perhitungan portal metode cross

7/25/2019 perhitungan portal metode cross

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I Balok :

b = 20 cm = 0.20 mh = 40 cm = 0.40 m

1/12*b*h^3 = 1/12*0.20*(0.40)^3 = 0.001066667

I Kolom :

b = 30 cm = 0.30 m

h = 20 cm = 0.20 m

1/12*b*h^3 = 1/12*0.30*(0.20)^3 = 0.0002

Faktor Kekakuan

Titik B

Kba = 5*EI(kolom)/L = 5*EI*0.0002/5 = 0.0002

Kbc = 5*2*EI(balok)/L = 5*2*E*0.001067/5 = 0.002134

0.002334

Titik C

Kcd = 5*EI(kolom)/L = 5*EI*0.0002/5 = 0.0002

Kcb = 5*2*EI(balok)/L = 5*2*E*0.001067/5 = 0.002134

0.002334

Faktor Distribusi

Kb =

Kc =


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Titik B

ba = Kba/Kb = 0.0002/0.00233 = 0.085689803

0.914310197

1

Titik C

cd = Kcd/Kc = 0.0002/0.00233 = 0.085689803

0.914310197

1

Momen rimer

B. Perhitungan Koefsien Distribusi

bc = Kbc/Kb = 0.00213/0.00233 =

Kontrol b= ba! bc=

cb= Kcb/Kc = 0.00213/0.00233 =

Kontrol b= ba! bc=


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Titik Simpul A

mAB = 0

Titik Simpul D

mDC = 0


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Titik Simpul B

Titik Simpul C

c. Pr!"! di!tribu!i mm"# $ Cr!! %


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d. P"r&itu#'a# (m"# D"!ai#

Kar"#a k#di!i b"ba# da# ra#'ka !im"tri!) maka dia#ali!i! Prtal

u#tuk itula& pr!"! di!tribu!i mm"# $cr!!% &a#*a !atu kali *ait

+ar'a mm"# d"!ai# !ama d"#'a# &ar'a cr!! dari b"ba# luar $l

(AB = -23. k'.m(BA = 2. k'.m

(BC = -2. k'.m

(CB = 2. k'.m

(CD = -2. k'.m

(DC = 23. k'.m

l. Free Bod untuk Perhitungan !eaksi Perletakan

Bata#' AB Bata#' CD

S(B = 0 C+ = -

A+ =$00.2%$23)5%-$2)%6/$% = 12.2k' ' D+ = -

S+ = 0

A+ B+ = P

B+ = P - A+ = 415.5k' '

Bata#' BC

S(C = 0

B7 =$300../2%$2)%-$2)%6/=$% 50.00k' '

S+ = 0

B7 C7 = 8

C7 = 8 - B7 = 50.00k' '


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m. Perhitungan "omen# $aa %intang dan $aa &ormal

Pt#'a# AB i#t"r9al Pt#'a#(:1 =A+.; - (AB 0 < ; < 2 (: = B7.

D:1 = A+ D: = B7

>:1 = - A7 = B7 >: = - B

(:2 =A+.$3;% - P.; - (AB 0 < ; < 3

D:2 = A+ - P

>:2 = - A7

Potongan 'B Potongan


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ta#pa P"r'*a#'a#.

akibat b"ba# luar $ta#pa p"r'*a#'a#%.

li&at ,umla& mm"# dari pr!"! cr!!%.

+= -12.3k' '

+= -415.5k' '


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BC i#t"r9al- 1/2.2. -: (BC 0 < ; <

.:

BC


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IIK ! " #

#!"!$% !" "! "# #" #&

'.&II"I 0.0000 0.0850 0.9140 0.0850 0.9140

'.I$&KI 0.5000 0.5000 0.5000 0.5000

+.,I+E -2.8800 4.3200 -6.2500 6.2500 -4.3200

+.,EL!!$!$ 0.0587 0.6316 -0.1641 -1.7640

+.I$&KI 0.0294 -0.0820 0.3158+.,EL!!$!$ 0.0070 0.0750 -0.0268 -0.2886

+.I$&KI 0.0035 -0.0134 0.0375

+.,EL!!$!$ 0.0011 0.0123 -0.0032 -0.0343

+.I$&KI 0.0006 -0.0016 0.0061

+.,EL!!$!$ 0.0001 0.0015 -0.0005 -0.0056

+.I$&KI 0.0001 -0.0003 0.0007

+.,EL!!$!$ 0.0000 0.0002 -0.0001 -0.0007

+.I$&KI 0.0000 0.0000 0.0001

+.,EL!!$!$ 0.0000 0.0000 0.0000 -0.0001

+.I$&KI 0.0000 0.0000 0.0000

+.,EL!!$!$ 0.0000 0.0000 0.0000 0.0000 0.0000

+.!KI -2.8464 4.3870 -5.6268 6.4156 -6.4133


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D

0.0000

2.8800

-0.20

-0.1443

-0.0151

-0.002

-0.0003

-0.0001

0.0000

1.333

-0.1

1.3


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1 +itu#'la& Prtal Tak B"r'*a#' b"rikut i#i d"#'a# ("td"

Di!tribu!i mm"#) Slp" D"?"cti#) da# (D>

Faktor Kekakuan

Titik B

Kba = 4*EI/L = 4*EI/5 = 0.

Kbc = 4*2*EI/L = 4*2EI*/5 = 1.

2.4

Titik C

Kcd = 4*EI/L = 4*EI/5 = 0.

