Reinforced Concrete Slabs - Cheat Sheet
Your 30-minute final review for one-way and two-way slab design, minimum thickness, flexural steel, shrinkage/temperature reinforcement, and coefficient/DDM methods. All formulas, classifications, and board-exam pitfalls in one place.
One-Way vs Two-Way Classification
Formulas
Aspect Ratio = L_long / L_short
Meaning
L_long = longer span; L_short = shorter span; both measured center-to-center of supports
Watch out
Do NOT use short/long backward; always divide LONGER by SHORTER. A slab on only two opposite sides is ALWAYS one-way, regardless of ratio.
When to use
Every slab design starts here — classify before choosing method
Important facts
- If aspect ratio is exactly 2.0, classify as TWO-WAY (≥ 2 means one-way; < 2 means two-way).
- Two-way slabs on columns (flat plates) use Direct Design Method (DDM) or Equivalent Frame Method.
- Two-way slabs on stiff beams use Coefficient Method with tabulated moment coefficients.
- All four edges supported is required for true two-way behaviour; cantilever or three-sided support → one-way.
Key definitions
One-Way Slab
Example
5 m × 2.4 m panel (5/2.4 = 2.08 ≥ 2) → one-way; or a 6 m cantilever off a beam → one-way.
Rectangular slab with L_long/L_short ≥ 2, or supported on only two opposite sides; bends primarily across the short span; designed as 1 m strip.
Two-Way Slab
Example
4 m × 3.5 m panel (4/3.5 = 1.14 < 2) → two-way slab on beams.
Rectangular slab with L_long/L_short < 2, supported on all four sides; bends in both directions; uses coefficient or DDM/EFM.
Diagrams to know
- Aspect ratio decision tree: L_long/L_short ≥ 2? → one-way; < 2 → two-way.
- Support configuration diagram: four-sided vs two-sided vs cantilever.
Minimum Thickness (Deflection Control)
Formulas
h_min = L / C
Meaning
L = clear span or effective span (NSCP 2015); C = coefficient based on support condition
Watch out
This h_min applies to SOLID slabs only. Use clear span, not center-to-center. If f_y ≠ 420 MPa, multiply by adjustment factor.
When to use
Whenever designing a one-way slab; if h ≥ h_min, deflection checks may be skipped
h_min (adjusted) = (L/C) × (0.4 + f_y/700)
Meaning
Adjustment factor for yield strength not equal to 420 MPa; f_y in MPa
Watch out
The adjustment is multiplicative. For f_y = 415 MPa: factor = 0.4 + 415/700 = 0.993; for f_y = 275: factor = 0.4 + 275/700 = 0.793.
When to use
When f_y = 275, 380, 415, or other non-standard value
Common values
Value
415 MPa
Symbol
f_y
Quantity
Standard yield strength
Value
275 MPa
Symbol
f_y
Quantity
Older/lower yield
Value
28 MPa (f'_c)
Symbol
f'_c
Quantity
Concrete strength (typical)
Important facts
- Use CLEAR SPAN (face-to-face of supports) or effective span per NSCP 2015.
- For prestressed slabs, h_min is reduced — consult NSCP or ACI 318.
- If actual h < h_min, perform deflection check per NSCP Section 421.5.3.
- Continuous slabs allow thinner sections because negative moments are smaller.
- Always check that chosen h satisfies both minimum thickness AND provides adequate concrete cover (typically 20–40 mm).
Key definitions
Simply Supported (SS)
Example
Span 3.5 m, f_y = 415 → h_min = (3500/20) × 0.993 = 174 mm.
Slab resting on supports at two ends; no moment continuity; h_min = L/20.
One End Continuous (1EC)
Example
Span 4.0 m, f_y = 415 → h_min = (4000/24) × 0.993 = 165 mm.
One end fixed, one end simply supported; h_min = L/24.
Both Ends Continuous (2EC)
Example
Span 4.2 m, f_y = 415 → h_min = (4200/28) × 0.993 = 149 mm.
Both ends fixed to beams or walls; h_min = L/28.
