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Slope-Deflection Method 1

4 Slope-Deflection Method

( ) Force Method

Slope-Deflection Displacement Method


Slope-Deflection (Beam) (Frame) Prismatic

Prismatic

Non-Prismatic


4.1 Slope-DeflectionSlope-Deflection Equations

End Distortion + Load

Mab = f (a , b , , Load)Mba = g (a , b , , Load)

(+)- (Mab , Mbc) - ( a , b ) - ()

Mab

Mba

ab

a bLoad


Mab Mba 4 a

b

Load Fixed-End Moments

LEI2

ML

EI4M aba

aab

=

= .......

LEI4

ML

EI2M bba

bab

=

= .......

2ba2ab LEI6

MLEI6

M

=

= '''''' .......

Maba

a b Mba

b = 0 , = 0

Mab ba b Mbaa = 0 , = 0

Mab a b

Mbaa = 0 , b = 0

MabF a b MbaFLoad

a = 0 , b = 0 = 0


Slope-Deflection

Fba2

baFbababababa

Fab2

baFababababab

MLEI6

LEI4

LEI2

MMMMM

MLEI6

LEI2

LEI4

MMMMM

+

+

=+++=

+

+

=+++=

'''

'''

Fbababa

Fabbaab

ML

32LEI2

M

ML

32LEI2

M

+

+=

+

+=

)(

)(


Moment 1 ( a )

- a Hinge - b Fixed EndConjugate Beam Rotation a (a) Condition 1) Moment Conjugate Beam a = 0

a = 02) Moment Conjugate Beam b = 0

b = 0

baMab

a Mba

a

MabEI Mba

EI

Elastic Load on Conjugate Beam


(1) (2)

... ...

=

=

=

=

20L3L

LEI

M21

3L2

LEI

M21

0M

03L2

LEI

M21

3L

LEI

M21

0M

abaab

b

baab

a

..........)()(

;

)()(

;

= 1M2M baab .............

.......L

EI2M

LEI4

M abaa

ab

=

=


Fixed-End MomentsP

L

L/28

PL8

PL WL12

WL2

12WL2

W

L

a

)( 2222

a3aL8L6L12

Wa+ )( a3L4

L12Wa

2

3

P

L

a2

2

LPab b

2

2

LbPa

ML

a)( a2b

LMb

2 b

)( ab2LMa

2

WL20

WL2

30WL2

W

L96WL5 2

96WL5 2

L/2

1

3

5

2

4

6

7


EX. Slope-Deflection ABCD

EI EI/2A800 kg.

4 m.

B C D

300 kg./m.

2 m. 2 m. 1 m.


1) Fixed End Moments

.. mkg40012

430012WL

M22

FAB =

=

=

.. mkg8008

480012

43008

PL12WL

M22

FBC =

=

=

EI EI/2A

800 kg.

4 m.

B C DW=300 kg./m.

2 m. 2 m. 1 m.

MABF MBAF MBCF MCBF

300 kg./m.A4 m.

BMABF MBAF

.. mkg40012WL

M2

FBA ==

300 kg./m.B CMBCF MCBF

800 kg.

2 m. 2 m... mkg800

8PL

12WL

M2

FCB =+=


2) Fixed End Moments Slope-Deflection () = 0

2 B C

4002EI

ML

32LEI2

M BF

ABBAAB =+

+= )(

400EIML

32LEI2

M BF

BABABA +=+

+= )(

80024EI

ML

32LEI2

M CBF

BCCBBC +=+

+= )()(

80024EI

ML

32LEI2

M CBF

CBCBCB ++=+

+= )()(


3) (2 )

MBA+ MBC= 0 MCB= 150 kg.-m.

4) 2 3

BMBA MBC

FBD. B

A C CMCB 150 kg.-m.

FBD. C

B D

=+++=+ 1080024EI

400EI0MM CBBBCBA ..........])([][...

=++= 215080024EI

150M CBCB .................................])([...


(2)

(1)

(3) (4)

=+ 3EI6002

2 CB ...................................................,

=+ 4EI6001

6 CB .......................................................,

., RadEI11

8005B = .