Kcb = 4*2EI/L = 4*2EI*/5 = 1.

2.4

Faktor Distribusi

Titik B

ba = Kba/Kb = 0./2.4= 0.3333333333

0.6666666667

1

Titik C

cd = Kcd/Kc = 0./2.4 = 0.3333333333

0.6666666667

1

Momen rimer

Titik "

+ab = -,ab/L = -6*3*2/5 = -2.88 .m

+ab = -2.88 .m

Kb =

Kc =

bc = Kbc/Kb = 1./1. =

Kontrol b= ba! bc=

cb= Kcb/Kc = 1./2.4 =

Kontrol b= ba! bc=


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Titik B

+ba = ,ab/L = 6*3*2/5 = 4.23 .m

+bc = -L/12 = -3*5/12 = -6.25 .m

+ba +bc = -2.02 m

Titik C

+cb = L/12 = 3*5/12 = 6.25 .m

+cd = -,ab/L = -6*3*2/5 = -4.32 .m

+cb +cd = 1.93 .m

Titik D

+dc = ,ab/L = 6*3*2/5 = 2. .m

+dc = 2. t.m

Titik Simpul B


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Titik Simpul C

Tabel Distribusi Momen

IIK ' B C

#!"!$% AB BA BC CB CD

'.&II"I 0.00 0.33 0.67 0.67 0.33

'.I$&KI 0.00 0.50 0.50 0.50 0.50

+.,I+E -2.88 4.32 -6.25 6.25 -4.32

+.,EL!!$!$ 0.00 0.64 1.29 -1.29 -0.64

+.I$&KI 0.32 0.00 -0.64 0.64 0.00

+.,EL!!$!$ 0.00 0.21 0.43 -0.43 -0.21

+.I$&KI 0.11 0.00 -0.21 0.21 0.00

+.,EL!!$!$ 0.00 0.07 0.14 -0.14 -0.07

+.I$&KI 0.04 0.00 -0.07 0.07 0.00

+.,EL!!$!$ 0.00 0.02 0.05 -0.05 -0.02

+.I$&KI 0.01 0.00 -0.02 0.02 0.00

+.,EL!!$!$ 0.00 0.01 0.02 -0.02 -0.01

+.I$&KI 0.00 0.00 -0.01 0.01 0.00

+.,EL!!$!$ 0.00 0.00 0.01 -0.01 0.00

+.I$&KI 0.00 0.00 0.00 0.00 0.00

+.,EL!!$!$ 0.00 0.00 0.00 0.00 0.00

+.!KI -2.40 5.28 -5.28 5.28 -5.28

d. Perhitungan "omen Desain


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Kar"#a k#di!i b"ba# da# ra#'ka !im"tri!) maka dia#ali!i! Prtal ta#pa P"r'*a#'a#.

u#tuk itula& pr!"! di!tribu!i mm"# $cr!!% &a#*a !atu kali *aitu akibat b"ba# luar $ta

+ar'a mm"# d"!ai# !ama d"#'a# &ar'a cr!! dari b"ba# luar $li&at ,umla& mm"# da

(AB = -23. k'.m

(BA = 2. k'.m

(BC = -2. k'.m

(CB = 2. k'.m(CD = -2. k'.m

(DC = 23. k'.m

l. Free Bod untuk Perhitungan !eaksi Perletakan

Bata#' AB Bata#' CD

S(B = 0 C+ = - B+= -12.3k' '

A+ =$00.2%$23)5%-$2)%6/$% = 12.2k' ' D+ = - A+= -415.5k' '

S+ = 0

A+ B+ = P

B+ = P - A+ = 415.5k' '

Bata#' BC

S(C = 0

B7 =$300../2%$2)%-$2)%6/=$% 50.00k' '

S+ = 0

B7 C7 = 8

C7 = 8 - B7 = 50.00k' '


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m. Perhitungan "omen# $aa %intang dan $aa &ormal

Pt#'a# AB i#t"r9al Pt#'a# BC

(:1 =A+.; - (AB 0 < ; < 2 (: = B7.: - 1/2.2. -: (BCD:1 = A+ D: = B7 - .:

>:1 = - A7 = B7 >: = - B+

(:2 =A+.$3;% - P.; - (AB 0 < ; < 3

D:2 = A+ - P

>:2 = - A7

Potongan 'B

(nter)al

0 < ; < 2

0 < ; < 3

Potongan BC (nter)al

0 < ; <


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D

DC

0.00

0.00

2.88

0.00

-0.32

0.00

-0.11

0.00

-0.04

0.00

-0.01

0.00

0.00

0.00

0.00

0.00

2.40


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pa p"r'*a#'a#%.

i pr!"! cr!!%.


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i#t"r9al

0 < ; <

* "* D* &*

0 -2.40 1.2 -5.0

1 -0. 1.2 -5.0

2 1.2 1.2 -5.0

3 3.05 1.2 -5.0

0 3.05 -4.15 -5.0

1 -1.10 -4.15 -5.0

2 -.2 -4.15 -5.0

* "* D* &*

0 -.2 5.0 -4.15

1 -1.1 .00 -4.15


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1 0.51 4.0 -4.15

2 2. 3.00 -4.15

2 3.51 1.0 -4.15

3 4.0 0.00 -4.15

3 3.51 -1.0 -4.15

4 2. -3.00 -4.15

4 0.51 -4.0 -4.15 -1.1 -.00 -4.15

-.2 -5.0 -4.15


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@


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perhitungan portal metode cross

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