Construction Materials and Testing - Cheat Sheet
Your last-minute revision companion for PRC Civil Engineer Licensure Exam. Concrete, aggregates, steel, acceptance criteria, and board-style numerals. Covers NSCP 2015, ACI 318, AISC 360.
CONCRETE — Fundamentals & Design
Formulas
w/c = W_water ÷ W_cement
Meaning
w/c = water-cement ratio (by weight); W = weight in kg or lb
Watch out
WEIGHT ratio, NOT volume. Common mistake: confusing litres with kg. Water ~1000 kg/m³.
When to use
Always when given cement and water masses; governs strength and durability
f'_c = P_failure ÷ A
Meaning
f'_c = compressive strength (MPa); P = failure load (N); A = cross-sectional area (mm²)
Watch out
Standard cylinder diameter = 150 mm, height = 300 mm. Convert load to Newtons. Result in MPa.
When to use
Always for cylinder/cube crushing tests; standard cylinder A = (π/4)(150)² mm²
A_cylinder = (π/4)d² = (π/4)(150)² ≈ 17,671 mm²
Meaning
Standard compressive-test cylinder cross-section; d = 150 mm (Philippines & ACI standard)
Watch out
Use millimetres (mm), not metres. 150 mm dia is fixed by ACI 318. Cubes (150 mm × 150 mm × 150 mm) also ≈17,671 mm².
When to use
Every time you compute compressive strength from cylinder test
f'_{cr} = max(f'_c + 1.34s, f'_c + 2.33s − 3.5) [f'_c ≤ 35 MPa]
Meaning
f'_cr = required average compressive strength; f'_c = specified target (MPa); s = standard deviation of trial tests (MPa)
Watch out
BOTH formulas are evaluated; take the LARGER value. First formula typically governs for small s. Check both always.
When to use
ACI 318 quality control acceptance for concretes ≤35 MPa; ensures ~99% pass rate
f'_{cr} = max(f'_c + 2.05s, 0.90f'_c + 2.33s) [f'_c > 35 MPa]
Meaning
Required average strength for higher-strength concretes (>35 MPa)
Watch out
Different coefficients. Second formula becomes more stringent for large s. Always compute both.
When to use
High-strength concrete mixes in PRC projects (HSC, ≥40 MPa target)
Common values
Value
17,671 mm² (diameter 150 mm)
Symbol
A_cyl
Quantity
Standard cylinder cross-section
Value
0.50–0.55
Symbol
w/c
Quantity
Typical w/c for 28 d strength ~30 MPa
Value
0.45–0.48
Symbol
w/c
Quantity
Typical w/c for 28 d strength ~35 MPa
Value
0.40–0.43
Symbol
w/c
Quantity
Typical w/c for 28 d strength ~40 MPa
Value
2–3.5 MPa
Symbol
s
Quantity
Standard deviation (good quality control)
Value
>5 MPa
Symbol
s
Quantity
Standard deviation (poor control)
Important facts
- Lower w/c → HIGHER strength, LOWER workability; typical range 0.40–0.60.
- Strength doubles roughly from 7 to 28 days; 28-day is reference point (ACI 318).
- Slump is NOT a measure of strength; high slump can mean weak (over-water) or strong (good plasticizer).
- w/c = 0.50 ≈ 30 MPa; w/c = 0.45 ≈ 35 MPa; w/c = 0.40 ≈ 40 MPa (approximate, depends on cement type & aggregate).
- Acceptance: if 2 consecutive cylinders <f'_c − 3.5 MPa OR average <f'_{cr}, investigate or reject batch (NSCP 2015, ACI 318).
- Standard test cylinder: 150 mm dia, 300 mm ht (Philippines, ACI standard); cured at 23°C, 95% RH until test.
- Concrete strength ∝ (cement content × cement hydration) − (w/c effect dominates).
- Admixtures (plasticizers, retarders, accelerators) alter w/c–strength relation; high-range water reducers (HRWR) → lower w/c, same slump.
Key definitions
Water-Cement Ratio (w/c)
Example
180 kg water ÷ 360 kg cement = 0.50 w/c; typical for 28-day strength ~30 MPa.
Ratio of water mass to cement mass; primary control on strength, durability, and workability (lower w/c → higher strength, lower workability).
Slump Test
Example
Slump 75–100 mm: normal consistency; <50 mm: stiff; >150 mm: wet/over-sanded.
Measures concrete workability (consistency/flowability); cone height 300 mm, dropped, vertical settlement recorded in mm.