Cantilever
Example
Cantilever overhang 1.2 m, f_y = 415 → h_min = (1200/10) × 0.993 = 119 mm.
Slab projecting beyond support; h_min = L/10 (much thicker than spanning slabs).
Diagrams to know
- Minimum thickness table by support condition and f_y.
- Adjustment factor curve for f_y vs (0.4 + f_y/700).
Flexural Design (One-Way, Per-Metre Strip)
Formulas
R_n = M_u / (φ × b × d²)
Meaning
R_n = nominal resistance factor (MPa); M_u = factored moment (N·mm); φ = 0.90 for flexure; b = 1000 mm (per-metre width); d = effective depth (mm)
Watch out
Convert M_u to N·mm if given in kN·m: M_u(N·mm) = M_u(kN·m) × 10⁶. Keep units consistent.
When to use
Always step 1 in slab flexural design; compute from factored moment
ρ = (0.85 × f'_c / f_y) × [1 − √(1 − (2 × R_n) / (0.85 × f'_c))]
Meaning
ρ = steel ratio (unitless); f'_c = concrete strength (MPa); f_y = yield strength (MPa); R_n from previous formula
Watch out
Do NOT use ρ_max; this formula gives ρ directly. If R_n is too large, the square root becomes imaginary → section is under-reinforced and moment capacity is insufficient.
When to use
Calculate ρ after finding R_n; this is the balanced ratio approach (NSCP/ACI 318)
A_s = ρ × b × d
Meaning
A_s = required steel area (mm²/m, per metre width); ρ = steel ratio; b = 1000 mm; d = effective depth (mm)
Watch out
A_s is in mm²/m — this is the area needed across a 1-metre-wide strip. Must check against shrinkage/temperature minimum.
When to use
Final step to get steel per metre; convert to bar spacing next
s = (A_b × 1000) / A_s
Meaning
s = bar spacing (mm, center-to-center); A_b = area of ONE bar (mm²); A_s = required area per metre (mm²/m)
Watch out
Spacing must satisfy s ≤ min(3h, 450 mm) for main steel. If s_calculated < min, reduce spacing; if > min, use min.
When to use
Convert per-metre steel to practical bar spacing for detailing
Common values
Value
1000 mm
Symbol
b
Quantity
Per-metre strip width
Value
20–40 mm
Symbol
cover
Quantity
Concrete cover (beams/slabs)
Value
78.5 mm²
Symbol
A_φ10
Quantity
10 mm φ bar area
Value
113.1 mm²
Symbol
A_φ12
Quantity
12 mm φ bar area
Value
201.1 mm²
Symbol
A_φ16
Quantity
16 mm φ bar area
Important facts
- Minimum steel ratio: ρ_min = max(0.0014, 1.4 × f_y / f'_c); but shrinkage/temperature steel often governs.
- For thin slabs with low moments, shrinkage/temperature minimum (ρ_temp = 0.0018) typically controls A_s.
- Always check A_s ≥ A_s,min; if not, use minimum and adjust spacing downward.
- Maximum steel ratio ρ_max ≈ 0.75 × ρ_balanced; over-reinforced sections fail suddenly (not acceptable).
- Bar spacing cannot exceed min(3h, 450 mm) for main steel; if spacing too large, add bars.
Key definitions
Per-Metre Strip Design
Example
A slab with A_s = 315 mm²/m and 10 mm φ bars (A_b = 78.5 mm²) requires s = 78.5 × 1000 / 315 = 249 mm spacing.
One-way slab analyzed as a 1 m wide rectangular beam with b = 1000 mm; all calculations (M_u, R_n, A_s) per unit width.
Effective Depth (d)
Example
h = 175 mm, cover = 20 mm, bar diameter 10 mm → d = 175 − 20 − 5 = 150 mm.
Distance from extreme compression fibre to centroid of tension steel; d = h − cover − φ_bar/2.
Diagrams to know
- Flow chart: M_u → R_n → ρ → A_s → spacing s.
- Cross-section of slab showing h, cover, d, and bar positions.
