Construction Methods, Equipment and Operations - Cheat Sheet
Your last-minute reference for equipment productivity, fleet matching, and earthwork operations. Master the formulas, spot common traps, and ace the exam.
Equipment Productivity Fundamentals
Formulas
Output = C × (3600 / t_cycle) × η × F_fill
Meaning
C = bucket/blade capacity (m³); t_cycle = cycle time (seconds); η = efficiency (decimal, e.g., 0.83); F_fill = fill factor (0.7–1.0 for buckets)
Watch out
Forget to convert cycle time to seconds (use 3600, not 60). Missing fill factor drops answer by 20–30%. Efficiency NOT the same as utilization — includes 50-min-hour AND job conditions.
When to use
Calculate hourly output of excavators, loaders, dozers; ALWAYS use this when given cycle time in seconds.
Efficiency η = (Work minutes/60) × Condition factor
Meaning
Work minutes = actual working minutes per hour (typically 45–55); Condition factor = management/weather/rest (0.75–0.95)
Watch out
Never assume η = 1.0. A 50-min hour alone gives η = 50/60 = 0.833 before any condition factor. Always multiply these separately.
When to use
When problem states 'works 50 minutes per hour' or gives site/weather conditions.
Cycles per hour = 3600 / t_cycle
Meaning
t_cycle in seconds; direct reciprocal scaled to hourly basis.
Watch out
If t_cycle is in minutes, divide by 60 FIRST, then take reciprocal. If in seconds, use 3600 directly.
When to use
Every time you have cycle time; it's the 'frequency' of the operation.
Common values
Value
25–40 seconds
Symbol
t_cycle
Quantity
Typical excavator cycle time
Value
0.80–0.95
Symbol
F_fill
Quantity
Typical bucket fill factor (loose soil)
Value
50/60 = 0.833
Symbol
η_base
Quantity
Productivity hour (50-min hour)
Value
20–35 seconds
Symbol
t_cycle
Quantity
Typical loader cycle time
Value
0.75–0.95
Symbol
f_cond
Quantity
Site condition efficiency factor
Important facts
- Output formula is MULTIPLICATIVE: all factors (capacity, cycles/hr, efficiency, fill factor) multiply together.
- Cycle time in SECONDS is standard; converting to hours requires 3600-second factor, not 60.
- Efficiency is NOT efficiency rating of the machine; it's the combined effect of working minutes per hour (50/60) PLUS site/management conditions.
- Fill factor < 1.0 is ALWAYS applied to buckets unless explicitly stated otherwise (loose materials, spillage, operator skill).
- A 10% increase in cycle time causes ~10% decrease in output (inverse relationship).
- Output units match capacity units: if C in m³, output in m³/hr.
Key definitions
Cycle time
Example
Truck: 2 min load + 8 min haul + 1 min dump + 5 min return = 16 min = 960 s.
Total time (seconds) for one complete operating cycle: load → haul → dump → return (for trucks); excavate → swing → dump → return (for excavators).
Bucket fill factor
Example
1.5 m³ bucket with F_fill = 0.9 → actual load = 1.35 m³.
Ratio of actual bucket volume filled to bucket rated capacity; accounts for loose soil, spillage, operator skill (typical 0.8–1.0).
50-minute hour (productivity hour)
Example
An excavator's raw output is 180 m³/hr, but with 50-min-hour efficiency = 180 × 0.833 = 150 m³/hr.
In typical construction, ~10 minutes/hour lost to breaks, delays, minor slowdowns; efficiency base is 50/60 = 0.833.
Production efficiency
Example
Poor site conditions → η = 0.70; excellent site, experienced crew → η = 0.90.
Decimal multiplier reflecting actual work time and job conditions relative to ideal operation (range 0.65–0.95).
Diagrams to know
- Loader cycle diagram: spot → dig → swing → dump → return
- Excavator swing pattern and reach envelope
- Truck haul route: load site → haul road → dump → return
Fleet Matching (Trucks & Loaders)
Formulas
N = T_cycle / T_load
Meaning
N = number of trucks; T_cycle = full truck cycle time (load + haul + dump + return); T_load = time to load one truck.
Watch out
ROUND UP, never down. 6.2 trucks → 7 trucks (you can't have 0.2 of a truck). T_cycle and T_load MUST be in same units (both minutes, or both seconds).
When to use
Determine how many haul units to keep a single loader/excavator continuously busy without idle time.
T_cycle = T_load + T_haul + T_dump + T_return
Meaning
Sum of all components in a truck's round trip.
