CELE Reinforced & Prestressed Concrete — Reinforced Concrete SlabsRevision Notes

Formulas

Exam Tips

• Always write the ratio as LONG ÷ SHORT. If your answer is less than 1, you inverted it — flip it.
• Board exams often present a borderline panel (ratio = 1.95 or 2.05) — be precise in your classification.
• When a problem says 'supported on two sides only,' classify as one-way immediately without computing the ratio.
• Memorise the boundary: ratio ≥ 2 → one-way; ratio < 2 → two-way (not ≤ 2, not > 2).

Key Points

• A rectangular slab supported on all four sides is classified by its aspect ratio: ratio = L_long / L_short.
• If L_long / L_short ≥ 2, the slab acts as a ONE-WAY slab — it bends primarily across the short span.
• If L_long / L_short < 2, the slab acts as a TWO-WAY slab — it bends significantly in both directions.
• A slab supported on only two opposite sides is ALWAYS one-way, regardless of the aspect ratio.
• One-way slabs are designed as a series of independent 1-metre wide beam strips spanning in the short direction.
• Two-way slabs require consideration of moments in both the long and short directions simultaneously.
• The critical distinction affects the entire design approach, load path, and reinforcement layout.
• Philippine practice follows NSCP 2015 Section 406 for one-way slabs and Section 408 for two-way slabs.

Definitions

Section Title

One-Way vs. Two-Way Slab Classification

Common Mistakes

• Inverting the ratio — computing L_short / L_long instead of L_long / L_short. The ratio must always be ≥ 1.
• Forgetting that a slab on only two opposite sides is always one-way, even if the panel is nearly square.
• Applying one-way formulas to a two-way panel and vice versa — this fundamentally changes the design.
• Using centre-to-centre beam spacings instead of clear spans for span ratios.

Formulas

Exam Tips

• Memorise the four divisors as a sequence: 20, 24, 28, 10 (SS → 1-end cont. → 2-end cont. → cantilever).
• Quick check: if fy = 420 MPa, the factor = exactly 1.0 — no adjustment needed. For fy = 415 MPa, factor ≈ 0.993 (very close to 1.0).
• For fy = 275 MPa, factor = 0.4 + 275/700 = 0.793 — significantly smaller, giving a thinner minimum slab.
• If the problem asks 'minimum thickness to satisfy deflection without calculation,' that is the h_min formula.
• Round the final answer UP — never round down a minimum requirement.

Key Points

• NSCP 2015 Section 406.3.1 (ACI 318-19 Table 7.3.1.1) provides minimum thicknesses for one-way solid slabs to waive explicit deflection calculations.
• The tabulated values apply for normal-weight concrete (wc ≈ 2400 kg/m³) and fy = 420 MPa.
• For other values of fy, multiply the tabulated h_min by the factor (0.4 + fy/700).
• Four support conditions are covered: simply supported, one end continuous, both ends continuous, and cantilever.
• The span L used in the formula is the CLEAR SPAN in the direction of bending.
• If the actual thickness provided is less than h_min, explicit deflection calculation per NSCP Section 406.6 is required.
• For two-way slabs, separate thickness criteria (including αf and βs) apply per NSCP 2015 Section 408.3.
• Always round UP to the nearest 5 mm or 10 mm increment in practice.

Definitions

Section Title

Minimum Slab Thickness for Deflection Control

Common Mistakes

• Using centre-to-centre span L instead of the clear span Ln in the h_min formula.
• Forgetting the (0.4 + fy/700) correction factor when fy ≠ 420 MPa (e.g., fy = 415 MPa gives factor = 0.993, not 1.0).
• Rounding DOWN instead of UP — always round up to the next millimetre or practical increment.
• Using the wrong divisor for the support condition — e.g., using L/20 for a continuous slab interior span instead of L/28.
• Applying the one-way minimum thickness table to two-way slab problems.

Formulas

Exam Tips

• Always convert Mu to N·mm: 1 kN·m = 10⁶ N·mm.
• Memorise common bar areas: 10 mm (78.5 mm²), 12 mm (113.1 mm²), 16 mm (201.1 mm²), 20 mm (314.2 mm²), 25 mm (490.9 mm²).
• After finding As from the ρ formula, always compare to As,temp = 0.0018bh and use the LARGER value.
• Round bar spacing DOWN to a convenient number (e.g., computed 249 mm → specify 200 mm) to ensure adequate steel.
• Check s_max = min(3h, 450 mm) as a final step — if computed spacing exceeds this, use s_max.

Key Points

• A one-way slab is designed as a rectangular beam of unit width b = 1000 mm.
• The factored moment Mu (in kN·m/m) is computed per unit width of slab.
• The design procedure follows beam flexure: compute Rn, solve for ρ, find As.
• The result As is in mm²/m — it represents the required steel area per 1 metre width of slab.
• Convert As to bar spacing: s = (Ab × 1000) / As, where Ab is the area of one bar (mm²).
• The minimum As for slabs in the main direction is governed by the shrinkage/temperature minimum on the full slab thickness h (not d).
• Maximum bar spacing for main steel: min(3h, 450 mm) per NSCP 2015 Section 406.7.3.
• Effective depth d = h − cover − half bar diameter; typical cover for slabs = 20 mm (protected) or 40 mm (exposed).
• Phi factor (φ) = 0.90 for tension-controlled flexure (NSCP 2015 Section 421.2.1).