,Rad

EI1120017

C

=


5) 2

..,, mkg115001

400EI11

80052EI

4002EI

M BAB

===

..,, mkg1120010

400EI11

8005EI400EIM BBA =+=+=

800EI1120017

EI118005

24EI

80024EI

M CBBC =+= ),,()(

.., mkg11

20010

=

800EI1120017

2EI11

80054EI

80024EI

M CBCB +=++= ),,()(

.. mkg150 =


6) FBD.

MA = 1,500/11 kg.-m. RA = 4,425/11 kg.RB = 43,825/22 kg. RC = 24,325/22 kg.

300 kg./m.1,500/11 10,200/11

4,425/11 8,775/11

B8,775/11 26,275/22

300 kg./m.10,200/11 150

26,275/22 17,725/22

800 kg150

300A

1,500/11

RA RB

C17,725/22 300

RC


EX. Slope-Deflection 1. 2. BMD. ABCD ( EI )

A

100 kg. B C D300 kg./m.

2 m. 2 m.

2 m.

50 kg.-m.



,0MM FBAFAB == 0MM

FCB

FBC ==

.. mkg10012

230012WL

M22

FCD =

=

=

.. mkg10012

230012WL

M22

FDC =

==

300 kg./m.C2 m.

DMCDF MDCF

A

100 kg. B C DW

2 m. 2 m.

2 m.

50 kg.-m. MCDF MDCF

W = 300 kg./m.


2) Fixed End Moments Slope-Deflection (= 0)

2 B C

BF

ABBAAB EIML32

LEI2

M =+

+= )(

BF

BABABA EI2ML32

LEI2

M =+

+= )(

)()( CBF

BCCBBC 2EIML32

LEI2

M +=+

+=

)()( CBF

BCCBCB 2EIML32

LEI2

M +=+

+=

100EI2ML

32LEI2

M CF

CDDCCD =+

+= )(

100EIML

32LEI2

M CF

CDDCDC +=+

+= )(


3) (2 ) B C

MBA+ MBC= 50 MCB + MCD = 0

CMCB

FBD. C

B DMCD

BMBA MBC

FBD. B

A

C100 kg.50 kg.-m.


4) 2 3

(1) (2)

.RadEI3

20B = .RadEI3

70C =

=++=+ 1502EIEI250MM CBBBCBA ....................)(...

=++=+ 20100EI22EI0MM CCBCDCB ..............)(...


5) B C 2

../)/( mkg320EI320EIEIM BAB ===

../)()( mkg3110EI3

70EI3

202EI2EIM CBBC =+=+=

../)/( mkg340EI320EI2EI2M BBA ===

../)()( mkg3160EI3

702

EI320

EI2EIM CBCB =+=+=

../ mkg3160100EI3

70EI2100EI2M CCD ===

../ mkg3370100EI3

70EI2100EIM CDC =+=+=


6) FBD.

MA = 20/3 kg.-m. RA,x = 10 kg.RA,Y = 45 kg. RC = 310 kg.MD = 370/3 kg.-m. RA,x = 110 kg.RD,Y = 335 kg. 1

A

20/345

10

1045 40/3

B 10100 kg.

50 kg.-m.

40/3

110/3110

45

45

110/3110

45 160/3110

45C

RC=310

11011045 265 300 kg./m.

160/3 370/3265110

335110 D


7) (BMD.)

2

A

C DB

110/3

160/320/3

40/3

370/3

185/3

BMD(kg.-m.)

++

--

+-


4.2 Slope-Deflection Joint Translation

Joint Translation

......

...Frame ...

=0

=0


Frame Symmetry () Load ( Sway )

=0

Centerline

Centerline

Centerline


Joint Translation

Frame Symmetry Load Symmetry

...Frame ...

1

2


EX. Slope-Deflection ( EI )

A

P B C

D

10 ft.

20 ft.


1) Side Sway - 1 B C (1 DOF Joint Translation)


0MM0MM0MM FDCFCD

FCB

FBC

FBA

FAB ====== ,

A

P B C

D10 ft.

