.250

24429.818

)400(

8

max

22

cm

kg

cm

kg

xx

M

S

wl

S

M

=

=⇒×

×===

τ

σσ

-. /�� �%�� 0 :

1- ��� 91> �� S3T �<��� # ���� �6���� ���� �� '!� % �‘ � �0 ‘� US8��%) @�� %0V

( ,�� W��.

2- @��13 �#:4( S3T �+� �6 ��8X� ���%3T ��-3 �6���� <� �!# ���� �� '!� ��� %� % �

�#�+T �� ,��� �� %Y� �1F+.

GZ ,�( ���� % ����� �+% 3 %Y� [��0 %6 <� 9�* '�%� /"( \ �% ��%� %7"8 � '�:16 �

� "0 �� �%-F �1F �6 � �3 ��F ���� ��.

±=′

−=

I

MY

A

P

N

p

σ

σ

I

MY

A

Pt ±−=σ

Page 10: 86

2

2

2

2

2400

800

107

101.2

5

6

cm

kg

s

cm

kg

all

cm

kg

all

cm

kg

S

E

E

=

=

×=

×=

σ

σ

cm

kg

Bcm

Kg

A 1111573

2

1410

2.18

2000,1331

573

2

14101

2.18

2000

55

4+=

×

+−

=−=

××

−−= σσ

�#:1(�#:1(�#:1(�#:1(::::

Q8�: ��<� ��P=10 tonH,�� ���I ��� 3�18T+ ���� ,12� %6�� /"(

^(��� �I ��<� �� ��P=PuH��� �� � �2( \ �B�� <� �!#

N( ��<� ��P=1.2PuH,�����I '�K� 90 )�B % _(

�( � "0 $%� % �500=allσ + ?=δ

Q8�(→=→∆=∆

+=

Ss

all

Ss

S

alls

AE

lF

AE

lFPlS

FFP

=

=

=

=+

tonF

tonF

FF

tonFF

S

all

allS

alS

9.5

1.4

44.1

10

^(

}tonAF laall 20200025800

?

==×== σ[�8T��� � �2( [� "#

Page 11: 86

8.252044.18.28122400. =×≤=×== tonAF Ssusσ��� � �2( ���

�"�� �� � �2( �� �a�8 b#�� +�%6.

tonPu 8.488.2820 =+=

N(

tonP 56.588.482.1 =×=

,�� ,#S3 �� 9!� % _(). �;%I58.5b>48.8,�� (

�(

tonPP

tonP

tonF

tonF

u

u

as

6.365.302.12.1

5.30185.12

185.1244.18.28

5.1225500

2 =×==

=+=

=×>=

=×=

���� ��� �� �� � ��� �� ��� ���)�� ����� � ��� ! " #$(

cmAE

FL

tonFs

19.012101.2

20024100

1.245.126.36

6

2

=⇒××

×==

=−=

δδ

Page 12: 86

12�� ���3-

42�� �' 5��� ���6� �7��

�F�( ���� 91> �� �0 ����� �+% 3 � [�X( /1;<� ��; ,8* � N�; ����� �� ,8* ��-

,�� :0%� <� .91> �� . �+% 3 � ,�� )�=� :0%� <� N�; �+% 3 p� �0 ���� C�� :0%� �

> ��1; %7"8 @+d=� �"0 %Y� �e%:

e M=P.

.

±= I

yM

A

� ,�� %��%� �e%> ���� ���3 %6 �� /"(:

.

+= I

eP

A

P yσ

<� �+2� �� 9�* /"( '��� ��%� %�� ���.

e

y

A

Iy 0

I

P.e

A

−=⇒= +=

,�� %�� 'T �� /"( �0 ,�� ��; �8�=�

Page 13: 86

�0 �=��� �0 �6� �� '�3 �8�=� �#� �� ��"� ,�d> P ���� %#< �� ���0 �+% 3 b# Z

��� �� �� �."; ���� ��� ��Z ���� ��%� . N+%; % � ,#:0 %� <� e/60 �."; ���� �� #

% �+ �� �6��; �+� C�� :0%� <�e ��� �� b#�:3 C�� :0%� �� �."; ���� \ �� # /#�:�� .

