Cara Perhitungan Kolom Balok Plat Xls

PERHITUNGAN PLAT LANTAI SLAB! P)%T )T&' &% %'%( TWO WAY SLAB

A. DATA BAHAN STRUKTUR Kuat tekan beton, Tegangan leleh baja untuk tulangan lentur,

 78 =  y =

#5 240

MPa MPa

)x = )y = h=

4.00 5.00 150

m m mm

B. DATA PLAT LANTAI Panjang bentang plat arah x, Panjang bentang plat arah y, Tebal plat lantai, Koei!ien momen plat untuk "

)y * )x =

1.25 KOEFISIEN MOMEN PLAT &% %'%( karena )y*)x+2 9lx = )apangan x 20 9ly = )apangan y 23 9tx = Tumpuan x 4 9ty = Tumpuan y 5 Tabe( % )en*an $ sisi ter+e,it

Æ = t! =

iameter tulangan yang /igunakan, Tebal ber!ih !elimut beton,

12 20

C. BEBAN PLAT LANTAI ". BEBAN MATI  DEAD LOAD!

o 1 2 #

Jenis Beban Mati

;erat !en/iri plat lantai k*m# ;erat finishing lantai k*m# ;erat plaon /an rangka k*m2

Berat satuan

24.0 22.0 0.2

Tebal m 0.15 0.05 

: k*m2 #.00 1.100 0.200

mm mm

4

;erat in!tala!i M k*m2 Total beban mati, %. BEBAN HIDUP  LIVE LOAD!

0.5



: =

;eban hi/up pa/a lantai bangunan =

:) =

0.500 5.400

#00 #.0

kg*m2 k*m2

11.230

k*m2

#.10 5.05# 11.551 10.1011.551

km*m km*m km*m km*m km*m

#. BEBAN RENCANA TERFAKTOR

;eban ren7ana teraktor,

:u = 1.2 ? : @ 1. ? :) =

$. MOMEN PLAT AKIBAT BEBAN TERFAKTOR

Momen lapangan arah x, Momen lapangan arah y, Momen tumpuan arah x, Momen tumpuan arah y, Momen ren7ana mak!imum plat,

Mulx = 9lx ? 0.001 ? :u ? )x2 = Muly = 9ly ? 0.001 ? :u ? )x2 = Mutx = 9tx ? 0.001 ? :u ? )x2 = Muty = 9ty ? 0.001 ? :u ? )x2 = Mu =

D. PENULANGAN PLAT

b1 =  b1 = 0.35  0.05 ?   78  #0 * - = 0.314235-14 aktor bentuk /i!tribu!i tegangan beton, 0.314235-14 1 = &ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,

'a!io tulangan pa/a kon/i!i balance,

rb = b1? 0.35 ?  78*  y ? 00 *  00 @  y  =

0.0-21

aktor tahanan momen mak!imum,

'max = 0.-5 ? rb ?  y ? B 1 C D? 0.-5 ? rb ?  y *  0.35 ?  78 E = f = aktor re/uk!i kekuatan lentur, /! = t! @ Æ * 2 = >arak tulangan terha/ap !i!i luar beton, / = h  /! = Tebal eekti plat lantai, b= itinjau plat lantai !elebar 1 m, Mn = Mu * f = Momen nominal ren7ana, 'n = Mn ? 10 *  b ? / 2  = aktor tahanan momen,

10.14-1 0.30 2.0 124.0 1000 14.4#3 0.<#<02

mm mm mm km

'n

+

'max

OK!

'a!io tulangan yang /iperlukan "

r = 0.35 ?  78 *  y ? B 1  B 1 C 2 ? 'n *  0.35 ?  78  E = 0.0040 rmin = 'a!io tulangan minimum, 0.0025 r= 'a!io tulangan yang /igunakan, 0.0040 %! = r * b ? / = )ua! tulangan yang /iperlukan, 4<# ! = p * 4 ? Æ2 ? b * %! = >arak tulangan yang /iperlukan, 22< !max = 2 ? h = >arak tulangan mak!imum, #00 !max = >arak tulangan mak!imum, 200 != >arak !engkang yang haru! /igunakan, 200 != iambil jarak !engkang " 200 & 12 200 igunakan tulangan, %! = p * 4 ? Æ2 ? b * ! = )ua! tulangan terpakai, 55

mm2 mm mm mm mm mm mm2

E. KONTROL LENDUTAN PLAT Mpa = *mm2 7 = 4-00?  78 = Mo/ulu! ela!ti! beton, 2-30 ! = 2.10@05 Mo/ulu! ela!ti! baja tulangan, : = : @ :) = ;eban merata tak teraktor pa/aplat, 3.400 )x = Panjang bentang plat, 4000 )x * 240 = ;ata! len/utan mak!imum yang /iijinkan, 1.Fg = 1*12 ? b ? h# = 231250000 Momen iner!ia brutto penampang plat,  r = 0.- ? 78 = 4.141255343 Mo/ulu! keruntuhan lentur beton, n = ! * 7 = ilai perban/ingan mo/ulu! ela!ti!, -.55 7 = n ? %! * b = >arak gari! netral terha/ap !i!i ata! beton, 4.2-1 Momen iner!ia penampang retak yang /itran!orma!ikan ke beton /ihitung !bb. " F7r = 1*# ? b ? 7# @ n ? %! ?  /  7  2 = 1243#05 yt = h * 2 = -5 M7r =  r ? Fg * yt = 1552<-0< Momen retak " Momen mak!imum akibat beban tanpa aktor beban " Ma = 1 * 3 ? : ? ) x2 = 1300000 Fner!ia eekti untuk perhitungan len/utan, Fe =  M7r * Ma # ? Fg @ B 1   M 7r * Ma # E ? F7r = 2#502#55 )en/utan ela!ti! !eketika akibat beban mati /an beban hi/up "

MPa MPa *mm mm mm mm# MPa mm mm4 mm mm mm mm4

de = 5 * #34 ? : ? ) x4 *  7 ? Fe  = r = %! *  b ? /  =

4.235 mm 'a!io tulangan !lab lantai " 0.004 aktor ketergantungan Haktu untuk beban mati jangka Haktu A 5 tahun, nilai " z= 2.0 l = z *  1 @ 50 ? r  = 1.23 )en/utan jangka panjang akibat rangkak /an !u!ut " dg = l ? 5 * #34 ? : ? ) x4 *  7 ? Fe  = .<-3 mm dtot = de @ dg = )en/utan total, 11.2# mm dtot )x * 240 ≤ $yarat " + AMAN OK! 11.2# 1.-

PERHITUNGAN BALOK LANTAI BEAM !

A. DATA BALOK LANTAI BAHAN STRUKTUR

Kuat tekan beton, Tegangan leleh baja /eorm untuk tulangan lentur, Tegangan leleh baja polo! untuk tulangan ge!er,

 78 =  y =  y =

2< 400 240

MPa MPa MPa

b= h= = P= t! =

00 50 22 1# -0

mm mm

#.1-0 141.##4 1-0.554

km km k

DIMENSI BALOK

)ebar balok Tinggi balok iameter tulangan /eorm yang /igunakan, iameter !engkang polo! yang /igunakan, Tebal ber!ih !elimut beton,

mm mm mm

MOMEN DAN GA'A GESER RENCANA

Momen ren7ana po!iti akibat beban teraktor, Momen ren7ana negati akibat beban teraktor, Iaya ge!er ren7ana akibat beban teraktor,

Mu@ = Mu  = Ju =

B. PERHITUNGAN TULANGAN

b1 = b1 = 0.35  0.05 ?   78  #0 * - = aktor bentuk /i!tribu!i tegangan beton, 1 = &ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,

0.35  0.35


rb = b1? 0.35 ?  7L*  y ? 00 *  00 @  y  =

0.0#14


'max = 0.-5 ? rb ?  y ? B1 C D?0.-5? rb ?  y *  0.35 ?  7L  E = f = aktor re/uk!i kekuatan lentur, /! = t! @ Æ @ *2 = >arak tulangan terha/ap !i!i luar beton, n! =  b  2 ? / ! *  25 @   = >umlah tulangan /lm !atu bari!, n! = igunakan jumlah tulangan /alam !atu bari!,

-.254 0.30 <4.00 3.-3

bh

##.-1 4-.00

mm mm

-3.<2 -0 530.00 0.#<12

km mm mm

mm

>arak hori!ontal pu!at ke pu!at antara tulangan,

x =  b  n ! ?   2 ? / !  *  n!  1  = y =  @ 25 = >arak ertikal pu!at ke pu!at antara tulangan, ". TULANGAN MOMEN POSITIF

Mn = Mu * f = Momen po!iti nominal ren7ana, /8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, / = h  /8 = Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = aktor tahanan momen, @

'n

+

'max

OK!


r = 0.35 ?  7L *  y ? B 1  ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.000<< rmin =  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##rmin = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 r= 'a!io tulangan yang /igunakan, 0.00#50 %! = r ? b ? / = )ua! tulangan yang /iperlukan, 1213 2 n = %! *  p * 4 ?   = >umlah tulangan yang /iperlukan, #.204 4  22 igunakan tulangan, %! = n ? p * 4 ? 2 = )ua! tulangan terpakai, 1521

mm2

mm2

nb = n * n! =

0.50

/8 = S B ni ? yi E * n =

<4.00

>umlah bari! tulangan,

nb ;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi

4 <4.00 0 0.00 0 0.00 S [ ni ? yi E = n= 4 )etak titik berat tulangan, A <4.00 Tinggi eekti balok, Momen nominal, Tahanan momen balok, f ? Mn $yarat " 20.523

#-.00 0.00 0.00 #- -0

,eriraan (a*i )/ NG!

/ = h  /8 = a = %! ?  y *  0.35 ?  78 ? b  = Mn = %! ?  y ?  /  a * 2  ? 10  = f ? Mn = Mu@ ≥

A

mm

#.1-0

55.00 41.12# #25.0 20.523

mm mm km km

AMAN OK!

%. TULANGAN MOMEN NEGATIF

Mn = Mu * f = Momen negati nominal ren7ana, /8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, / = h  /8 = Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = aktor tahanan momen, 

'n

+

'max

1-.50 00.00 0.31-<

km mm mm

OK!


r = 0.35 ?  7L *  y ? B 1  ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.00203 rmin =  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##r min = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 r= 'a!io tulangan yang /igunakan, 0.00#50 %! = r ? b ? / = )ua! tulangan yang /iperlukan, 120 n = %! *  p * 4 ? 2  = >umlah tulangan yang /iperlukan, #.#15 4  22 igunakan tulangan, %! = n ? p * 4 ? 2 = )ua! tulangan terpakai, 1521 nb = n * n! = >umlah bari! tulangan, 0.50

mm2

mm2

nb

;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi


#-.00 0.00 0.00 #-

/8 = S B ni ? yi E * n = 50

mm


/ = h  /8 = a = %! ?  y *  0.35 ?  78 ? b  = Mn = %! ?  y ?  /  a * 2  ? 10  = f ? Mn = Mu ≥

A

<4.00

141.##4

55.0 41.12# #25.0 20.523

mm mm km km

AMAN OK!

#. TULANGAN GESER

Iaya ge!er ultimit ren7ana, aktor re/uk!i kekuatan ge!er, Tegangan leleh tulangan ge!er, Kuat ge!er beton, Tahanan ge!er beton,

Ju = f=  y = J7 =   78 *  ? b ? / ? 10 # = f * J7 =

1-0.554 0.0 240 #12.#40 13-.404

k MPa k k

Han0a ,er(u tu(.*eser 1in

f * J! = Ju  f * J7 = Tahanan ge!er !engkang,  J! = 1-0.554 Kuat ge!er !engkang, 2 P 1# igunakan !engkang berpenampang " % = n! ? p * 4 ? P2 = )ua! tulangan ge!er !engkang, 25.4 ! = % ?  y ? / *  J! ? 10#  = >arak !engkang yang /iperlukan " 21. !max = / * 2 = >arak !engkang mak!imum, 2-3.00 !max = >arak !engkang mak!imum, 250.00 != >arak !engkang yang haru! /igunakan, 21.

k k mm2 mm mm mm mm

iambil jarak !engkang " igunakan !engkang,

!= 2

P

1#

210

210

mm

PERHITUNGAN BALOK LANTAI BEAM !

A. DATA BALOK LANTAI BAHAN STRUKTUR

Kuat tekan beton, Tegangan leleh baja /eorm untuk tulangan lentur, Tegangan leleh baja polo! untuk tulangan ge!er,

 78 =  y =  y =

2< 400 240

MPa MPa MPa

b= h= = P= t! =

00 50 22 1# -0

mm mm

#.1-0 141.##4 1-0.554

km km k

DIMENSI BALOK

)ebar balok Tinggi balok iameter tulangan /eorm yang /igunakan, iameter !engkang polo! yang /igunakan, Tebal ber!ih !elimut beton,

mm mm mm

MOMEN DAN GA'A GESER RENCANA

Momen ren7ana po!iti akibat beban teraktor, Momen ren7ana negati akibat beban teraktor, Iaya ge!er ren7ana akibat beban teraktor,

Mu@ = Mu  = Ju =

B. PERHITUNGAN TULANGAN

b1 = b1 = 0.35  0.05 ?   78  #0 * - = aktor bentuk /i!tribu!i tegangan beton, 1 = &ntuk "  78 ≤ #0 MPa, &ntuk "  78 A #0 MPa,

0.35  0.35


rb = b1? 0.35 ?  7L*  y ? 00 *  00 @  y  =

0.0#14


'max = 0.-5 ? rb ?  y ? B1 C D?0.-5? rb ?  y *  0.35 ?  7L  E = f = aktor re/uk!i kekuatan lentur, /! = t! @ Æ @ *2 = >arak tulangan terha/ap !i!i luar beton, n! =  b  2 ? / ! *  25 @   = >umlah tulangan /lm !atu bari!, n! = igunakan jumlah tulangan /alam !atu bari!,

-.254 0.30 <4.00 3.-3

bh

##.-1 4-.00

mm mm

-3.<2 -0 530.00 0.#<12

km mm mm

mm

>arak hori!ontal pu!at ke pu!at antara tulangan,

x =  b  n ! ?   2 ? / !  *  n!  1  = y =  @ 25 = >arak ertikal pu!at ke pu!at antara tulangan, ". TULANGAN MOMEN POSITIF

Mn = Mu * f = Momen po!iti nominal ren7ana, /8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, / = h  /8 = Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = aktor tahanan momen, @

'n

+

'max

OK!


r = 0.35 ?  7L *  y ? B 1  ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.000<< rmin =  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##rmin = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 r= 'a!io tulangan yang /igunakan, 0.00#50 %! = r ? b ? / = )ua! tulangan yang /iperlukan, 1213 2 n = %! *  p * 4 ?   = >umlah tulangan yang /iperlukan, #.204 4  22 igunakan tulangan, %! = n ? p * 4 ? 2 = )ua! tulangan terpakai, 1521

mm2

mm2

nb = n * n! =

0.50

/8 = S B ni ? yi E * n =

<4.00

>umlah bari! tulangan,

nb ;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi


#-.00 0.00 0.00 #- -0


/ = h  /8 = a = %! ?  y *  0.35 ?  78 ? b  = Mn = %! ?  y ?  /  a * 2  ? 10  = f ? Mn = Mu@ ≥

A

mm

#.1-0

55.00 41.12# #25.0 20.523

mm mm km km

AMAN OK!

%. TULANGAN MOMEN NEGATIF

Mn = Mu * f = Momen negati nominal ren7ana, /8 = iperkirakan jarak pu!at tulangan lentur ke !i!i beton, / = h  /8 = Tinggi eekti balok, 'n = Mn ? 10 *  b ? / 2  = aktor tahanan momen, 

'n

+

'max

1-.50 00.00 0.31-<

km mm mm

OK!


r = 0.35 ?  7L *  y ? B 1  ? B1 C 2 ? 'n *  0.35 ?  7L  E = 0.00203 rmin =  78 *  4 ?  y  = 'a!io tulangan minimum, 0.00##r min = 1.4 *  y = 'a!io tulangan minimum, 0.00#50 r= 'a!io tulangan yang /igunakan, 0.00#50 %! = r ? b ? / = )ua! tulangan yang /iperlukan, 120 n = %! *  p * 4 ? 2  = >umlah tulangan yang /iperlukan, #.#15 4  22 igunakan tulangan, %! = n ? p * 4 ? 2 = )ua! tulangan terpakai, 1521 nb = n * n! = >umlah bari! tulangan, 0.50

mm2

mm2

nb

;ari! ke 1 2 #

-

#

OK!