20 ft.


3) Fixed End Moments Slope-Deflection

3 B , C

)()( =++= 320200EI

ML

32LEI2

M BF

ABAB

BAAB

)()( =++= 3400200EI

ML

32LEI2

M BF

BAAB

BABA

)()( CBF

BCBC

CBBC 4080200EI

ML

32LEI2

M +=+

+=

)()( CBF

CBBC

CBCB 8040200EI

ML

32LEI2

M +=+

+=

)()( =++= 340200EI

ML

32LEI2

M CF

CDCD

DCCD

)()( =++= 320200EI

ML

32LEI2

M CF

DCCD

DCDC


4) (3 ) B C

MBA+ MBC= 0 MCB + MCD = 0 1

FBD. B

BMBA

MBC

A

CP

0P2

MM2

MM DCCDBAAB =++

++ )()(20MM BAAB /)( + 20MM DCCD /)( +

A

P B C

DMAB MDC

FBD. C

BMCD

MCB

D

C


5) 3 4

=+

=+=+

6EI

P4001126060

5031204040340120

CB

CB

CB

.................................................,......................................................................................................................

=++=+ 104080200EI

340200EI

0MM CBBBCBA .......)()(...

=++=+ 20340200EI

8040200EI

0MM CCBCDCB .......)()(...

201

340200EI

320200EI

0P2

MM2

MMBB

DCCDBAAB +=++

++ )]()([)()(

=+++ 30P201

320200EI

340200EI

CC ...................)]()([


(4) , (5) (6)

6) 3

Note (Anti-Symmetry) Unknown 1

( Yuan-Yu Hsieh)

.RadEI13P100

CB == .,

ftEI39

P0016=

13P70

EI39P0016

3EI13P100

20200EI

MAB

== ),(

13P60

EI39P0016

3EI13P100

40200EI

MBA

== ),(

13P60

EI13P100

40EI13P100

80200EI

MBC =+= )(

ABDCBACDBCCB MMMMMM === ;;



A

300 kg.

B C

D

2.5 m.

4 m.

600 kg./m.

1.5 m.

1.5 m.

1 m.


1) Sidesway B C

2) Fixed End MomentsA

300 kg.B C

D2.5 m.

600 kg./m.

4 m.1.5 m.

1.5 m.1 m.

A300 kg. B

MABF

MBAF

1.5 m.1.5 m.

C

600 kg./m.

BMBCF MCBF

2.5 m.

.... mkg531212

5260012WL

M22

FBC =

=

=

... mkg531212WL

M2

FCB ==

... mkg51128

33008PL

MFAB =

=

=

... mkg51128

33008

PLMFBA =

==

.. mkg0MM FDCFCD ==



4 B , C , D

51123EI2

ML

32LEI2

M BF

ABAB

BAAB .)()( =+

+=

511223EI2

ML

32LEI2

M BF

BAAB

BABA .)()( +=+

+=

531225EI4

ML

32LEI2

M CBF

BCBC

CBBC .)()( +=+

+=

531225EI4

ML

32LEI2

M CBF

CBBC

CBCB .)()( ++=+

+=

)()(4

32

2EI

ML

32LEI2

M DCF

CDCD

DCCD

+=+

+=

)()(4

32

2EI

ML

32LEI2

M DCF

DCCD

DCDC

+=+

+=


4) (4 ) B , C D

MBA+ MBC= 0 MDC = 0 MCB + MCD = 0

1

FBD. BBMBA

MBC

A

C

03004

MM3

450MM DCCDBAAB =++

++ )()(

351300MM BAAB /).( +

4MM DCCD /)( +

MDC

FBD. D

300 kg.

MAB MDC

600 kg./m.

