8/16/2019 Centroid Plastis
1/28
b = 250 fc' = 25 N/mm2h = 500 fy = 400 N/mm2
d' = 50 D = 19 mmAs tul = 283.5287 mm2
d = h - d'
d = 450 As = 850.5862As' = 850.5862
d - h/2 = 200
d - d' = 400
0.85 x fc' x h x b x d - h/2! " As' x fy x d - d'! 667#343#793.75 200.000.85 x fc' x h x b " As " As'! x fy 3336718.9687676
b = 250 fc' = 25 N/mm2h = 600 fy = 400 N/mm2
d' = 50 D = 19 mmAs tul = 283.5287 mm2
d = h - d'
d = 550 As = 850.5862As' = 850.5862
d - h/2 = 250
d - d' = 500
0.85 x fc' x h x b x d - h/2! " As' x fy x d - d'! 966#992#242.19 250.000.85 x fc' x h x b " As " As'! x fy 3867968.9687676
8/16/2019 Centroid Plastis
2/28
b = 250 fc' = 25 N/mm2h = 500 fy = 400 N/mm2
d' = 40 D = 19 mmAs tul = 283.5287 mm2
d = h - d'd = 460 As = 850.5862
As' = 850.5862d - h/2 = 210
d - d' = 420
0.85 x fc' x h x b x d - h/2! " As' x fy x d - d'! 700#710#983.44 210.000.85 x fc' x h x b " As " As'! x fy 3336718.9687676
b = 250 fc' = 25 N/mm2h = 500 fy = 400 N/mm2
d' = 50 D = 19 mmAs tul = 283.5287 mm2
d = h - d'
d = 450 As = 1134.115 ==>PERHATAN JIKA TULAAs' = 850.5862
d - h/2 = 200
d - d' = 400
0.85 x fc' x h x b x d - h/2! " As' x fy x d - d'! 667#343#793.75 193.430.85 x fc' x h x b " As " As'! x fy 3450130.4635621
8/16/2019 Centroid Plastis
3/28
b = 250 fc' = 25 N/mm2h = 600 fy = 400 N/mm2
d' = 40 D = 19 mmAs tul = 283.5287 mm2
d = h - d'd = 560 As = 1134.115
As' = 850.5862d - h/2 = 260
d - d' = 520
0.85 x fc' x h x b x d - h/2! " As' x fy x d - d'! 1#005#671#931.88 252.590.85 x fc' x h x b " As " As'! x fy 3981380.4635621
8/16/2019 Centroid Plastis
4/28
8/16/2019 Centroid Plastis
5/28
NGAN TIDAK SERAGAM
ACER:BERGESER KE ARAH TULANGAN
YANG LEBIH BANYAK UNTUKMENCAPAI KESEIMBANGAN(LEBIH DEKAT KE AS YANGBESAR)
8/16/2019 Centroid Plastis
6/28
8/16/2019 Centroid Plastis
7/28
b = 250 mm fc' = 27 N/mm2h = 600 mm fy = 400 N/mm2
d' = 50 mm D = 16 mmAs tul = 201.0619298297 mm2
d = h - d'd = 550 mm As = 3 D 16 603.1857894892
As' = 3 D 16 603.1857894892
Statis Momen terhadap t !an"an tari#$ As %
d - h/2 = 250 mm
d - d' = 500 mm
d $ = 0.85 x fc' x h x b x d - h/2! " As' x fy x d - d'! = 981#262#157.90 =0.85 x fc' x h x b " As " As'! x fy 3#925#048.63
Statis Momen terhadap tepi atas &!o# te"' Te#an &eton %