>umlah

>arak

>uml. >arak

ni

yi

ni ? yi


#-.00 0.00 0.00 #-

/8 = S B ni ? yi E * n = 50

mm


/ = h  /8 = a = %! ?  y *  0.35 ?  78 ? b  = Mn = %! ?  y ?  /  a * 2  ? 10  = f ? Mn = Mu ≥

A

<4.00

141.##4

55.0 41.12# #25.0 20.523

mm mm km km

AMAN OK!

#. TULANGAN GESER

Iaya ge!er ultimit ren7ana, aktor re/uk!i kekuatan ge!er, Tegangan leleh tulangan ge!er, Kuat ge!er beton, Tahanan ge!er beton,

Ju = f=  y = J7 =   78 *  ? b ? / ? 10 # = f * J7 =

1-0.554 0.0 240 #12.#40 13-.404

k MPa k k

Han0a ,er(u tu(.*eser 1in

f * J! = Ju  f * J7 = Tahanan ge!er !engkang,  J! = 1-0.554 Kuat ge!er !engkang, 2 P 1# igunakan !engkang berpenampang " % = n! ? p * 4 ? P2 = )ua! tulangan ge!er !engkang, 25.4 ! = % ?  y ? / *  J! ? 10#  = >arak !engkang yang /iperlukan " 21. !max = / * 2 = >arak !engkang mak!imum, 2-3.00 !max = >arak !engkang mak!imum, 250.00 != >arak !engkang yang haru! /igunakan, 21.

k k mm2 mm mm mm mm

iambil jarak !engkang " igunakan !engkang,

!= 2

P

1#

210

210

mm

Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi

ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham

K6 K6)6M

K2

INPUT DATA KOLOM

 78 = 20 MPa  y = #<0 MPa b = 250 mm h = 250 mm /! = 40 mm n = 4 buah  = 1< mm

Kuat tekan beton, Tegangan leleh baja, )ebar kolom, Tinggi kolom, Tebal brutto !elimut beton, >umlah tulangan, iameter tulangan, PERHITUNGAN DIAGRAM INTERAKSI

! = untuk 78 £ #0 MPa untuk 78 A #0 MPa N1 = %! = n ? p * 4 ? 2 = x = h  2?/! = r = %! * %g =

Mo/ulu! ela!ti! baja, = 0.35 1 = 0.35  0.003  78  #0 1 aktor /i!tribu!i tegangan, )ua! tulangan total, >arak antara tulangan, 'a!io tulangan, aktor re/uk!i kekuatan, f = 0.5 untuk Pn O 0.1 ? 78 ? b ? h f = 0.30 untuk Pn = 0

&ntuk " 0

≤

2@05 MPa

0.35 11#4 mm2 1-0.00 mm 1.31

Pn ≤ 0.1 ?  78 ? b ? h

f = 0.5 @ 0.15 ?  Pno  Pn  * Pno


N2 Luas 1asin*&1asin* tu(an*an

%!1 = 2*4 ? %! = 5- mm2 1 %!2 = 2*4 ? %! = 5- mm2 2 %! = 11#4 mm2 Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 "

Jara tu(an*an t3). sisi bet2n

/1 = x @ /! = /2 = /! =

210 mm 40 mm

Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E?10# = 1133 k 0.1 ?  78 ? b ? h ?10 # = 125 k 7 = 7b = 00 * 00 @  y ? /1 = 12-.# mm Pa/a kon/i!i balan7e " Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " 'egangan pa/a ma!ingma!ing baja tulangan " !i = 0.00# ?  7  / i  * 7 Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q maka " !i = e!i? ! &ntuk Q !i Q maka " !i =Q !i Q * e!i?  y &ntuk → D7 = 2.2#21 >umlah interal jarak gr! netral = 112 URAIAN PERHITUNGAN

PERSAMAAN

UNIT

Iayagaya internal pa/a ma!ingma!ing baja tulangan " 'e!ultan gaya internal baja tulangan " Momen akibat gaya internal ma!ingma!ing baja tulangan " Momen total akibat gaya internal baja tulangan " Tinggi blok tegangan tekan beton, Iaya internal pa/a beton tekan " Momen akibat gaya internal tekan beton " Iaya ak!ial nominal " Momen nominal " Iaya ak!ial ren7ana "

!i = %!i ?  !i ? 10# 9! = B S !i E?10# M!i = !i?h*2  /i M! = S M!i a = N1 ? 7 97 = 0.35 ?  78 ? b ? a ? 10# M7 = 97 ? h  a * 2 Pn = 9! @ 97 Mn = M7 @ M!?10# Pu = f Pn

k k kmm kmm mm k kmm k km k


N2 Luas 1asin*&1asin* tu(an*an


%!1 = 2*4 ? %! = 5- mm %!2 = 2*4 ? %! = 5- mm2 %! = 11#4 mm2 Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " 1 2

2

/1 = x @ /! = /2 = /! =

210 mm 40 mm

Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E?10# = 1133 k 0.1 ?  78 ? b ? h ?10 # = 125 k 7 = 7b = 00 * 00 @  y ? /1 = 12-.# mm Pa/a kon/i!i balan7e " Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " 'egangan pa/a ma!ingma!ing baja tulangan " !i = 0.00# ?  7  / i  * 7 Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q maka " !i = e!i? ! &ntuk Q !i Q maka " !i =Q !i Q * e!i?  y &ntuk → D7 = 2.2#21 >umlah interal jarak gr! netral = 112 URAIAN PERHITUNGAN

PERSAMAAN

UNIT


!i = %!i ?  !i ? 10 9! = B S !i E?10# M!i = !i?h*2  /i M! = S M!i a = N1 ? 7 97 = 0.35 ?  78 ? b ? a ? 10# M7 = 97 ? h  a * 2 Pn = 9! @ 97 Mn = M7 @ M!?10# Pu = f Pn #



Momen ren7ana "

Mu = f

Mn

km

1000.00 <50.00 <00.00 350.00 300.00 -50.00 -00.00 ) N k ( n P . f

50.00 00.00 550.00 500.00 450.00

b = 250 mm h = 250 mm $

D

"4

 78 = 20 MPa  y = #<0 MPa

400.00

Pu

Mu

#50.00

k

km

#00.00

112.

11.-

250.00

12<.-

10.-

200.00

124.0

11.<

150.00

32.3

1#.0

100.00

1#.0

1#.5

50.00

11.5

10.2

0.00

114.2

15.-

-2.<

1-.#

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 2 . 4 . , . 3 . 1 0 . 1 2 . 1 4 . 1 , . 1 3 . 2 0 . 2 2 . 2 4 . 2 , . 2 3 . # 0 . # 2 . # 4 . # , . # 3 . 4 0 . 4 2 . 4 4 . 4 , . 4 3 . 5 0 .


Mu = f

Momen ren7ana "

Mn

km

1000.00 <50.00 <00.00 350.00 300.00 -50.00 -00.00 ) N k ( n P . f

50.00

b = 250 mm h = 250 mm

00.00 550.00

$

D

"4

 78 = 20 MPa  y = #<0 MPa

500.00 450.00 400.00

Pu

Mu

#50.00

k

km

#00.00

112.

11.-

250.00

12<.-

10.-

200.00

124.0

11.<

150.00

32.3

1#.0

100.00

1#.0

1#.5

50.00

11.5

10.2

0.00

114.2

15.-

-2.<

1-.#

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 2 . 4 . , . 3 . 1 0 . 1 2 . 1 4 . 1 , . 1 3 . 2 0 . 2 2 . 2 4 . 2 , . 2 3 . # 0 . # 2 . # 4 . # , . # 3 . 4 0 . 4 2 . 4 4 . 4 , . 4 3 . 5 0 .


f.Mn (kNm)

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI 7



!1



!2

mm









!2

9

M

M

M

a

9

M

MPa

MPa

k

k

k

kmm

kmm

kmm

mm

k

kmm

!1

!2

!1

!

!1

!2

!

7

7

KONDISI TEKAN AKSIAL SENTRIS

SSS 0.000-1 0.0025 SSS 0.000< 0.0025 SSS 0.000- 0.0025 SSS 0.0005 0.00255 SSS 0.000# 0.00255 SSS 0.0001 0.00255 SSS 0.0005< 0.00254 SSS 0.0005- 0.00254 SSS 0.00055 0.0025# SSS 0.0005# 0.0025# SSS 0.00051 0.0025# SSS 0.00043 0.00252 SSS 0.0004 0.00252 SSS 0.00044 0.00251 SSS 0.00042 0.00251 SSS 0.000#< 0.00250 SSS 0.000#- 0.00250 SSS 0.000#4 0.0024< SSS 0.000#2 0.0024< SSS 0.0002< 0.00243 SSS 0.0002- 0.00243 SSS 0.00024 0.0024SSS 0.00021 0.0024SSS 0.00013 0.0024 SSS 0.00015 0.0024 SSS 0.0001# 0.00245 SSS 0.00010 0.00245 SSS 0.0000- 0.00244 SSS 0.00004 0.00244 SSS 0.00000 0.0024# SSS 0.0000# 0.00242 SSS 0.0000 0.00242 SSS 0.0000< 0.00241

141.32 1#3.01#4.2 1#0.#3 12.44 122.44 113.# 114.22 110.00 105.-1 101.#4 <.<0 <2.#3-.-3#.03 -3.#0 -#.4# 3.4#.42 53.25#.02 4-.42.21 #.5 #0.<25.11<.2 1#.22 -.0 0.- 5.12.2# 13.<5

#<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00

30.42 -3.2< -.1# -#.<# -1.-0 <.4# -.12 4.-2.#3 5<.<4 5-.454.<5 52.#3 4<.-4-.11 44.40 41.4 #3.3# #5.< ##.04 #0.02-.0# 2#.<4 20.-3 1-.5 14.210.<2 -.50 4.00 0.4# #.21 .<4 10.-4

221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15

#01.52<<.45 2<-.23 2<5.0< 2<2.35 2<0.53 233.2235.<2 23#.5# 231.10 2-3.2 2-.10 2-#.5# 2-0.<2 23.2 25.55 22.-< 25<.<3 25-.12 254.20 251.22 243.13 245.0< 241.<# 2#3.-1 2#5.4# 2#2.0223.5 225.1 221.5< 21-.<4 214.21 210.41

3#5.2 54.<0 4-1.1< 234.4# 0<4.54 5<01.4# 5-05.02 5505.24 5#01.<< 50<5.13 4334.-1 4-0.4< 4452.42 42#0.#< 4004.#0 #--4.02 #5#<.45 ##00.4#05.<4 2303.-# 2555.-1 22<-.-5 20#4.3 1-.#14<2.4 121#.#4 <23.2< #-.#2 #40.2# #.34 2-#.0 53<.< <1#.2

13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.<

11<2.#4 1214#.0 12#2.- 1251#.52 12-0#.42 123<.5# 1#0<2.<# 1#2<2.-2 1#4<5.<1#-02.-3 1#<1#.25 1412-.4 14#45.5# 145-.5 14-<#. 1502#.<# 15253.50 154<-.4< 15-41.02 15<3<.22 1242.24 1500.21 1-#.21-0#1.5< 1-#05.#1 1-534.1 1-3<. 1310.# 1345-.-2 13-1.11 1<0-1.02 1<#3-.5 1<-11.22

2##.-5 2#1.35 22<.< 223.0 22.1 224.2 222.#220.4213.521.214.-3 212.33 210.<3 20<.03 20-.1< 205.2< 20#.#< 201.50 1<<.0 1<-.-0 1<5.30 1<#.<1 1<2.01 1<0.11 133.21 13.#2 134.42 132.52 130.# 1-3.-# 1-.3# 1-4.<# 1-#.04

<<#.44 <35.#<--.#1 <<.25 <1.13 <5#.12 <45.0 <#.<< <23.<# <20.3 <12.30 <04.-4 3<.333.1 330.55 3-2.43 34.42 35.# 343.2< 340.2# 3#2.1324.10 31.04 30-.<-<<.<1 -<1.35 -3#.-3 --5.-2 --. -5<.5< -51.5# -4#.4-#5.40

30-1.3 3<40.<5 <-<4.<2 10##.5< 1145.< 1225.0# 1#05-.30 1#3#5.23 145<-.45 15#44.#2 10-5.<0 1-<2.11-4<#.15 131-3.3# 1334<.21 1<504.2< 20144.0 20-3.55 21#--.-# 21<-1.1 22550.1< 2#11#.42#1.4 241<4.14 24-11.5# 2521#.1 25-00.40 21-1.3< 223.03 2-03.<2-4<4.55 2-<04.35 232<<.34

Pn k 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1130.34 11-0.21 115<.5# 1143.31 11#3.04 112-.21 111.#4 1105.41 10<4.4# 103#.#3 10-2.2< 101.1# 104<.<1 10#3.2 102-.21015.3 1004.#<<2.31 <31.13 <<.4<5-.3 <45.31

Mn

R

km 0.00 20.0# 21.03 22.12 2#.15 24.1 25.1 2.15 2-.1# 23.0< 2<.05 2<.<< #0.<2 #1.34 #2.-5 ##.4 #4.5# #5.40 #.2#-.12 #-.< #3.-< #<.1 40.42 41.2# 42.02 42.30 4#.544.## 45.0< 45.3# 4.54-.2< 43.01

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

R.Pn k --2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--.54 -0.4 -5#.-0 -4.-# -#<.-2 -#2.< -25.2 -13.52 -11.#3 -04.20 <.<< 3<.-# 32.44 -5.11 -.-# 0.#1 52.34 45.## #-.-#0.15 22.4< 14.-3

R.Mn km 0.00 1#.02 1#.-0 14.#3 15.05 15.-0 1.# 1-.00 1-.# 13.2 13.33 1<.4< 20.10 20.-0 21.2< 21.322.44 2#.01 2#.524.1# 24.25.22 25.-5 2.23 2.30 2-.#1 2-.32 23.#2 23.32 2<.#1 2<.-< #0.2#0.-4 #1.21


f.Mn (kNm)




!1



!2

mm









!2

9

M

M

M

a

9

M

MPa

MPa

k

k

k

kmm

kmm

kmm

mm

k

kmm

!1

!2

!1

!

!1

!2

!

