Perhitungan Beton Bertulang MN vs PN

B. Perhitungan Grafik Mn dan Pn

F`c = 30 Mpa Fy = 350 Mpa d` = 50 mm  b = 500 mm h = 700 mm Ag = ( b x h ) Data beban Pu = 3000 kN Mu = 200 kNm =500 x 700 = 350000 mm 2 Misal Ast = 1% Ast = 1% x 350000 = 3500 mm 2 As = As` =

 Ast  2

3500 

2



1750 mm

2

Dalam keadaan desak aksial ( Mu = 0 ) 

Pu = 0.85 x f`c x ( Ag-Ast ) + ( Ast x fy ) =0.85 x 30 x (350000-3500) + (3500 x 350 ) = 10060750 N = 10060.75 KN

Dalam Keadaan seimbang ( Fs = Fy ) 

d = h-d` 700-50 = 650 mm









   d  600  Fy   

 Xb  

600

 Xb

 600      650  410.52632mm  600 350   

a



0.85  Xb

a



0.85 410 410. 52632  348 348.94737mm

 Xb  d `  fs`   600   Xb    410.52632  50      600  526.92308 Mpa   Fy 410 . 52632  

 fs` 

 jadi dipakai f`s = 350 Mpa

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

 d    Xb   fs    600   Xb   650  410.52632    600  350 Mpa   Fy  410.52632 

 fs  

 jadi dipakai fs = 350 Mpa 







Cc



Cc



Cs



Cs



Ts



Ts



 Pu

0.85   f  `c  a  b 1000 0.85  30  348.94737  500   1000



4449.0789 KN 

 As` fs`0.85   f  `c  1000



1750  350  0.85  30



1000



567.875 KN 

 As   fs 1000 1750  350 1000



Cc  Cs



612.5 KN 

_ Ts

 Pu  4449.0789  567 567. 875 875  612 612.5  4404.4539 KN  

 h a   h     h     Cs    d `  Ts d     2 2   2     2 

 Mu  Cc  

 Mu

700   700 348.94737   700      4449.0789     50   612.5   650    567.875    2 2     2     2    

Mu = 1135042.9 KNmm=1135.0429 KNmm=1135.0429 KNm 

eb

eb

 Mn 

 Pn 1135.0429





0.2577034

4404.4539

Dalam Keadaan Patah desak d 

h

d 

`

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 X    1.5  410  615 410.52632   615.78947mm





a



0.85  X  

a



0.85 615 615. 78947  523 523.42105mm

 X   d `  fs`   600   X    615.78947  50      600  551.28205 Mpa   Fy  615.78947 

 fs` 

 jadi Fs` dipakai = 350 Mpa 

 d    X    fs    600   X     650  615.78947    600  33.333 Mpa   Fy 615 . 78947  

 fs  

 jadi fs dipakai = 33.333 Mpa 







Cc  Cc



Cs



Cs



Ts



Ts



 Pu

0.85   f  `c  b  a 1000 0.85  30  500  523.42105   1000

6673.6184 KN 

 As` fs`0.85   f  `c  1000



1750  350  0.85  30 1000





567.875 KN 

 As   fs 1000 1750  33.333





1000 Cc  Cs



58.333 KN 

_ Ts

 Pu  6673.6184  567 567.875 87   5  58.333 333  7183.1601 KN  

 h a   h     h     Cs    d `  Ts d     2 2   2     2 

 Mu  Cc  

 700

523 42105 

 700

 

 

700 

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

 Mn

eb



 Pn 777.07276

eb



7183.1601



0.1081798

Dalam Keadaan Patah tarik 

d 



h



d 

`

d   700 700  50  650 650mm 

 X 



0.5   Xb

 205  X    0.5  410 410.52632   205.26316mm 



a



0.85  X  

a



0.85 205 205. 26316  174 174.47368mm

 X   d `  fs`   600   X    205.26316  50      600  453.84615 MPa   Fy  205.26316 

 fs` 

Dipakai fs` = 350 MPa 

 d    X    fs    600   X     650  205.26316   600  1300 MPa   Fy    205 . 26316  

 fs  

Dipakai fs = 350 Mpa 



Cc  Cc



Cs



Cs 

0.85   f  `c  b  a 1000 0.85  30  500  174.47368   1000



2224.5395 KN 

 As` fs`0.85   f  `c  1000



1750  350  0.85  30 1000

 As   fs





567.875 KN 

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



 Pu



Cc  Cs _ Ts

 Pu



2224.5395  567. 875 _ 612.5  2179.9145 KN 

 h a   h     h     Cs    d `  Ts d     2 2   2     2 

 Mu  Cc  

700   700 174.47368   700      2224.5395     50   612.5   650    567.875    2 2     2     2    

 Mu

Mu=938639.52 KNmm = 938.63952 KNm 

eb

eb

 Mn 

 Pn 938.63952



2179.9145



0.43

Dalam keadaan Lentur murni 

a

a 



 Pu

 As   fy 0.85   f  `c  b 1750  350   0.85  30  500 



0

   

 Mu   As   fy   d  



48.039216mm

   

a 



2 

 Mu  1750  350   650 

48.039216  2

  

Mu = 383412990 KNmm = 383.41299 KNm