Two-Way Flexural Analysis

Kuat Lentur Pelat Beton Dua Arah — Metode Kekuatan (LRFD)

SNI 2847:2019SNI 1727:2020ACI 318M

Parameter Input

Nilai default terisi, ubah bila perlu lalu klik Hitung.

Material & Geometri
MPa
mm
mm
MPa
Momen Arah X
kNm/m
kNm/m
Momen Arah Y
kNm/m
kNm/m
Tul. X — Bawah (Mxx⁺)
Tul. X — Atas (Mxx⁻)
Tul. Y — Bawah (Myy⁺)
Tul. Y — Atas (Myy⁻)
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Potongan Penampang — 4 Lapis Tulangan

tinjauan lebar 1000 mm
h = 200 mmATAS (Mu⁻): ● X D10-150 · ▬ Y D10-150BAWAH (Mu⁺): ● X D10-150 · ▬ Y D10-150
X atas D10-150 Y atas D10-150 X bawah D10-150 Y bawah D10-150
SR X — Mxx⁺ / Mxx⁻
0.59 / 0.59
SR Y — Myy⁺ / Myy⁻
0.63 / 0.63
ρ Arah X (As/Ac)
0.299 %
ρ Arah Y (As/Ac)
0.317 %

Rasio Luas Tulangan terhadap Luas Beton (ρ)

arah X & Y vs batas SNI 2847:2019

ρ = As / (b·d) — luas tulangan baja per satuan luas penampang beton (b = 1000 mm). Dibandingkan terhadap ρmin (Ps. 9.6 / 7.6) dan ρmax pada εt = 0.004 (Ps. 9.3.3.1). ρb = rasio pada kondisi berimbang (balanced).

Arah / LokasiTulanganAs (mm²/m)d (mm)ρ = As/(b·d)ρminρmaxρbStatus
Arah X — Bawah (Mxx⁺) D10-150 524 175.0 0.299% 0.333% 2.175% 2.985% ρ<ρmin
Arah X — Atas (Mxx⁻) D10-150 524 175.0 0.299% 0.333% 2.175% 2.985% ρ<ρmin
Arah Y — Bawah (Myy⁺) D10-150 524 165.0 0.317% 0.333% 2.175% 2.985% ρ<ρmin
Arah Y — Atas (Myy⁻) D10-150 524 165.0 0.317% 0.333% 2.175% 2.985% ρ<ρmin

Syarat SNI: ρmin ≤ ρ ≤ ρmax. ρ < ρmin → penampang kurang tulangan (getas saat retak); ρ > ρmax → over-reinforced (gagal tekan mendadak, tidak daktail). ρmin lentur = maks(0.25√f'c/fy ; 1.4/fy); untuk pelat, tulangan susut-suhu minimum 0.0018·b·h juga berlaku.

Rasio Berat Baja terhadap Volume Beton

indeks pemakaian besi · per 1 m²
Berat baja total
16.44 kg/m²
Volume beton
0.200 m³/m²
Rasio baja
82.2 kg/m³
Setara
16.4 kg/m² pelat
Vbaja = Σ As · L = (524+524+524+524)·1000 = 2,094,395 mm³ per m²
Wbaja = Vbaja · ρbaja = 2,094,395·10⁻⁹·7850 = 16.44 kg/m²
Vbeton = 1·1·h = 1·1·0.200 = 0.200 m³/m²
Rasio = Wbaja / Vbeton = 16.44 / 0.200 = 82.2 kg/m³

Kontribusi per arah: X bawah 4.1 · X atas 4.1 · Y bawah 4.1 · Y atas 4.1 kg/m². Densitas baja 7850 kg/m³. Nilai wajar pelat umumnya ±80–150 kg/m³ (belum termasuk tulangan susut/pembagi & overlap).

Tampak Atas Penulangan

jaring X (horizontal) & Y (vertikal) · per 1 m²
Lapis BAWAH — momen positif (Mxx⁺, Myy⁺)
Tulangan Bawah1000 mm1000 mmX D10-150 (8 btg)Y D10-150 (8 btg)
Lapis ATAS — momen negatif (Mxx⁻, Myy⁻)
Tulangan Atas1000 mm1000 mmX D10-150 (8 btg)Y D10-150 (8 btg)

Garis mendatar penuh = tulangan arah X, garis tegak penuh = tulangan arah Y. Jumlah batang mengikuti jarak s pada bidang 1000×1000 mm.

Simulasi 3D Penulangan & Beton

1 m × 1 m · stek keluar 40D · drag untuk memutar
Transparansi beton

Beton transparan 1000×1000×200 mm. Tulangan atas & bawah arah X/Y ditampilkan; stek (kaitan) menonjol keluar sepanjang 40·D di tiap sisi.