Shrinkage & Temperature Steel
Formulas
A_s,temp = ρ_temp × b × h
Meaning
A_s,temp = minimum steel perpendicular to main steel (mm²/m); ρ_temp = shrinkage/temperature ratio; b = 1000 mm (per metre); h = slab thickness (mm)
Watch out
Use FULL thickness h, not effective depth d. This is a separate, minimum requirement — always check. ρ_temp varies with f_y.
When to use
EVERY slab design must provide temperature steel perpendicular to main flexural steel
ρ_temp = 0.0018 (for f_y = 415–420 MPa); ρ_temp = 0.0020 (for f_y = 275 MPa)
Meaning
Shrinkage/temperature ratio specified by NSCP based on steel grade
Watch out
Do NOT confuse with main flexural steel ratio ρ. Temperature steel is a code minimum independent of moment.
When to use
Plug into A_s,temp formula; standard values per NSCP 2015
s_temp = (A_b × 1000) / A_s,temp
Meaning
s_temp = bar spacing for temperature steel (mm); A_b = bar area; A_s,temp = area per metre
Watch out
Maximum spacing for temperature steel: s ≤ min(5h, 450 mm). Tighter spacing required than for main steel.
When to use
Convert A_s,temp to practical bar spacing
Common values
Value
0.0018
Symbol
ρ_temp
Quantity
Temperature ratio (f_y = 415 MPa)
Value
0.0020
Symbol
ρ_temp
Quantity
Temperature ratio (f_y = 275 MPa)
Value
min(3h, 450) mm
Symbol
s_max
Quantity
Max spacing main steel
Value
min(5h, 450) mm
Symbol
s_temp,max
Quantity
Max spacing temp steel
Important facts
- Temperature steel is perpendicular to main flexural steel (one-way slabs: temperature steel runs parallel to span, main steel perpendicular).
- Maximum spacing: main steel ≤ min(3h, 450 mm); temperature steel ≤ min(5h, 450 mm).
- If computed A_s,main < A_s,temp, use A_s,temp and adjust spacing for both directions.
- Slab shrinkage ratio ρ_temp is constant per NSCP — does NOT depend on moment or span.
- Two-way slabs require temperature steel in BOTH directions (each way gets minimum ρ_temp).
Key definitions
Shrinkage & Temperature Cracking
Example
A slab 175 mm thick will shrink ~0.04–0.06% of its length; temperature steel prevents one large crack and creates many small ones.
Uncontrolled cracking in concrete slabs due to drying shrinkage and thermal expansion/contraction; minimum reinforcement (ρ = 0.0018) distributes cracks and limits crack width.
Diagrams to know
- Slab reinforcement plan showing main steel and perpendicular temperature steel with spacings.
- Cross-section showing location of temperature bars relative to main bars.
Two-Way Slabs: Coefficient Method (Slabs on Beams)
Formulas
M_x = C_x × w × L_s²; M_y = C_y × w × L_s²
Meaning
M_x, M_y = moments in two directions (kN·m/m); C_x, C_y = tabulated coefficients (NSCP Table); w = uniform service load (kN/m²); L_s = shorter span (m)
Watch out
Use SHORTER span L_s, not longer span. Coefficients depend on aspect ratio L_long/L_short and which edges are continuous.
When to use
Two-way slab supported on all four sides by stiff beams; use tabulated coefficients for specific edge condition
Common values
Value
0.5 to 2.0
Symbol
L_long / L_short
Quantity
Typical aspect ratio range
Important facts
- Coefficients are tabulated in NSCP Section 2.11 (or ACI 318, Table 13.6) for various aspect ratios (0.5 to 2.0) and edge conditions.
- Common edge conditions: simple support (S), continuous (C); typical cases: 4 continuous edges, 3 continuous, 2 opposite continuous, etc.
- After calculating moments M_x and M_y, design each direction as a one-way slab per metre width (same procedure as one-way flexural design).
- Deflection checks less commonly required for thin slabs if minimum thickness is met.
- Shear in two-way slabs around concentrated loads requires special treatment (punching shear); not covered in basic coefficient method.