7

7


SSS 0.000-1 0.0025 SSS 0.000< 0.0025 SSS 0.000- 0.0025 SSS 0.0005 0.00255 SSS 0.000# 0.00255 SSS 0.0001 0.00255 SSS 0.0005< 0.00254 SSS 0.0005- 0.00254 SSS 0.00055 0.0025# SSS 0.0005# 0.0025# SSS 0.00051 0.0025# SSS 0.00043 0.00252 SSS 0.0004 0.00252 SSS 0.00044 0.00251 SSS 0.00042 0.00251 SSS 0.000#< 0.00250 SSS 0.000#- 0.00250 SSS 0.000#4 0.0024< SSS 0.000#2 0.0024< SSS 0.0002< 0.00243 SSS 0.0002- 0.00243 SSS 0.00024 0.0024SSS 0.00021 0.0024SSS 0.00013 0.0024 SSS 0.00015 0.0024 SSS 0.0001# 0.00245 SSS 0.00010 0.00245 SSS 0.0000- 0.00244 SSS 0.00004 0.00244 SSS 0.00000 0.0024# SSS 0.0000# 0.00242 SSS 0.0000 0.00242 SSS 0.0000< 0.00241

141.32 1#3.01#4.2 1#0.#3 12.44 122.44 113.# 114.22 110.00 105.-1 101.#4 <.<0 <2.#3-.-3#.03 -3.#0 -#.4# 3.4#.42 53.25#.02 4-.42.21 #.5 #0.<25.11<.2 1#.22 -.0 0.- 5.12.2# 13.<5

#<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00

30.42 -3.2< -.1# -#.<# -1.-0 <.4# -.12 4.-2.#3 5<.<4 5-.454.<5 52.#3 4<.-4-.11 44.40 41.4 #3.3# #5.< ##.04 #0.02-.0# 2#.<4 20.-3 1-.5 14.210.<2 -.50 4.00 0.4# #.21 .<4 10.-4

221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15

#01.52<<.45 2<-.23 2<5.0< 2<2.35 2<0.53 233.2235.<2 23#.5# 231.10 2-3.2 2-.10 2-#.5# 2-0.<2 23.2 25.55 22.-< 25<.<3 25-.12 254.20 251.22 243.13 245.0< 241.<# 2#3.-1 2#5.4# 2#2.0223.5 225.1 221.5< 21-.<4 214.21 210.41

3#5.2 54.<0 4-1.1< 234.4# 0<4.54 5<01.4# 5-05.02 5505.24 5#01.<< 50<5.13 4334.-1 4-0.4< 4452.42 42#0.#< 4004.#0 #--4.02 #5#<.45 ##00.4#05.<4 2303.-# 2555.-1 22<-.-5 20#4.3 1-.#14<2.4 121#.#4 <23.2< #-.#2 #40.2# #.34 2-#.0 53<.< <1#.2

13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.<

11<2.#4 1214#.0 12#2.- 1251#.52 12-0#.42 123<.5# 1#0<2.<# 1#2<2.-2 1#4<5.<1#-02.-3 1#<1#.25 1412-.4 14#45.5# 145-.5 14-<#. 1502#.<# 15253.50 154<-.4< 15-41.02 15<3<.22 1242.24 1500.21 1-#.21-0#1.5< 1-#05.#1 1-534.1 1-3<. 1310.# 1345-.-2 13-1.11 1<0-1.02 1<#3-.5 1<-11.22

2##.-5 2#1.35 22<.< 223.0 22.1 224.2 222.#220.4213.521.214.-3 212.33 210.<3 20<.03 20-.1< 205.2< 20#.#< 201.50 1<<.0 1<-.-0 1<5.30 1<#.<1 1<2.01 1<0.11 133.21 13.#2 134.42 132.52 130.# 1-3.-# 1-.3# 1-4.<# 1-#.04

<<#.44 <35.#<--.#1 <<.25 <1.13 <5#.12 <45.0 <#.<< <23.<# <20.3 <12.30 <04.-4 3<.333.1 330.55 3-2.43 34.42 35.# 343.2< 340.2# 3#2.1324.10 31.04 30-.<-<<.<1 -<1.35 -3#.-3 --5.-2 --. -5<.5< -51.5# -4#.4-#5.40

30-1.3 3<40.<5 <-<4.<2 10##.5< 1145.< 1225.0# 1#05-.30 1#3#5.23 145<-.45 15#44.#2 10-5.<0 1-<2.11-4<#.15 131-3.3# 1334<.21 1<504.2< 20144.0 20-3.55 21#--.-# 21<-1.1 22550.1< 2#11#.42#1.4 241<4.14 24-11.5# 2521#.1 25-00.40 21-1.3< 223.03 2-03.<2-4<4.55 2-<04.35 232<<.34

Pn k 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1133.42 1130.34 11-0.21 115<.5# 1143.31 11#3.04 112-.21 111.#4 1105.41 10<4.4# 103#.#3 10-2.2< 101.1# 104<.<1 10#3.2 102-.21015.3 1004.#<<2.31 <31.13 <<.4<5-.3 <45.31

Mn

R

R.Pn k --2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--2.4--.54 -0.4 -5#.-0 -4.-# -#<.-2 -#2.< -25.2 -13.52 -11.#3 -04.20 <.<< 3<.-# 32.44 -5.11 -.-# 0.#1 52.34 45.## #-.-#0.15 22.4< 14.-3

R.Mn

km 0.00 20.0# 21.03 22.12 2#.15 24.1 25.1 2.15 2-.1# 23.0< 2<.05 2<.<< #0.<2 #1.34 #2.-5 ##.4 #4.5# #5.40 #.2#-.12 #-.< #3.-< #<.1 40.42 41.2# 42.02 42.30 4#.544.## 45.0< 45.3# 4.54-.2< 43.01

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

km 0.00 1#.02 1#.-0 14.#3 15.05 15.-0 1.# 1-.00 1-.# 13.2 13.33 1<.4< 20.10 20.-0 21.2< 21.322.44 2#.01 2#.524.1# 24.25.22 25.-5 2.23 2.30 2-.#1 2-.32 23.#2 23.32 2<.#1 2<.-< #0.2#0.-4 #1.21

Mn

R

R.Pn

R.Mn

km 43.-2 4<.42 50.12 50.31 51.4< 52.1 52.3# 5#.4< 54.14 54.-< 55.44 5.03 5.-1 5-.#4 5-.<53.0 5<.22 5<.34 0.4 1.03 1.-0 2.#1 2.<# #.5 4.13 4.31 5.44 .03 .-2 -.#3.0# 3.-0 <.#3 -0.0-0.03 <.<# <.-

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 0-.01 5<<.13 5<1.2< 53#.#5 5-5.#4 5-.2 55<.12 550.<1 542.# 5#4.2525.3# 51-.#1 503.-1 500.0# 4<1.25 432.#3 4-#.41 44.## 455.15 445.34#.4 42.<4 41-.2< 40-.51 #<-.5< #3-.5# #--.#1 #.<5 #5.41 #45.-0 ##4.32 #2#.-4 #12.4 #00.<2<4.5 23<.#2 234.03

km #1.#2.1# #2.53 ##.02 ##.4##.<0 #4.#4 #4.-#5.1< #5.2 #.0# #.45 #.3 #-.2#-.3 #3.0< #3.4< #3.<0 #<.#0 #<.-0 40.10 40.50 40.<1 41.#1 41.-2 42.12 42.54 42.<5 4#.#4#.-< 44.22 44.5 45.10 45.55 45.55 45.45 45.#4


7 mm SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS



!1

0.0001# 0.0001 0.00020 0.00024 0.00020.000#1 0.000#5 0.000#< 0.0004# 0.00043 0.00052 0.0005 0.0001 0.000 0.000-0 0.000-5 0.00030 0.0003 0.000<1 0.000< 0.00102 0.00103 0.00114 0.00120 0.0012 0.001## 0.00140 0.00140.00154 0.0011 0.001< 0.001-0.00135 0.001<# 0.00202 0.00211 0.00221



!2

0.00240 0.00240 0.002#< 0.002#3 0.002#3 0.002#0.002# 0.002#5 0.002#5 0.002#4 0.002## 0.002#2 0.002#1 0.002#0 0.0022< 0.0022< 0.00223 0.00220.0022 0.00224 0.0022# 0.00222 0.00221 0.00220 0.0021< 0.00213 0.0021 0.00215 0.00214 0.00212 0.00211 0.0020< 0.00203 0.0020 0.00204 0.0020# 0.00201



!1





MPa 25.31 #2.3# 40.00 4-.#4 54.35 2.54 -0.40 -3.4 3.-2 <5.110#.34 112.-# 121.34 1#1.1< 140.-< 150.4 10.-5 1-1.15 131.3# 1<2.31 204.10 215.-2 22-.3 240.00 252.< 25.-2-<.25 2<#.1 #0-.52 #22.#5 ##-.#5#.51 #<.<0 #3.35 #<0.00 #<0.00 #<0.00

MPa #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00

k 14.4 13.1 22.3 2.34 #1.10 #5.4 #<.<2 44.4< 4<.15#.<53.33 #.<2 <.0< -4.#< -<.3# 35.42 <1.1 <-.05 10#.11 10<.## 115.-4 122.## 12<.11 1#.0< 14#.2< 150.-1 153.#5 1.24 1-4.#3 132.-< 1<1.43 200.4 20<.-5 21<.#221.15 221.15 221.15

!2

!1



!2

k 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15

9

!

k 20.52 202.54 1<3.41<4.#1 1<0.05 135.< 131.2# 1-. 1-1.<3 1-.13 12.215-.2# 152.0 14.- 141.#2 1#5.-# 1#0.00 124.10 113.05 111.32 105.41 <3.3# <2.04 35.0 --.3 -0.45 2.30 54.<1 4.-#3.# 2<.20.< 11.40 1.-3 0.00 0.00 0.00

M

!1

kmm 1244.01 1532.11<23.00 2231.- 24#.-2 #014.1< ##<#.4 #-31.34 41-<.453-.#0 5005.10 54##.44 53-2.-4 #2#.4# -35.<4 -20.-5 --43.# 324<.2< 3-4.10 <2<#.#<3#-.-2 10#<-.30 10<-4.#1 115-.<121-<.51230<.<# 1#45<.<# 141#0.50 14322.# 155#-.#12-5.31-0#<.#1 1-323.<< 134.23 13-<-.< 13-<-.< 13-<-.<

M

M

kmm 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.<

kmm 20041.< 20#30.12 20-25.<5 210-<.-1 21441.3 21312.15 221<1.41 225-<.-< 22<--.2 2##35.25 2#30#.05 242#1.40 24-0.-0 25121.#3 2553#.3< 2053.-0 254.#1 2-04-.25 2-52.0 230<1.## 23#5.3 2<1<5.- 2<--2.2 #0#5.<# #0<--.5# #10-.3< #225-.3< #2<23.45 ##20.53 #4##5.## #50-#.32 #53#-.2#2.<4 #-444.2# #-5<5.<1 #-5<5.<1 #-5<5.<1

!2

!

a mm 1-1.14 1<.24 1-.#4 15.45 1#.55 11.5 15<.-5 15-.3 155.< 154.0 152.1150.2143.#14.4144.53 142.3 140.-3 1#3.33 1#.<< 1#5.0< 1##.1< 1#1.2< 12<.40 12-.50 125.0 12#.-1 121.31 11<.<1 113.01 11.12 114.22 112.#2 110.42 103.5# 10.# 104.-# 102.3#

9

7

k -2-.#4 -1<.2-11.21 -0#.15 <5.03 3-.02 -3.< -0.3< 2.3# 54.-4.-0 #3.4 #0.522.51 14.45 0.#3 5<3.#2 5<0.2 532.1< 5-4.1# 5.0553.00 54<.<4 541.33 5##.31 525.-5 51-.3 50<.2 501.5 4<#.4< 435.4# 4--.#4<.#0 41.24 45#.13 445.11 4#-.05

M

7

kmm 23-<.5# 2<04#.<2 2<#<#.01 2<-2.31 #0045.#0 #0#43.50 #0#.40 #0<03.<< #11.2< #1403.2< #1#4.<< #134.#< #2042.4< #222#.2< #2#33.-< #25#3.<< #2-#.<0 #2-<#.50 #23<-.31 #2<3.31 ##00.52 ##113.<# ##12.04 ##13<.34 ##202.#5 ##1<<.5 ##131.4##143.0< ##0<<.40 ##0#5.41 #2<5.12 #231.54 #2-51.5 #22.4#2435.<< #2##0.20 #215<.12

Pn k <##.3 <21.31 <0<.3 3<-.4 335.1# 3-2.-1 30.1< 34-.55 3#4.31 321.<5 303.<-<5.3-32.4 -<.2-55.--42.12 -23.#2 -14.# -00.24 35.<5 -1.43 5.3# 41.<3 2.<# 11.5<.20 530.43 54.5# 543.## 5#1.35 515.10 4<3.0 430.-0 4#.02 45#.13 445.11 4#-.05


7 mm SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS



!1

0.0001# 0.0001 0.00020 0.00024 0.00020.000#1 0.000#5 0.000#< 0.0004# 0.00043 0.00052 0.0005 0.0001 0.000 0.000-0 0.000-5 0.00030 0.0003 0.000<1 0.000< 0.00102 0.00103 0.00114 0.00120 0.0012 0.001## 0.00140 0.00140.00154 0.0011 0.001< 0.001-0.00135 0.001<# 0.00202 0.00211 0.00221



!2

0.00240 0.00240 0.002#< 0.002#3 0.002#3 0.002#0.002# 0.002#5 0.002#5 0.002#4 0.002## 0.002#2 0.002#1 0.002#0 0.0022< 0.0022< 0.00223 0.00220.0022 0.00224 0.0022# 0.00222 0.00221 0.00220 0.0021< 0.00213 0.0021 0.00215 0.00214 0.00212 0.00211 0.0020< 0.00203 0.0020 0.00204 0.0020# 0.00201



!1





MPa 25.31 #2.3# 40.00 4-.#4 54.35 2.54 -0.40 -3.4 3.-2 <5.110#.34 112.-# 121.34 1#1.1< 140.-< 150.4 10.-5 1-1.15 131.3# 1<2.31 204.10 215.-2 22-.3 240.00 252.< 25.-2-<.25 2<#.1 #0-.52 #22.#5 ##-.#5#.51 #<.<0 #3.35 #<0.00 #<0.00 #<0.00

MPa #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00

k 14.4 13.1 22.3 2.34 #1.10 #5.4 #<.<2 44.4< 4<.15#.<53.33 #.<2 <.0< -4.#< -<.3# 35.42 <1.1 <-.05 10#.11 10<.## 115.-4 122.## 12<.11 1#.0< 14#.2< 150.-1 153.#5 1.24 1-4.#3 132.-< 1<1.43 200.4 20<.-5 21<.#221.15 221.15 221.15

!2

!1

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k 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15

9

!

k 20.52 202.54 1<3.41<4.#1 1<0.05 135.< 131.2# 1-. 1-1.<3 1-.13 12.215-.2# 152.0 14.- 141.#2 1#5.-# 1#0.00 124.10 113.05 111.32 105.41 <3.3# <2.04 35.0 --.3 -0.45 2.30 54.<1 4.-#3.# 2<.20.< 11.40 1.-3 0.00 0.00 0.00

M

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kmm 1244.01 1532.11<23.00 2231.- 24#.-2 #014.1< ##<#.4 #-31.34 41-<.453-.#0 5005.10 54##.44 53-2.-4 #2#.4# -35.<4 -20.-5 --43.# 324<.2< 3-4.10 <2<#.#<3#-.-2 10#<-.30 10<-4.#1 115-.<121-<.51230<.<# 1#45<.<# 141#0.50 14322.# 155#-.#12-5.31-0#<.#1 1-323.<< 134.23 13-<-.< 13-<-.< 13-<-.<

M

M

kmm 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.<

kmm 20041.< 20#30.12 20-25.<5 210-<.-1 21441.3 21312.15 221<1.41 225-<.-< 22<--.2 2##35.25 2#30#.05 242#1.40 24-0.-0 25121.#3 2553#.3< 2053.-0 254.#1 2-04-.25 2-52.0 230<1.## 23#5.3 2<1<5.- 2<--2.2 #0#5.<# #0<--.5# #10-.3< #225-.3< #2<23.45 ##20.53 #4##5.## #50-#.32 #53#-.2#2.<4 #-444.2# #-5<5.<1 #-5<5.<1 #-5<5.<1

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a mm 1-1.14 1<.24 1-.#4 15.45 1#.55 11.5 15<.-5 15-.3 155.< 154.0 152.1150.2143.#14.4144.53 142.3 140.-3 1#3.33 1#.<< 1#5.0< 1##.1< 1#1.2< 12<.40 12-.50 125.0 12#.-1 121.31 11<.<1 113.01 11.12 114.22 112.#2 110.42 103.5# 10.# 104.-# 102.3#

9

7

k -2-.#4 -1<.2-11.21 -0#.15 <5.03 3-.02 -3.< -0.3< 2.3# 54.-4.-0 #3.4 #0.522.51 14.45 0.#3 5<3.#2 5<0.2 532.1< 5-4.1# 5.0553.00 54<.<4 541.33 5##.31 525.-5 51-.3 50<.2 501.5 4<#.4< 435.4# 4--.#4<.#0 41.24 45#.13 445.11 4#-.05

M

7

kmm 23-<.5# 2<04#.<2 2<#<#.01 2<-2.31 #0045.#0 #0#43.50 #0#.40 #0<03.<< #11.2< #1403.2< #1#4.<< #134.#< #2042.4< #222#.2< #2#33.-< #25#3.<< #2-#.<0 #2-<#.50 #23<-.31 #2<3.31 ##00.52 ##113.<# ##12.04 ##13<.34 ##202.#5 ##1<<.5 ##131.4##143.0< ##0<<.40 ##0#5.41 #2<5.12 #231.54 #2-51.5 #22.4#2435.<< #2##0.20 #215<.12

