Engineer Concrete cheat sheet

Absolute volume method: V_aggregate = 1 m³ − (V_cement + V_water + V_air); cement volume = mass / (relative density × 1000 kg/m³).

ACI 211.1 water content for 75–100 mm slump, non-air-entrained: about 180 kg/m³ for 25 mm aggregate, 170 kg/m³ for 37.5 mm, 160 kg/m³ for 50 mm; air-entrained mixes use about 15–25 kg/m³ less.

Water/cementitious ratio controls strength: w/c ≈ 0.40 gives roughly 40–45 MPa at 28 days; w/c ≈ 0.60 gives roughly 25–30 MPa (ordinary Portland cement, moist-cured).

Air entrainment: 4.5–7.5% by volume for 12.5–50 mm maximum aggregate size; each 1% air typically costs about 4–6% compressive strength.

Bulk relative density (SSD) of aggregate converts mass to absolute volume; use saturated-surface-dry mass for absorption correction in batch weights.

Supplementary cementitious materials: Class F fly ash typically 15–25% replacement, Class C 15–35%, GGBFS 30–50%, silica fume 5–10% of cementitious mass.

Alkali–silica reaction mitigation: use low-alkali cement (Na2Oeq ≤ 0.60%), non-reactive aggregate, or ≥25% Class F fly ash or ≥35–50% slag replacement.

Sulfate exposure: use Type V or sulfate-resisting cement where water-soluble sulfate exceeds 0.20% in soil or 1500 mg/L in water (ACI 318 exposure classes S1–S3).

Slump test (ASTM C143) measures consistency only; not suitable for very dry or very wet mixes, and does not measure stability or placeability.

Slump ranges: 25–50 mm (stiff, mass concrete), 75–100 mm (normal), 125–175 mm (pumped or congested sections); slump flow test is used for self-consolidating concrete (500–700 mm typical).

Segregation is indicated by coarse aggregate separating from mortar; bleeding is water rising to the surface, worsened by high w/c, low fines, or excessive vibration.

Placement: free fall limited to 1.0–1.5 m; layers of 300–500 mm; concrete temperature 10–32°C during placement for normal work; hot weather limits per ACI 305.

Consolidation: internal vibrator spacing about 1.5 times the radius of action (typically 450–600 mm), penetrate 100–150 mm into the previous lift, withdraw slowly.

Overvibration causes segregation and bleeding; undervibration leaves honeycomb and entrapped air voids (bug holes).

Pumping: line pressure depends on slump, aggregate size, and bend radius; a 125 mm line handles up to 25–37.5 mm aggregate; prime with grout or a lubricating mix.

Formwork pressure: fresh concrete exerts lateral pressure up to full hydrostatic (γh) unless it sets; pressure reduces with low slump, low temperature, and slow placement rate.

Curing: keep concrete moist and above 5–10°C; ASTM C31/C192 standard curing is 20 ± 2°C, ≥95% RH; field curing per ACI 308 lasts 7 days (3 days for Type I at 27°C) or longer for low w/c and SCM mixes.

Maturity index: M = Σ(T − T0)·Δt, with datum temperature T0 ≈ −10°C for Type I cement; strength–maturity relationship is mix-specific and requires calibration.

Early-age cracking: plastic shrinkage occurs when evaporation exceeds about 1.0 kg/m²·h; use windbreaks, fog spray, evaporation retarder, or cure immediately.

Thermal cracking: maximum temperature rise in thick sections is roughly 10–15°C per 100 kg/m³ of cement; limit differential temperature to about 20°C.

Finishing sequence: screed, bull float, wait for bleed water to disappear, then float, trowel, and broom or texture; never finish while bleed water is present.

Saw-cut joints: cut when concrete can support the saw without raveling, typically 4–12 hours after finishing; depth is 1/4 of slab thickness (minimum 25 mm).

Removal of forms: vertical faces 24–48 h; soffits of beams/slabs typically 7 days (props remain longer); prestressing transfer at 70–80% of specified strength.