d $ = 0.85 x fc' x h x b x h/2! " As' x fy x d'! " As x fy x d! 1177514589.47742 =0.85 x fc' x h x b " As " As'! x fy 3#925#048.63
Statis Momen terhadap t !an"an te#an$ As( %
h/2 - d' = 250 mm
d - d' = 500 mm
d $ = 0.85 x fc' x h x b x h/2 - d'! " As x fy x d - d'! = 981#262#157.90 =0.85 x fc' x h x b " As " As'! x fy 3#925#048.63
8/16/2019 Centroid Plastis
8/28
Statis Momen terhadap titi# ) %
x = 125 mm d%& (%& s )*t&%l +*)%m+%)( b*t,) * %)%)
1 = x 1 = 125 mm2 = h/2 - d' - x 2 = 125 mm3 = d - d' - 2 3 = 375 mm
d $ = 0.85 x fc' x h x b x 1! - As' x fy x 2! " As x fy x 3! 490#631#078.95 =0.85 x fc' x h x b " As " As'! x fy 3#925#048.63
Statis Momen terhadap "aris netra! penampan" &eton %
1 = x 1 = 0 mm
8/16/2019 Centroid Plastis
9/28
2 = h/2 - d' 2 = 250 mm3 = d - h/2 3 = 250 mm
d $ = 0.85 x fc' x h x b x 1! - As' x fy x 2! " As x fy x 3! - =0.85 x fc' x h x b " As " As'! x fy 3#925#048.63
8/16/2019 Centroid Plastis
10/28
mm2mm2
250.00 mm d%& tul%)(%) t%&
300.00 mm d%& t*+ %t%s bl, t*(. * %) b*t,)
250.00 mm d%& tul%)(%) t* %)
8/16/2019 Centroid Plastis
11/28
125.00 mm d%& t t x
8/16/2019 Centroid Plastis
12/28
- mm d%& d%& (%& s )*t&%l +*)%m+%)(
8/16/2019 Centroid Plastis
13/28
MENGHITUNG d( *+ENTR,ID PLASTIS-
D = 19 mmfc' = 27 N/mm2 As = 283.5287 mm2fy = 400 N/mm2
As1 = 1417.644 mm2b = 400 mm As2 = 567.0575 mm2h = 400 mm As3 = 567.0575 mm2
% = h# As4 = 567.0575 mm2 % = 400 mm As5 = 1417.644 mm2
d' = 50 mmd = h - d'd = 350 mm
. Statis Momen terhadap "aris netra! penampan" &eton %
50
50 mm
125 mm
200 mm
275 mm
350 mm
c = h/2 - %/2 c = 0 mm1 = h/2 - d1 1 = 150 mm2 = h/2 - d2 2 = 75 mm3 = h/2 - d3 3 = 0 mm4 = d4 - h/2 4 = 75 mm5 = d5 - h/2 5 = 150 mm
d$ = 0.85 x fc' x h x b x c! " As1x fy x 1! " As2x fy x 2! " As3x fy x 3! - As4x fy x 4! - As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
0 = - mm dari garis netral 5#486#583.92
d = dc " - 1! h - 2dc ! / N - 1!
dc = d' dc =
d1 =
d2 =
d3 =
d4 =
d5 =
h = 400
b = 400
s5 s4 s3 s2 s1
c
d1d2
d3
d4
d5
124
5
8/16/2019 Centroid Plastis
14/28
/ Statis Momen terhadap tepi atas &!o# te"an"an te#an &eton %
50 mm
125 mm
200 mm
275 mm350 mm
c = h/2 c = 200 mm1 = d1 1 = 50 mm2 = d2 2 = 125 mm3 = d3 3 = 200 mm4 = d4 4 = 275 mm5 = d5 5 = 350 mm
d$ = 0.85 x fc' x h x b x c! " As1x fy x 1 " As2x fy x 2! " As3x fy x 3! " As4x fy x 4! " As5x fy x 5!