Pn k <##.3 <21.31 <0<.3 3<-.4 335.1# 3-2.-1 30.1< 34-.55 3#4.31 321.<5 303.<-<5.3-32.4 -<.2-55.--42.12 -23.#2 -14.# -00.24 35.<5 -1.43 5.3# 41.<3 2.<# 11.5<.20 530.43 54.5# 543.## 5#1.35 515.10 4<3.0 430.-0 4#.02 45#.13 445.11 4#-.05

Mn

R

R.Pn

R.Mn

km 43.-2 4<.42 50.12 50.31 51.4< 52.1 52.3# 5#.4< 54.14 54.-< 55.44 5.03 5.-1 5-.#4 5-.<53.0 5<.22 5<.34 0.4 1.03 1.-0 2.#1 2.<# #.5 4.13 4.31 5.44 .03 .-2 -.#3.0# 3.-0 <.#3 -0.0-0.03 <.<# <.-

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 0-.01 5<<.13 5<1.2< 53#.#5 5-5.#4 5-.2 55<.12 550.<1 542.# 5#4.2525.3# 51-.#1 503.-1 500.0# 4<1.25 432.#3 4-#.41 44.## 455.15 445.34#.4 42.<4 41-.2< 40-.51 #<-.5< #3-.5# #--.#1 #.<5 #5.41 #45.-0 ##4.32 #2#.-4 #12.4 #00.<2<4.5 23<.#2 234.03

km #1.#2.1# #2.53 ##.02 ##.4##.<0 #4.#4 #4.-#5.1< #5.2 #.0# #.45 #.3 #-.2#-.3 #3.0< #3.4< #3.<0 #<.#0 #<.-0 40.10 40.50 40.<1 41.#1 41.-2 42.12 42.54 42.<5 4#.#4#.-< 44.22 44.5 45.10 45.55 45.55 45.45 45.#4

Mn

R

R.Pn

R.Mn

km <.5<.#<.15 3.-2 3.2 -.-3 -.2.-4 .13 5.0 4.<< 4.#5 #.3 2.<3 2.25 1.4< 0.-0 5<.35<.00 53.0< 5-.14 5.15 55.11 54.02 52.33 51.3 50.42 4<.0< 4-.-0 4.22 44.5 4#.<1 4#.1 41.#5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0. 0.3 0.-0 0.-# 0.-5 0.- 0.-0.30

k 2-3.34 2-#.0 23.# 21.5254.-# 24-.32 240.3# 2##.-22.# 21<.41 212.0< 204.3 1<-.1 13<.52 131.-1-#.33 15.35 15-. 14<.#1 140.-3 1#2.05 12#.10 11#.<1 104.4<4.-# 34.3 -5.-4 .5.5# 45.1#2.4# 2.22 1<.#.#1

km 45.22 45.0< 44.<5 44.44.#44.0 4#.-# 4#.#3 4#.02 42.4 42.24 41.3# 41.#< 40.<4 40.4#<.<#<.45 #3.<1 #3.#5 #-.- #-.14 #.50 #5.32 #5.11 #4.###.5< ##.42 ##.52 ##.5 ##.52 ##.#< ##.#1 ##.20 #2.3-


7 mm SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS



!1

0.002#1 0.00241 0.00251 0.0022 0.002-4 0.0023 0.002<3 0.00#11 0.00#24 0.00##< 0.00#5# 0.00#< 0.00#35 0.00402 0.00420 0.004#< 0.0045< 0.00430 0.00502 0.00525 0.00550 0.005-0.0005 0.00#5 0.000.00-01 0.00-#3 0.00--0.00320 0.003 0.00<10.00<41 0.00<5 0.0102



!2

0.001<< 0.001<0.001<5 0.001<# 0.001<1 0.00133 0.0013 0.00134 0.00131 0.001-3 0.001- 0.001-# 0.001-0 0.001 0.001# 0.0015< 0.00155 0.00151 0.00140.0014# 0.001#3 0.001## 0.00123 0.00122 0.0011 0.0010< 0.00102 0.000<5 0.00030.000-3 0.0003 0.0004 0.0005< 0.0004-



!1

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MPa #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00

MPa #<0.00 #<0.00 #<0.00 #35.32 #31.4 #-.<# #-2.20 #-.2#2.12 #5.-4 #51.11 #45.21 ##<.0# ##2.54 #25.-1 #13.5# #10.<#02.<3 2<4.55 235.1 2-.14 2.0< 255.#3 24#.<2#1.-3 213.-2 204.-1 13<.2 1-#.## 155.-0 1#.55 12-.4# 11-.<# <4.-4

k 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15

!2

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KONDISI TEKAN AKSIAL KECIL 5 Pn 6 7." 8 9:/ 8 b 8 3



!2

9

k 221.15 221.15 221.15 213.-3 21.#1 21#.-4 211.0 203.2 205.#5 202.2< 1<<.10 1<5.- 1<2.25 133.5134.-0 130.# 1-.#4 1-1.31 1-.02 11.< 15.5< 150.3< 144.32 1#3.#5 1#1.4# 124.0# 11.03 10-.52 <3.2< 33.2< --.4# -2.2 .33 5#.-2

k 0.00 0.00 0.00 2.#4.34 -.41 10.0< 12.3< 15.31 13.3 22.05 25.40 23.<0 #2.53 #.45 40.5# 44.32 4<.#4 54.1# 5<.1< 4.5 -0.2-.## 32.31 3<.-2 <-.12 105.011#.# 122.3 1#2.3 14#.-2 143.3< 154.23 1-.4#

!

M

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kmm 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.<

kmm 13-<-.< 13-<-.< 13-<-.< 135<.#2 13#3.4< 131-.< 1-<40.1 1--02.50 1-454.## 1-1<4.<# 1<2#.52 1#<.24 1#41.1 1023.2 15<<.#< 15#5#.#0 14<33.1 140#.-141<-.0 1#-.5 1##10.14 12325.# 12#0<.51 11-5<.50 111-1.31 10542.44 <3.30 <1#<.53 3#54.5 -504.34 531.-3 141.<# 534.41 45.#0

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a mm 100.<4 <<.04 <-.14 <5.25 <#.#5 <1.45 3<.55 3-. 35.- 3#.3 31.< 30.0-3.1-.2-4.#-2.43 -0.53 3.3 .-< 4.3< 2.<< 1.0< 5<.20 5-.#0 55.40 5#.50 51.1 4<.-1 4-.31 45.<2 44.02 4#.142.#2 40.#3

9

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k 423.<3 420.<2 412.3 404.-< #<.-# #33.#30.0 #-2.54 #4.43 #5.41 #43.#5 #40.23 ##2.22 #24.1 #1.0< #03.0# 2<<.<2<1.<0 23#.34 2-5.-3 2-.-1 25<.5 251.53 24#.52 2#5.4 22-.#< 21<.## 211.220#.20 1<5.14 13-.03 13#.4 1-<.35 1-1.5<

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Pn k 423.<3 420.<2 412.3 402.42 #<1.3< #31.25 #-0.51 #5<.5 #43.##-.55 #2.#0 #14.3< #0#.#2 2<1.52-<.4 2-.50 255.15 242.5 22<.-1 21.53 20#.15 13<.#3 1-5.25 10.-2 145.-4 1#0.2114.2 <-.4 30.#4 2.23 4#.# #4.525.54.1

31.25 31.25

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0.002#1 0.00241 0.00251 0.0022 0.002-4 0.0023 0.002<3 0.00#11 0.00#24 0.00##< 0.00#5# 0.00#< 0.00#35 0.00402 0.00420 0.004#< 0.0045< 0.00430 0.00502 0.00525 0.00550 0.005-0.0005 0.00#5 0.000.00-01 0.00-#3 0.00--0.00320 0.003 0.00<10.00<41 0.00<5 0.0102



!2

0.001<< 0.001<0.001<5 0.001<# 0.001<1 0.00133 0.0013 0.00134 0.00131 0.001-3 0.001- 0.001-# 0.001-0 0.001 0.001# 0.0015< 0.00155 0.00151 0.00140.0014# 0.001#3 0.001## 0.00123 0.00122 0.0011 0.0010< 0.00102 0.000<5 0.00030.000-3 0.0003 0.0004 0.0005< 0.0004-



!1





MPa #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00 #<0.00

MPa #<0.00 #<0.00 #<0.00 #35.32 #31.4 #-.<# #-2.20 #-.2#2.12 #5.-4 #51.11 #45.21 ##<.0# ##2.54 #25.-1 #13.5# #10.<#02.<3 2<4.55 235.1 2-.14 2.0< 255.#3 24#.<2#1.-3 213.-2 204.-1 13<.2 1-#.## 155.-0 1#.55 12-.4# 11-.<# <4.-4

k 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15 221.15

!2

!1



!2

9

k 221.15 221.15 221.15 213.-3 21.#1 21#.-4 211.0 203.2 205.#5 202.2< 1<<.10 1<5.- 1<2.25 133.5134.-0 130.# 1-.#4 1-1.31 1-.02 11.< 15.5< 150.3< 144.32 1#3.#5 1#1.4# 124.0# 11.03 10-.52 <3.2< 33.2< --.4# -2.2 .33 5#.-2

k 0.00 0.00 0.00 2.#4.34 -.41 10.0< 12.3< 15.31 13.3 22.05 25.40 23.<0 #2.53 #.45 40.5# 44.32 4<.#4 54.1# 5<.1< 4.5 -0.2-.## 32.31 3<.-2 <-.12 105.011#.# 122.3 1#2.3 14#.-2 143.3< 154.23 1-.4#

!

M

M

kmm 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.< 13-<-.<

kmm 13-<-.< 13-<-.< 13-<-.< 135<.#2 13#3.4< 131-.< 1-<40.1 1--02.50 1-454.## 1-1<4.<# 1<2#.52 1#<.24 1#41.1 1023.2 15<<.#< 15#5#.#0 14<33.1 140#.-141<-.0 1#-.5 1##10.14 12325.# 12#0<.51 11-5<.50 111-1.31 10542.44 <3.30 <1#<.53 3#54.5 -504.34 531.-3 141.<# 534.41 45.#0

!1

!2

M

!

kmm #-5<5.<1 #-5<5.<1 #-5<5.<1 #-#<4.23 #-134.45 #<5.<1 #-#3.12 #500.4 #252.2< #5<<2.33 #5-21.4#54#-.20 #51#<.12 #432.22 #44<-.#5 #4151.2 ##-3.5 ##401.-2 #2<<5.01 #254.52 #2103.0< #12#.#2 #110-.4 #055-.45 2<<<.- 2<#40.40 234.- 2-<#-.54 2-152.0 2#02.30 25#-<.-# 24<#<.33 24432.# 2##4.2

a mm 100.<4 <<.04 <-.14 <5.25 <#.#5 <1.45 3<.55 3-. 35.- 3#.3 31.< 30.0-3.1-.2-4.#-2.43 -0.53 3.3 .-< 4.3< 2.<< 1.0< 5<.20 5-.#0 55.40 5#.50 51.1 4<.-1 4-.31 45.<2 44.02 4#.142.#2 40.#3

9

7

k 423.<3 420.<2 412.3 404.-< #<.-# #33.#30.0 #-2.54 #4.43 #5.41 #43.#5 #40.23 ##2.22 #24.1 #1.0< #03.0# 2<<.<2<1.<0 23#.34 2-5.-3 2-.-1 25<.5 251.53 24#.52 2#5.4 22-.#< 21<.## 211.220#.20 1<5.14 13-.03 13#.4 1-<.35 1-1.5<

M

7

kmm #1<-2.-4 #1--1.0 #1554.03 #1#21.30 #10-4.22 #0311.#5 #05##.1#02#<.< 2<<#0.<2 2<0.34 2<2-.423<12.30 23542.3# 2315-.55 2--5.<3 2-#41.11 2<0<.<4 24#.42001.-1 25524.4 250#2.224524.1 24001.4 2#4#.#3 22<0<.31 22#40.<5 21-5.-< 2115-.## 20542.51<<12.51 1<2-.15 13<-#.0 13-5.<1 1-<35.1-

Pn k 423.<3 420.<2 412.3 402.42 #<1.3< #31.25 #-0.51 #5<.5 #43.##-.55 #2.#0 #14.3< #0#.#2 2<1.52-<.4 2-.50 255.15 242.5 22<.-1 21.53 20#.15 13<.#3 1-5.25 10.-2 145.-4 1#0.2114.2 <-.4 30.#4 2.23 4#.# #4.525.54.1

Mn

R

R.Pn

R.Mn

km <.5<.#<.15 3.-2 3.2 -.-3 -.2.-4 .13 5.0 4.<< 4.#5 #.3 2.<3 2.25 1.4< 0.-0 5<.35<.00 53.0< 5-.14 5.15 55.11 54.02 52.33 51.3 50.42 4<.0< 4-.-0 4.22 44.5 4#.<1 4#.1 41.#5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0. 0.3 0.-0 0.-# 0.-5 0.- 0.-0.30

k 2-3.34 2-#.0 23.# 21.5254.-# 24-.32 240.3# 2##.-22.# 21<.41 212.0< 204.3 1<-.1 13<.52 131.-1-#.33 15.35 15-. 14<.#1 140.-3 1#2.05 12#.10 11#.<1 104.4<4.-# 34.3 -5.-4 .5.5# 45.1#2.4# 2.22 1<.#.#1

km 45.22 45.0< 44.<5 44.44.#44.0 4#.-# 4#.#3 4#.02 42.4 42.24 41.3# 41.#< 40.<4 40.4#<.<#<.45 #3.<1 #3.#5 #-.- #-.14 #.50 #5.32 #5.11 #4.###.5< ##.42 ##.52 ##.5 ##.52 ##.#< ##.#1 ##.20 #2.3-

31.25 31.25

KONDISI TEKAN AKSIAL KECIL 5 Pn 6 7." 8 9:/ 8 b 8 3

0.00 50.00


7



!1



mm

!2









9

MPa

MPa

k

k

k

!1

!2

!1

!2

!

M

!1

kmm

M

!2

kmm

M

a

9

M

Pn

Mn

kmm

mm

k

kmm

k

km

#-5<5.<1

103.13

!

7

7

R

R.Pn

R.Mn

k

km

KONDISI BALANCE

SSS 0.001<5 0.0020 #<0.00 #<0.00 221.15

221.15

0.00 13-<-.< 13-<-.<

45<.-- #202.0-

45<.--

-0.20

0.5

0.00 2<3.35

0.00 45.#


7



!1



!2

mm









9

MPa

MPa

k

k

k

!1

!2

!1

!2

!

M

M

a

9

M

Pn

Mn

kmm

mm

k

kmm

k

km

#-5<5.<1

103.13

M

!1

!2

kmm

kmm

!

