Evaluasi Desain Tulangan Balok
Lebar Balok
Tinggi Balok
Lebar Tinggi Balok, b Balok, h
Tebal Selimut Beton
Jarak Serat Tinggi Tekan Efektif Terluar Balok ke Pusat Tulanga n Tekan
Diameter Diameter Tebal Tulangan Tulangan Selimut Tarik, φD Geser, φS Beton, s
= h - d' = 40 + (s+1/2.φ φS + D+φS) 1/2. φD'
Asumsi Asumsi Diameter Diameter Tulangan Tulangan Utama Geser
Kuat Tekan Karakter istik 28 Hari (Mutu Beton)
Kuat Luluh Baja (Mutu Baja)
d
f c' c'
f y
Diameter Modulus Modulus Tulangan Elastisitas Elastisitas Bahan Tarik, φD Beton Baja (mm)
Es
= 2x10 MPa
5
Ec = 4700. f c' c'0.5
Hitung a : Hitung εcu : Tinggi Blok Hitung c : Regangan Diameter Jumlah Tulangan Tulangan tegangan Jumlah Jarak serat Batas/Luluh Tulangan batang batang Tarik Tekan tekan tekan terluar Beton yang tulangan Tekan, φD' tulangan terpasang, terpasang, persegi ke garis Menerima tarik, ns tekan, ns' As (mm2) As' (mm2) ekivalen (mm) neutral, (mm) Tekanan Whitney (mm/mm) (mm)
Diameter Diameter ns Tulangan =Jumlah Tulangan Tarik atau Batang Tekan atau Tulangan Tulangan Tulangan Tarik Positif, φD negatif, φD'
ns' Luas Luas =Jumlah Tulangan Tulangan Batang Tarik Tekan Tulangan Terpasang Terpasang Tekan As As'
c
Hitung εy : Regangan Batas/Luluh Baja Tulangan Tarik/Tekan (mm/mm)
= a/β1, β1
= 0.85 IF f c' c' ≤ a = (AsAs').f y/0.85. y/0.85. 30 MPa, IF fc' > 30 MPa, β1 f c'. c'.b = 0.850.008(fc'-30)
Regangan Tekan Beton, cu
y = f y/ y/Es
mm
mm
mm
mm
mm
mm
MPa
MPa
MP MPa
MPa
mm
-
mm
-
mm2
mm2
mm
mm
500
900
22
8
40
841.0
59.0
20
240
20 200000
21 21019
22
4
18
2
1520.5
508.9
28.6
33.6
0.003
0
500 500 500 500 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
900 700 700 700 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
23 24 25 26 27 28 29 30 22 23 22 27.5 22 27 28 29 30 30 30 30 30 30 30 30 30 30
8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 8 8 8 8 8 8 8 8 8
40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
840.5 640.0 639.5 639.0 438.5 438.0 437.5 437.0 439.0 438.5 439.0 436.3 439.0 436.5 436.0 435.5 435.0 437.0 437.0 437.0 437.0 437.0 437.0 437.0 437.0 437.0
59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 61.0 61.5 61.0 63.8 61.0 63.5 64.0 64.5 65.0 63.0 63.0 63.0 63.0 63.0 63.0 63.0 63.0 63.0
20 20 20 20 20 20 20 20 20 20 20 20 25 20 20 20 20 20 20 20 20 20 20 20 20 20
240 240 240 240 240 240 240 240 240 240 300 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240
200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000
21019 21019 21019 21019 21019 21019 21019 21019 21019 21019 21019 21019 23500 21019 21019 21019 21019 21019 21019 21019 21019 21019 21019 21019 21019 21019
23 24 25 26 27 28 29 30 22 23 22 27.5 22 27 28 29 30 22 23 24 25 26 27 28 29 30
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1661.9
508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9 508.9
32.6 36.7 41.1 45.6 100.6 110.3 120.5 130.9 57.1 65.1 71.4 105.4 45.7 100.6 110.3 120.5 130.9 57.1 65.1 73.4 82.1 91.2 100.6 110.3 120.5 130.9
38.3 43.2 48.3 53.6 118.3 129.8 141.7 154.0 67.2 76.6 84.0 124.0 53.8 118.3 129.8 141.7 154.0 67.2 76.6 86.4 96.6 107.3 118.3 129.8 141.7 154.0
0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
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
mm
18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1809.6 1963.5 2123.7 2290.2 2463.0 2642.1 2827.4 1520.5 1661.9 1520.5 2375.8 1520.5 2290.2 2463.0 2642.1 2827.4 1520.5 1661.9 1809.6 1963.5 2123.7 2290.2 2463.0 2642.1 2827.4
mm/mm
mm/mm
Kontrol Regangan Hitung εs : Hitung εs' : Baja : If εs > εy Regangan Regangan and εs' > εy --> Baja Baja Tulangan Tulangan Kondisi I, if εs > εy Tarik Tekan and εs' < εy --> (mm/mm) (mm/mm) Kondisi II
Koefisien c 2 of ac 2 + bc + c = 0
Koefisien c
IF s ≥ y AND s' ≥ y ==> First s = (dc).