Hot weather per ACI 305: limit concrete temperature to 35°C, cool aggregates or use ice, and use retarders; cold weather per ACI 306 requires protection below 5°C and insulation until strength gain.

Compressive strength: 150 mm cube (Europe/Asia) or 150 × 300 mm cylinder (ASTM); cylinder strength ≈ 0.8 × cube strength; standard moist curing 28 days.

Tensile strength: modulus of rupture fr ≈ 0.62 √f'c (SI, MPa); split-cylinder ≈ 0.56 √f'c; direct tension ≈ 0.5 fr.

Modulus of elasticity: Ec ≈ 4700 √f'c MPa (normal-weight, ACI 318); increases with compressive strength and aggregate stiffness.

Stress–strain: peak at strain ≈ 0.002, crushing at ≈ 0.003–0.0035; confined concrete can reach much higher strain.

Non-destructive tests: rebound hammer (surface hardness, ±25% accuracy), ultrasonic pulse velocity (crack detection, uniformity), and pullout; all require correlation with cores.

Cores: ASTM C42; test diameter ≥ 3 × maximum aggregate size; strength correction for length/diameter ratio and moisture; cores typically 75–85% of standard cylinder strength.

Drying shrinkage: 400–800 microstrain typical; restrained shrinkage causes cracking; creep coefficient ≈ 1.5–3.0 at 1 year under sustained load.

Permeability and durability indices: rapid chloride permeability (ASTM C1202) ratings - <1000 C very low, 1000–2000 C low, 2000–4000 C moderate; surface resistivity and water absorption also used.

Flexural design (ACI 318): Mn = As fy (d − a/2), a = As fy / (0.85 f'c b); strength reduction factor φ = 0.90 for tension-controlled sections.

Tension-controlled limit: εt ≥ 0.005; compression-controlled: εt ≤ 0.002 (φ = 0.65 for tied, 0.75 for spiral); transition between.

Minimum reinforcement: As,min = max(0.25 √f'c / fy, 1.4 / fy) · bw · d (SI, MPa).

Balanced ratio: ρb = 0.85 β1 (f'c / fy) · (0.003 / (0.003 + fy/Es)); design ρ should stay below about 0.75 ρb for ductility.

Shear: Vc = 0.17 λ √f'c bw d (SI); Vs = Av fy d / s; φ = 0.75; minimum stirrups required when Vu > 0.5 φ Vc.

Development length: ld = (fy ψt ψe / (1.1 λ √f'c)) · db / (cb/db factor) - simplified; check bar size, cover, and confinement factors.

Columns: tied φ = 0.65, spiral φ = 0.75; minimum longitudinal steel 1% (tied) or 1% (spiral), maximum 8%; ties ≥ 10 mm at spacing ≤ 16 db or 48 dt.

Serviceability: deflection limit L/240 (total) or L/360 (live load); crack width limit ≈ 0.3–0.4 mm for interior/exterior exposure; one-way slab minimum thickness L/20 to L/28 depending on support.

Prestress types: pre-tensioned (strands stressed before casting, transfer at 70–80% f'c) and post-tensioned (stressed after hardening, grouted or unbonded).

Prestress force: P = Aps · fpi; effective prestress after losses (elastic shortening, creep, shrinkage, relaxation, friction, anchorage set) is typically 70–85% of initial.

Friction loss in post-tensioning: ΔfpF = fpi (μ α + K L); μ ≈ 0.15–0.25, K ≈ 0.001–0.005 per meter depending on tendon type.

Flexural design: Mn = Aps fps (d − a/2); fps for bonded tendons ≈ fpu (1 − (γp/β1)(ρp fpu / f'c)).

Prestressed members are classified as uncracked (Class U), transition (Class T), or cracked (Class C) based on extreme fiber tensile stress vs 0.62 √f'c.