Compressive Strength (f'_c)
Example
Cylinder fails at 530 kN → f'_c = 530,000 N ÷ 17,671 mm² ≈ 30.0 MPa.
Crushing capacity of hardened concrete at 28 days; measured from standard cylinders (150 mm dia × 300 mm ht) or 150 mm cubes; reported in MPa.
Standard Deviation (s)
Example
Trial tests: 28, 29, 31, 30 MPa → s ≈ 1.2 MPa (tight); requires f'_{cr} only slightly above f'_c.
Statistical spread of compressive test results; higher s → more variability → higher required average strength.
Curing
Example
Wet curing (moist burlap, 7 days) → ~30 MPa at 28 d; air-dry → ~20–25 MPa (strength loss).
Process of maintaining concrete temperature and moisture post-placement (7–28 days minimum); affects strength development and durability.
Diagrams to know
- w/c vs Strength curve (inverse power law; flattens at very low w/c)
- Slump cone diagram (300 mm ht, 100 mm top, 200 mm base)
- Cylinder compressive test setup (axial load, failure cone ~45°)
- Strength-development curve (log scale: 7d, 28d, 56d, 90d)
- Acceptance sampling flowchart (average, std dev, two-formula check)
AGGREGATES — Classification & Properties
Formulas
Fineness Modulus (FM) = (Σ% retained on standard sieves) ÷ 100
Meaning
Measure of aggregate size distribution (higher FM → coarser). Standard sieves: 150, 300, 600 µm, 1.18, 2.36, 4.75, 9.5, 19, 37.5, 75 mm
Watch out
Poorly graded aggregate (high or low FM) increases cement paste demand, raises cost, reduces durability.
When to use
Check aggregate gradation acceptance; fine aggregate FM ≈ 2.8–3.0; coarse FM ≈ 6.5–7.5 (NSCP 2015)
Absorption (%) = [(SSD − OD) ÷ OD] × 100
Meaning
SSD = saturated-surface-dry mass (g); OD = oven-dry mass (g); indicates aggregate pore porosity
Watch out
Lightweight aggregate (porous) can have absorption >10%; dense aggregate <1%. Affects mix design.
When to use
Affects fresh concrete water demand; high absorption → adjust w/c downward to maintain strength
Specific Gravity (SG) = OD mass ÷ volume (displaced water)
Meaning
Density indicator; typical fine aggregate 2.60–2.65; coarse 2.65–2.75 (granite, basalt)
Watch out
Confuse specific gravity with unit weight. SG is density relative to water (unitless); unit weight = SG × 9.81 kN/m³.
When to use
Concrete mix design calculations; higher SG → denser, heavier aggregate
Common values
Value
2.60–2.65
Symbol
SG_fine
Quantity
Fine aggregate specific gravity
Value
2.65–2.75
Symbol
SG_coarse
Quantity
Coarse aggregate specific gravity
Value
2.8–3.0
Symbol
FM_fine
Quantity
Fine aggregate fineness modulus (ideal)
Value
6.5–7.5
Symbol
FM_coarse
Quantity
Coarse aggregate fineness modulus (typical 19 mm)
Value
~1,600 kg/m³
Symbol
γ_fine
Quantity
Fine aggregate unit weight (loose)
Value
~1,750 kg/m³
Symbol
γ_coarse
Quantity
Coarse aggregate unit weight (loose)
Important facts
- Aggregate is ~75–80% of concrete by mass; quality & gradation directly affect strength, durability, workability, and cost.
- Maximum nominal size: typically 37.5 mm (coarse) or 19 mm for high-strength; smaller max size → higher strength (more matrix), more cost.
- Poorly graded or gap-graded aggregate: high void ratio → more cement paste needed → higher w/c → lower strength.
- Fine aggregate FM should be 2.8–3.0 (medium sand preferred); <2.5 = too fine (high paste demand); >3.2 = too coarse (poor workability).
- Coarse aggregate should be angular (crushed) for better interlock; rounded (river gravel) less ideal but acceptable.
- Absorption affects concrete water demand: high-absorption aggregate must be pre-wetted or w/c adjusted to maintain strength.
- Deleterious materials (shale, coal, mica, salt) reduce strength and durability; NSCP 2015 limits ≤1–5% by mass.
- Sulfate in aggregate & water: can cause ettringite expansion; use sulfate-resistant cement (Type II/III, SR-3/SR-4) if SO₄²⁻ >1,500 mg/L.
Key definitions
Fine Aggregate
Example
Natural sand, manufactured sand (crusher dust); FM 2.8–3.0 is ideal.