/c
cu
mm/mm
s' = (cd').
/c
cu
mm/mm
0.0721
0
0.0628 0.0414 0.0367 0.0327 0.0081 0.0071 0.0063 0.0055 0.0166 0.0142 0.0127 0.0076 0.0215 0.0081 0.0071 0.0062 0.0055 0.0165 0.0141 0.0122 0.0106 0.0092 0.0081 0.0071 0.0063 0.0055
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
Condition, IF s ≥ y AND s' < y ==> Second Condition
of c2 = 0.85.f c'. c'.b.β1 a
b
of c = ( cu.Es.As'As.f y) y)
Konstanta untuk c untuk c
Hitung fs' : Revisi c = Jarak Tegangan Perhitungan Serat Tekan Kontrol fs': Tulangan a: Tinggi Blok Terluar ke IF fs' < fy Baja Tegangan G.N. yang --> OK! Tekan Persegi direvisi (MPa) Whitney (mm)
Hitung ND1: kN
Hitung ND2: kN
Hitung ΣND = ND1+ND2, kN
Resultan Hitung Tegangan Hitung Hitung ΣMn = Tarik dari Mn1, kN Mn2, kN Mn1 + Tulangan Mn2, kN Baja, NT
IF f s' s' ≥ f y a = β1.c, β1 = NT = ==> First 0.85 IF f c' c' ≤ ND1 = ΣND = ND2 = As.f y. y. = s'. Es Condition, 30 MPa. IF 0.85.f c'. c'.a. 0.85.f c'.a.b c'.a.b c of c = c = {-b±(b2As'.f s'. s'. IF Kontrol: = ( c IF f s' s ' < f y f c' c ' > 30 MPa, b. s'. -d'( cu.Es.As') 4ac)0.5}/2a Cond. 1 or + As'.f s'. ==> Cond. 1 or d'). cu.Es/c β1=0.85Cond. 1 or ΣND = NT 2: 2 Second 2: ==> OK! 0.008.x. Condition Cond. 1 or 2: f s' s'
-
mm2
mm
-
mm
MPa
Kondisi II
7225.0
-59564.6
-18016405.55
54.2
-52.8
Kondisi II Kondisi II Kondisi II Kondisi II Kondisi I Kondisi I Kondisi I Kondisi I Kondisi II Kondisi II Kondisi II Kondisi I Kondisi II Kondisi I Kondisi I Kondisi I Kondisi I Kondisi II Kondisi II Kondisi II Kondisi II Kondisi I Kondisi I Kondisi I Kondisi I Kondisi I
7225.0 7225.0 7225 7225 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 4515.63 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5 3612.5
-93493.8 -128930.96 -165876.09 -204329.19 -244290.24 -285759.27 -328736.26 -373221.21 -59564.6 -93493.8 -150796.45 -264836.26 -59564.6 -244290.24 -285759.27 -328736.26 -373221.21 -59564.6 -93493.8 -128930.96 -165876.09 -204329.19 -244290.24 -285759.27 -328736.26 -373221.21
-18169086.95 -18321768.36 -18474449.76 -18627131.16 -18779812.56 -18932493.97 -19085175.37 -19237856.77 -18627131.16 -18779812.56 -18627131.16 -19466878.88 -18627131.16 -19390538.18 -19543219.58 -19695900.98 -19848582.39 -19237856.77 -19237856.77 -19237856.77 -19237856.77 -19237856.77 -19237856.77 -19237856.77 -19237856.77 -19237856.77