:0%� <� N�; ���0 �+% 3 %Y� ���3 �0 �=� �� P ���� ���� �6���� <� �!# �+� ��

,�% �6��; f��� ���� �6���� )�* '�:16 ���� /1; �3���3 ��%� �e%>.

DKg� % � %Y� ���3 f P� �� ey , ez �6���� )�* ��1; �6%7"8 � 6� /#13

y , z %��%� h (%( �� ���> ���� P.ez ,P.ey ��� �"6��; . f��� �#� ��.

fDKg� �� �e%> ���� <� �� ���3 �� �"#T %� ���1> /"(z, y � ,�� %��%� :

..

++= z

y

y

z

I

eP

I

eP

A

).�:

^�ABC ���3 �� ���� �8�8 +� '��� i�F � B C�� �8�8 %6 ,�� @�� 9 !�(

����29.103 cmA =, �Kg8 �+K� 48820 cmI = �F�; %�� +cmd 3.27= ���� .

$%� � �� ^� �� ����+ ���0 �6 /"( %.0��*kgP 1350= � mL 4.2=� ,8.1=H

� "0 �� 5 .

Page 14: 86

9*: kgmM B 1620=

mLHAB 34.28.12222 =+=+='��(

8.0sin,6.03

8.1cos ==== αα

AB

H

xPxP

xRM xA 5404.0)8.0)(2

(sin ==== ����� ��1;%7"8 X <�A

kgmM B 1620)3(540 ==⇒0��* ���3�� ��1;%7"8%.B��� �� .

αα cos2

cosP

RP A ==⇒)�B%��%��� ����� �+% 3AB� ,�� %��%�+ ,�Y

I

yM

A

P

I

M

A

P By +−=+=2

cosασ���� �� ^� �� ���� + ���0 �S�"( %.0��*B ��� ��

( )I

dM

A

P B

c

)2

(

2

cosmax

−−=α

σ ���� �3��� �( �� ���� /"( %.0��* B �� ���

( )2max

6.254)8820)(2(

)3.27)(162000(

)4.103)(2(

)6.0)(1350(

cm

kgc =−−=σ

28.246

)2

(

2

cos)(

cm

kgB

tI

dM

A

P=+

−=

ασ ���� �3K�( �( �� ���0 /"( %.0��*B,�� %��%�

).� :

���� �� 9!� ��%� ���� � �� � b# ���� C�� mm ,�� @�� QD3 . /"( %.0��*

@�� ���� + ���0 ���� %Y� ,�( �� � @�� bI�0 ���� �� p � "0 ^2* .

Page 15: 86

���� )�* ���� �#�y ���� �� ���1> /"( ���� ��%� /1; ,�( z ���� <� y %��%�

� ,��:

I

M

A

P z+=σ

)121(2

))((

4

2)(

23

3121 a

z

a

p

a

zpa

aa

Pa

+=+

���� �� ���0 /"( %.0��*4

az = �%� + ��� �� � ,�� %�:

2

84max )()(

a

Pat z === σσ

���� �� ���� /"( %.0��* 4

az −= � ,�� %��%� + ��� �� :

2max

4)

4()(

a

pazc −=−== σσ

Page 16: 86

).�:

���� �K26 I%#< 9!� <� �"(�-> ���� �#� fDg�� � "0 �� 5 ��:

444 84.941544,27346 cmAcmIcmI yZ ===

cmAz

Ie

cnAy

Ie

y

z

81.1)9)(84.94(

1544

96.13)65.20)(84.94(

27346

2

1

==−=

==−=

���� �� �<�8 b# ���:� �K26 �#�%�"�876 12

92.27

e

+}22

62.3

e

��� ��.

Page 17: 86

).�:

@�� �K;� :#%0; ����S73 ��%� @�� ��� �e%> ���� �0 �#"� C8D� <� ���* ���#�

,��. j�Dg� '<+ �#"�=1.8 t/m3 γ ��� �� . ��� k;q �"0 �� ���+ ���#� %� ��

%��%� ���#� �5 �� 'T %.0��* �����+ �"0 ��% _( ��; ���� ���#� l�(�� �� �0.5t/m2 1 ,��

.H � "0 ^2* ���#� �5 �� �� �1 " �+ �1#:0� ���� �6 /"(

)��� ���#� <� �K12�L=1m ��F ��

[ "0 �mmm ,12� �#� �'��( �� ��

,�% %a3 �� �� @%B @% ( b# f��D�

��� ���% / 3K�( �SK3� �� �0 .

i��; '<+ %Y� ,�( �� @%B % ( �#�

�e%> ���� ��� �� @�%�� k; ���+

,��� �6��; �� /"( �#%K� � ���#� �5�� .