FBD. CB

MCD

MCB

D

C


5) 3 4

=+++ 10531225EI4

511223EI2

CBB ...........)(.)(

=

++++ 204

32

2EI

531225EI4

DCCB ............)(.)(

31

450511223EI2

51123EI2

BB ++ ].)(.)([

=+

++

++ 3030041

43

22EI

43

22EI

DCDC .......)]()([

=

+ 404

32

2EI

DC .........................................................)(


(5) (8)

=+ 50003EI10EI12EI44 CB ...............................................,

=++ 650012EI20EI15EI104EI32 DCB .............................,

=++ 760021EI54EI91EI54EI96 DCB ...............................,

=+ 80EI8EI3EI4 DC ...........................................

.. RadEI

8244B =

.. mEI

3572=

.. RadEI

6170C

=

.RadEI

300D =


6) B , C , D 3

MAB = -330.9 kg.-m. MBA = 57.34 kg.-m. MBC = -57.34 kg.-m. MCB = 235.3 kg.-m. MCD = -235.3 kg.-m. MDC = 0 kg.-m.



A

BC

D

1.5 T.

/m.5 m.

10 m.E

12 m. 12 m.


1) Sidesway 1 2


A

BC

D

1.5 T.

/m.

5 m.

10 m.E

12 m. 12 m.

1 2

A1.5 T.

/m.

B

MABF

MBAF

10 m..... mT512

121051

12WL

M22

FAB =

=

=

... mT51212WL

M2

FBA ==

...sin. mT12531213

13551

M2

FBC =

=

B1.5

T./m.

MABF

MBAF

13 m.C

...sin. mT12531213

13551

M2

FCB =

=


3) Rotation 1 2

Rotation AB = Rotation BC =

Rotation CD = Rotation DE =

101 /

1013SIN21221 )( =

1013SIN22121 )( =

102 /

A

BC

D

1.5 T.

/m.

5 m.

10 m.E

12 m. 12 m.

1 2

1/10 2/10



51210

35EI

ML

32LEI2

M 1BF

ABAB

BAAB .)()(

=+

+=

51210

32

5EI

ML

32LEI2

M 1BF

BAAB

BABA .)()( +

=+

+=

125310

32

13EI2

ML

32LEI2

M 12CBF

BCBC

CBBC .])([)( +=++=

125310

32

13EI2

ML

32LEI2

M 12CBF

CBBC

CBCB .])([)( ++=++=

])([)(10

32

13EI2

ML

32LEI2

M 21DCF

CDCD

DCCD

+=+

+=

])([)(10

32

13EI2

ML

32LEI2

M 21DCF

DCCD

DCDC

+=+

+=


5 B , C , D , 1 2

5) (5 ) - B , C D

][)(10

32

10EI2

ML

32LEI2

M 2EDF

DEDE

EDDE

+=+

+=

][)(10

32

10EI2

ML

32LEI2

M 2EDF

EDDE

EDED

+=+

+=

=+= 10MM0M BCBAB ..........................................................;

=+= 20MM0M CDCBC ..........................................................;

=+= 30MM0M DEDCD ..........................................................;


HA HE

E

D

MED

MDEVD

VE

HE

HD010HMM0M EEDDED =++= ;

)( EDDEE MM101

H +=

1551HH0F EAX =+= .;

A1.5 T.

/m.

B

MAB

MBAVB

VA

HA

HB 05105110HMM0M ABAABB =++= .;

)(. BAABA MM101

57H +=

522MM101

MM101

57 EDDEBAAB .)()(. =++

=+++ 4150MMMM EDDEBAAB ....................................


VA VE

EDDECDE M241

M81

M121

V =

0VV0F EAY =+= ;

057155112V15HMM0M AACBABC =+++= ..;

CBBAABA M121

M81

M241

68754V ++= .

0M241

M81

M121

M121

M81

M241

68754 EDDECDCBBAAB =+++.

=+++ 505112MM3M2M2M3M EDDECDCBBAAB .............

A1.5

T./m. B

MAB

MCB

VA

HA

HCC

VC

12V15HMM0M EEEDCDC =++= ;

E

D

MED

MCD VC

VE

HE

HC C


6) Slope-Deflection 5

7) (6) (10)

=+ 638609EI3EI90EI10EI46 21CB .....................................

=++ 73120EIEI4EI DCB .........................................................