7

7

R

R.Pn

R.Mn

k

km

KONDISI BALANCE

SSS 0.001<5 0.0020 #<0.00 #<0.00 221.15

221.15

0.00 13-<-.< 13-<-.<

45<.-- #202.0-

45<.--



K6 K6)6M

K#

INPUT DATA KOLOM

Kuat tekan beton, Tegangan leleh baja, )ebar kolom, Tinggi kolom, Tebal brutto !elimut beton, >umlah tulangan, iameter tulangan,

 78 =  y = b= h= /! = n= =

20 #<0 250 250 40 3 1

MPa MPa mm mm mm buah mm

PERHITUNGAN DIAGRAM INTERAKSI

! = 2@05 MPa untuk 78 £ #0 MPa untuk 78 A #0 MPa N1 = 0.35 aktor /i!tribu!i tegangan, %! = n ? p * 4 ? 2 = 103 mm2 )ua! tulangan total, x =  h  2?/!  * 2 = 35.000 mm >arak antara tulangan, r = %! * %g = 2.5- 'a!io tulangan, Mo/ulu! ela!ti! baja, N1 = 0.35 N1 = 0.35  0.003  78  #0

aktor re/uk!i kekuatan, f = 0.5 untuk Pn O 0.1 ? 78 ? b ? h f = 0.30 untuk Pn = 0

&ntuk " 0

≤

Pn ≤ 0.1 ?  78 ? b ? h

f = 0.5 @ 0.15 ?  P no  Pn  * Pno

-0.20

0.5

0.00 2<3.35

0.00 45.#



K#

K6 K6)6M INPUT DATA KOLOM

 78 =  y = b= h= /! = n= =

Kuat tekan beton, Tegangan leleh baja, )ebar kolom, Tinggi kolom, Tebal brutto !elimut beton, >umlah tulangan, iameter tulangan,

20 #<0 250 250 40 3 1

MPa MPa mm mm mm buah mm

PERHITUNGAN DIAGRAM INTERAKSI

! = 2@05 MPa untuk 78 £ #0 MPa untuk 78 A #0 MPa N1 = 0.35 aktor /i!tribu!i tegangan, %! = n ? p * 4 ? 2 = 103 mm2 )ua! tulangan total, x =  h  2?/!  * 2 = 35.000 mm >arak antara tulangan, r = %! * %g = 2.5- 'a!io tulangan, Mo/ulu! ela!ti! baja, N1 = 0.35 N1 = 0.35  0.003  78  #0

aktor re/uk!i kekuatan, f = 0.5 untuk Pn O 0.1 ? 78 ? b ? h f = 0.30 untuk Pn = 0

&ntuk " 0

≤

Pn ≤ 0.1 ?  78 ? b ? h

f = 0.5 @ 0.15 ?  P no  Pn  * Pno


1000.00 <50.00 <00.00 350.00 300.00 -50.00 -00.00 ) N k ( n P . f

b= h=

50.00 00.00

Tul. "

550.00

;

 78 =  y =

500.00 450.00

250 250

mm mm

D

"<

20 #<0

400.00

Pu

Mu

#50.00

k

km

#00.00

112.54

2#.#20

250.00

12<.-03

21.#14

200.00

124.013

2#.33

150.00

32.32<

25.<15

100.00

1#.043

2.<<#

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

50.00 0.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . . . . . 0 0 . 2 . 4 0 . 0 . 2 . 4 . , . 3 . 1 0 . 1 2 . 1 4 . 1 , . 1 3 . 2 0 . 2 2 . 2 4 . 2 , 2 3 # 0 # 2 # 4 # , # 3 4 , . 4 3 . 5 0 . 4 4 4

f.Mn (kNm)

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI

MPa MPa


1000.00 <50.00 <00.00 350.00 300.00 -50.00 -00.00 ) N k ( n P . f

b= h=

50.00 00.00

Tul. "

550.00

;

 78 =  y =

500.00 450.00

250 250

mm mm

D

"<

20 #<0

400.00

Pu

Mu

#50.00

k

km

#00.00

112.54

2#.#20

250.00

12<.-03

21.#14

200.00

124.013

2#.33

150.00

32.32<

25.<15

100.00

1#.043

2.<<#

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

50.00 0.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . . . . . 0 0 . 2 . 4 0 . 0 . 2 . 4 . , . 3 . 1 0 . 1 2 . 1 4 . 1 , . 1 3 . 2 0 . 2 2 . 2 4 . 2 , 2 3 # 0 # 2 # 4 # , # 3 4 , . 4 3 . 5 0 . 4 4 4

f.Mn (kNm)

MPa MPa

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI


N2

1 2 #

Luas 1asin*&1asin* tu(an*an

%!1 = #*3 ? %! = 0# %!2 = 2*3 ? %! = 402 %!# = #*3 ? %! = 0#


mm2 mm2 mm2

/1 = 2?x @ / ! = /2 = x @ /! = /# = /! =

210 125 40

mm mm mm

Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E?10#

Pno =

1##0 k 0.1 ? 78 ? b ? h ?10 = 125 k Pa/a kon/i!i balan7e " 7 = 7b = 00 * 00 @  y ? /1 = 12-.2- mm

%! = 103 mm2 Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " !i = 0.00# ?  7  / i  * 7 'egangan pa/a ma!ingma!ing baja tulangan " Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q +  y * ! maka "  !i = e!i? ! &ntuk Q !i Q ³  y * ! maka "  !i =Q !i Q * e!i?  y &ntuk >umlah interal jarak gr! netral =

→

#

125

→

D7 = 2.0000

URAIAN PERHITUNGAN

PERSAMAAN

UNIT


!i = %!i ?  !i ? 10# 9! = B S !i E?10# M!i = !i?h*2  /i M! = S M!i a = N1 ? 7 97 = 0.35 ?  78 ? b ? a ? 10 # M7 = 97 ? h  a * 2 Pn = 9! @ 97 Mn = M7 @ M!?10# Pu = f Pn



N2

Luas 1asin*&1asin* tu(an*an

%!1 = #*3 ? %! = 0# %!2 = 2*3 ? %! = 402 %!# = #*3 ? %! = 0#

1 2 #


mm2 mm2 mm2

/1 = 2?x @ / ! = /2 = x @ /! = /# = /! =

210 125 40

mm mm mm

Pa/a kon/i!i tekan ak!ial !entri! Mno = 0 " Pno = 0.30?B 0.35? 78 ?b?h @ %!? y  0.35? 78E?10#

Pno =

1##0 k 0.1 ? 78 ? b ? h ?10 = 125 k Pa/a kon/i!i balan7e " 7 = 7b = 00 * 00 @  y ? /1 = 12-.2- mm →

#

%! = 103 mm2 Pa/a kon/i!i gari! netral terletak pa/a jarak 7 /ari !i!i beton tekan terluar " !i = 0.00# ?  7  / i  * 7 'egangan pa/a ma!ingma!ing baja tulangan " Tegangan pa/a ma!ingma!ing baja tulangan " Q !i Q +  y * ! maka "  !i = e!i? ! &ntuk Q !i Q ³  y * ! maka "  !i =Q !i Q * e!i?  y &ntuk >umlah interal jarak gr! netral =

125

URAIAN PERHITUNGAN

PERSAMAAN


!i = %!i ?  !i ? 10 9! = B S !i E?10# M!i = !i?h*2  /i M! = S M!i a = N1 ? 7 97 = 0.35 ?  78 ? b ? a ? 10 # M7 = 97 ? h  a * 2 Pn = 9! @ 97 Mn = M7 @ M!?10# Pu = f Pn

→

D7 = 2.0000 UNIT

#



1000.00 <50.00 <00.00 350.00 300.00 -50.00 -00.00 ) N k ( n P . f

b= h=

50.00 00.00

Tul. "

550.00

;

 78 =  y =

500.00 450.00 400.00 #50.00 #00.00

250 250 D

20 #<0

Pu

Mu

k

km

112.54

2#.#20

12<.-03

21.#14

150.00

124.013

2#.33

100.00

32.32<

25.<15

50.00

1#.043

2.<<#

0.00

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

250.00 200.00

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 3 . 4 0 . 2 . 4 . , . 3 . 1 0 . 1 2 . 1 4 . 1 , . 1 3 . 2 0 . 2 2 . 2 4 . 2 , . 2 3 . # 0 . # 2 . # 4 . # , . # 0 4 2 . 4 4 . 4 , . 4 3 . 5 0 .

f.Mn (kNm)

mm mm "<

MPa MPa


1000.00 <50.00 <00.00 350.00 300.00 -50.00 -00.00 ) N k ( n P . f

b= h=

50.00 00.00

Tul. "

550.00

;

 78 =  y =

500.00 450.00 400.00 #50.00 #00.00

250 250 D

"<

20 #<0

Pu

Mu

k

km

112.54

2#.#20

12<.-03

21.#14

150.00

124.013

2#.33

100.00

32.32<

25.<15

50.00

1#.043

2.<<#

0.00

11.54<

20.454

114.222

#1.#22

-2.350

#4.-3

250.00 200.00

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 3 . 4 0 . 2 . 4 . , . 3 . 1 0 . 1 2 . 1 4 . 1 , . 1 3 . 2 0 . 2 2 . 2 4 . 2 , . 2 3 . # 0 . # 2 . # 4 . # , . # 0 4 2 . 4 4 . 4 , . 4 3 . 5 0 .

f.Mn (kNm)

mm mm MPa MPa


Momen ren7ana "   7 !1

Mu = f !2



!#

mm

Mn













9

MPa

MPa

MPa

k

k

k

k

kmm

141.313 1#3.42 1#5.055 1#1.5<< 123.0<0 124.523 120.<1# 11-.241 11#.514 10<.-23 105.332 101.<- <3.003 <#.<- 3<.3-< 35.-14 31.431 --.1-3 -2.30# 3.#54 #.3#0 5<.2254.545 4<.-32 44.<#4 40.000 #4.<-3 2<.34 24.53 1<.#55 1#.<5# 3.451 2.344 2.3-1 3.<

#2-.2-# #25.2-5 #2#.24#21.1<0 #1<.101 #1.<31 #14.32< #12.44 #10.425 #03.1-1 #05.332 #0#.55#01.1<5 2<3.-<5 2<.#5 2<#.3-3 2<1.#53 233.-<23.1<2 23#.544 230.351 2-3.112 2-5.#25 2-2.43< 2<.04 2.2#.-20.## 25-.5#4 254.#-3 251.1# 24-.33244.550 241.143 2#-.31

#<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000

1#1.04 1#0.301 12<.<35 12<.153 123.#13 12-.4 12.00 125.-21 124.32< 12#.<2# 12#.00# 122.03 121.113 120.15# 11<.1-2 113.1-5 11-.12 11.1#2 115.035 114.020 112.<#111.3#5 110.-15 10<.5-4 103.414 10-.2## 10.0#1 104.3010#.51 102.2<1 100.<<< <<.31 <3.##< <.<-1 <5.5--

2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242

452.#3< 44<.51 44.<1 44#.--< 440.32# 4#-.322 4#4.--5 4#1.32 423.541 425.#52 422.112 413.321 415.4-412.030 403.23 405.11< 401.55# #<-.<2#<4.241 #<0.4<# #3.31 #32.30# #-3.353 #-4.344 #-0.-0 #.0# #2.#-1 #53.0# #5#.- #4<.203 #44.53 #40.021 ##5.2<##0.432 #25.5-5

-2-1.1# -0<<.0# <24.#< -4-.1 5-.2#34. 1<<.23 011.0 531<.<# 525.32 5423.5223.40 5024.<5 4313.22 403.14 4#<4.4 41--.2 #<5-.00 #-#2.< #504.5< #2-2.0 #0#.4 2-<.5< 2552.#5 2#0#.30 2050.3# 1-<#.## 15#1.1 124.21 <<2.#4 -15.41 4##.2145.-< 14-.1< 445.3#

!1

!2

!#

!1

!2

!#

!

M

!1

M

!2

kmm

km M

a

kmm

kmm

mm

1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1

12-24.43 123<.53 1#0-1.21 1#243.45 1#423.#4 1#10.<4 1#-<.## 1#<34.55 141-5.3 14#<.-< 145.<4 14--.20 14<-0. 151--.#< 15#3-.4 1500.<1531-.<< 10#3.1 122.<2 14<1.02 1-2#.01 1<53.<1-1<<.02 1-44#.2 1-<1.31 1-<44.-3 13202.23 1344.44 13-#1.40 1<00#.21<230.20 1<52.## 1<34<.32 20142.30 20441.44

M

!#

!


2-5.000 2-#.000 2-1.000 2<.000 2-.000 25.000 2#.000 21.000 25<.000 25-.000 255.000 25#.000 251.000 24<.000 24-.000 245.000 24#.000 241.000 2#<.000 2#-.000 2#5.000 2##.000 2#1.000 22<.000 22-.000 225.000 22#.000 221.000 21<.000 21-.000 215.000 21#.000 211.000 20<.000 20-.000

0.000-1 0.000< 0.0003 0.000 0.0004 0.0002 0.0000 0.0005< 0.00050.00055 0.0005# 0.00051 0.0004< 0.00040.00045 0.0004# 0.00041 0.000#< 0.000# 0.000#4 0.000#2 0.000#0 0.00020.00025 0.00022 0.00020 0.00010.00015 0.00012 0.00010 0.00000.00004 0.00001 0.00001 0.00004

0.0014 0.001# 0.0012 0.0011 0.0010 0.00153 0.00150.0015 0.00155 0.00154 0.0015# 0.00152 0.00151 0.0014< 0.00143 0.00140.0014 0.00144 0.0014# 0.00142 0.00140 0.001#< 0.001#3 0.001# 0.001#5 0.001## 0.001#2 0.001#0 0.0012< 0.00120.0012 0.00124 0.00122 0.00121 0.0011<

0.0025 0.0025 0.0025 0.00255 0.00255 0.00255 0.00254 0.00254 0.00254 0.0025# 0.0025# 0.0025# 0.00252 0.00252 0.00251 0.00251 0.00251 0.00250 0.00250 0.0024< 0.0024< 0.00243 0.00243 0.00243 0.00240.00240.0024 0.0024 0.00245 0.00245 0.00244 0.00244 0.0024# 0.0024# 0.00242

35.54# 3#.513 31.4# -<.#-3 --.22 -5.114 -2.<## -0.-13 3.4-0 .13 #.31.511 5<.115.35 54.21# 51.-02 4<.143 4.55# 4#.<14 41.2#0 #3.501 #5.-25 #2.<01 #0.023 2-.104 24.1221.0<3 13.014 14.3-# 11.-5 3.415.0<1.-15 1.-#2 5.245

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2##.-5 2#2.05 2#0.#5 223.5 22.<5 225.25 22#.55 221.35 220.15 213.45 21.-5 215.05 21#.#5 211.5 20<.<5 203.25 20.55 204.35 20#.15 201.45 1<<.-5 1<3.05 1<.#5 1<4.5 1<2.<5 1<1.25 13<.55 13-.35 13.15 134.45 132.-5 131.05 1-<.#5 1--.5 1-5.<5


Momen ren7ana "   7 !1

Mu = f 

!2

!#













9

MPa

MPa

MPa

k

k

k

k

kmm

141.313 1#3.42 1#5.055 1#1.5<< 123.0<0 124.523 120.<1# 11-.241 11#.514 10<.-23 105.332 101.<- <3.003 <#.<- 3<.3-< 35.-14 31.431 --.1-3 -2.30# 3.#54 #.3#0 5<.2254.545 4<.-32 44.<#4 40.000 #4.<-3 2<.34 24.53 1<.#55 1#.<5# 3.451 2.344 2.3-1 3.<

#2-.2-# #25.2-5 #2#.24#21.1<0 #1<.101 #1.<31 #14.32< #12.44 #10.425 #03.1-1 #05.332 #0#.55#01.1<5 2<3.-<5 2<.#5 2<#.3-3 2<1.#53 233.-<23.1<2 23#.544 230.351 2-3.112 2-5.#25 2-2.43< 2<.04 2.2#.-20.## 25-.5#4 254.#-3 251.1# 24-.33244.550 241.143 2#-.31

#<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000

1#1.04 1#0.301 12<.<35 12<.153 123.#13 12-.4 12.00 125.-21 124.32< 12#.<2# 12#.00# 122.03 121.113 120.15# 11<.1-2 113.1-5 11-.12 11.1#2 115.035 114.020 112.<#111.3#5 110.-15 10<.5-4 103.414 10-.2## 10.0#1 104.3010#.51 102.2<1 100.<<< <<.31 <3.##< <.<-1 <5.5--

2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242

452.#3< 44<.51 44.<1 44#.--< 440.32# 4#-.322 4#4.--5 4#1.32 423.541 425.#52 422.112 413.321 415.4-412.030 403.23 405.11< 401.55# #<-.<2#<4.241 #<0.4<# #3.31 #32.30# #-3.353 #-4.344 #-0.-0 #.0# #2.#-1 #53.0# #5#.- #4<.203 #44.53 #40.021 ##5.2<##0.432 #25.5-5

-2-1.1# -0<<.0# <24.#< -4-.1 5-.2#34. 1<<.23 011.0 531<.<# 525.32 5423.5223.40 5024.<5 4313.22 403.14 4#<4.4 41--.2 #<5-.00 #-#2.< #504.5< #2-2.0 #0#.4 2-<.5< 2552.#5 2#0#.30 2050.3# 1-<#.## 15#1.1 124.21 <<2.#4 -15.41 4##.2145.-< 14-.1< 445.3#

!1

mm

Mn

!2

!#

!1

!2

!#

!