P : � @�� ��F ,12� '<+%��%21 QQS

M

A

P+±=σ

TQQP

cThaLQ

cTLabhQ

34.1148.686.4

48.6)8.1)(1)(8.0)(5.4(

86.4)8.1)(1)(8.02)(5.4()(

21

22

121

21

1

=+=+=

====

==−=−=

γ

γ

Page 18: 86

��1; %7"8M �6 '<+ %7"8 l�14� � %��%� 1Q+2Q ���� )�* k;��� �"#T%�+ Z �0 ,��

�"0 �� ��-> ���#� �5�� �e%> ���� C�� :0%�<�.

MThhqab

Qbab

aQM .15.2)5.4)(5.1()6.0)(48.6()2.0)(86.4()3

(2

)22

()23

( 2

61max

21 =+−=+−−−−

+=

'�I22mblA ==+6

2Lb

S =�#��� ��� ��6

M

A

−=σ

2/21.367.562.0

15.2

2

34.11mt±−=±−=σ

���3 �� �1#:0 � ���� /"(A ���3 �� �1 " � ���� /"(+ B ��� �� .

288.821.367.5max m

t−=−−=σ : �1#:0� ���� /"(

246.221.367.5min m

t−=+−=σ : ���� /"(�1 " �

).�:

,�� @�� @��� '�3 �.�.� ���� � �"K� �� b# . �6 /"( �#<�( � =( ,2�����

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�0 $%� �:4� % ( b# f��D� �n0 ���� %� ��1> ,SF �� �� % ( �"S5 �#.�K� j�Dg� '<+

AO ,�� h=!� %K� %� �(� 3 �� 0 .

Page 19: 86

mKN��ريI

MC

A

w

mKN��ريI

MC

A

w

mKNwHM

knPW

KNVH

hhVH

A

2

2

2

0

2

1

/7.602.235.37

/3.142.235.37

12

8.1

9.5.12

18.1

5.67

.5.12)3.0)(5.67()9.0)(4.36)3.0()9.0(

5.6725)1)(3)(8.1(2

1

4.36)1)(7.2()10)(7.2)(2

1(

1

−=−−=−−=

−=+−=×

−=+−

=

=−=−=

=

==

=

==

××==

σ

σ

γ

).�:

���I % ( b# mm 100∗150 ����� �� ,;��"!# @�%K2 �� b# 91�( ��%� M �� 0

�36� �� �(� 3G ��%� @��K�� ���� �%K� ���� ./"( %.0��* ^2* �36� o�+ �� �� ��1;

� "0 � =( �� �."; �( 9�� ���� '16 ��%�+ � "0) . � "0 %a3 p%� % ( '<+ <� . (

Page 20: 86

}

47373

30cos

1025.1)100)(150(12

11081.2)150)(100(

12

1

.3.1)2

3(5.1cos.5.1

8

34

8

mmII

mKNMMmKNWL

M

yZ

Z

×==×==

====×

== α

6103.1 ×

=±±=y

Y

Z

z

I

ZM

I

yMσ

آ�

آ��

mm

NB

mm

NA

2

2

47.0347.3

47.6347.3

=−+=

=++=

σ

σ

آ�

��ري

mm

mm

Nc

2

2

47.0347.3

47.6347.3

−=+−=

−=−−=

σ

σ

).� :

� �6 /"( :F �� �� %YX� �1#:0 bI�0 ,#S3 �� qC,B,A � "0 �-��� .

) ��% �-��� ���3 �� �� �#� S�"( [1((

Page 21: 86

��3��2 7 �� �- �809 )��3��2 7 ��3- ��6(

).�).�).�).�(((( C�� �+� �� �#� �0 �#6 /"( � =( ,�� ^���� AB :F ( �""0 %Y� �.�.� q:F <�

�31� ��� )�=( �� bI�0.

