CELE Reinforced & Prestressed Concrete — Reinforced Concrete SlabsCheat Sheet
One-page cheat sheet for CELE Reinforced & Prestressed Concrete — Reinforced Concrete Slabs. Every formula, definition, and key fact you need for this chapter, condensed to a single printable page. Designed for the final review session before the CELE 2026.
Exam context
On the CELE 2026, the Reinforced & Prestressed Concrete subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Reinforced Concrete Slabs lands at position 5th out of 7 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Reinforced & Prestressed Concrete on a typical CELE paper.
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.
Sections
Formulas
Formula
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
Section Title
One-Way vs Two-Way Classification
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
Term
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.
Definition
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.
Term
Two-Way Slab
Example
4 m × 3.5 m panel (4/3.5 = 1.14 < 2) → two-way slab on beams.
Definition
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.
Formulas
Formula
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
Formula
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)
Section Title
Minimum Thickness (Deflection Control)
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
Term
Simply Supported (SS)
Example
Span 3.5 m, f_y = 415 → h_min = (3500/20) × 0.993 = 174 mm.
Definition
Slab resting on supports at two ends; no moment continuity; h_min = L/20.
Term
One End Continuous (1EC)
Example
Span 4.0 m, f_y = 415 → h_min = (4000/24) × 0.993 = 165 mm.
Definition
One end fixed, one end simply supported; h_min = L/24.
Term
Both Ends Continuous (2EC)
Example
Span 4.2 m, f_y = 415 → h_min = (4200/28) × 0.993 = 149 mm.
Definition
Both ends fixed to beams or walls; h_min = L/28.
Term
Cantilever
Example
Cantilever overhang 1.2 m, f_y = 415 → h_min = (1200/10) × 0.993 = 119 mm.
Definition
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).
Formulas
Formula
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
Formula
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)
Formula
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
Formula
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
Section Title
Flexural Design (One-Way, Per-Metre Strip)
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
Term
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.
Definition
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.
Term
Effective Depth (d)
Example
h = 175 mm, cover = 20 mm, bar diameter 10 mm → d = 175 − 20 − 5 = 150 mm.
Definition
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.
Formulas
Formula
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
Formula
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
Formula
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
Section Title
Shrinkage & Temperature 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
Term
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.
Definition
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.
Formulas
Formula
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
Section Title
Two-Way Slabs: Coefficient Method (Slabs on Beams)
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
Term
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.
Definition
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).
Formulas
Formula
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
Formula
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)
Section Title
Two-Way Slabs: Direct Design Method (DDM) — Flat Plates/Slabs on Columns
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
Term
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.
Definition
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.
Term
Column Strip
Example
For L_2 = 4 m, column strip width ≈ 1 m; carries majority of moment.
Definition
Central portion of slab above/below column (typically width = min(L_2/4, L_n/4)); resists ~60–75% of total moment.
Term
Middle Strip
Example
Remaining 2 m width on each side of the 1 m column strip.
Definition
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.
Section Title
Key Equations & Conversions
Diagrams To Know
- Moment diagram for continuous vs simply-supported beams/slabs (shape of M affects minimum thickness).
Reactions Or Equations
Note
Always ensure units match: if R_n formula uses d in mm, M_u must be in N·mm.
Equation
M (kN·m) × 10⁶ = M (N·mm)
Conditions
Unit conversion for moment; essential when using R_n = M_u / (φ b d²)
Note
Example: 10 mm φ bar (78.5 mm²) with A_s = 315 mm²/m → s = 249 mm ≈ 250 mm.
Equation
A_bar × 1000 / A_s = s (mm spacing)
Conditions
Converting per-metre steel area to practical bar spacing; A_bar in mm², A_s in mm²/m
Note
Always measure span center-to-center or clear span consistently.
Equation
Aspect Ratio = L_long / L_short
Conditions
If ≥ 2.0 → one-way; if < 2.0 → two-way
Note
Round up to nearest 10 or 25 mm for practical thickness. This h_min assumes fy = 415 MPa baseline.
Equation
h_min = (L / C) × (0.4 + f_y / 700)
Conditions
Deflection control; C = 20 (SS), 24 (1EC), 28 (2EC), 10 (cantilever); f_y in MPa
Must Remember
Item
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
Item
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
Item
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
Item
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
Item
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
Item
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
Item
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
Item
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
Item
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
Item
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
Tip
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
Tip
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
Tip
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
Tip
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
Tip
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
Rows
Values
- ≥ 2.0
- < 2.0
Property
Aspect Ratio (L_long / L_short)
Values
- Two opposite sides OR any length
- All four sides on stiff supports
Property
Support Condition
Values
- One direction (across short span)
- Both directions (x and y)
Property
Bending Direction
Values
- Per-metre strip (b = 1000 mm); flexural formulas for beam
- Coefficient method (beams) or DDM/EFM (flat plate)
Property
Design Method
Values
- M_u based on L_short²
- M_x = C_x w L_s²; M_y = C_y w L_s²
Property
Typical Moments
Values
- One direction (perpendicular to main)
- Both directions (each way min ρ = 0.0018)
Property
Temperature Steel
Values
- Very common; ~60% of slab problems
- Common; ~40%; often with coefficient table provided
Property
Board-Exam Frequency
Columns
- Property
- One-Way Slab
- Two-Way Slab
Table Title
One-Way vs Two-Way Slabs: Quick Reference
Rows
Values
- 20
- L/20
- 200 mm
Property
Simply Supported
Values
- 24
- L/24
- 167 mm
Property
One End Continuous
Values
- 28
- L/28
- 143 mm
Property
Both Ends Continuous
Values
- 10
- L/10
- 400 mm
Property
Cantilever
Columns
- Support Condition
- Coefficient C
- h_min = L/C
- Example (L = 4.0 m)
Table Title
Minimum Thickness by Support Condition (f_y = 415 MPa Baseline)
Rows
Values
- 78.5
- 249 mm
- 196 mm
- 157 mm
Property
10
Values
- 113.1
- 359 mm
- 283 mm
- 226 mm
Property
12
Values
- 201.1
- 638 mm
- 503 mm
- 402 mm
Property
16
Columns
- 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
Table Title
Common Bar Areas & Spacings for Slabs
Previous chapter
Reinforced Concrete Columns
Next chapter
Reinforced Concrete Footings, Bond and Development
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