Key definitions
Coefficient Method
Example
4.0 m × 3.0 m slab (L_short = 3.0 m) with all edges continuous and w = 6 kN/m² gives M_x and M_y from NSCP coefficient tables.
Empirical moment distribution for two-way slabs on beams; moments determined from tables based on aspect ratio and boundary conditions; simple and conservative.
Diagrams to know
- Two-way slab panel showing principal directions (x and y), moment distribution pattern.
- Moment coefficient table layout (rows: aspect ratios; columns: edge conditions; cells: C_x, C_y values).
Two-Way Slabs: Direct Design Method (DDM) — Flat Plates/Slabs on Columns
Formulas
M_o = (w_u × L_2 × L_n²) / 8
Meaning
M_o = total static moment (kN·m per strip); w_u = factored load (kN/m²); L_2 = span perpendicular to direction of analysis (m, center-to-center); L_n = clear span (m, face-to-face of supports) in direction being analyzed
Watch out
Use FACTORED load w_u, not service load. L_n is CLEAR span (subtract column width); L_2 is full span center-to-center. Sign error: M_o is always positive (magnitude).
When to use
DDM for flat plate/slab on columns (no beams); compute total moment for each strip, then distribute to column/middle strips
M_column = 0.75 × M_o × ν; M_middle = 0.25 × M_o × ν
Meaning
M_column, M_middle = moments allocated to column and middle strips; ν = distribution factor (fraction of M_o); typical ν ≈ 1.0 for rectangular panels
Watch out
Distribution depends on geometry and loading; values given here are approximate. Consult NSCP Section 2.12 or ACI 318 for exact ν.
When to use
After computing M_o, split into column strip (typically 60–75%) and middle strip (25–40%)
Common values
Value
10–12 kN/m²
Symbol
w_u
Quantity
Typical factored load (residential)
Value
12–16 kN/m²
Symbol
w_u
Quantity
Typical factored load (office)
Important facts
- DDM is simpler than Equivalent Frame Method (EFM) but less accurate for irregular geometry.
- Limitation: DDM applies to regular rectangular slab panels; panels with significantly different spans or asymmetric loading require EFM.
- Negative moments occur over columns (critical for punching shear); positive moments at mid-span.
- Total static moment M_o is a reference value; actual moments vary across the strip.
- After design, check SHEAR around columns (punching shear per ACI 318 Section 8.6) — often governs flat-plate thickness more than bending.
Key definitions
Direct Design Method (DDM)
Example
5 m × 4 m flat slab, clear spans L_nx = 4.8 m, L_ny = 3.8 m, w_u = 12 kN/m² → M_o,x = (12 × 4 × 4.8²) / 8 = 55.3 kN·m.
Simplified procedure for flat plates/slabs on columns; computes total static moment M_o, then distributes to column and middle strips without detailed frame analysis.
Column Strip
Example
For L_2 = 4 m, column strip width ≈ 1 m; carries majority of moment.
Central portion of slab above/below column (typically width = min(L_2/4, L_n/4)); resists ~60–75% of total moment.
Middle Strip
Example
Remaining 2 m width on each side of the 1 m column strip.
Remaining portion of slab between column strips; resists ~25% of total moment; lighter reinforcement.
Diagrams to know
- Flat slab plan view showing column grid, span directions (L_2, L_n), column strips, and middle strips.
- Moment distribution diagram across the span showing parabolic shape of M (positive mid-span, negative over columns).
- Column strip vs middle strip moment allocation sketch.
Key Equations & Conversions
Diagrams to know
- Moment diagram for continuous vs simply-supported beams/slabs (shape of M affects minimum thickness).
Reactions or equations
M (kN·m) × 10⁶ = M (N·mm)
Note
Always ensure units match: if R_n formula uses d in mm, M_u must be in N·mm.
Conditions
Unit conversion for moment; essential when using R_n = M_u / (φ b d²)
A_bar × 1000 / A_s = s (mm spacing)
Note
Example: 10 mm φ bar (78.5 mm²) with A_s = 315 mm²/m → s = 249 mm ≈ 250 mm.