αααα sin1sin2cos2cos3 4321 ==== FFFF

NNFFFFN 29.1sincossincos 4321 =⇒+−−= αααα ∑ =+→

0)(FnFx

NSFFFFS 12.2cossincossin 4321 =⇒−−+= αααα ∑ = 0Fs

Page 22: 86

Nx 12.2=τ NX 29.1=σ

θσθθτθθτθσσ

θθθθ

22

4321

sincossinsincoscos

0sincossincos0

dAdAxydAxydAdA

FFFFNXF

yxx +++=

=−−−==′

� �%B <�dA* �� � "! � p�

θτθ

σθ

σσ 2sin2

)2cos1(

2

)2cos1(xyyxx +

−+

+=′

r��� �� ���� b# <�"( 9#�-( %7#�

) 1 ( θτθσσσσ

σ 2sin2cos22

xy

yxyx

x +−

++

=′

)A( θτθσσ

τ 2cos2sin2

xy

yx

yx +−

−=′′

) G (θτθσσσσ

σ 2sin2cos22

xy

yxyx

y −−

−+

=′

Page 23: 86

r������ ) �(�F �� οθ , θθ += 90 6� �� ��%� r���� + � ) G (,����#T �� .

yxyx′′′′ τσσ ,,�"0 �� W�� ,SF o�� ,�� 9-� ���3 '16 �� .

,�Y=+=+=+⇒+ ′′ 21)31( σσσσσσ yxyx

��� �-)Maxmin,) (��:'(

����� �I q�<� ��θ \ x′σ��� �� �1#:0� .

θτθσσσσ

σ 2sin2cos22

xy

yxyx

x +−

++

=′

r���� <� % � )� (�� ,-23θ �6 /"( � 6� ��%� %�� �+2� �� 9�* �4 K3 + �#% 7� sK��

����)Maxmin, (�"#T �� ,�� ��.

02cos2sin22

=+−

−=′ θτθσσ

θσ

xy

yxx

d

d

′+=′′

−=

11

1

21802

2

2

)(2tan

θθ

θ

σστ

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Page 28: 86

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Page 29: 86

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Page 34: 86

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Page 35: 86

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Page 36: 86

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Page 37: 86

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Page 39: 86

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Page 40: 86

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2

2

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M

dx

vd−=

2

2

Page 48: 86

Vdx

dm−=

�!م{��"�

vEIdx

vdEIM

EI

M

dx

vd′′−=−=→−=

2

2

2

2

vEIdx

vdEIV ′′−=−=

3

3

��%�

vEIdx

vdEIq ′′′′−=−=

4

4

+% 3)@%K2 ��(

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00 =→= Mx �#��� h �

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=

=

=

0

0

0

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Page 49: 86

vArcV ′=′= tan,tan θθ

222dvdxds +=

ds

dx

dx

vArcd

ds

dk

)tan(1 ′===

θρ

[ ] 21

22

1

2 )(1)(1 Vdx

dv

dx

ds′+=

+=

[ ])3(

)(1

1)2(),1(

)2()(1

)tan(

2

32

2

v

v

ds

dK

v

vvArc

dx

d

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′+

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θρ

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��6���:

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�>4(�� �"�"� h �=′== vdx

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/1;}

=′′==�!م��"�

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2

2

i%�=′′== vEIdx

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3

3

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vdEIq

4

4

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).�

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% ( �>4(�� �"�"� r���� � =( ,2�����

�� �<%� v%�Lx

LV

MLM

=←

=

+=

0)(

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=

=

0)0(

0)0(

θ

v

�<%� o#�%�

12

2

MMdx

vdEI ==��1; %7"8

0)0( 331 ==′→+= CvEIcxMdx

dvEIh �

xccxMEIvxMdx

dvEI 34

2

11 21 ++=→=

EIxMv

2

2

1=⇒== 0)0( 4CEIV

� ,1� �� �>4(�� �"�"� '!� % _( �0�6� �� '�3 @��T ,�� �� �4 K3 ,-.� ,�d>

��� ��.