Sand, particles 75 µm–4.75 mm; constitutes ~35–40% concrete volume; improves workability and fills voids.
Coarse Aggregate
Example
19 mm nominal size (3/4 in); coarse FM ~7.0; reduces cement paste demand.
Gravel or crushed stone, particles >4.75 mm (typically 9.5–37.5 mm); constitutes ~40–45% concrete volume; provides strength-bearing skeleton.
Well-Graded Aggregate
Example
50% pass 4.75 mm, 35% pass 9.5 mm, 20% pass 19 mm; vs. single-size (poorly graded) = high void ratio.
Continuous particle size distribution from fine to coarse; minimizes voids, reduces cement paste & water demand, improves strength.
Aggregate Cleanliness (Sand Equivalent)
Example
Beach sand (salt, silt) often <60%; quarried sand typically 80–95%.
Test measuring clay/silt content; higher value (>75%) = clean; <50% = contaminated (reduces strength, durability).
Unit Weight (Bulk Density)
Example
Granite: ~1,750 kg/m³; lightweight: ~1,200 kg/m³; used in mix design & concrete unit weight estimation.
Mass of aggregate per unit volume (in-place, with voids); typical 1,600–1,800 kg/m³ for natural aggregates.
Diagrams to know
- Sieve analysis graph (% passing vs. sieve size); well-graded vs. gap-graded curves
- Fineness modulus calculation table (retained %, cumulative %)
- Fine vs. coarse aggregate particle-size ranges with micron/mm scales
- Aggregate grading envelope (NSCP/ACI acceptable zone)
STEEL REINFORCEMENT & STRUCTURAL STEEL
Formulas
Stress = P ÷ A; Strain = ΔL ÷ L₀
Meaning
P = axial load (N); A = cross-sectional area (mm²); ΔL = extension (mm); L₀ = original length (mm)
Watch out
Stress in MPa (N/mm²); strain is unitless (dimensionless ratio). Watch unit conversion (mm² from nominal diameter).
When to use
Tension test analysis for yield strength, ultimate strength, and ductility (elongation)
Modulus of Elasticity (E) = Stress ÷ Strain = (P/A) ÷ (ΔL/L₀)
Meaning
E = Young's modulus (MPa or GPa); slope of elastic region of stress–strain curve
Watch out
Linear only in elastic region (up to yield, ~250–400 MPa for rebar). Nonlinear beyond yield.
When to use
Steel reinforcing: E ≈ 200 GPa (200,000 MPa); used for deflection calculations (NSCP 2015, ACI 318)
Yield Strength (f_y); Ultimate Strength (f_u); Elongation % = (L_f − L₀) ÷ L₀ × 100
Meaning
f_y = stress at permanent set (~0.2% offset); f_u = maximum stress; elongation = ductility indicator (%)
Watch out
Philippines: deformed bar Grade 275 MPa (old 40 ksi), Grade 415 MPa (60 ksi) are standard. Elongation ≥12% required for ductility.
When to use
Classification of reinforcing steel (Grade 230, 275, 415 MPa NSCP 2015) and structural steel (AISC 360)
Common values
Value
200 GPa (200,000 MPa)
Symbol
E_s
Quantity
Steel modulus of elasticity
Value
280 MPa
Symbol
f_y
Quantity
Grade 275 rebar yield stress (minimum)
Value
420 MPa
Symbol
f_y
Quantity
Grade 415 rebar yield stress (minimum)
Value
620–640 MPa
Symbol
f_u
Quantity
Grade 415 rebar ultimate stress (typical)
Value
12%
Symbol
ε_min
Quantity
Minimum elongation (200 mm gauge)
Value
1.58 kg/m
Symbol
ω
Quantity
Typical rebar unit weight (16 mm Ø)
Important facts
- Reinforcing steel grades (NSCP 2015): Grade 275 MPa (f_y ≥ 280 MPa) [old 40 ksi], Grade 415 MPa (f_y ≥ 420 MPa) [60 ksi]; Grade 415 preferred in PRC.
- Structural steel (AISC 360): Grade 250 (f_y = 250 MPa, f_u = 400 MPa); Grade 345 (f_y = 345 MPa); Grade 450 (f_y = 450 MPa high-strength); A36 (f_y = 250 MPa) common US.
- Modulus of elasticity: steel E ≈ 200 GPa (200,000 MPa) regardless of grade; concrete E_c ≈ 20–30 GPa (depends on f'_c).