M

!1

M

!2

kmm

km M

a

kmm

kmm

mm

1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1

12-24.43 123<.53 1#0-1.21 1#243.45 1#423.#4 1#10.<4 1#-<.## 1#<34.55 141-5.3 14#<.-< 145.<4 14--.20 14<-0. 151--.#< 15#3-.4 1500.<1531-.<< 10#3.1 122.<2 14<1.02 1-2#.01 1<53.<1-1<<.02 1-44#.2 1-<1.31 1-<44.-3 13202.23 1344.44 13-#1.40 1<00#.21<230.20 1<52.## 1<34<.32 20142.30 20441.44

M

!#

!


2-5.000 2-#.000 2-1.000 2<.000 2-.000 25.000 2#.000 21.000 25<.000 25-.000 255.000 25#.000 251.000 24<.000 24-.000 245.000 24#.000 241.000 2#<.000 2#-.000 2#5.000 2##.000 2#1.000 22<.000 22-.000 225.000 22#.000 221.000 21<.000 21-.000 215.000 21#.000 211.000 20<.000 20-.000

0.000-1 0.000< 0.0003 0.000 0.0004 0.0002 0.0000 0.0005< 0.00050.00055 0.0005# 0.00051 0.0004< 0.00040.00045 0.0004# 0.00041 0.000#< 0.000# 0.000#4 0.000#2 0.000#0 0.00020.00025 0.00022 0.00020 0.00010.00015 0.00012 0.00010 0.00000.00004 0.00001 0.00001 0.00004

0.0014 0.001# 0.0012 0.0011 0.0010 0.00153 0.00150.0015 0.00155 0.00154 0.0015# 0.00152 0.00151 0.0014< 0.00143 0.00140.0014 0.00144 0.0014# 0.00142 0.00140 0.001#< 0.001#3 0.001# 0.001#5 0.001## 0.001#2 0.001#0 0.0012< 0.00120.0012 0.00124 0.00122 0.00121 0.0011<

0.0025 0.0025 0.0025 0.00255 0.00255 0.00255 0.00254 0.00254 0.00254 0.0025# 0.0025# 0.0025# 0.00252 0.00252 0.00251 0.00251 0.00251 0.00250 0.00250 0.0024< 0.0024< 0.00243 0.00243 0.00243 0.00240.00240.0024 0.0024 0.00245 0.00245 0.00244 0.00244 0.0024# 0.0024# 0.00242

35.54# 3#.513 31.4# -<.#-3 --.22 -5.114 -2.<## -0.-13 3.4-0 .13 #.31.511 5<.115.35 54.21# 51.-02 4<.143 4.55# 4#.<14 41.2#0 #3.501 #5.-25 #2.<01 #0.023 2-.104 24.1221.0<3 13.014 14.3-# 11.-5 3.415.0<1.-15 1.-#2 5.245

Analisis Kekuatan Kolom Beton Bertulang Dengan Dia gram Interaksi


M

k

kmm

7

<<#.44 <3.21 <-3.<< <-1.- <4.54 <5-.#1 <50.0< <42.3 <#5.4 <23.41 <21.1< <1#.< <0.-4 3<<.51 3<2.2< 335.0 3--.34 3-0.1 3#.#< 35.1 343.<4 341.-1 3#4.4< 32-.2 320.04 312.31 305.5< -<3.# -<1.14 -3#.<1 --.< -<.4 -2.24 -55.01 -4-.-<

7

30-1.3 3351.2 <13.55 10#-#.5 1111.2< 1134.-4 1254.<1 1#2-0.-< 1#<4.#< 1445.-1 15#14.-4 15<-1.4< 115.< 1-243.15 1-33.0 134-5.3 1<0-1.02 1<54.03 20224.35 20-3#.#4 21#2<.55 213#.43 22#35.1# 223<4.4< 2##<1.52#3-.#24#43.33 2430<.11 2525-.0 25<2.-# 211.12 252-.22 2<2.04 2-#12.53 2-3.3#

Pn

Mn

k 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#22.21 1#11.5< 1#00.<2 12<0.13 12-<.#< 123.54 125-.# 124. 12#5.2 1224.52 121#.#5 1202.11 11<0.30 11-<.42 11-.< 115.4# 1144.31 11##.12 1121.#5 110<.43 10<-.5# 1035.4< 10-#.#

km 0.00 20.30 21.-5 22.< 2#.2 24.54 25.4 2.# 2-.2 23.14 2<.02 2<.33 #0.-4 #1.5< #2.4# ##.2 #4.03 #4.3< #5.< #.4< #-.2#3.05 #3.32 #<.53 40.#4 41.03 41.32 42.55 4#.24#.<< 44.-0 45.40 4.0< 4.-3 4-.4 43.1#

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 35<.44 352.54 345.5< 3#3.2 3#1.0 324.55 31-.4 310.## 30#.15 -<5.<4 -33.-31.#--4.02 -.2 -5<.1-51.3 -44.1# -#.5# -23.3-21.1 -1#.40 -05.5<-.<

R.Mn km 0.00 1#.52 14.14 14.-5 15.#5 15.<5 1.55 1-.1# 1-.-2 13.2< 13.3 1<.42 1<.<3 20.5# 21.03 21.2 22.15 22.3 2#.20 2#.-2 24.2# 24.-# 25.2# 25.-# 2.22 2.-0 2-.13 2-. 23.1# 23.5< 2<.05 2<.51 2<.< #0.40 #0.35 #1.23

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2##.-5 2#2.05 2#0.#5 223.5 22.<5 225.25 22#.55 221.35 220.15 213.45 21.-5 215.05 21#.#5 211.5 20<.<5 203.25 20.55 204.35 20#.15 201.45 1<<.-5 1<3.05 1<.#5 1<4.5 1<2.<5 1<1.25 13<.55 13-.35 13.15 134.45 132.-5 131.05 1-<.#5 1--.5 1-5.<5

Analisis Kekuatan Kolom Beton Bertulang Dengan Dia gram Interaksi


M

k

kmm

7

7

<<#.44 <3.21 <-3.<< <-1.- <4.54 <5-.#1 <50.0< <42.3 <#5.4 <23.41 <21.1< <1#.< <0.-4 3<<.51 3<2.2< 335.0 3--.34 3-0.1 3#.#< 35.1 343.<4 341.-1 3#4.4< 32-.2 320.04 312.31 305.5< -<3.# -<1.14 -3#.<1 --.< -<.4 -2.24 -55.01 -4-.-<

30-1.3 3351.2 <13.55 10#-#.5 1111.2< 1134.-4 1254.<1 1#2-0.-< 1#<4.#< 1445.-1 15#14.-4 15<-1.4< 115.< 1-243.15 1-33.0 134-5.3 1<0-1.02 1<54.03 20224.35 20-3#.#4 21#2<.55 213#.43 22#35.1# 223<4.4< 2##<1.52#3-.#24#43.33 2430<.11 2525-.0 25<2.-# 211.12 252-.22 2<2.04 2-#12.53 2-3.3#

Pn

Mn

k 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#2<.<3 1#22.21 1#11.5< 1#00.<2 12<0.13 12-<.#< 123.54 125-.# 124. 12#5.2 1224.52 121#.#5 1202.11 11<0.30 11-<.42 11-.< 115.4# 1144.31 11##.12 1121.#5 110<.43 10<-.5# 1035.4< 10-#.#

km 0.00 20.30 21.-5 22.< 2#.2 24.54 25.4 2.# 2-.2 23.14 2<.02 2<.33 #0.-4 #1.5< #2.4# ##.2 #4.03 #4.3< #5.< #.4< #-.2#3.05 #3.32 #<.53 40.#4 41.03 41.32 42.55 4#.24#.<< 44.-0 45.40 4.0< 4.-3 4-.4 43.1#

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 34.43 35<.44 352.54 345.5< 3#3.2 3#1.0 324.55 31-.4 310.## 30#.15 -<5.<4 -33.-31.#--4.02 -.2 -5<.1-51.3 -44.1# -#.5# -23.3-21.1 -1#.40 -05.5<-.<

R.Mn km 0.00 1#.52 14.14 14.-5 15.#5 15.<5 1.55 1-.1# 1-.-2 13.2< 13.3 1<.42 1<.<3 20.5# 21.03 21.2 22.15 22.3 2#.20 2#.-2 24.2# 24.-# 25.2# 25.-# 2.22 2.-0 2-.13 2-. 23.1# 23.5< 2<.05 2<.51 2<.< #0.40 #0.35 #1.23


7 mm 205.000 20#.000 201.000 1<<.000 1<-.000 1<5.000 1<#.000 1<1.000 13<.000 13-.000 135.000 13#.000 131.000 1-<.000 1--.000 1-5.000 1-#.000 1-1.000 1<.000 1-.000 15.000 1#.000 11.000 15<.000 15-.000 155.000 15#.000 151.000 14<.000 14-.000 145.000 14#.000 141.000 1#<.000 1#-.000 1#5.000 1##.000



!1

0.00000.00010 0.0001# 0.00010.00020 0.0002# 0.0002 0.000#0 0.000## 0.000#0.00041 0.00044 0.00043 0.00052 0.0005 0.0000 0.0004 0.0003 0.000-# 0.000-0.00032 0.00030.000<1 0.000< 0.00101 0.0010 0.00112 0.00110.0012# 0.0012< 0.001#4 0.00141 0.00140.0015# 0.0010 0.0010.001-4



!2

0.00110.00115 0.0011# 0.00112 0.00110 0.00103 0.0010 0.00104 0.00102 0.000<< 0.000<0.000<5 0.000<# 0.000<1 0.00033 0.0003 0.0003# 0.00031 0.000-3 0.000-5 0.000-# 0.000-0 0.0000.0004 0.0001 0.00053 0.00055 0.00052 0.00043 0.00045 0.00041 0.000#3 0.000#4 0.000#0 0.0002 0.00022 0.00013



!#

0.00241 0.00241 0.00240 0.00240 0.002#< 0.002#3 0.002#3 0.002#0.002#0.002# 0.002#5 0.002#4 0.002#4 0.002## 0.002#2 0.002#1 0.002#1 0.002#0 0.0022< 0.00223 0.00220.0022 0.00225 0.00225 0.00224 0.0022# 0.00222 0.00221 0.0021< 0.00213 0.00210.0021 0.00215 0.00214 0.00212 0.00211 0.00210



!1

MPa 14.#4 20.<0 2.3 ##.1 #<.5<4 4.154 52.350 5<.3 .-#.-<31.031 33.525 <.1## 10#.<11 111.34 120.000 123.#24 1#.342 145.52 154.4<1 1#.# 1-#.00 132.0< 1<2.45# 202.543 212.<0# 22#.52< 2#4.4#245.#3 25-.14# 23.< 231.11< 2<#.1#0.4-5 #1<.-03 ###.### #4-.#3



!2

MPa 2#4.14 2#0.542 22.3 22#.11 21<.23< 215.#35 211.#<< 20-.##0 20#.1-5 1<3.<#0 1<4.5<5 1<0.14 135.#5 131.00 1-.2-1 1-1.42< 1.4-4 11.404 15.21# 150.3<3 145.455 1#<.3-1#4.11 123.#02 122.2<# 11.12< 10<.304 10#.#11 <.44 3<.-< 32.-5< -5.524 3.035 0.4#2 52.555 44.444 #.0<0



!#

MPa #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000



!1

k 3.3212.430 1.205 20.005 2#.332 2-.3#< #1.3-3 #.002 40.212 44.51# 43.<05#.#<5-.<3 2.--.4-5 -2.#32 --.40# 32.541 3-.301 <#.13<3.-0# 104.#55 110.1411.035 122.1-4 123.420 1#4.3#0 141.40< 143.15 155.105 12.2# 1<.51--.10 134.31 1<2.34# 201.02 20<.523



!2

k <4.15 <2.-0 <1.223 3<.-20 33.131 3.11 35.00< 3#.#-2 31.-01 -<.<<5 -3.251 -.4< -4.43 -2.-3-0.33# 3.<# .<4# 4.<04 2.310.30 53.4<1 5.243 5#.<50 51.5<# 4<.1-4.<3 44.155 41.544 #3.3# #.10< ##.2-< #0.#-0 2-.#-< 24.#01 21.1#4 1-.3-2 14.51#



!#

k 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242

9

!

k #20.5-1 #15.4< #10.2 #04.<52<<.541 2<4.014 233.#-# 232.1# 2-.-#1 2-0.-24 24.53253.#15 251.<05 245.#52 2#3.50 2#1.-< 224.-3# 21-.05 210.253 202.-#5 1<5.0#0 13-.1# 1-<.045 1-0.-51 12.245 15#.521 144.51#5.#-125.<40 11.2410.235 <.04 35.515 -4.32 #.5## 52.05# 40.223

M

!1

kmm -50.#0 100.-3 1#--.42 1-00.44 20#0.01 2#.#4 2-0<.5 #00.14 #413.05 #-3#.2 415-.0< 45#3.-# 4<23.-< 5#2-.53 5-#5.#3 152.50 5-<.2 -01.00 -4#.0< -<20.33 3#3<.-33-0.1 <#2.4< <3-.21 10#34.-3 10<15.-2 1140.5# 1201<.-3 125<4.0# 1#13#.<2 1#-<0.03 1441#.1< 1505#.<3 15-1#.21 1#<1.3 1-0<0.2 1-30<.35

M

!2

kmm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M

!#

kmm 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1

M

!

kmm 20-45.<1 2105.#3 21#-#.0# 21<.05 22025.2 22#1.<5 22-05.2 2#055.-5 2#41#. 2#--<.2# 24152.-0 245#4.## 24<24.40 25#2#.1< 25-#0.<< 2143.10 25-4.32-011.1 2-453.< 2-<1.4< 23#35.#2335.-2<#53.10 2<32.32 #0#30.#< #0<11.## #145.14 #2015.#3 #253<.4 ##1-<.5# ##-35.3 #4403.30 #504<.5< #5-03.32 ##3-.2< #-035.3#-305.4

a mm 1-4.25 1-2.55 1-0.35 1<.15 1-.45 15.-5 14.05 12.#5 10.5 153.<5 15-.25 155.55 15#.35 152.15 150.45 143.-5 14-.05 145.#5 14#.5 141.<5 140.25 1#3.55 1#.35 1#5.15 1##.45 1#1.-5 1#0.05 123.#5 12.5 124.<5 12#.25 121.55 11<.35 113.15 11.45 114.-5 11#.05




7 mm 205.000 20#.000 201.000 1<<.000 1<-.000 1<5.000 1<#.000 1<1.000 13<.000 13-.000 135.000 13#.000 131.000 1-<.000 1--.000 1-5.000 1-#.000 1-1.000 1<.000 1-.000 15.000 1#.000 11.000 15<.000 15-.000 155.000 15#.000 151.000 14<.000 14-.000 145.000 14#.000 141.000 1#<.000 1#-.000 1#5.000 1##.000



!1

0.00000.00010 0.0001# 0.00010.00020 0.0002# 0.0002 0.000#0 0.000## 0.000#0.00041 0.00044 0.00043 0.00052 0.0005 0.0000 0.0004 0.0003 0.000-# 0.000-0.00032 0.00030.000<1 0.000< 0.00101 0.0010 0.00112 0.00110.0012# 0.0012< 0.001#4 0.00141 0.00140.0015# 0.0010 0.0010.001-4



!2

0.00110.00115 0.0011# 0.00112 0.00110 0.00103 0.0010 0.00104 0.00102 0.000<< 0.000<0.000<5 0.000<# 0.000<1 0.00033 0.0003 0.0003# 0.00031 0.000-3 0.000-5 0.000-# 0.000-0 0.0000.0004 0.0001 0.00053 0.00055 0.00052 0.00043 0.00045 0.00041 0.000#3 0.000#4 0.000#0 0.0002 0.00022 0.00013



!#



!1

0.00241 0.00241 0.00240 0.00240 0.002#< 0.002#3 0.002#3 0.002#0.002#0.002# 0.002#5 0.002#4 0.002#4 0.002## 0.002#2 0.002#1 0.002#1 0.002#0 0.0022< 0.00223 0.00220.0022 0.00225 0.00225 0.00224 0.0022# 0.00222 0.00221 0.0021< 0.00213 0.00210.0021 0.00215 0.00214 0.00212 0.00211 0.00210