����� �#%K �:�v �� X=L�6� �� �� .2� ��<T �SK3� �� �>4(�� h � �+EI

LM1+ �� '#���

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).�

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�-��� �#T �� ��F�� ��(��T �� �0 �1#:0� � �1325101.2

mmNEst ×=

P

yE−=σ mmy 10=���3 �#%(� ����

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).�:

#b,�� $+%�� � �5 p%B �� ,;��"!# @�%K2 �� ,�( @�� % ( . %m ( ��1; �"�"�E I

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^ :[�SI �F�� 9 23�%�#� �8�=� <� @��K�� �

Page 52: 86

EI

LwvLxat

BxLLEI

vL

xCx

xxLc

384

52/

)()2(2432424

4

0max

4330

4

03

4

0

=⇒=

+−−

=⇒++

=++ ωωω

20)(

20

0

LwRLRBLLO

A

LBR

B

BA

M ο==+−⇒=↵

−=+

∑− ω

ω

}0

43

4

0

3

0

3

3

0

2

0

2

0

2

2

2412)(

64

22

CxCxLx

EIVA

CxLx

dx

dvEI

xLxM

dx

vdEI

++−=

+−=

−==

ωω

ωω

ωωο

����� ��A ����� C3 � 6� �� ��%� ��

}

00)0( 4

0

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CEIv

x

#)0(v

24

3

0

3

LC

ω−=⇒= 0)(LEIv

Page 53: 86

�SI �F�� 9�23�%��� �8�=� <� @��K�� � 9*

103

3

0

4

4

Cxdx

vdELq

dx

vdEL +−=→−== ωω)^

21

2

02

2

2cxc

x

dx

vdEL ++−= ω

==′′=

=⇒=′′=

0)(,0)(

02,0)0(,,0)0(

LvELorLM

CvEIorM�<%� i+�

220

11

2

0 LCLC

L ωω =⇒+−=

�� '!� % _( %.0��*2

Lx =� �#� '��� ��%� ��6� �� �� ����� �� ����B �����

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EIL

v384

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Page 54: 86

=

==

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β

α

2

122

816

5

60

x

xLLxxxv

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=⇒==

00

00

03

4

Cdx

dv

Cv

0: ω−=′′

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xd

vdEIq %K2 ��@�

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3

Cxdx

vdEIV +−== ω) 1(

21

2

02

2

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x

dx

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32

3

1

3

0

22: CxC

xCx

dx

dvEI +++−= ωθ h � )3(

43

2

2

3

1

4

0

2624: CxC

xCxCxv EIv ++++−=

ω[%� % _()4(

=++−=

=++−=

=

02

0

02624

0

21

2

02

2

2

3

1

4

04

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M

LC

LC

Lv

LX

ω

ω

8

2

2

WLC

−= +

8

51

WLC = : A �8�=� A )�S4�

[%� % _( �8�=�

×+−=

1668

5

24

234

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816

5

6

223

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EIv

dx

dv ωθ

A��"� �%7#� + ,-.� �!# ^��F

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8)0( 0

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8

5 0 LRaV

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ω=−=→

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8

3)( 0L

RLV b

ω==

Page 55: 86

b# �>4(�� �"�"� ,;��"!# @�%K2 �� %Y� ,�( @�� % (q� "0 �� 5 �� .

,�� %�� �36� o�+ �� �4#� �"�"� h �.

22

2qxqLxM −=

���� �� ��1; %7"8x� �I @ � !( <

( ) ( )24

02

12

0

)(6422

3

1

)(

1

322

2

2

qLCVدرLxV

ACqxqlx

dx

dvEI

qxqLxVEI

EI

M

dx

vd

A

−==′⇒==′

+±−=⇒−=′′⇒−

=

2464

332qLqxqLx

vEI +±−

=′ ����� C1 �8�=� �� �� A� 6� ��%�.

��x =0 v =0 2

333

242412c

xqLqxqLxEIV ++±

−=<� A�#% �� )�%7 K3� .

( ) )(224

233 BLXXLEI

qxV µ±−= % ( �>4(�� �"�"� �8�=� ⇒=⇒== 00)0( 2CV

�1#:0� '!� % _()δ ( �36� o�+ �� '��� ��%m� m�+ �m�- � % (2

1=x �m8�=� ��B �m�

��#T �� ,��

%7#� ��#%Bqdx

vdEI ==

4

4

EI

qLV

384

5 4

max ==δ

{0

21

2

2CxC

qxvEI ++=′′ 13

3

Cqxdx

vdEI +=

Page 56: 86

�"�� �� %�� % ( �SK3� +� �� ��1; �6%7"8 + 6 '!�% _(

{

024

,0,2

0)()0(

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26

4

3

321

0

43

2

2

3

1

4

32

2

1

3

===−

=⇒==

++++===⇒

+++=′

cql

ccql

clvv

cxcx

cx

cqx

EIvLvv

cxcx

cqx

vEI

0122424

334

+++−=qlxxqlqx

EIv

).�:

1#:0� h � + �1#:0� '!� % _( + �>4(�� �"�"�@�%K2 �� ,�( �0 �� @%B % ( �

�#�+T �� ,�� �� ��� ,;��"!#.