Conditions
Converting per-metre steel area to practical bar spacing; A_bar in mm², A_s in mm²/m
Aspect Ratio = L_long / L_short
Note
Always measure span center-to-center or clear span consistently.
Conditions
If ≥ 2.0 → one-way; if < 2.0 → two-way
h_min = (L / C) × (0.4 + f_y / 700)
Note
Round up to nearest 10 or 25 mm for practical thickness. This h_min assumes fy = 415 MPa baseline.
Conditions
Deflection control; C = 20 (SS), 24 (1EC), 28 (2EC), 10 (cantilever); f_y in MPa
Must remember
ASPECT RATIO CLASSIFICATION: Always divide LONGER by SHORTER span. If ≥ 2.0 → one-way; < 2.0 → two-way. A slab on only two opposite sides is ALWAYS one-way, regardless of ratio.
Order
1
MINIMUM THICKNESS FORMULA: h_min = (L/C) × (0.4 + f_y/700). Use clear or effective span. C = 20 (SS), 24 (1EC), 28 (2EC), 10 (cantilever). Adjust for f_y ≠ 415 MPa. If h < h_min, perform deflection check.
Order
2
SHRINKAGE/TEMPERATURE STEEL ALWAYS REQUIRED: ρ_temp = 0.0018 (f_y = 415 MPa) or 0.0020 (f_y = 275 MPa). A_s,temp = ρ_temp × 1000 × h (full thickness). If A_s,flexural < A_s,temp, USE MINIMUM.
Order
3
PER-METRE DESIGN PROCEDURE (One-Way): (1) Factor moment M_u → (2) Compute R_n = M_u / (0.90 × 1000 × d²) → (3) Solve for ρ → (4) Get A_s = ρ × 1000 × d (mm²/m) → (5) Convert to bar spacing s = A_bar × 1000 / A_s. Keep units: if M_u in kN·m, convert to N·mm.
Order
4
BAR SPACING LIMITS: Main steel s ≤ min(3h, 450 mm); Temperature steel s ≤ min(5h, 450 mm). If calculated spacing exceeds limit, reduce it. If spacing becomes impractically small, use larger bar size.
Order
5
TWO-WAY COEFFICIENT METHOD: M_x = C_x × w × L_s²; M_y = C_y × w × L_s². Use SERVICE load w (or factor to w_u), SHORTER span L_s, and coefficients from NSCP Table 2.11 based on aspect ratio and edge condition. Design each direction as one-way.
Order
6
TWO-WAY DDM FOR FLAT PLATES: M_o = (w_u × L_2 × L_n²) / 8. Use FACTORED load w_u, clear span L_n in direction analyzed, perpendicular span L_2 (center-to-center). Distribute M_o to column strip (~75%) and middle strip (~25%); design each for bending and check punching shear.
Order
7
MINIMUM STEEL RATIO GOVERNING: Thin slabs with small moments often have A_s,minimum (from shrinkage/temperature, ρ = 0.0018) control the design. Always check A_s,calculated ≥ A_s,minimum. If not, use minimum and adjust spacing downward.
Order
8
EFFECTIVE DEPTH d: Calculate d = h − cover − bar diameter/2. For slabs, cover is typically 20–30 mm on bottom, 30–40 mm on top (depending on environment and code). Small d significantly increases R_n and ρ; verify cover in design assumptions.
Order
9
COMMON BOARD-EXAM MISTAKES: (1) Wrong span ratio (short/long instead of long/short). (2) Forgetting f_y adjustment on h_min. (3) Missing shrinkage/temperature minimum. (4) Using center-to-center span instead of clear span for h_min. (5) Confusion between per-metre steel A_s and bar spacing s. (6) Over-reinforcement (ρ > ρ_balanced) — section fails suddenly. Check bounds 0.0014 ≤ ρ ≤ ρ_balanced.
Order
10
Last minute tips
ASPECT RATIO TRAP: Many students flip long/short. Quick check: if one span is obviously much longer (e.g., 6 m vs 2.4 m), ratio = 2.5 → one-way. If both spans similar (e.g., 4 m vs 3.5 m), ratio = 1.14 → two-way. Never assume — calculate both ways if unsure.