- Bend test: 180° cold-bend around mandrel; no cracking indicates ductility; required for quality control (NSCP, ACI 318).
- Tensile test sample: minimum 3 coupons per lot; if 1 specimen fails, test 3 more; all must pass for acceptance.
- Elongation requirement: minimum 12% on 200 mm gauge length (NSCP 2015); lower elongation (<5%) typical of work-hardened or high-strength steel.
- Stress–strain curve: elastic region (linear E), yield plateau, strain-hardening region, rupture; stress drops at necking.
- Rebars are supplied in bundles; weight per metre depends on diameter: 12 mm ≈ 0.89 kg/m, 16 mm ≈ 1.58 kg/m, 20 mm ≈ 2.47 kg/m.
Key definitions
Deformed Reinforcing Bar (Rebar)
Example
16 mm Ø, Grade 415 rebar; yield ~420 MPa, ultimate ~620 MPa; elongation ≥12%.
Steel bar with surface deformations (ribs); improves bond with concrete; grades 275 MPa (280 MPa yield min), 415 MPa (420 MPa yield min) common in PRC.
Plain Round Bar (Wire)
Example
Historical use; now replaced by welded wire fabric (WWF) or deformed rebar.
Smooth steel wire or bar; lower bond capacity than deformed; generally obsolete for structural use (NSCP 2015 discourages).
Yield Strength (f_y)
Example
16 mm Grade 415 rebar: f_y ≈ 420 MPa; design yield stress used in flexural/axial capacity equations.
Stress at which steel begins permanent plastic deformation (0.2% offset yield); for PRC Grade 415, ~420 MPa minimum.
Ductility (Elongation)
Example
Bar elongates 15% before rupture; indicates ductile behavior; <5% = brittle (unacceptable for seismic regions).
Percentage extension at rupture; minimum 12% required (NSCP 2015) to ensure warning before sudden failure; allows plastic hinge redistribution.
Mill Certificate
Example
Certificate confirms 16 mm Ø Grade 415, f_y = 420 MPa, f_u = 640 MPa, elongation = 13%; must match project specification.
Document from steel manufacturer certifying grade, yield, ultimate, elongation, bend-test results; required for material acceptance (RA 544).
Diagrams to know
- Stress–strain curve for steel (elastic, yield plateau, strain-hardening, rupture)
- Rebar deformation pattern (rib spacing, height profile)
- Tensile test setup (gripped specimen, extensometer, load cell)
- Bend-test mandrel schematic (diameter D, rebar diameter d, 180° bend)
ACCEPTANCE CRITERIA & QUALITY CONTROL (NSCP 2015, ACI 318)
Formulas
Sample statistic: Mean f'_test = Σf'_i ÷ n; Standard Deviation s = √[Σ(f'_i − Mean)² ÷ (n−1)]
Meaning
n = number of cylinders tested (typically n=3–6 per batch); f'_i = individual strength result (MPa)
Watch out
Use n−1 denominator (sample s), NOT n (population σ). Small n (3–4) → high s → high required f'_{cr}.
When to use
Always compute mean and std dev for acceptance decision; required by ACI 318, NSCP 2015
Acceptance Rule 1 (NSCP): All individual cylinders ≥ f'_c − 3.5 MPa
Meaning
No cylinder more than 3.5 MPa below target; if even 1 fails, batch rejected or further investigation required
Watch out
Single low result can reject entire batch. Common in poor QC. Must investigate: curing, testing error, or actual concrete defect.
When to use
First check; ensures minimum margin; violation = automatic failure regardless of average
Acceptance Rule 2 (NSCP): Average strength ≥ f'_{cr} (computed from ACI two-formula)
Meaning
f'_{cr} = max(f'_c + 1.34s, f'_c + 2.33s − 3.5) for f'_c ≤ 35 MPa
Watch out
Both rules must pass. High s → high f'_{cr} → need stronger trial mix. If s > 5 MPa, investigate process (water control, curing, cement variation).
When to use
Second check; ensures average exceeds target by safety margin proportional to variability
Coefficient of Variation (CV) = s ÷ Mean × 100 (%)
Meaning
Normalized measure of QC consistency; lower CV = better control (target <10% in PRC)
Watch out
CV depends on mean strength. High mean (40 MPa) with s=3 → CV=7.5% (good); low mean (20 MPa) same s → CV=15% (poor relative to target).