−=

−−=

)(

2

)( 2

xLqV

xLqM

2)(

)(2

2

2xL

qMdx

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v

−−==

′′876

60)0(

3

1

qLCV =⇒=′,�� %�� %��%� h � @ � !( ��

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1

3

6)(

)( cxL

qMdx

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v

+−−==

Page 57: 86

2

222

21

422

)46(24

)(

24

)()33(

6(A)

CxLxLEI

qxvB

CxCxlq

EIvxLxLEI

qxv

++−=

++−

=→+−=′

)46(24

0 222

2 xllEI

qxvc x

�'�دل&���� +−= →=⇒ @ � !( 9���� ��* v:�0)0( =v

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��#T �� ,��

EI

qLLvA

6)()(

3

=′=θ EI

qLLvB

8)()(

4

==δ

(���. �9�� � �'�F8� ����>� @7�

)(13

3

4

4

kCqxdx

vdEIq

dx

vdEI +=→=

�� ��%� �+% 3 '�Ix =L��� �� %�� f��� �� ��* v%�#< %:

�8�=���K + � 6� �� ��%� � 6� �� ����� � �"3� � ��→−=⇒= qLCdx

vd13

3

0

Page 58: 86

).�(

%.0��* f�� � �.�.� �� �0 �� �� @�� % ( '!�% _( �"�"� �8�=�0q �"0 �� 91�( ��

� "0 � =(

)�=� ,�� �#+% 3 �.�.� �� �"#T%�

2

qoLF ��B� ��

2L

@ � !( <�B

∑ =→= )3

(2

)(0 LLqLRM o

AB

32

00 LqR

LqRR BBA =⇒=+ ∑ ↑ =⇒=

+

06

0

yFLq

RA

362000 LqLqLq

RB =−=

300

0

0

66)

3)()()((

2

1

2)( x

L

qx

Lqxq

L

xxx

LqxM −=−= M

dx

vdEI ==

2

2

1

4020

300

2

2

2412

66

CxL

qx

Lq

dx

dvEI

xL

qx

Lq

dx

vdEI

+−=

==

21

5030

12036cxcx

l

qx

lqEIv ++−=

Page 59: 86

L

xqy

x

L

y

q 00 =→=

0326

=+××+−

Mxx

L

xqx

Lq οο

)2(0)(),1(0)0( == Lvv��* o#�%�

)7103(360

360

7:0

12036)2(

0)1(

42240

3

011

5

0

4

0

2

LxLxEIL

xqv

LqCLCL

LqLq

C

++−=

==+−⇒

=⇒

� ��#%B[�SI �-(%� 9 23�%�#� �8�=� <� @��K�� � [+

xl

q

l

xqq

dx

vdEI 00

4

4

===

1

20

3

3

2Cx

l

lq

dx

vdEI +=

)�( 21

30

2

2

6CCx

l

q

dx

vdEI X ++=

)A( 32

2

1

40

21

24CxCxCx

l

q

dx

dvEI +++=

)G( } }0

43

2

0

2

3

1

050

21

6120CxCxCxC

lqx

l

qEIV ++++=

��* o#�%�

00)0( 4

3 =→= Cv

00)0( 2

1 =→=′′ Cv

Page 60: 86

≤≤−

≤≤=

LxL

xM

axxL

M

M

0)1(

0ο

660)(

360

70

661200)(

011

2

01

3

033

4

0

4

03

LqCLC

LqLv

LqCLCLqLq

Lv

=→+→=′′

=→=+×

−→=

)7103(360

42240 LxLxEIL

xqV +−= ⇒ ����� �� %#��� �"#:7#F)G(

).�:

:0%1K� %7"8 b# %Y� ,�( �0 �� �� @�� % ( '!� % _( �"�"� �8�=�οM � =( ��� ��

� "0.