=+ 80EI90EI3EI46EI10 21DC .............................................

=+ 9250EI20EI20EIEI 21DB ............................................

=+ 1016120EI390EI390EIEI 21DB .....................................

.. RadEI3289

B =

.. mEI5612

1 =

.. RadEI

8655C

= .. Rad

EI8113

D =

.. mEI1010

2 =


8) 7 Slope-Deflection ( 4) MAB = -69.99 T.-m. MBA = -27.12 T.-m. MBC = 27.12 T.-m. MCB = 11.04 T.-m. MCD = -11.04 T.-m. MDC = 15.06 T.-m. MDE = -15.06 T.-m. MED = -37.82 T.-m.


EX. Slope-Deflection 1. B C 2. B 3. BMD ( EI )

A B

C D

9 m.2I

100 kN./m.

4 m.

6 m.

2I I


1) Sidesway

- AB CD AB = -CD = -vB

- BC BC = 0

2) 2

- B (B) - C (C)

A B

C D

9 m.2I

100 kN./m.

4 m.

6 m.

2I I

-AB

-CD

A B

C D

9 m.2I

100 kN./m.

4 m.

6 m.

2I I

B

C



4) Slope-Deflection ( 6 )

A D = 0

D

100 kg./m.C

MCDF MDCF

9 m.

.. mkg67512

910012WL

M22

FCD =

=

=

.. mkg67512WL

M2

FDC ==

.. mkg0MMMM FCBFBC

FBA

FAB ====

0EIv3330EI6670EI3331M BBAAB +++= ...0EIv3330EI3331EI6770M BBABA +++= ...

0EIv0000EI0001EI002M BCBBC +++= ...0EIv0000EI0002EI001M BCBCB +++= ...

675EIv0740EI2220EI4440M BDCCD += ...675EIv0740EI4440EI2220M BDCCD ++= ...


5) (3 )

MBA+ MBC= 0 MCB + MCD = 0

FBD. C

CMCB

MCD

B

D

FBD. BA

MCBMBA

C

B

A B

C D

9 m.2I

100 kN./m.

4 m.

6 m.

2I ICDDCCDABBAAB LMMLMM /)(/)( +++

0L1002L100 CDCD =+ )/(


6) 4 5

7) (1) , (2) (3)

1,2

=+++ 100EIv3330EI0001EI3333 BCB .................................

=+ 20675EIv0740EI4442EI0001 BCB ..............................

=+ 30450EIv1280EI0740EI3330 BCB ...........................

.. RadEI

1519B =

.., mEI

49334vB

=

.. RadEI

785C

=


8) 7 Slope-Deflection 4 MAB = -1,298.4 kN.-m. MBA = -952.4 kN.-m. MBC = 952.4 kN.-m.MCB = 347.7 kN.-m. MCD = -347.7 kN.-m. MDC = 1,021.4 kN.-m.

9)

3-1,298.4

-1,021.4

-347.7-347.7 952.4

952.4

356

BMD.(kN.-m.)

A B

C D


EX. Slope-Deflection 1. C D 2. C D 3. D ( EI )

A BC D

8 m.

60 kN.

4 m.

6 m. 6 m.E



.. mkN0MMMM FCEFEC

FDC

FCD ====

.. mkN908

12608PL

MFAC =

==

MCAFMACFA B

C D

8 m.

60 kN.

4 m.

6 m. 6 m.E

60 kNA

12 m.C

MACF MCAFB .. mkN908PL

MFCA ==


2) Fixed End Moments Slope-Deflection (= 0)

2 C D

90EI1670EI3330ML

32LEI2

M CAF

ACCAAC +=+

+= ..)(

90EI3330EI1670ML

32LEI2

M CAF

CACACA ++=+

+= ..)(

DCF

CDDCCD EI250EI50ML32

LEI2

M +=+

+= ..)(

DCF

DCCBDC EI50EI250ML32

LEI2

M +=+

+= ..)(

ECF

CEECCE EI50EIML32

LEI2

M +=+

+= .)(

ECF

ECECEC EIEI50ML32

LEI2

M +=+

+= .)(


3) (2 ) B C

MCA+ MCD+ MCE= 0 MDC = 0

4) 2 3

FBD. D

DMDC

FBD. C

MCA MCDC

MCE

=+ 190EI250EI8331 DC ................................................