When to use
Trend analysis over many batches; CV >15% indicates poor process control
Common values
Value
f'_c − 3.5 MPa
Symbol
f'_min
Quantity
Minimum rejection threshold (single cylinder)
Value
≥0.85 f'_c
Symbol
ratio
Quantity
Core strength acceptance ratio
Value
<0.75 f'_c
Symbol
ratio
Quantity
Minimum core strength for outright rejection
Value
2–3 MPa
Symbol
s
Quantity
Typical good-control standard deviation
Value
>5 MPa
Symbol
s
Quantity
Typical poor-control standard deviation
Important facts
- ACI 318 & NSCP 2015 use two-formula approach for f'_{cr} to balance cost vs. safety; first formula dominates when s is small (tight control).
- If s > 4 MPa, contractor must investigate: inadequate water control, inconsistent curing, cement variations, testing error, or batch segregation.
- Standard deviation is estimated from trial tests (pilot batches); assumed constant for field batches of same mix design and source.
- Acceptance is TWO-PART: (1) no single cylinder <f'_c−3.5 MPa [NSCP Rule 1], AND (2) average ≥f'_{cr} [NSCP Rule 2]. Both must pass.
- Field-cured cylinders (cured at job site in same conditions as structure) are more representative than lab-cured; ACI 318 recognizes both approaches.
- Core tests: drill ~3–4 cores from suspicious area; strength ≥0.85f'_c → structure acceptable; <0.75f'_c → reject; 0.75–0.85 → case-by-case review.
- Strength gain: 7-day strength ≈ 60–70% of 28-day; 14-day ≈ 80–85%; early tests indicate trend but are NOT acceptance basis (28-day is reference).
- RA 544 (Philippine Architects and Engineers Law): engineer responsible for QC; must document test records, certifications, and corrective actions.
Key definitions
Specified Strength (f'_c)
Example
f'_c = 28 MPa; contractor trial mix may yield 32 MPa average (with s=2.5) → accepted with margin.
Design target compressive strength (MPa) selected for structural design; e.g., 28 MPa, 35 MPa. Not necessarily what contractor achieves on first try.
Required Average Strength (f'_{cr})
Example
f'_c = 28 MPa, s = 3 MPa → f'_{cr} = max(28+4.02, 28+6.99−3.5) = 31.5 MPa; contractor must hit 31.5 MPa average.
Statistical target: average of trial/control test cylinders must equal or exceed f'_{cr} to ensure ~99% of field concrete meets f'_c.
Standard Deviation (s)
Example
Trial tests: 30, 31, 29, 32 MPa → mean=30.5, s≈1.3 (tight); 20, 35, 25, 30 MPa → mean=27.5, s≈6.1 (poor).
Measure of scatter in cylinder test results; higher s → tighter control required. Depends on contractor QC, curing consistency, testing precision.
Test Batch / Acceptance Unit
Example
1-day pour of 75 m³ → 3 cylinders sampled and tested at 28 days; if all ≥f'_c−3.5 and avg ≥f'_{cr}, batch accepted.
Quantity of concrete from which samples are taken (typically 50–100 m³ or per NSCP 2015 specification); minimum 3 cylinders per batch.
Rejection & Investigation
Example
Cylinders: 26, 27, 29 MPa (avg=27.3) for f'_c=28; if f'_{cr}=31.5, batch fails; cores drilled from slab; if core avg ≥0.85f'_c, structure may be accepted with engineer approval.
If average <f'_{cr} OR any cylinder <f'_c−3.5 MPa: batch flagged; cores cut from structure for strength verification (IS 1199 core test); if cores insufficient, structural analysis & remedial work required.
Diagrams to know
- Acceptance flowchart: compute mean, s → check Rule 1 (all ≥f'_c−3.5) → check Rule 2 (avg ≥f'_{cr}) → PASS/REJECT/INVESTIGATE
- Histogram of cylinder strengths (normal distribution, mean, ±1s, ±2s bands relative to f'_c)
- Required average strength vs. specified strength graph (varying s; f'_{cr} curves for different w/c mixes)
TESTING PROCEDURES & STANDARDS
Common values
Value
150 mm
Symbol
d
Quantity
Standard cylinder diameter
Value
300 mm (height:diameter = 2:1)
Symbol
h
Quantity
Standard cylinder height
Value
300 mm
Symbol
h_cone
Quantity
Slump cone height
Value
0.07–0.12 f'_c
Symbol
f_t
Quantity
Typical splitting tensile strength ratio
Value
0.10–0.15 f'_c
Symbol
f_r
Quantity
Typical flexural strength ratio
Value
E_c = 3,320 √f'_c + 6,900 (MPa for f'_c in MPa) [ACI 318]
Symbol
E_c
Quantity
Modulus of elasticity for concrete (rough estimate)
Important facts
- All tests must follow NSCP 2015 (Philippine standard based on ACI 318 & ASTM) or relevant ASTM standard; documentation required for acceptance.