L

MRRRF

L

MRLRM

MLRA

ABAy

BB

BM

ο

οο

ο

=→=+→=

−=→−=

=+→=

∑ ↑

+

+←

00

0)(0

ax ≤≤0

xL

MxRM A

ο==⇒

Lxa ≤≤

Page 61: 86

)1( −=−=−=⇒L

xMMx

L

MMxRM A οο

οο

�SK12� �� �� '!� % _( �"�"� �8�=�AC + CB h (%( �� 1v+2v13 �� ��

≤≤−==

≤≤==

LxaL

xMM

dx

vdEI

axxL

MM

dx

vdEI

)1(

0

2

2

2

2

ο

ο

}

}

≤≤+−=

≤≤+=

LxaCLxL

M

dx

dvEI

axCxL

M

dx

dvEI

x

v

v

2

22

1

21

)2

1(

02

2

1

ο

ο

≤≤++−=

≤≤++=

LxaCxCLxxL

MEIV

axCxCxL

MEIV

42

2302

31

301

)2

1

6

1(

0

��* o#�%�:

03

1 =→ C0)0(1 =v

)3()()(

)2(0)(

21

2

avav

lv

=

=

2

201

2021 )

21(

2)4()()( CLaa

L

MCa

L

Mavav +−=+⇒→=′

)5( aMCC 021 +=

Page 62: 86

)6(3

10)6

12

1()2( 2

02442

330 LMLCCCLCLLL

M+−=⇒=+++−⇒

42

230

1

30 )2

16

1(6

)3( CaCLaaL

MaCa

L

M++−=+⇒

)7(2

142

2

01 CaCaMaC ++−=

o��+� 9* <�5 ( 7��� �� �4 K3

)623(6

220

1 LaLaL

MC −+−=

)23(6

220

2 LaL

MC +−=

2

2

0

4

aMC =

ax ≤≤0 )236(6

22201 xLaaL

LEI

xMv −−−=

� Lxa ≤≤

+

+−−=

26

23

6

1

2

1 222320

2

Lax

LaxLx

LEI

xMv

���3 '!� % _( ��0 ,8* ��C 9!� %�� Q8g� )� (

��� �� . %7"8 �0 �K�+M0 ���+ % ( �36� o�+ ,���

��� �)2

1=a(

���3c9!� ,��� �6��g3 '!� % _( )A(

Page 63: 86

).�:

�� ,�( i��<T �SK3� �� �0 �� �� @%B @% ( b# '!� % _( �"�"� �8�=� P ��� ��

,����#�+T . '!� % _(δ �#+�< + θ� "0 �-��� : 3 �� ��<T �SK3� .

}

}

} }0

2

0

1

32

1

2

2

2

)3

1(2

)2

1(:

)(

CxCxLxPEIV

CxLxPdx

dvEI

xLpMdx

vdEL

v

v

++−−=

+−−=

−−==

′′

θ

��* o#�%�

00)0( 2 =⇒= CV

00)0( 1 =⇒=′ CV

)3(6

2

LxEI

PxV −=

EI

PLLPPLLLLpLV

EI

pLLL

EI

pLLV

22)

21)(()(

3)3(

6)(

2222

32

−=+−=−−==

−=−==

θ

δ

Page 64: 86

).�:

,12� '!� % _( �"�"� AB% ( ABC ���3 �� �0 �� A + ���� ��%� 9#� �!��n @ � !(

,12� ��BC�.� ���� �� ,�( % ( '!� % _( 9 23�%�#� �8�=� <� @��K�� � ��- � �.

� "0 � =( . �36� �� '!� % _( �1#:0�AB,�� ���I i�����+ 40 �� .

==+−⇒=

=+=⇒=

6:0

460cos0

3:)

3(

40

0 qLR

qLRRF

qLR

LL

qLLRMA

ABAy

BB

Lx ≤≤0 xqL

xRMvEI A12

60cos 0 −=−=−=′′

21

3

1

2

72

24

CxCxqL

EIv

CxqL

vEI

++−=

+−=′

0)1( 2 =⇒ C )2( 0)( =Lv) 1 (0)0( =v

Page 65: 86

72

3

1

qLC = : 0

72)2( 1

4

=+−⇒ LCqL

)3 ()(72

22xL

qLxEIv −=

sK�� �1#:0� '!� % _( 9�� � =( ��%�v� 6� �� ��%� %�� �+2� .