!2

MPa 14.#4 20.<0 2.3 ##.1 #<.5<4 4.154 52.350 5<.3 .-#.-<31.031 33.525 <.1## 10#.<11 111.34 120.000 123.#24 1#.342 145.52 154.4<1 1#.# 1-#.00 132.0< 1<2.45# 202.543 212.<0# 22#.52< 2#4.4#245.#3 25-.14# 23.< 231.11< 2<#.1#0.4-5 #1<.-03 ###.### #4-.#3

MPa 2#4.14 2#0.542 22.3 22#.11 21<.23< 215.#35 211.#<< 20-.##0 20#.1-5 1<3.<#0 1<4.5<5 1<0.14 135.#5 131.00 1-.2-1 1-1.42< 1.4-4 11.404 15.21# 150.3<3 145.455 1#<.3-1#4.11 123.#02 122.2<# 11.12< 10<.304 10#.#11 <.44 3<.-< 32.-5< -5.524 3.035 0.4#2 52.555 44.444 #.0<0



!#

MPa #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000



!1

k 3.3212.430 1.205 20.005 2#.332 2-.3#< #1.3-3 #.002 40.212 44.51# 43.<05#.#<5-.<3 2.--.4-5 -2.#32 --.40# 32.541 3-.301 <#.13<3.-0# 104.#55 110.1411.035 122.1-4 123.420 1#4.3#0 141.40< 143.15 155.105 12.2# 1<.51--.10 134.31 1<2.34# 201.02 20<.523



!2

k <4.15 <2.-0 <1.223 3<.-20 33.131 3.11 35.00< 3#.#-2 31.-01 -<.<<5 -3.251 -.4< -4.43 -2.-3-0.33# 3.<# .<4# 4.<04 2.310.30 53.4<1 5.243 5#.<50 51.5<# 4<.1-4.<3 44.155 41.544 #3.3# #.10< ##.2-< #0.#-0 2-.#-< 24.#01 21.1#4 1-.3-2 14.51#



!#

k 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242

9

!

k #20.5-1 #15.4< #10.2 #04.<52<<.541 2<4.014 233.#-# 232.1# 2-.-#1 2-0.-24 24.53253.#15 251.<05 245.#52 2#3.50 2#1.-< 224.-3# 21-.05 210.253 202.-#5 1<5.0#0 13-.1# 1-<.045 1-0.-51 12.245 15#.521 144.51#5.#-125.<40 11.2410.235 <.04 35.515 -4.32 #.5## 52.05# 40.223

M

!1

kmm -50.#0 100.-3 1#--.42 1-00.44 20#0.01 2#.#4 2-0<.5 #00.14 #413.05 #-3#.2 415-.0< 45#3.-# 4<23.-< 5#2-.53 5-#5.#3 152.50 5-<.2 -01.00 -4#.0< -<20.33 3#3<.-33-0.1 <#2.4< <3-.21 10#34.-3 10<15.-2 1140.5# 1201<.-3 125<4.0# 1#13#.<2 1#-<0.03 1441#.1< 1505#.<3 15-1#.21 1#<1.3 1-0<0.2 1-30<.35


9

7

k -40.5 -##.#4 -2.11 -13.3< -11. -04.44 <-.21 3<.<< 32.- -5.54 3.#1 1.0< 5#.3 4.4 #<.41 #2.1< 24.< 1-.-4 10.51 0#.2< 5<.0 533.34 531.1 5-4.#< 5-.1 55<.<4 552.-1 545.4< 5#3.2 5#1.04 52#.31 51.5< 50<.# 502.14 4<4.<1 43-.< 430.4

M

7

kmm 23043.30 23#<3.4< 23-#5.<0 2<01.0# 2<#-#.32<-4.4# 2<<2.-1 #02#3.-0 #0502.41 #0-5#.34 #0<<2.<< #121<.3 #14#4.44 #1#.-4 #132.- #2004.4< #21<.<4 #2#2#.11 #244.00 #25<2.1 #2-03.<# #2312.<#2<04.-# #2<34.20 ##051.#< ##10.#0 ##143.<# ##1-<.23 ##1<-.#4 ##20#.12 ##1<.2 ##1--.3# ##14.- ##10#.41 ##04-.-3 #2<-<.3#23<<.-

Pn

Mn

k 101.1# 1043.31 10#.#3 102#.34 1011.20 <<3.45 <35.5< <-2.0 <5<.4< <4.2 <#2.<0 <1<.40 <05.-3<1.<< 3-3.0 3#.<3 34<.-5 3#5.#4 320.-30.02 -<1.0< --5.<-0. -45.14 -2<.41 -1#.4 <-.23 30.3 4.20 4-.23 #0.10 12.# 5<4.33 5-.32 553.45 5#<.-4 520.<

km 43.-< 4<.45 50.11 50.- 51.40 52.04 52.5#.2< 5#.<2 54.5# 55.15 55.-5 5.# 5.< 5-.5 53.15 53.-4 5<.## 5<.<2 0.51 1.0< 1.3 2.2 2.35 #.4# 4.02 4.1 5.1< 5.-< .#3 .<3 -.5< 3.20 3.31 <.44 -0.0-0.-1

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 3<.-4 31.-2 -#.5 5.50 5-.23 43.<< 40.# #2.1< 2#.15.00.#3 5<-.1 533.-5 5-<.-< 5-0.-4 51.5< 552.## 542.<5##.50 52#.<1 514.21 504.#3 4<4.4# 434.#4 4-4.12 4#.-5 45#.2# 442.5 4#1.-# 420.-# 40<.5 #<3.21 #3.#-4.<# #2.<< #50.3# ##3.45

R.Mn km #1.-2 #2.15 #2.5#2.<< ##.41 ##.32 #4.2# #4.4 #5.05 #5.45 #5.34 #.24 #.# #-.02 #-.41 #-.30 #3.13 #3.5#3.<5 #<.## #<.-1 40.0< 40.440.35 41.2# 41.1 41.<< 42.#3 42.- 4#.15 4#.54 4#.<# 44.## 44.-# 45.1# 45.54 45.<

M

!2

kmm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M

!#

kmm 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1

M

!

kmm 20-45.<1 2105.#3 21#-#.0# 21<.05 22025.2 22#1.<5 22-05.2 2#055.-5 2#41#. 2#--<.2# 24152.-0 245#4.## 24<24.40 25#2#.1< 25-#0.<< 2143.10 25-4.32-011.1 2-453.< 2-<1.4< 23#35.#2335.-2<#53.10 2<32.32 #0#30.#< #0<11.## #145.14 #2015.#3 #253<.4 ##1-<.5# ##-35.3 #4403.30 #504<.5< #5-03.32 ##3-.2< #-035.3#-305.4

a mm 1-4.25 1-2.55 1-0.35 1<.15 1-.45 15.-5 14.05 12.#5 10.5 153.<5 15-.25 155.55 15#.35 152.15 150.45 143.-5 14-.05 145.#5 14#.5 141.<5 140.25 1#3.55 1#.35 1#5.15 1##.45 1#1.-5 1#0.05 123.#5 12.5 124.<5 12#.25 121.55 11<.35 113.15 11.45 114.-5 11#.05


9

M

7

7

k -40.5 -##.#4 -2.11 -13.3< -11. -04.44 <-.21 3<.<< 32.- -5.54 3.#1 1.0< 5#.3 4.4 #<.41 #2.1< 24.< 1-.-4 10.51 0#.2< 5<.0 533.34 531.1 5-4.#< 5-.1 55<.<4 552.-1 545.4< 5#3.2 5#1.04 52#.31 51.5< 50<.# 502.14 4<4.<1 43-.< 430.4

kmm 23043.30 23#<3.4< 23-#5.<0 2<01.0# 2<#-#.32<-4.4# 2<<2.-1 #02#3.-0 #0502.41 #0-5#.34 #0<<2.<< #121<.3 #14#4.44 #1#.-4 #132.- #2004.4< #21<.<4 #2#2#.11 #244.00 #25<2.1 #2-03.<# #2312.<#2<04.-# #2<34.20 ##051.#< ##10.#0 ##143.<# ##1-<.23 ##1<-.#4 ##20#.12 ##1<.2 ##1--.3# ##14.- ##10#.41 ##04-.-3 #2<-<.3#23<<.-

Pn

Mn

k 101.1# 1043.31 10#.#3 102#.34 1011.20 <<3.45 <35.5< <-2.0 <5<.4< <4.2 <#2.<0 <1<.40 <05.-3<1.<< 3-3.0 3#.<3 34<.-5 3#5.#4 320.-30.02 -<1.0< --5.<-0. -45.14 -2<.41 -1#.4 <-.23 30.3 4.20 4-.23 #0.10 12.# 5<4.33 5-.32 553.45 5#<.-4 520.<

km 43.-< 4<.45 50.11 50.- 51.40 52.04 52.5#.2< 5#.<2 54.5# 55.15 55.-5 5.# 5.< 5-.5 53.15 53.-4 5<.## 5<.<2 0.51 1.0< 1.3 2.2 2.35 #.4# 4.02 4.1 5.1< 5.-< .#3 .<3 -.5< 3.20 3.31 <.44 -0.0-0.-1

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

k 3<.-4 31.-2 -#.5 5.50 5-.23 43.<< 40.# #2.1< 2#.15.00.#3 5<-.1 533.-5 5-<.-< 5-0.-4 51.5< 552.## 542.<5##.50 52#.<1 514.21 504.#3 4<4.4# 434.#4 4-4.12 4#.-5 45#.2# 442.5 4#1.-# 420.-# 40<.5 #<3.21 #3.#-4.<# #2.<< #50.3# ##3.45

R.Mn km #1.-2 #2.15 #2.5#2.<< ##.41 ##.32 #4.2# #4.4 #5.05 #5.45 #5.34 #.24 #.# #-.02 #-.41 #-.30 #3.13 #3.5#3.<5 #<.## #<.-1 40.0< 40.440.35 41.2# 41.1 41.<< 42.#3 42.- 4#.15 4#.54 4#.<# 44.## 44.-# 45.1# 45.54 45.<


7 mm 1#1.000 12<.000 12-.000 125.000 12#.000 121.000 11<.000 11-.000 115.000 11#.000 111.000 10<.000 10-.000 105.000 10#.000 101.000 <<.000 <-.000 <5.000 <#.000 <1.000 3<.000 3-.000 35.000 3#.000 31.000 -<.000 --.000 -5.000 -#.000 -1.000 3.000



!1

0.00131 0.00133 0.001< 0.00204 0.00212 0.00221 0.0022< 0.002#3 0.00243 0.00253 0.0023 0.002-3 0.0023< 0.00#00 0.00#12 0.00#24 0.00## 0.00#4< 0.00## 0.00#-0.00#<2 0.00403 0.00424 0.00441 0.0045< 0.004-3 0.004<0.00513 0.00540 0.005# 0.00530.002



!2

0.00014 0.0000< 0.00005 0.00000 0.00005 0.00010 0.00015 0.00021 0.0002 0.000#2 0.000#3 0.00044 0.00050 0.00050.0004 0.000-1 0.000-< 0.00030.000<5 0.0010# 0.00112 0.00121 0.001#1 0.00141 0.00152 0.001# 0.001-5 0.00130.00200 0.00214 0.00223 0.00251



!#

0.00203 0.00200.0020 0.00204 0.00202 0.00201 0.001<< 0.001<0.001< 0.001<4 0.001<2 0.001<0 0.00133 0.0013 0.0013# 0.00131 0.001-< 0.001- 0.001-4 0.001-1 0.0013 0.0015 0.0012 0.0015< 0.00155 0.00152 0.00143 0.00144 0.00140 0.001# 0.001#1 0.00124



!1

MPa #1.3#2 #-.-44 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000

KONDISI TEKAN AKSIAL KECIL 5 Pn 6 7." 8 9:/ 8 b 8 3 KONDISI BALANCE



!2

MPa 2-.431 13.05 <.44< 0.000 <.-5 1<.3#5 #0.252 41.02 52.1-4 #.-1-5.- 33.0-# 100.<#5 114.23 123.155 142.5-4 15-.5- 1-#.1< 13<.4-4 20.452 224.1- 242.<22.0< 232.#5# #0#.14 #25.<2 #4<.##-4.02 #<0.000 #<0.000 #<0.000 #<0.000



!#

MPa #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #3-.11 #3#.-34 #-<.31#-5.-01 #-1.42< #.<<0 #2.#- #5-.5- #52.5-#4-.#3 #41.<#5 ##.24 ##0.###24.1#3 #1-.4#10.34# #0#.-04 2<.20# 233.#12 230.000 2-1.2## 21.<-2 24-.05<



!1

k 213.252 22-.242#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242



!2

k 11.051 -.431 #.300 0.000 #.<2# -.<- 12.15 1.4<20.<30 25.22 #0.4#1 #5.41 40.533 45.<551.5#4 5-.### #.#5 <.4 -.1<2 3#.01< <0.14 <-.5<4 105.#34 11#.541 122.0<1 1#1.0# 140.43< 150.405 15.323 15.323 15.323 15.323



!#

k 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2##.301 2#1.4<# 22<.100 22.1224.040 221.## 213.530 215.35 212.-0 20<.523 20.251 202.3#0 1<<.255 1<5.515 1<1.00 13-.4< 13#.1<0 1-3.5 1-#.<0 13.3<2 1#.04 153.013 14<.022

9

!

k 23.041 15.4-#.300 0.000 #.<2# -.<- 12.15 1.4<20.<30 2-.0# #4.131 41.55< 4<.21# 5-.15< 5.41# -#.<<5 32.<2# <2.21< 101.<0112.011 122.55< 1##.532 145.111 15-.13# 1<.3#13#.115 1<-.0 211.-42 22#.1-< 223.42#4.05# 24#.043

M

!1

kmm 13551.42 1<#15.<1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1

M

!2

kmm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M

!#

kmm 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<3-#.10 1<-.<0 1<4-#.4< 1<22.43 1<04#.44 13315.33 135-<.#2 13###.1< 130-.<2 1-30<.35 1-5#1.#0 1-240.51 1<#.4 113.31 123.02 15<#-.1< 155-1.1# 1513.54 14-31.<14#55.32 1#<0.#2 1#4#1.50 12.<0

M

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kmm #354-.0# #<#11.53 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<33.-1 #<-2.51 #<4<.10 #<253.0< #<0#<.05 #3311.4< #35-4.<# #3#23.30 #30-2.5# #-305.4 #-52.<1 #-2#.12 #<#2.25 #14.42 #231.# #5<#2.-< #55.-4 #5132.15 #4---.53 #4#51.4# ##<01.<# ##42-.11 #22.51

a mm 111.#5 10<.5 10-.<5 10.25 104.55 102.35 101.15 <<.45 <-.-5 <.05 <4.#5 <2.5 <0.<5 3<.25 3-.55 35.35 34.15 32.45 30.-5 -<.05 --.#5 -5.5 -#.<5 -2.25 -0.55 3.35 -.15 5.45 #.-5 2.05 0.#5 5-.30




7 mm 1#1.000 12<.000 12-.000 125.000 12#.000 121.000 11<.000 11-.000 115.000 11#.000 111.000 10<.000 10-.000 105.000 10#.000 101.000 <<.000 <-.000 <5.000 <#.000 <1.000 3<.000 3-.000 35.000 3#.000 31.000 -<.000 --.000 -5.000 -#.000 -1.000 3.000



!1

0.00131 0.00133 0.001< 0.00204 0.00212 0.00221 0.0022< 0.002#3 0.00243 0.00253 0.0023 0.002-3 0.0023< 0.00#00 0.00#12 0.00#24 0.00## 0.00#4< 0.00## 0.00#-0.00#<2 0.00403 0.00424 0.00441 0.0045< 0.004-3 0.004<0.00513 0.00540 0.005# 0.00530.002



!2

0.00014 0.0000< 0.00005 0.00000 0.00005 0.00010 0.00015 0.00021 0.0002 0.000#2 0.000#3 0.00044 0.00050 0.00050.0004 0.000-1 0.000-< 0.00030.000<5 0.0010# 0.00112 0.00121 0.001#1 0.00141 0.00152 0.001# 0.001-5 0.00130.00200 0.00214 0.00223 0.00251