Watch out
Missing any component (esp. return time) throws off the calculation. Return time is often 40–60% of loaded haul time.
When to use
Build the full cycle time before applying fleet-matching formula.
Common values
Value
2–5 minutes
Symbol
T_load
Quantity
Typical truck load time
Value
10–20 minutes (haul + return)
Symbol
T_haul + T_return
Quantity
Typical haul distance cycle
Value
15–30 minutes
Symbol
T_cycle
Quantity
Typical full truck cycle
Value
4–8 trucks
Symbol
N
Quantity
Optimal fleet size (small excavator)
Important facts
- Optimal N minimizes both queuing (cost of extra trucks) and starvation (cost of idle loader).
- N = T_cycle / T_load assumes continuous one-loader operation; for multiple loaders, scale accordingly.
- Load time is typically 2–5 minutes; haul and return often dominate cycle time on distant sites.
- If N fractional, round UP to ensure loader never starves (slight over-match is cheaper than under-match).
- Dispatch strategy matters: if trucks queue, consider staging, pre-positioning, or additional loading zones.
- Earthwork projects often use this formula to size the truck fleet at project start.
Key definitions
Truck cycle time
Example
3 min load + 10 min haul + 1 min dump + 7 min return = 21 min.
Total elapsed time from arrival at loader until return to loader, including load, haul, dump, and empty return.
Fleet matching
Example
21-min truck cycle ÷ 3-min load time = 7 trucks needed.
Sizing the number of haul units to balance loader productivity and truck utilization, minimizing queuing and idle time.
Queuing
Example
9 trucks assigned when only 7 are needed → trucks queue, loader busy, but high fuel/labor cost.
Wait time at the loader when too many trucks are assigned; indicates over-matching (cost waste).
Starving the loader
Example
Only 4 trucks for a fleet needing 7 → loader idle, production lost.
Under-matching (too few trucks); loader idle, waiting for return of the haul unit.
Diagrams to know
- Truck cycle timeline: load → haul → dump → return
- Queuing diagram at loader (one queue, multiple servers)
- Cycle time breakdown bar chart
Earthwork Volumes: Swell & Shrinkage
Formulas
V_loose = V_bank × (1 + S_swell)
Meaning
V_loose = volume to haul (loose); V_bank = in-place (bank) volume; S_swell = swell factor as decimal (e.g., 0.25 for 25% swell).
Watch out
Swell is a PERCENTAGE increase. 25% swell = multiply by 1.25, NOT 0.25. Forgetting (1 + S_swell) is a common exam trap.
When to use
Convert bank (in-place) volume to loose volume for haul accounting; loose volume always EXCEEDS bank for most soils.
V_bank = V_compacted / (1 - S_shrinkage)
Meaning
V_compacted = final compacted fill volume; S_shrinkage = shrinkage factor (e.g., 0.10 for 10% shrinkage); V_bank = source bank volume needed.
Watch out
Shrinkage reduces volume, so denominator is (1 − shrinkage), not (1 + shrinkage). If 10% shrinkage, divide by 0.90.
When to use
Determine how much bank material must be excavated to achieve a specified compacted fill volume.
V_compacted = V_bank × (1 - S_shrinkage)
Meaning
Rearranged form: compacted volume is bank volume reduced by shrinkage factor.
Watch out
This is the REVERSE of the previous formula. Know which direction you're going: bank → loose (swell) vs. bank → compacted (shrinkage).
When to use
Direct calculation if bank volume is known; alternative form of the shrinkage equation.
Common values
Value
0.30–0.40
Symbol
S_swell
Quantity
Swell factor — clay
Value
0.15–0.25
Symbol
S_swell
Quantity
Swell factor — sand
Value
0.40–0.60
Symbol
S_swell
Quantity
Swell factor — rock (rippable)
Value
0.08–0.15
Symbol
S_shrinkage
Quantity
Shrinkage factor — fill compaction
Value
12–18 m³
Symbol
C_truck
Quantity
Typical truck payload (loose soil)
Important facts
- Bank volume is the REFERENCE; swell and shrinkage are departures from it.
- Swell increases haul-truck requirements and disposal cost.
- Shrinkage increases cut/excavation requirements; you must excavate MORE bank material than the final compacted volume.
- Swell factor varies by soil type: clay >30%, sand ~20%, fine gravel ~15%, rock fragments >50%.
- Shrinkage typically 8–15% for compacted earthfill; higher compaction effort → higher shrinkage.