0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
1097316783.3 = 200.00 mm dari tepi atas blok tegangan tekan beton 5#486#583.92
d1 =
d2 =
d3 =
d4 =d5 =
h = 400
b = 400
s5 s4 s3 s2 s1
c
d1d2
d3
d4
d5
12
3 = c
45
8/16/2019 Centroid Plastis
15/28
0 Statis Momen terhadap As1 %
50 mm
125 mm200 mm
275 mm
350 mm
c = d - h/2 c = 150 mm1 = d - d1 1 = 300 mm2 = d - d2 2 = 225 mm3 = d - d3 3 = 150 mm
4 = d - d4 4 = 75 mm5 = d - d 5 = 0 mm
d$ = 0.85 x fc' x h x b x c! " As1x fy x 1! " As2x fy x 2! " As3x fy x 3! " As4x fy x 4! " As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
822987587.51 = 150.00 mm dari As5 5#486#583.92
d1 =
d2=
d3 =
d4 =
d5 =
h = 400
b = 400
s5 s4 s3 s2 s1
c
4
d1d2
d3
d4
d5
3 = c
21
8/16/2019 Centroid Plastis
16/28
2 Statis Momen terhadap As2 %
50 mm
125 mm200 mm
275 mm
350 mm
c = d4 - h/2 c = 75 mm1 = d4 - d1 1 = 225 mm2 = d4 - d2 2 = 150 mm3 = d4 - d3 3 = 75 mm4 = d4 - d4 4 = 0 mm
5 = d5 - d4 5 = 75 mm
d$ = 0.85 x fc' x h x b x c! " As1x fy x 1! " As2x fy x 2! " As3x fy x 3! " As4x fy x 4! - As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
411493793.75 = 75.00 mm dari As4 5#486#583.92
d1 =
d2=
d3 =
d4 =
d5 =
h = 400
b = 400
s5 s4 s3 s2 s1
c
d1d2
d3
d4
d5
12
3 = c5
8/16/2019 Centroid Plastis
17/28
8/16/2019 Centroid Plastis
18/28
3 Statis Momen terhadap As/ %
50 mm
125 mm
200 mm275 mm
350 mm
c = h/2 - d2 c = 75 mm1 = d2 - d1 1 = 75 mm
2 = d2 - d2 2 = 0 mm3 = d3 - d2 3 = 75 mm4 = d4 - d2 4 = 150 mm5 = d5 - d2 5 = 225 mm
d$ = - 0.85 x fc' x h x b x c! " As1x fy x 1! " As2x fy x 2! - As3x fy x 3! - As4x fy x 4! - As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
-411493793.8 = (75.00) mm dari As2 5#486#583.92
A A
d$ = 0.85 x fc' x h x b x c! - As1x fy x 1! - As2x fy x 2! " As3x fy x 3! " As4x fy x 4! " As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
411493793.75 = 75.00 mm dari As2
5#486#583.92
d1 =
d2 =
d3 =d4 =
d5 =
h = 400
b = 400
s5 s4 s3 s2 s1
c
d1d2
d3
d4
d5
134
5
8/16/2019 Centroid Plastis
19/28
4 Statis Momen terhadap As. %
50 mm
125 mm
200 mm275 mm
350 mm
c = h/2 - d1 c = 150 mm1 = d1 - d1 1 = 0 mm
2 = d2 - d1 2 = 75 mm3 = d3 - d1 3 = 150 mm4 = d4 - d1 4 = 225 mm5 = d5 - d1 5 = 300 mm
d$ = - 0.85 x fc' x h x b x c! " As1x fy x 1! - As2x fy x 2! - As3x fy x 3! - As4x fy x 4! - As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
-822987587.5 = (150.00) mm dari As2 5#486#583.92
A A
d$ = 0.85 x fc' x h x b x c! - As1x fy x 1! " As2x fy x 2! " As3x fy x 3! " As4x fy x 4! " As5x fy x 5!0.85 x fc' x h x b! " As1" As2 " As3 " As4 " As5! x fy
822987587.51 = 150.00 mm dari As2 5#486#583.92
d1 =
d2 =
d3 =d4 =
d5 =
h = 400
b = 400
s5 s4 s3 s2 s1