=+ 20EI50EI250 DC ......................................................


5) (1) (2) 4

1

6) Slope-Deflection MAC = -98.8 kN.-m. MDC = 0 kN.-m. MCA = 72.4 kN.-m. MCE = -52.7 kN.-m. MCD = -19.8 kN.-m. MEC = -26.3 kN.-m. 2

7) D

3

.. RadEI

752C

= .. Rad

EI326

D =

CDYC M8D0M ==

.. kN472D Y =FBD. CD

DMCD CVCD

NCDDY

DX


EX. Slope-Deflection 1. B 2. B 3. A ( EI )

AB C

4 m.

10 kN./m.

3I

6 m.

I


1) Sidesway

- AB CD AB = BC = -

2) 1

- B (B)

A B C

4 m.

10 kN./m.

3I

6 m.

I

A B C

4 m.

10 kN./m.

3I

6 m.

I



4) Slope-Deflection ( 4 )

B

10 kN./m.A

MABF MBCF

6 m.

.. mkN3012

61012WL

M22

FAB =

=

=

.. mkN3012WL

M2

FBA ==

.. mkN0MM FCBFBC ==

30EI50EIML32LEI2M BFABABABBAABABAB =++= .)/(/

30EI50EI2ML32LEI2M BFBAABABBAABABBA +=++= .)/(/

0EI3750EIML32LEI2M BFBCBCBCCBBCBCBC ++=++= .)/(/

0EI3750EI50ML32LEI2M BFCBBCBCCBBCBCCB ++=++= ..)/(/


5) (2 )

MBA+ MBC= 0 VAB - VCB = (10)(6)

6) 4 5

= 130EI1250EI3 B ........................................................

FBD. BA

MBCMBACB

FBD.A

VCBVABCB

=+ 230EI3540EI1250 B ..................................................

BCCBBCCBABBAABAB LMMVL3610MMV /)(;/)( +=+=


7) (1) (2)

1,2

8) 7 Slope-Deflection ( 3) MAB = -77.8 kN-m. 3

.. RadEI

66B

= .. m

EI482

=

บทที่ 4 (slope-deflection) - civil...

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Deflection Testing marketing1.ppt

Structure Analysis I Chapter 9 - الصفحات الشخصيةsite.iugaza.edu.ps/malqedra/files/Chapter-9.pdf · Structure Analysis I Chapter 9. Deflection Energy MethodEnergy Method

Ver 4.0.0. 개정내용 2016(v1.1) Release Notesadmin.midasuser.com/UploadFiles2/74/SoilWorks 2016(v1.1...• Optimization method is introduced in slope stability analysis using LEM

Testof%Opcal%Stochasc%Cooling% in%CESRdlr/osc/documentation/... · 2017-09-13 · deflection from the s axis Therefore, the peak angular deflection is Define the deflection parameter

บทที่ 2 Slope-Deflection Methodeng.sut.ac.th/ce/oldce/anapptpdf50/analysis2.pdf · · 2007-12-189 10 2.2 Slope-Deflection Equations ความสัมพันธ ระหว

Policy とDeflection...2. Deflection Type をEnable Real Time Deflection にする。 Part 1: Policy とDeflection の活用 10 / 13 紀伊國屋書店 OCLC センター修正が必要な例3

Analisis Struktur Statis Tak Tentu dengan Metode Slope-Deflection · a home base to excellence Analisis Portal Tak Bergoyang Metode Slope-Deflection Example 11.7 Tentukan momen pada

6.6 EULER’S METHOD - McGraw Hill · PDF fileHowever, Euler’s method does not provide particularly accu- ... equation tells us that the slope of the tangent line to the solution

Chapter 10: Deflection of beam (Ch. 12 in Shames) 9... · 2019. 9. 5. · Chapter 10: Deflection of beam ... - Differential equations for deflection of symmetric beams - Statically