Deflection control: prestress camber must be balanced against dead-load deflection; check at transfer, at erection, and in service.

Special systems: two-way flat plates (punching shear check, stud rails), shear walls (ACI 318 Chapter 11/18 provisions), and moment frames with special detailing.

Seismic detailing (ACI 318 Chapter 18): special moment frames require confinement, strong-column/weak-beam ratio ≥ 1.2, and joint shear checks.

Chloride-induced corrosion: threshold ≈ 0.4% chloride by mass of cement (acid-soluble); critical for marine and deicing exposure; use low w/c (≤0.40) and adequate cover.

Carbonation: CO2 reacts with Ca(OH)2 lowering pH below ~9, depassivating steel; carbonation depth ≈ k √t, with k ≈ 1–3 mm/√year for good concrete.

Freeze–thaw: air entrainment 4.5–7.5% with spacing factor ≤ 0.20 mm (ASTM C457) provides resistance; deicing salts require higher air content and low w/c.

Sulfate attack: external sulfates form ettringite/gypsum causing expansion; use sulfate-resisting cement, low w/c, and SCMs; Class S0–S3 exposure per ACI 318.

Alkali–silica reaction: reactive silica + high-alkali pore solution forms expansive gel; mitigate with low-alkali cement, fly ash/slag, or lithium nitrate.

Abrasion and erosion: high-strength, low w/c concrete with hard aggregate; for hydraulic structures, use silica fume or steel fibers.

Service life prediction: fib Model Code / Durability Design uses chloride diffusion (Fick's second law) and carbonation models; cover depth and quality are dominant parameters.

Repair durability: patch repairs must match substrate modulus and thermal expansion; use bonding agents, proper surface preparation, and cure; avoid incipient anode effect around patches.

Acceptance testing: sample per ASTM C172 (composite sample), cure cylinders per ASTM C31, test per ASTM C39; frequency typically 1 set per 100–150 m³ or per day of placement.

Acceptance criteria (ACI 318): average of 3 consecutive tests ≥ f'c; no single test < f'c − 3.5 MPa; cores required if criteria fail.

Slump and air content tested at point of discharge; air content per ASTM C231 (pressure method) or C173 (volumetric).

Formwork design: lateral pressure per ACI 347; deflection limit L/360 for visible surfaces; stripping strength verified by field-cured cylinders.

Inspection checkpoints: reinforcement cover and spacing, embedment, formwork tightness, vibration, construction joints, curing method and duration.

Quality control charts: track slump, air, temperature, and 28-day strength; investigate trends beyond control limits before failure.

Tolerances (ACI 117): vertical alignment ±25 mm for columns, slab thickness ±10 mm, cover tolerance ±10 mm for cast-in-place.

Documentation: batch tickets, delivery times (limit 90 minutes or 300 drum revolutions), placement records, and nonconformance reports.

Forensic method: define failure mode, collect as-built data, test (cores, cover meter, half-cell potential, petrography), and model the mechanism before repair.

Half-cell potential (ASTM C876): < −200 mV vs CSE indicates low corrosion risk, > −350 mV indicates high risk; map potentials to locate anodic regions.

Cover meter and ground-penetrating radar locate reinforcement and voids; verify with local chipping before drilling or cutting.

Repair materials: cementitious patching, epoxy mortar, and polymer-modified concrete; match thermal expansion and modulus to substrate to avoid debonding.

Structural rehabilitation: section enlargement, FRP wrapping (flexural and shear strengthening), external post-tensioning, and steel plate bonding.

Crack repair: epoxy injection for structural cracks >0.3 mm; routing and sealing for non-structural; stitch cracks with dowels for movement control.

Cathodic protection and chloride extraction: electrochemical methods for chloride-contaminated structures; CP systems require monitoring and maintenance.

Failure investigation: check concrete strength vs design, reinforcement placement, construction joints, and environmental exposure; use petrography to identify ASR, sulfate attack, or freeze–thaw damage.