Diagram Interaksi φMn vs Jarak

f'c 30 · fy 420
Mxx⁺ (X bawah) D10
7157432814080120160200240280Jarak s (mm)φMn (kNm/m)Mu=20.0s=34
Mxx⁻ (X atas) D10
7157432814080120160200240280Jarak s (mm)φMn (kNm/m)Mu=20.0s=34
Myy⁺ (Y bawah) D10
6754402713080120160200240280Jarak s (mm)φMn (kNm/m)Mu=20.0s=32
Myy⁻ (Y atas) D10
6754402713080120160200240280Jarak s (mm)φMn (kNm/m)Mu=20.0s=32

Detail Perhitungan — Mn, φMn, ρ & Strength Ratio

SNI 2847:2019 Ps. 22.2 & 9.3
Arah X — Bawah (Mxx⁺) · D10-150 · Mu = 20.0 kNm/m
d = 175.0 mm · As = ¼π·10²·(1000/150) = 523.6 mm²/m (7 btg/m)
a = As·fy/(0.85f'c·b) = 8.62 mm · c = a/β₁ = 10.32 mm · εt = 0.0479 terkendali tarik, φ=0.90 ✓
Mn = As·fy·(d − a/2) = 523.6·420·(175.0 − 8.62/2) = 37.54 kNm/m
φMn = 0.90 · Mn = 33.78 kNm/m
ρ = As/(b·d)
0.299%
ρmin
0.333%
ρmax (εt=0.004)
2.175%
Cek ρ: 0.333% ≤ ρ = 0.299% ≤ 2.175% → ρ < ρmin, tambah tulangan
ρb (balanced) = 2.985%
Strength Ratio = |Mu| / φMn = 20.0 / 33.78 = 0.592 AMAN ✓
Arah X — Atas (Mxx⁻) · D10-150 · Mu = 20.0 kNm/m
d = 175.0 mm · As = ¼π·10²·(1000/150) = 523.6 mm²/m (7 btg/m)
a = As·fy/(0.85f'c·b) = 8.62 mm · c = a/β₁ = 10.32 mm · εt = 0.0479 terkendali tarik, φ=0.90 ✓
Mn = As·fy·(d − a/2) = 523.6·420·(175.0 − 8.62/2) = 37.54 kNm/m
φMn = 0.90 · Mn = 33.78 kNm/m
ρ = As/(b·d)
0.299%
ρmin
0.333%
ρmax (εt=0.004)
2.175%
Cek ρ: 0.333% ≤ ρ = 0.299% ≤ 2.175% → ρ < ρmin, tambah tulangan
ρb (balanced) = 2.985%
Strength Ratio = |Mu| / φMn = 20.0 / 33.78 = 0.592 AMAN ✓
Arah Y — Bawah (Myy⁺) · D10-150 · Mu = 20.0 kNm/m
d = 165.0 mm · As = ¼π·10²·(1000/150) = 523.6 mm²/m (7 btg/m)
a = As·fy/(0.85f'c·b) = 8.62 mm · c = a/β₁ = 10.32 mm · εt = 0.0450 terkendali tarik, φ=0.90 ✓
Mn = As·fy·(d − a/2) = 523.6·420·(165.0 − 8.62/2) = 35.34 kNm/m
φMn = 0.90 · Mn = 31.80 kNm/m
ρ = As/(b·d)
0.317%
ρmin
0.333%
ρmax (εt=0.004)
2.175%
Cek ρ: 0.333% ≤ ρ = 0.317% ≤ 2.175% → ρ < ρmin, tambah tulangan
ρb (balanced) = 2.985%
Strength Ratio = |Mu| / φMn = 20.0 / 31.80 = 0.629 AMAN ✓
Arah Y — Atas (Myy⁻) · D10-150 · Mu = 20.0 kNm/m
d = 165.0 mm · As = ¼π·10²·(1000/150) = 523.6 mm²/m (7 btg/m)
a = As·fy/(0.85f'c·b) = 8.62 mm · c = a/β₁ = 10.32 mm · εt = 0.0450 terkendali tarik, φ=0.90 ✓
Mn = As·fy·(d − a/2) = 523.6·420·(165.0 − 8.62/2) = 35.34 kNm/m
φMn = 0.90 · Mn = 31.80 kNm/m
ρ = As/(b·d)
0.317%
ρmin
0.333%
ρmax (εt=0.004)
2.175%
Cek ρ: 0.333% ≤ ρ = 0.317% ≤ 2.175% → ρ < ρmin, tambah tulangan
ρb (balanced) = 2.985%
Strength Ratio = |Mu| / φMn = 20.0 / 31.80 = 0.629 AMAN ✓
LokasiTul.MuφMnρ(%)ρminρmaxSRStatus
Mxx⁺ (X bawah)D10-15020.033.78 0.2990.3332.175 0.592AMAN
Mxx⁻ (X atas)D10-15020.033.78 0.2990.3332.175 0.592AMAN
Myy⁺ (Y bawah)D10-15020.031.80 0.3170.3332.175 0.629AMAN
Myy⁻ (Y atas)D10-15020.031.80 0.3170.3332.175 0.629AMAN
Dihitung berdasarkan SNI 2847:2019 — Pelat Dua Arah, Metode Kekuatan (LRFD) · ρmin & ρmax Ps. 9.3 & 21.2.
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