Definitions

Section Title

Flexural Steel Design — Per-Metre Strip Method

Common Mistakes

• Forgetting to convert Mu from kN·m to N·mm (multiply by 10⁶) before computing Rn.
• Using h (total thickness) instead of d (effective depth) in the Rn formula.
• Not checking the computed As against the minimum (shrinkage/temperature steel on h) — the minimum often governs for thin slabs.
• Rounding bar spacing UP instead of DOWN (rounding UP gives fewer bars and less steel than required).
• Using φ = 0.85 (for shear) instead of φ = 0.90 (for flexure).

Formulas

Exam Tips

• Two values to memorise: ρ_temp = 0.0018 (fy = 415/420 MPa) and ρ_temp = 0.0020 (fy = 275 MPa).
• Temperature steel always uses FULL THICKNESS h, not d. Main steel uses d in moment calculations but h for the minimum check.
• When a problem gives both Mu (for main steel) and asks for temperature steel — two separate calculations, both per 1 m strip.
• If As,calc from flexure < As,temp from temperature minimum, use the temperature minimum as the ACTUAL As to provide.
• Spacing: compute s, check against min(5h, 450) for temperature bars. Round computed spacing DOWN.

Key Points

• Temperature and shrinkage reinforcement is placed perpendicular to the main flexural steel to control cracking.
• It resists cracking caused by concrete drying shrinkage and thermal deformation — not flexure.
• The minimum ratio ρ_temp depends on fy: use 0.0020 for fy = 275 MPa (Grade 40) and 0.0018 for fy = 415–420 MPa (Grade 60).
• As,temp is computed on the FULL slab thickness h (not effective depth d).
• Maximum spacing for temperature steel: min(5h, 450 mm) per NSCP 2015.
• In the main direction of a thin slab, As from the flexure calculation may be less than As,temp — in that case, the temperature minimum governs.
• Temperature steel is provided in BOTH faces for thick slabs (h > 300 mm is a common practical threshold).
• NSCP 2015 Section 406.6 (ACI 318 Section 7.6.1) provides these minimum ratios.

Definitions

Section Title

Shrinkage and Temperature Steel

Common Mistakes

• Computing As,temp using d (effective depth) instead of h (full thickness) — always use total thickness for temperature steel.
• Applying ρ_temp = 0.0018 when fy = 275 MPa — the correct value is 0.0020 for Grade 40 steel.
• Forgetting to check temperature minimum against the computed main steel As — the larger governs.
• Using the temperature spacing limit (min 5h, 450 mm) for main steel, or vice versa — they have different limits.

Formulas

Exam Tips

• Mo = wu L2 Ln² / 8 — think of it as an equivalent simply-supported span beam moment.
• For interior spans (DDM): split Mo as 65% negative, 35% positive. For end spans: use NSCP Table 408.10.4.2 (varies by edge condition).
• Verify DDM applicability before applying it — board exam problems sometimes test whether conditions are met.
• The coefficient method uses SHORT SPAN in M = C w Ls²; coefficients Ca (short direction) and Cb (long direction) are read from separate tables.
• Two-way punching shear at columns is a separate check — do not confuse it with flexural design.

Key Points

• Two-way slabs develop bending moments in both the short and long directions simultaneously.
• Three main analysis methods are used: (1) Coefficient Method, (2) Direct Design Method (DDM), (3) Equivalent Frame Method (EFM).
• The Coefficient Method is used for slabs supported on stiff beams (not flat plates). Moments = C × w × Ls², with C tabulated by edge condition and aspect ratio.
• DDM and EFM are applicable to flat plates and flat slabs supported directly on columns.
• DDM requires: minimum 3 spans, rectangular panels, successive span ratio ≤ 1/3, no offset columns, and LL/DL ≤ 2 (NSCP 2015 Sec. 408.10).
• The total static moment Mo is the starting point for DDM — distributed to column and middle strips.
• Column strip occupies the middle half of each panel width (L2/2 centred on the column line).
• Middle strip is the remainder between two column strips in adjacent panels.
• NSCP 2015 specifies the percentage of Mo distributed to positive and negative moment regions and to column vs. middle strips.

Definitions

Section Title

Two-Way Slab Analysis

Common Mistakes

• Using the full panel span L instead of the clear span Ln in the Mo formula.
• Confusing L2 (transverse span) and Ln (clear span in direction of analysis) — they are different lengths.
• Applying DDM to slabs that violate the applicability conditions (e.g., LL/DL > 2, irregular panels).
• Assigning 100% of the column strip moment fraction to only ONE direction of reinforcement.
• Using the coefficient method coefficients for flat plates (they only apply to slabs on stiff beams).