Order
1
MINIMUM THICKNESS FREQUENCY: On nearly every board problem, the chosen h ends up being dictated by h_min, not by moment capacity. Always compute h_min as your FIRST step; if candidate h ≥ h_min, you're safe. If h < h_min, flag for deflection check (rarely required if h is chosen correctly).
Order
2
UNIT CONVERSION FOR R_n: If problem gives moment in kN·m and you forget to convert to N·mm, your R_n will be off by 10⁶. Always double-check: R_n = M_u(N·mm) / [0.90 × 1000(mm) × d²(mm²)]. Result in MPa.
Order
3
BAR SPACING QUICK CALCULATION: s = (A_bar × 1000) / A_s is fast. Memorize key bar areas: φ10 = 78.5 mm², φ12 = 113 mm², φ16 = 201 mm². If A_s = 315 mm²/m and φ10 → s ≈ 250 mm (handy to verify). If s_calc > min(3h, 450), reduce it.
Order
4
TWO-WAY COEFFICIENT TABLE OFTEN PROVIDED: On the exam, if you see a two-way slab, the problem usually includes a coefficient table or directs you to NSCP Table 2.11. Use the table, don't try to memorize coefficients. BUT be sure to use shorter span L_s, not longer span, in M = C w L_s².
Order
5
Comparison tables
One-Way vs Two-Way Slabs: Quick Reference
| Property | One-Way Slab | Two-Way Slab |
|---|---|---|
| Aspect Ratio (L_long / L_short) | ≥ 2.0 | < 2.0 |
| Support Condition | Two opposite sides OR any length | All four sides on stiff supports |
| Bending Direction | One direction (across short span) | Both directions (x and y) |
| Design Method | Per-metre strip (b = 1000 mm); flexural formulas for beam | Coefficient method (beams) or DDM/EFM (flat plate) |
| Typical Moments | M_u based on L_short² | M_x = C_x w L_s²; M_y = C_y w L_s² |
| Temperature Steel | One direction (perpendicular to main) | Both directions (each way min ρ = 0.0018) |
| Board-Exam Frequency | Very common; ~60% of slab problems | Common; ~40%; often with coefficient table provided |
Minimum Thickness by Support Condition (f_y = 415 MPa Baseline)
| Support Condition | Coefficient C | h_min = L/C | Example (L = 4.0 m) |
|---|---|---|---|
| Simply Supported | 20 | L/20 | 200 mm |
| One End Continuous | 24 | L/24 | 167 mm |
| Both Ends Continuous | 28 | L/28 | 143 mm |
| Cantilever | 10 | L/10 | 400 mm |
Common Bar Areas & Spacings for Slabs
| Bar Size (mm φ) | Area (mm²) | Spacing for A_s = 315 mm²/m | Spacing for A_s = 400 mm²/m | Spacing for A_s = 500 mm²/m |
|---|---|---|---|---|
| 10 | 78.5 | 249 mm | 196 mm | 157 mm |
| 12 | 113.1 | 359 mm | 283 mm | 226 mm |
| 16 | 201.1 | 638 mm | 503 mm | 402 mm |
Diagrams
Slab Classification & Design Method Decision Tree
Step-by-step flowchart to classify a slab as one-way or two-way and select the correct design method. Branches on support condition, aspect ratio, and support type (beams vs columns).
One-Way Slab Flexural Design Formula Map
Mind map showing the hierarchical five-step process for designing one-way slab flexural steel, from factored moment through bar spacing and limits.
Minimum Thickness (Deflection Control) – Quick Calculator
Flowchart guiding selection of support condition coefficient and yield strength adjustment to compute minimum thickness quickly. Common values highlighted.
Slab Design Workflow State Diagram
State diagram tracking the design workflow from initial classification through final bar spacing, showing decision points and state transitions.
Typical Slab Problem Distribution on Board Exams
Pie chart showing typical distribution of slab problem types on PRC licensure exams. One-way and two-way flexural design dominate; minimum thickness and special cases less frequent.