c
d1d2
d3
d4
d5
3
5
4
2
8/16/2019 Centroid Plastis
20/28
h = 400
b = 400
s5 s4 s3 s2 s1
c
8/16/2019 Centroid Plastis
21/28
75 50
400
400
200
50 75 75 75
8/16/2019 Centroid Plastis
22/28
75 50
400
400
50
200
50 75 75 75
8/16/2019 Centroid Plastis
23/28
600
50 100 100 1 00 100 1 00
50
100
50
200
50100
50
8/16/2019 Centroid Plastis
24/28
D *t%hu utu b*t,) utu b% %
b = mm fc ' = 25 % fy = %bf = mm = 25 N/mm2 = N/mm2h = mmhf = mm ,dulus :l%st s t%s ;*t,) ,dulud :l%st s t%s ;% %# :yh - hf = mm :c = :y = 200#000 %
:c = 23500 N/mm2
8/16/2019 Centroid Plastis
25/28
Centroid plastis, d"t%t s ,m*) * t*+ b% %h +*)%m+%)(
Ac1 = 0.85 x fc x hf x bf = 2#550#000 N c1 = 1/2.hf " h - hf! c1 = mmAc2 = 0.85 x fc x h - hf! x b = 2#125#000 N c2 = 1/2 h- hf ! c2 = mm
As1 = 6 As = 2#280.80 mm2 d1 = 50 mm 1 = d7 1 = mmAs2 = 6 As = 2#280.80 mm2 d2 = mm 2 = d6 2 = mmAs3 = 2 As = 760.27 mm2 d3 = mm 3 = d5 3 = mmAs4 = 2 As = 760.27 mm2 d4 = mm 4 = d4 4 = mmAs5 = 2 As = 760.27 mm2 d5 = mm 5 = d3 5 = mmAs6 = 2 As = 760.27 mm2 d6 = mm 6 = d2 6 = mmAs7 = 2 As = 760.27 mm2 d7 = mm 7 = d1 7 = 50 mm
Ac1 " Ac2! " As1 " As2 " As3 " As4 " As5 " As6 " As7! x fy
d $ = 3#536#164#919.01 = 440.909 mm d%& t*+ b% %h +*)%m+%)( ,l,m 8#020#167.86
*mbu t %)h - d$ = - 259.091 = 440.909 mm d%& t*+ b% %h +*)%m+%)( ,l,m -OK bangeets…!
d$ " d$ = " = 0OK bangeets…!
D *t%hu utu b*t,) utu b% %
b = mm fc ' = 25 % fy = %bf = mm = 25 N/mm2 = N/mm2h = mmhf = mm ,dulus :l%st s t%s ;*t,) ,dulud :l%st s t%s ;% %# :yh - hf = mm :c = :y = 200#000 %
:c = 23500 N/mm2
8/16/2019 Centroid Plastis
26/28
D = 22As = 380.13 mm2
ul%)(%) = 22 D 22
Centroid plastis, d"t%t s ,m*) * t*+ & +*)%m+%)(
Ac1 = 0.85 x fc x hf x bf = 2#550#000 N c1 = 1/2.bf c1 = mmAc2 = 0.85 x fc x h - hf! x b = 2#125#000 N c2 = 1/2.bf c2 = mm
As1 = 2 As = 760.27 mm2 d1 = 50 mm 1 = d1 1 = 50 mmAs2 = 2 As = 760.27 mm2 d2 = mm 2 = d2 2 = mmAs3 = 7 As = 2#660.93 mm2 d3 = mm 3 = d3 3 = mmAs4 = 7 As = 2#660.93 mm2 d4 = mm 4 = d4 4 = mmAs5 = 2 As = 760.27 mm2 d5 = mm 5 = d5 5 = mmAs6 = 2 As = 760.27 mm2 d6 = mm 6 = d6 6 = mmAs7 = 0 As = - mm2 d7 = 0 mm 7 = d7 7 = 0 mm
22 b%t%)( D %.22
Ac1 " Ac2! " As1 " As2 " As3 " As4 " As5 " As6 " As7! x fy
d $ = 2#406#050#357.26 = 300 mm d%& t*+ & +*)%m+%)( ,l,m 8#020#167.86
d $ = Ac1 x c1 " Ac2 x c2! " As1 x fy x 1 " As2 x fy x 2 " As3 x fy x 3 " As4 x fy x 4 " As5 x fy x 5 " As6 x fy x 6 " As7 x fy x 7!
8/16/2019 Centroid Plastis
27/28
D *t%hu utu b*t,) utu b% %
b = mm fc ' = 25 % fy = %bf = mm = 25 N/mm2 = N/mm2h = mmhf = mm ,dulus :l%st s t%s ;*t,) ,dulud :l%st s t%s ;% %# :yh - hf = mm :c = :y = 200#000 %
:c = 23500 N/mm2
8/16/2019 Centroid Plastis
28/28