- Field samples (cylinders) cast from same batch at time of placement; at least 1 set per day or per 50 m³, whichever is more frequent.
- Standard curing: 23±2°C, 95% RH until 28 days; field-cured cylinders wrapped in wet burlap approximate job-site conditions.
- Strength measured at 28 days (reference age); early tests at 7 or 14 days indicate trend; not acceptance basis unless specified.
- Testing rate/speed: compression ~0.25 MPa/s (slow); tension ~0.01–0.05 mm/s extension rate; affects results (strain-rate sensitivity).
- NSCP 2015 cylinder standard: 150 mm dia × 300 mm ht (aspect ratio 2:1); cubes 150×150×150 mm also acceptable; results differ slightly (~3–5% higher for cubes).
- Quality assurance: 3rd-party testing lab (independent from contractor) is preferred in PRC for major projects; accreditation required (ISO 17025).
- Aggregates: cleanliness, gradation, absorption, specific gravity, and soundness (freeze–thaw, sulfate attack) all tested per NSCP; deleterious content limits ≤1–5%.
Key definitions
Slump Test (ASTM C143 / NSCP 2015)
Example
Normal slump 75–100 mm (plastic concrete); <50 mm stiff (poor flow); >150 mm wet/over-sanded (often weak).
Cone 300 mm tall, 100 mm top dia, 200 mm base; filled with concrete, lifted, vertical settlement measured; indicates workability.
Compressive Strength Test (ASTM C39 / NSCP 2015)
Example
Cylinder fails at 530 kN → f'_c = 530 kN ÷ 0.01767 m² = 30.0 MPa.
Standard cylinder 150 mm dia × 300 mm ht (or 150 mm cube); tested in compression at 28 days at 23±2°C; loading rate ~0.25 MPa/s.
Tensile (Split-Cylinder) Test (ASTM C496 / NSCP 2015)
Example
f'_c = 30 MPa → f_t ≈ 2.0–3.5 MPa; used for pavement, precast design.
Cylinder loaded diametrically; splitting stress = 2P/(πDL) where D=dia, L=length; gives indirect tensile strength f_t ≈ 0.07–0.12 f'_c.
Flexural Strength (Modulus of Rupture) Test (ASTM C78 / NSCP 2015)
Example
f'_c = 30 MPa → f_r ≈ 3.0–4.5 MPa; critical for pavements, slabs.
Beam 150×150×750 mm, third-point loading; stress f_r = PL/(bd²) where P=load, L=span, b=width, d=depth; f_r ≈ 0.10–0.15 f'_c.
Air Content Test (ASTM C173 / NSCP 2015)
Example
Measured 6.2% air → within acceptable range for freeze–thaw durability in northern PRC regions (not typical in tropical Philippines).
Measures entrapped + entrained air in fresh concrete (percent by volume); target 4–6% in air-entrained concrete; excess air reduces strength (~3–5% strength loss per 1% air).
Setting Time Test (ASTM C807 / NSCP 2015)
Example
Initial set at 5 hours → forms can be struck after 12–18 hours; accelerators reduce to 2–3 hours.
Vicat apparatus: initial set (resistance to 2.5 mm penetration) typically 4–6 hours; final set (0 mm penetration) ~10–12 hours; important for form removal timing.
Sieve Analysis / Gradation Test (ASTM C136 / NSCP 2015)
Example
Fine aggregate: % passing 4.75 mm ≈ 85%, 2.36 mm ≈ 70%, 1.18 mm ≈ 50%; FM ≈ 2.9 (medium sand, acceptable).
Aggregate sieved through standard series (75 µm to 75 mm); % passing each sieve plotted; fineness modulus calculated; checks conformity to gradation envelope.
Tensile Test (Steel Reinforcement ASTM A370 / NSCP 2015)
Example
16 mm Grade 415: f_y ≈ 420 MPa, f_u ≈ 630 MPa, elongation 13%; passed bend test → accepted for use.
Rebar tensioned to rupture; yield stress (0.2% offset), ultimate stress, elongation measured; bend test 180° around mandrel, no cracking required.