- In volume accounting: bank → loose (×swell factor) and bank → compacted (÷shrinkage factor).
- Loose-to-compacted conversion: V_compacted = V_loose × (1 + S_swell)⁻¹ × (1 − S_shrinkage) — rarely needed directly.
Key definitions
Bank volume (in-place)
Example
A cut of undisturbed earth measuring 100 m³.
Original volume of soil in its natural, undisturbed state in the ground.
Loose volume
Example
100 m³ bank soil becomes 125 m³ loose (at 25% swell).
Volume of excavated soil after disturbance; always larger than bank volume due to air voids introduced during excavation.
Swell
Example
Sandy soil: ~20% swell; clay: ~30% swell; rock: ~50% swell (rippable).
Percentage increase in volume when soil is excavated and loosened; typical 10–40% depending on soil type (clay, sand, rock).
Compacted volume
Example
Compaction shrinkage of 10% means 100 m³ bank → 90 m³ compacted.
Volume of soil after mechanical compaction in-place (fill); always smaller than bank due to removal of air voids.
Shrinkage
Example
Fill requires 800 m³ compacted; at 10% shrinkage, need 800 / 0.90 = 889 m³ bank material.
Percentage reduction in volume when bank soil is compacted to specification (typically 8–15%).
Diagrams to know
- Volume transformation diagram: bank → loose → compacted with swell/shrinkage percentages
- Soil type vs. swell factor table (rock, clay, sand, gravel)
- Haul truck capacity vs. loose volume conversion
Concreting Operations
Formulas
Concrete output = (Mixer capacity) × (Cycles per hour) × η
Meaning
Mixer capacity (m³/batch); cycles/hr = 60 / (mixing + loading time in minutes); η = efficiency.
Watch out
Cycle time for concrete includes MIX time (not excavation load), which is often 90–120 seconds. Don't confuse with earthwork cycles.
When to use
Estimate concrete production rate from batching/mixer capacity.
Pump output = Q_pump × η_pump
Meaning
Q_pump = pump rated capacity (m³/hr); η_pump = on-site efficiency (typically 0.70–0.85) accounting for standby, line prep, cleanup.
Watch out
Pump efficiency < rated because of setup, line blowouts, operator delays. Never assume 100% utilization.
When to use
Estimate concrete delivery/placement rate from pump specifications.
Concrete volume = Plan area × Depth
Meaning
Direct geometry; apply waste factor (1.05–1.10) for spills, over-pours, measurement variance.
Watch out
Slabs, walls, beams all use similar logic; don't forget to subtract voids (windows, conduits, rebar volume is negligible).
When to use
Order concrete; account for ~5% waste in estimates.
Common values
Value
6–10 m³
Symbol
C_mixer
Quantity
Typical transit mixer capacity
Value
20–40 m³/hr
Symbol
Q_pump
Quantity
Typical concrete pump output
Value
5–8 minutes
Symbol
t_batch
Quantity
Batch cycle time (central batching)
Value
75–150 mm
Symbol
Slump
Quantity
Concrete slump range (typical)
Value
~90 minutes
Symbol
t_set
Quantity
Initial set time
Important facts
- Concrete operations span batching (central or on-site), transport (truck mixer, pump), placement, consolidation, and curing.
- ACI 318-19 requires proper vibration and curing to achieve specified strength.
- Pump efficiency typically 70–85% due to line setup, pressure test, operator coordination.
- Waste factor 5–10% accounts for over-pours, spills, measurement tolerance.
- Concrete sets (initial set ~90 min) but doesn't reach design strength until 28 days; early loading risk.
- Slump consistency ensures uniform workability; too low → poor placement, too high → segregation.
- Curing per ACI 318: moist for minimum 7 days (or equivalent strength gain method).
Key definitions
Batch cycle time
Example
Transit mixer: 3 min load + 4 min mix + 1 min discharge = 8 min cycle.
Time for one complete concrete batch: charge hopper → mix → discharge → return hopper (typically 5–8 minutes for transit-mix).
Slump
Example
Target slump 100 mm for vibrated slab; higher slump = more fluid, lower = stiffer.
Measure of concrete workability; vertical distance concrete slumps when slump cone is lifted (ACI 318); typical 75–150 mm for placement.
Consolidation (vibration)
Example
Internal vibrator: 10–30 seconds per placement zone.
Process of removing entrapped air from fresh concrete via internal or external vibration; required per ACI 318 for full strength.