DISPLACEMENT METHOD OF ANALYSIS: SLOPE DEFLECTION …austin/ence353.d/lecture-material2014/Slope... · 1! e! ents! on! nts Span! s Beams! ay! ay DISPLACEMENT METHOD OF ANALYSIS: SLOPE

Especificação Técnica de Projeto N.º 002 002.pdf · ASTM D 648 standard Test Method for Deflection Temperature of Plastics Under Flexural Load in the Edgewise Position

Slope Deflection Method

2. (principle and method of procedure used for examinations) · Linear method C 0 = คา intercept = b, C 1 = slope = m, delta Abs = คาการดูดกลืนแสงจากการตรวจวัดคาของตัวอยางตรวจ

Deflection Expose - 025

SISTEM PENGENDALIAN SUSPENSI SEMI-AKTIF ...repository.its.ac.id/76260/1/2114105048-Undergraduate...Supensi deflection m Zb−Zu conector deflection m Zu−Zr Tire deflection m Ż u−Żr

Buckling of Rigid Frames – I - UMass Lowellfaculty.uml.edu/.../documents/SS_LN06_0228_Bucklingofrigidframes-I.pdfBuckling of Rigid Frames – I ... Slope Deflection Method • Slope

Slope Deflection Bergoyang

Analisis Struktur Statis Tak Tentu dengan Metode Slope ... · PDF filea home base to excellence Analisis Struktur Statis Tak Tentu dengan Metode Slope-Deflection Pertemuan - 12 Mata

DISPLACEMENT METHOD OF ANALYSIS: SLOPE ......2011/11/03 · DISPLACEMENT METHOD OF ANALYSIS: SLOPE DEFLECTION EQUATIONS 2 Slope Œ Deflection Equations settlement = ∆j i P j k w

MODUL 3 : METODA “ Slope Deflection” 3.1. Judul : Metoda ... · struktur statis tidak tertentu. 3.1.2. Perumusan Momen Batang Momen batang dapat ditimbulkan dengan adanya beban

An Improved Deflection Energy Method to Normalise … · deflection energy versus deflection for the thorax are of constant slope. The deflection energy is the ... using a deflection

Slope Stability Analysis Using Graphical Method تبسيط الطريقة البيانية في تحليل المنحدرات الصخرية

Metode Slope Deflection

Estimation of Scale and Slope Information for …yamashita/paper/B/B191Final.pdfOverview of proposed method. Firstly, original 3D map that has no absolute slope and scale information

RANCANG BANGUN DAN ANALISA STRUKTURMESIN …/Rancan… · melalui gaya geser momen lentur yang muncul akibat beban yang diberikan pada rangka menggunakan metode slope deflection yang

Deflection and member deformation

METODA SLOPE DEFLECTION · Balok AB yang merupakan elemen dari sebuah struktur yang lengkap, akibat beban luar yang bekerja akan berdeformasi seperti tergambar ( mengalami rotasi

TAM 251 EQUATION SHEETmechref.engr.illinois.edu/sol/FormulaSheet.pdfTAM 251 Equation Sheet Page 2 Apr. 2019. Beam Deflection Diagram Max. Deflection Slope at End Elastic Curve ymax

Mechanics of Materials - Memphis Deflection by... · Mechanics of Materials CIVL 3322 / MECH 3322 ... slope, and deflection curves identifying the maximum, minimum, and zero points

07- ASSTT- Metode Slope- Deflection

03b slope deflection 2 SWAY.pdf

Resolución Problema Slope Deflection

إ - مجلس الخدمة المدنية · Web viewStatically indeterminate beams, 3 moments equation. Truss. Deflection of structures: Virtual work method Castigliano’s 2nd theorem

DISPLACEMENT METHOD OF ANALYSIS: SLOPE … e! ents! on! nts Span! s Beams! ay! ay DISPLACEMENT METHOD OF ANALYSIS: SLOPE DEFLECTION EQUATIONS

Rock Slope Stability Analysis: Limit Equilibrium Method