!#



!1

0.00203 0.00200.0020 0.00204 0.00202 0.00201 0.001<< 0.001<0.001< 0.001<4 0.001<2 0.001<0 0.00133 0.0013 0.0013# 0.00131 0.001-< 0.001- 0.001-4 0.001-1 0.0013 0.0015 0.0012 0.0015< 0.00155 0.00152 0.00143 0.00144 0.00140 0.001# 0.001#1 0.00124

!2

MPa #1.3#2 #-.-44 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000

MPa 2-.431 13.05 <.44< 0.000 <.-5 1<.3#5 #0.252 41.02 52.1-4 #.-1-5.- 33.0-# 100.<#5 114.23 123.155 142.5-4 15-.5- 1-#.1< 13<.4-4 20.452 224.1- 242.<22.0< 232.#5# #0#.14 #25.<2 #4<.##-4.02 #<0.000 #<0.000 #<0.000 #<0.000



!#

MPa #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #<0.000 #3-.11 #3#.-34 #-<.31#-5.-01 #-1.42< #.<<0 #2.#- #5-.5- #52.5-#4-.#3 #41.<#5 ##.24 ##0.###24.1#3 #1-.4#10.34# #0#.-04 2<.20# 233.#12 230.000 2-1.2## 21.<-2 24-.05<



!1

k 213.252 22-.242#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242



!2

k 11.051 -.431 #.300 0.000 #.<2# -.<- 12.15 1.4<20.<30 25.22 #0.4#1 #5.41 40.533 45.<551.5#4 5-.### #.#5 <.4 -.1<2 3#.01< <0.14 <-.5<4 105.#34 11#.541 122.0<1 1#1.0# 140.43< 150.405 15.323 15.323 15.323 15.323



!#

k 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2#5.242 2##.301 2#1.4<# 22<.100 22.1224.040 221.## 213.530 215.35 212.-0 20<.523 20.251 202.3#0 1<<.255 1<5.515 1<1.00 13-.4< 13#.1<0 1-3.5 1-#.<0 13.3<2 1#.04 153.013 14<.022

9

!

k 23.041 15.4-#.300 0.000 #.<2# -.<- 12.15 1.4<20.<30 2-.0# #4.131 41.55< 4<.21# 5-.15< 5.41# -#.<<5 32.<2# <2.21< 101.<0112.011 122.55< 1##.532 145.111 15-.13# 1<.3#13#.115 1<-.0 211.-42 22#.1-< 223.42#4.05# 24#.043

M

kmm 13551.42 1<#15.<1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1

KONDISI TEKAN AKSIAL KECIL 5 Pn 6 7." 8 9:/ 8 b 8 3 KONDISI BALANCE


9

7

k 4-#.24 4.01 453.-< 451.5 444.#4 4#-.11 42<.3< 422. 415.44 403.21 400.<< #<#.- #3.54 #-<.#1 #-2.0< #4.3 #5-.4 #50.41 #4#.1< ##5.< #23.-4 #21.51 #14.2< #0-.0 2<<.34 2<2.1 235.#< 2-3.1 2-0.<4 2#.-1 25.4< 245.5

M

7

kmm #230-.1< #2-02.4# #2535.#3 #245.05 #2#14.44 #210.55 #1<<4.#3 #1315.<2 #125.13 #1422.1 #120.35 #0<-<.2 #0-#<.#< #043-.24 #0222.31 2<<4.0< 2<5-.0< 2<#55.31 2<042.24 23-1.#< 23#-3.2 2302-.35 2-5.1 2-2<0.13 2<02.<2 250#.#3 20<1.55 25-.44 252#1.05 24-32.#3 24#21.4# 2#0.<-

Pn

Mn

k 501.23 431.4< 42.5< 451.5 440.41 42<.14 41-.-2 40.1#<4.4 #31.15 #.31 #52.20 ##-.#2 #22.15 #0.2<0.32-4.-1 253.1< 241.23 22#.<5 20.13 13-.<# 1<.13 14<.33 1#0.00 10<.50 33.#2 .42 4-.- #5.25 22.4# 2.0

km -1.#5 -2.01 -2.53 -2.45 -2.#1 -2.15 -1.<< -1.31 -1.2 -1.2< -0.33 -0.45 -0.00 <.5# <.0# 3.52 -.<< -.4# .35 .24 5.1 4.< 4.23 #.52.34 2.01.20.45 5<.53 53.3 5-.-5 5.2-

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.0.< 0.-2 0.-4 0.- 0.-0.30

R.Mn

k #25.3# #12.<#00.3 2<#.52 23.22-3.<4 2-1.52 24.01 25.40 24-.-5 2#3.42 223.<# 21<.2 20<.40 1<<.#4 13<.0 1-3.5 1-.3# 15.3# 145.51#4.02 122.15 10<.< <-.42 34.50 -#.21 1.#0 4-.34 #5.42.-1 1-.#4 2.0-

km 4.#3 4.31 4-.14-.0< 4-.00 4.<0 4.-< 4.4.55 4.#4 4.045.-< 45.50 45.1< 44.344.54 44.1< 4#.3# 4#.45 4#.0 42.5 42.22 41.-3 41.#2 40.34 41.50 42.52 4#.54 44.25 44.444.4 44.34

31.25 31.25

0.00 50.00

0.00

0.00

!1

M

!2

kmm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M

!#

kmm 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<<<5.1 1<3-#.10 1<-.<0 1<4-#.4< 1<22.43 1<04#.44 13315.33 135-<.#2 13###.1< 130-.<2 1-30<.35 1-5#1.#0 1-240.51 1<#.4 113.31 123.02 15<#-.1< 155-1.1# 1513.54 14-31.<14#55.32 1#<0.#2 1#4#1.50 12.<0

M

!

kmm #354-.0# #<#11.53 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<<<1.22 #<33.-1 #<-2.51 #<4<.10 #<253.0< #<0#<.05 #3311.4< #35-4.<# #3#23.30 #30-2.5# #-305.4 #-52.<1 #-2#.12 #<#2.25 #14.42 #231.# #5<#2.-< #55.-4 #5132.15 #4---.53 #4#51.4# ##<01.<# ##42-.11 #22.51

a mm 111.#5 10<.5 10-.<5 10.25 104.55 102.35 101.15 <<.45 <-.-5 <.05 <4.#5 <2.5 <0.<5 3<.25 3-.55 35.35 34.15 32.45 30.-5 -<.05 --.#5 -5.5 -#.<5 -2.25 -0.55 3.35 -.15 5.45 #.-5 2.05 0.#5 5-.30


9

M

7

7

k 4-#.24 4.01 453.-< 451.5 444.#4 4#-.11 42<.3< 422. 415.44 403.21 400.<< #<#.- #3.54 #-<.#1 #-2.0< #4.3 #5-.4 #50.41 #4#.1< ##5.< #23.-4 #21.51 #14.2< #0-.0 2<<.34 2<2.1 235.#< 2-3.1 2-0.<4 2#.-1 25.4< 245.5

kmm #230-.1< #2-02.4# #2535.#3 #245.05 #2#14.44 #210.55 #1<<4.#3 #1315.<2 #125.13 #1422.1 #120.35 #0<-<.2 #0-#<.#< #043-.24 #0222.31 2<<4.0< 2<5-.0< 2<#55.31 2<042.24 23-1.#< 23#-3.2 2302-.35 2-5.1 2-2<0.13 2<02.<2 250#.#3 20<1.55 25-.44 252#1.05 24-32.#3 24#21.4# 2#0.<-

Pn

Mn

k 501.23 431.4< 42.5< 451.5 440.41 42<.14 41-.-2 40.1#<4.4 #31.15 #.31 #52.20 ##-.#2 #22.15 #0.2<0.32-4.-1 253.1< 241.23 22#.<5 20.13 13-.<# 1<.13 14<.33 1#0.00 10<.50 33.#2 .42 4-.- #5.25 22.4# 2.0

km -1.#5 -2.01 -2.53 -2.45 -2.#1 -2.15 -1.<< -1.31 -1.2 -1.2< -0.33 -0.45 -0.00 <.5# <.0# 3.52 -.<< -.4# .35 .24 5.1 4.< 4.23 #.52.34 2.01.20.45 5<.53 53.3 5-.-5 5.2-

R.Pn

R 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.0.< 0.-2 0.-4 0.- 0.-0.30

R.Mn

k #25.3# #12.<#00.3 2<#.52 23.22-3.<4 2-1.52 24.01 25.40 24-.-5 2#3.42 223.<# 21<.2 20<.40 1<<.#4 13<.0 1-3.5 1-.3# 15.3# 145.51#4.02 122.15 10<.< <-.42 34.50 -#.21 1.#0 4-.34 #5.42.-1 1-.#4 2.0-

km 4.#3 4.31 4-.14-.0< 4-.00 4.<0 4.-< 4.4.55 4.#4 4.045.-< 45.50 45.1< 44.344.54 44.1< 4#.3# 4#.45 4#.0 42.5 42.22 41.-3 41.#2 40.34 41.50 42.52 4#.54 44.25 44.444.4 44.34

31.25 31.25

0.00 50.00

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0.00


7 mm 12-

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!1

0.001<5

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!2

0.00005

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0.0020

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MPa #<0.000

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MPa 10.-14

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MPa #<0.000



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9

k 2#5.242

k 4.#03

k 2#5.242

k kmm 4.#03 1<<<5.1

!1

!2

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!

M

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M

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kmm 0.00

M

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kmm 1<<<5.1

M

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kmm #<<<1.22

a mm 103.13


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7 mm 12-

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0.00005

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0.0020

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MPa 10.-14

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MPa #<0.000



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9

k 2#5.242

k 4.#03

k 2#5.242

k kmm 4.#03 1<<<5.1

!1

!2

!#

!

M


9

7

k 45<.--

M

7

kmm #202.0-

Pn

Mn

k 44.03

km -2.5<

R.Pn

R 0.5

k #01.5

R.Mn km 4-.1<

!1

M

!2

kmm 0.00

M

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kmm 1<<<5.1

M

!

kmm #<<<1.22

a mm 103.13


9

7

k 45<.--

M

7

kmm #202.0-

Pn

Mn

k 44.03

km -2.5<

R.Pn

R 0.5

k #01.5

R.Mn km 4-.1<

Maka s diambil 300 mm. Tipe

Lx (mm)

Ly (mm)

1(III)

2150

2650

2(IX)

1150

2150

3 (III)

2150

3000

4(VIII)

1000

2450

5(II)

1650

2450

6(II)

1150

2450

7(IX)

950

2000

8(IX)

1500

2000

9

1000

3550

10

1050

2800

11(IX)

2500

2800

12(VIII)

1050

2000

13(VI)

2200

3550

14(VIII)

1000

1350

15(IX)

1350

2800

16(III)

2250

3800

17(V)

2000

2250

18(III)

2200

3600

Tipe

Mlx/Φ (N mm)

Mly/Φ (N mm)

x/Φ (N m

1(III)

1568298 69

1032782 06

213099 7

Mty/Φ 28305

Maka s diambil 300 mm. Tipe

Lx (mm)

Ly (mm)

1(III)

2150

2650

2(IX)

1150

2150

3 (III)

2150

3000

4(VIII)

1000

2450

5(II)

1650

2450

6(II)

1150

2450

7(IX)

950

2000

8(IX)

1500

2000

9

1000

3550

10

1050

2800

11(IX)

2500

2800

12(VIII)

1050

2000

13(VI)

2200

3550

14(VIII)

1000

1350

15(IX)

1350

2800

16(III)

2250

3800

17(V)

2000

2250

18(III)

2200

3600

Tipe

Mlx/Φ (N mm)

Mly/Φ (N mm)

x/Φ (N m

1(III)

1568298,69

1032782,06

213099,7

28305

2(IX)

612846,50

186042,69

902854,22

5800

3 (III)

1989061,75

879777,31

710365,1

29453

4(VIII)

653725,00

132400,00

001275,0

6040

5(II)

1025055,28

371723,34

689651,5

12255

6(II)

634733,88

164155,31

897382,38

5800

7(IX)

433154,88

126959,19

619859,56

3958

8(IX)

763368,75

372375,00

359168,7

10240

9

591250

-

918750

10

651250

-

1012500

11(IX)

1680859,38

1189531,25

361718,7

12(VIII)

611253,56

159655,78

13(VI)

2843621,00

1201530,00

-

44456

14(VIII)

388925,00

190325,00

728200,00

6123

15(IX)

874708,88

256380,19

251738,5

7691

16(III)

2681100,00

879735,94

587194,5

32256

17(V)

1324000,00

662000,00

515600,0

18(III)

2563264,00

841071,00

385584,5

012673,81

Mty/Φ

28186 6933

30839

Tipe

Aslx

Asly

Astx

Asty

ρlx

ρly

1(III)

54,09

41,05

111,86

114,08

0,00054

0,00041

2(IX)

21,02

7,35

31,02

22,98

0,00021

0,00007

3 (III)

68,76

34,93

129,55

118,81

0,00069

0,00035

4(VIII)

22,43

5,23

34,42

23,94

0,00022

0,00005

5(II)

35,24

14,70

58,31

48,79

0,00035

0,00015

6(II)

21,78

6,48

30,83

22,98

0,00022

0,00006

7(IX)

14,84

5,01

21,26

15,66

0,00015

0,00005

8(IX)

26,21

14,73

46,82

40,70

0,00026

0,00015

9

20

-

32

-

0,0002

-

10

22

-

35

-

0,00022

-

11(IX)

58,01

47,34

117,14

113,59

0,00058

0,00047

12(VIII)

20,97

6,31

34,82

27,49

0,00021

0,00006

13(VI)

98,79

47,82

-

181,49

0,00099

0,00048

14(VIII)

13,33

7,52

25,00

24,27

0,00013

0,00008

15(IX)

30,05

10,13

43,09

30,51

0,00030

0,00010

16(III)

93,06

34,93

161,00

130,41

0,00093

0 ,00035

17(V)

45,60

26,24

87,23

-

0,00046

0,00026

18(III)

88,91

33,39

153,74

124,53

0,00089

0 ,00033

m, sehingga diambil ρ minimu m sebesar 0,00! sebagai tulangan susut dan suhu. "engan ρ # 0,00! didapatk an spasi antar tulangan sebesar $00 mm, tetapi jarak ma%imu m antar tulangan adalah 3t atau $00 mm, diambil spasi sebesar 3t &300

Pada kolom tipe slab tabel di atas, terdapat keterangan jenis slab, berikut Slab Jenis : Slab dengan keempat sisi menerus. : Slab dengan satu sisi panjang menerus, satu Slab Jenis : Slab dengan dua sisi panjang menerus dan dua sisi pendek ti Slab Jenis : Slab dengan satu sisi pendek menerus dan ketiga sisi lainnya Slab Jenis : Slab dengan satu sisi panjang tidak menerus dan ketiga sisi la Slab Jenis : Slab dengan satu sisi pendek tidak menerus dan ketiga sisi lai

Ly/Lx

Jenis

123,255,814

Dua arah

1,869,565,217

Dua arah

1,395,348,837

Dua arah

2,45

Dua arah

1,484,848,485

Dua arah

2,130,434,783

Dua arah

2,105,263,158

Dua arah

1,333,333,333

Dua arah

3,55

Satu arah

2,666,666,667

Satu arah

1,12

Dua arah

1,904,761,905

Dua arah

1,613,636,364

Dua arah

1,35

Dua arah

2,074,074,074

Dua arah

1,688,888,889

Dua arah

1,125

Dua arah

1,636,363,636

Dua arah

N mm)

Mtix/Φ (N mm)

y/Φ (N mm)

87,88

784149,34

516391,03

5,44

-

93021,34

41,44

994530,88

439888,66

5,00

326862,50

-

60,60

-

-

5,44

-

-

3,94

-

63479,59

31,25

-

186187,50

517500

-

570000

-

71,88

-

594765,63

2,25

305626,78

-

61,00

1421810,50

600765,00

0,00

194462,50

-

0,56

-

128190,09

98,44

1340550,00

439867,97

-

331000,00

1281632,00

420535,50

27,00

ρtx

ρty

0,00112

0,00114

0,00031

0,00023

0,00130

0,00119

0,00034

0,00024

0,00058

0,00049

0,00031

0,00023

Cara Perhitungan Kolom Balok Plat Xls

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