57.0 60.1 63.3 66.8 113.4 122.0 131.3 141.1 80.5 86.2 95.7 118.7 71.2 114.5 123.1 132.2 142.0 81.7 87.1 93.0 99.5 106.5 114.2 122.6 131.5 141.1
-26.0 0.6 26.8 52.5 274.7 295.2 314.3 332.0 145.5 171.9 217.4 277.8 85.7 267.3 288.0 307.3 325.4 137.2 165.8 193.4 219.9 245.2 269.1 291.6 312.5 332.0
-
fs' < fy fs' < fy fs' < fy fs' < fy fs' < fy fs' => fy fs' => fy fs' => fy fs' => fy fs' < fy fs' < fy fs' < fy fs' => fy fs' < fy fs' => fy fs' => fy fs' => fy fs' => fy fs' < fy fs' < fy fs' < fy fs' < fy fs' => fy fs' => fy fs' => fy fs' => fy fs' => fy
Mn1
=
ND1.z1
= ND1.(da/2)
Mn2
=
ND2.z2
=
ND2.(dd')
ΣM = n
Mn1
+
Mn2
MR = φ ΣMn
MR = 0.80.ΣMn
mm
kN
kN
kN
kN
kN.m
kN.m
kN.m
kN.m
46.1
391.8
-26.9
364.9
364.9
320.5
-21.0
299.5
239.57
48.5 51.1 53.8 56.8 100.6 110.3 120.5 130.9 68.4 73.3 81.3 105.4 60.5 100.6 110.3 120.5 130.9 69.4 74.0 79.0 84.5 91.2 100.6 110.3 120.5 130.9
412.1 434.0 457.6 483.0 427.5 469.0 512.0 556.4 290.9 311.4 345.5 448.1 321.3 427.5 469.0 512.0 556.4 295.1 314.5 335.9 359.3 387.5 427.5 469.0 512.0 556.4
-13.2 0.3 13.7 26.7 122.1 122.1 122.1 122.1 74.0 87.5 110.6 122.1 43.6 122.1 122.1 122.1 122.1 69.8 84.4 98.4 111.9 122.1 122.1 122.1 122.1 122.1
398.9 434.3 471.2 509.7 549.7 591.1 634.1 678.6 364.9 398.9 456.2 570.2 364.9 549.7 591.1 634.1 678.6 364.9 398.9 434.3 471.2 509.7 549.7 591.1 634.1 678.6
398.9 434.3 471.2 509.7 549.7 591.1 634.1 678.6 364.9 398.9 456.2 570.2 364.9 549.7 591.1 634.1 678.6 364.9 398.9 434.3 471.2 509.7 549.7 591.1 634.1 678.6
336.4 266.7 280.3 294.9 166.0 179.5 193.1 206.7 117.7 125.1 137.6 171.8 131.3 165.1 178.6 192.1 205.6 118.7 125.8 133.5 141.8 151.7 165.3 179.1 192.9 206.7
-10.3 0.2 7.9 15.4 46.0 45.9 45.8 45.7 28.0 33.0 41.8 45.5 16.5 45.6 45.4 45.3 45.2 26.1 31.6 36.8 41.9 45.7 45.7 45.7 45.7 45.7
326.0 266.9 288.2 310.3 212.0 225.5 238.9 252.4 145.7 158.1 179.5 217.3 147.8 210.7 224.0 237.4 250.8 144.8 157.3 170.3 183.7 197.4 211.0 224.7 238.6 252.4
260.83 213.48 230.57 248.27 169.61 180.37 191.16 201.94 116.59 126.49 143.57 173.88 118.26 168.53 179.23 189.95 200.65 115.86 125.88 136.25 146.95 157.90 168.80 179.80 190.86 201.94