Diagrams to know
- Slump cone assembly (dimensions 300 mm ht, 100 mm top dia, 200 mm base dia)
- Cylinder failure mode (axial splitting, conical fracture, mushroom cap)
- Flexural test beam setup (third-point loading, mid-span deflection)
- Vicat penetrometer for setting time (needle depth vs. time graph)
- Stress–strain curve for tensile test (linear elastic to yield, strain-hardening, rupture with necking)
- Sieve size series with % passing curve (well-graded vs. gap-graded)
Must remember
- 1. w/c is BY WEIGHT (water ÷ cement, kg/kg); lower w/c → higher strength & lower workability. Typical: w/c=0.50→30 MPa, w/c=0.45→35 MPa.
- 2. Standard cylinder: 150 mm dia × 300 mm ht; cross-section A≈17,671 mm²; test at 28 days; f'_c = P(N) ÷ A(mm²) in MPa.
- 3. Acceptance TWO RULES (both must pass): Rule 1: No cylinder <f'_c−3.5 MPa; Rule 2: Average ≥f'_{cr}=max(f'_c+1.34s, f'_c+2.33s−3.5).
- 4. Standard deviation s reflects QC variability; s=2–3 MPa is good, s>5 MPa is poor → investigate process.
- 5. Slump test measures WORKABILITY (consistency), NOT strength; typical 75–100 mm is normal; high slump ≠ high strength (can indicate over-watering).
- 6. Grade 415 MPa rebar (f_y≥420 MPa, f_u≈620–640 MPa, elongation≥12%) is standard in PRC; Grade 275 being phased out.
- 7. Aggregate gradation: fine FM 2.8–3.0, coarse FM 6.5–7.5; well-graded reduces paste demand & cost; gap-graded increases voids & cement demand.
- 8. Steel E≈200 GPa (constant); concrete E_c≈3,320√f'_c + 6,900 (MPa); E_c ≈ 20–30 GPa for typical concrete.
- 9. Tensile strength f_t ≈ 0.07–0.12 f'_c; flexural strength f_r ≈ 0.10–0.15 f'_c; neither can be designed for in NSCP (design for shear, not tension).
- 10. Core test acceptance: ≥0.85f'_c → accept structure; <0.75f'_c → reject; 0.75–0.85 → engineer case-by-case review (per NSCP 2015, ACI 318).
Last minute tips
- TIP 1 — w/c Calculation Pitfall: Always CHECK UNITS. If cement=360 kg, water=180 L (≈180 kg), then w/c=180÷360=0.50. Confusing kg with L is the #1 error. Remember: water ≈1000 kg/m³.
- TIP 2 — Acceptance Formula Memory: f'_{cr} is the LARGER of two values; first formula (1.34s) governs for tight control; second formula (2.33s−3.5) governs for high variability (s>4 MPa). Always compute BOTH, then max.
- TIP 3 — Cylinder Strength Calculation: Area = π/4 × 150² ≈ 17,671 mm². If load given in kN, convert to N first (×1,000). Stress = P(N) ÷ A(mm²) automatically gives MPa. Wrong units = wrong answer.
- TIP 4 — Aggregate Fineness Modulus: FM = (% retained on all sieves in series) ÷ 100. Higher FM = coarser; fine sand FM 2.8–3.0 ideal; if FM outside range, mix design must adjust cement or w/c proportions.
- TIP 5 — Board Exam Pattern: Expect 2–3 questions on w/c & strength, 1 on acceptance criteria (compute f'_{cr}), 1 on rebar tensile properties, 1 on aggregate gradation. Fastest = have f'_{cr} formula memorized & understand when each sub-formula governs.