3

Lx = :0)3(

72

22 =−=′ xLEI

qlV

�"#:7#F �3

Lx = �8�=��� )3 (�#T �� ,�� �� �1#:0� '!� % _(.

EI

qLv

3108

4

max =

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04

4

=−= qdx

vdEI

21 CxCvEI +=′′ 13

3

Cdx

vdEI =

02

16

1443

2

2

3

1 =→+++= CCxCxCxCEIv 32

2

121 CxCxCvEI ++=′

��* o#�%�:

}0)0(0)()0(

02

=′′==′′=C

vlvv

1234)( 11

qLCLC

LqLMLvEI B =⇒=

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'!�% _( �"�"� �8�=� 43T <�+ �% )�%7K3� ,�Y �SI W�� ��* v%� �SI <� @��K�� �

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Page 66: 86

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L

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AL

EAr

A

Pcr

cr ===2

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2

=

r

L

Ecr

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2

5102mm

NE ×=

Page 67: 86

+�%��� 42���' 5��� ���

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M

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crcr

cr

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+=+=

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1

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max

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max

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maxmax

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max

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r

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EI

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Page 68: 86

409.71 cmI y = ) %K� =e ( ��� �� .

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e

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4

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=××

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=

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Page 70: 86

kNFS

PPP

mN

A

P

cr

all

ycr

y

cr

cr

cr

56.85.2

21385)4

%7.90972.01044

10277.4

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6

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σ

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510125.0mm

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Q8� ( ��100 �(� 3 �� 0

^ ( ��200 �"0 91�( �� �(� 3 �� 0 .

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LPI

L

EIP

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EISF

mLKNP

cr

cr

cr

×=×

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==→=

==

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π

Page 71: 86

mmaa

mmP

A

mm

N

aA

P

all

1.12916667

1666712

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23

22

3

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Page 72: 86

).� : '�K�AB )��� 2.45 @�� �K;� \ @�� @��� fDg�� � �B�� �� � 3 b# <� %K�

,�� .

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all

all

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cr

==

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crP

PeV :0%� <� N�; ��)^

Page 73: 86

2

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P

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��P� �0 ��� �6��; �1#:0� �K�+ + �� �BC,AB �""0 �310 '�:16 .

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ABcrAB

===

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Page 75: 86

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Page 76: 86

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Page 77: 86

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π

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Page 78: 86

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55

4050

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CD( �� mmmm =mmmmm "0 �� �mmmm �

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Page 79: 86

���3 �� 6 '!� % _( �� <� v%� � "0 %a3 p%� '�K� ����� 9!� % _( <� % �C

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48,

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5,

34

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PLF

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FL

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EI

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PL

=⇒=⇒′=

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5

L

EIP

EIPLcr ==

π

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Page 80: 86

==→=

==→=

آ��P

FP

FF

��ريP

FP

FF

x

y

3:

3260cos0

3:

230cos0

12

1

11

1

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x

y

360cos)(0

30

314

2

13

2

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2

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==→=

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x

y

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2

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Page 82: 86

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Page 83: 86

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EIP Z

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Page 84: 86

مادسیج

نینو یریادگیبه یپنجره ا ،جیمادس

مفهوم اشاره نیا در باشد. یم رانیدهکده علم و دانش ا یبه معنا یو در مفهوم بوم ییدانا فتهیش یبه معنا madsageمخفف کلمه جیمادس

باشد. ی( مرانیاقوام ا نیاز اول یکیکشورمان( و ماد ) یبایز یاز روستاها یکی) جیبه دو کلمه س

در ،هرچه راحت تر جامعه بزرگ علمی ایران یو دسترس یعلم شرفتیبا هدف بهبود پ( IRESNET) جیمادس یژوهشپ -شیشبکه آموز

دانش آموخته رشته یرضا محمود یارشد جناب آقا ینامه کارشناس انیاز طرح پا جیمادس هی. هسته اولفضای مجازی ایجاد شده است

باشد، بر گرفته یمهر البرز م یمعاون دانشگاه مجاز یدکتر عباد یاستاد گرانقدر جناب آقا ییکه با راهنما تهراندانشگاه یآموزش تیریمد

. شده است

رانپژوهشی ای –شبکه آموزشی