Comparison tables
Concrete Strength Classes vs. w/c & Typical Uses
| Strength Class (MPa) | Typical w/c Range | Typical Application | Acceptance f'_{cr} Approx. (s=3) | 28-day Slump Expected |
|---|---|---|---|---|
| f'_c = 21 MPa | 0.60–0.65 | Lean concrete, non-structural fill | ~26 MPa | 100–150 mm |
| f'_c = 28 MPa | 0.50–0.55 | Typical structural floor, wall (most PRC buildings) | ~31.5 MPa | 75–100 mm |
| f'_c = 35 MPa | 0.45–0.48 | High-rise, bridge deck, stronger requirements | ~40 MPa | 50–75 mm |
| f'_c ≥ 40 MPa (HSC) | 0.35–0.42 | High-strength columns, T-beams, precast; requires HRWR | ~46 MPa (using 2nd formula) | 50–75 mm |
Fine vs. Coarse Aggregate — Key Distinctions
| Property | Fine Aggregate (Sand) | Coarse Aggregate (Gravel/Stone) |
|---|---|---|
| Size Range | 75 µm – 4.75 mm | >4.75 mm (typically 9.5–37.5 mm) |
| Fineness Modulus (FM) | 2.8–3.0 (ideal); <2.5 too fine, >3.2 too coarse | 6.5–7.5 (19 mm nom.); 7.0–8.0 (25 mm nom.) |
| Typical Specific Gravity | 2.60–2.65 | 2.65–2.75 |
| % in Concrete (by volume) | ~35–40% | ~40–45% |
| Function | Fills voids, improves workability & consolidation | Load-bearing skeleton, reduces paste demand |
| High Absorption Effect | Beach sand (salt, silt); reduces strength & durability | Porous limestone; adjusts w/c downward to maintain strength |
Acceptance Rules — Single vs. Average (NSCP 2015)
| Rule | Condition | Action If Failed | Example (f'_c=28 MPa, s=3) |
|---|---|---|---|
| Rule 1: Individual Minimum | No cylinder <f'_c − 3.5 MPa | Any value <24.5 MPa → BATCH REJECTED or investigate cores | If cylinders are 26, 27, 29 MPa; 26 < 24.5? No, all pass. |
| Rule 2: Average Strength | Mean ≥ f'_{cr} = max(f'_c+1.34s, f'_c+2.33s−3.5) | If mean <f'_{cr} → BATCH REJECTED or investigate cores | f'_{cr} = max(32.02, 32.66) = 32.66 MPa; if mean=31 < 32.66 → fail. |
| Both Rules Must Pass | Single violation → batch flagged | Drill cores from structure; core avg ≥0.85f'_c → acceptable with engineer approval | Rule 1 passes (all ≥24.5) but Rule 2 fails (avg<32.66) → cores required. |
Steel Reinforcement Grades (NSCP 2015) vs. Historical US Grades
| Grade (MPa) | Yield Stress f_y (min) | Ultimate Stress f_u | Elongation (min, %) | Common Region/Notes |
|---|---|---|---|---|
| Grade 275 (≡ 40 ksi) | 280 MPa | ~420 MPa | 12% | Older PRC buildings; being phased out; 40 ksi US equiv. |
| Grade 415 (≡ 60 ksi) | 420 MPa | 620–640 MPa | 12% | Standard in modern PRC; 60 ksi US equivalent; RECOMMENDED |
| Grade 500 (high-strength) | 500 MPa | 700+ MPa | ≥8% | Emerging in PRC; used in high-rise, bridge; requires special detailing. |
| A36 (US structural steel) | 250 MPa | 400 MPa | ≥20% | For structural steel sections (beams, columns); f_y = 36 ksi. |
Concrete Tensile & Flexural Strength Estimates
| Compressive Strength f'_c | Approximate f_t (Split) | Approximate f_r (Flexural) | Ratio to f'_c |
|---|---|---|---|
| 21 MPa | 1.5–2.0 MPa | 2.1–3.2 MPa | ~0.10–0.15 f'_c |
| 28 MPa | 2.0–2.5 MPa | 2.8–4.2 MPa | ~0.10–0.15 f'_c |
| 35 MPa | 2.5–3.2 MPa | 3.5–5.2 MPa | ~0.10–0.15 f'_c |
| 40 MPa | 2.8–3.6 MPa | 4.0–6.0 MPa | ~0.10–0.15 f'_c |
Diagrams
Concrete Strength Hierarchy — w/c, Testing & Acceptance
Mind map showing hierarchy of concrete strength factors: w/c and its effect on strength/workability; cylinder testing protocol; acceptance rules (individual & average); and standard deviation role in quality control.
Concrete Batch Acceptance Decision Tree (NSCP 2015, ACI 318)
Decision flowchart for concrete batch acceptance per NSCP 2015. Shows two-rule check (individual & average), core drilling threshold, and final disposition (accept/reject/remedial).
Steel Reinforcement Quality Acceptance — Tensile & Bend Tests
Quality acceptance flowchart for steel reinforcement: tensile test (yield, ultimate, elongation), bend test (ductility), and mill certificate verification per NSCP 2015.
Concrete Constituent Distribution by Volume (Typical Mix)
Pie chart showing typical volume distribution in concrete: aggregates dominate (~80%), paste ~18%, air ~3%. Illustrates why aggregate gradation & quality are critical.
Concrete Strength Development Over Time
State diagram showing concrete strength development timeline: early hydration (~60–70% at 7d), maturation (28d reference), and continued long-term gain. Indicates key testing ages and form-striking windows.