Curing
Example
Standard curing: cover with plastic sheeting or wet burlap; check at 7 and 28 days per ACI 318-19.
Maintaining moisture and temperature after placement to allow cement hydration and strength gain; minimum 7 days (moist) per ACI 318.
Concrete strength gain timeline
Example
ACI 318: design strength typically based on 28-day cylinder tests.
At 1 day ~25%, at 7 days ~70%, at 28 days ~100% (reference), at 90+ days continued gain (design strength achieved).
Diagrams to know
- Concrete supply chain: batch plant → truck mixer → pump → placement → vibration → curing
- Slump cone diagram and typical slump ranges
- Concrete strength gain curve (1-day, 7-day, 28-day, 90-day milestones)
Formwork & Falsework (Critical for Failures)
Formulas
Lateral pressure (fresh concrete) = γ_c × h + (Pouring rate × T_fill)
Meaning
γ_c ≈ 24 kN/m³ (concrete unit weight); h = depth of concrete; pouring rate and fill time account for dynamic pressure (simplified; full ACI formula more complex).
Watch out
Lateral pressure is NOT just γ_c·h (hydrostatic). Rapid pour rate increases dynamic pressure significantly. ACI 347 provides detailed formulas.
When to use
Estimate formwork bending moment and bracing requirements; critical for safety (forms collapse if underdesigned).
Maximum bending moment = (Lateral pressure) × (Span²) / 8
Meaning
Standard beam formula for uniformly loaded formwork panel (span in meters, pressure in kN/m²).
Watch out
Span of formwork is critical — doubling span quadruples moment. Use shortest practical span; increase bracing density if needed.
When to use
Design formwork sheathing, joists, stringers; ensure moment capacity of lumber/steel.
Common values
Value
24 kN/m³
Symbol
γ_c
Quantity
Fresh concrete unit weight
Value
1–3 m/hr (vertical rise)
Symbol
R_pour
Quantity
Typical concrete pour rate (ready-mix)
Value
~90 minutes
Symbol
t_set
Quantity
Initial set time (standard Portland)
Value
L/240 to L/180 (span-dependent)
Symbol
Δ_allow
Quantity
Allowable formwork deflection
Value
1.5–2.5 m
Symbol
Spacing
Quantity
Typical prop spacing (slab formwork)
Important facts
- Formwork failures are a leading cause of construction accidents and collapse-related fatalities in the Philippines.
- Lateral concrete pressure depends on height, pouring rate, concrete temperature, and concrete mix design.
- ACI 347 (Guide to Concrete Formwork) and NSCP 2015 specify minimum formwork design requirements.
- Improper removal of props/bracing before concrete reaches adequate strength is a common failure mode.
- Deflection and settlement of formwork can cause uneven surfaces, cracks, and non-plumb walls.
- Temperature effects: cold concrete hydrates slower → longer formwork time; warm concrete faster hydration → earlier stripping possible.
- Safety inspections of formwork BEFORE concrete placement are mandatory (PRC licensing requires awareness).
- Reusable systems (falsework) must be engineered and load-rated for each project; no one-size-fits-all.
Key definitions
Fresh concrete pressure
Example
1 m depth at 2 m/hr pour rate → pressure ~30–40 kN/m² (simplified).
Lateral load exerted by plastic (not-yet-set) concrete on vertical formwork; varies with depth, temperature, and pouring rate.
Formwork failure
Example
Wall form collapse during pour — structural and human safety disaster; leads to litigation, project delays, prosecutions.
Loss of structural integrity of temporary concrete mold; catastrophic, typically from inadequate bracing, underestimated pressure, or material defect.
Shoring/bracing
Example
Vertical props at 2 m spacing supporting slab formwork.
Temporary internal and external supports (props, braces, ties) preventing formwork displacement under concrete load.
Stripping time
Example
Slab: 7 days at standard curing; wall: 2–7 days depending on temperature and next-stage loads.
Time at which formwork can be safely removed; depends on concrete strength gain (typically 7–28 days per ACI 318) and load requirements.
Deflection (formwork)
Example
Allowable deflection typically L/240 (span ÷ 240).
Inward/outward movement of formwork under concrete load; must be limited to prevent surface defects or instability.
Diagrams to know
- Lateral pressure diagram: pressure increasing with depth on vertical form
- Formwork bending moment diagram: max moment at center of span
- Bracing layout: typical prop and diagonal brace spacing for walls/slabs
- Formwork failure modes: outward movement (pressure), inward deflection, loss of plumb
Common Construction Equipment & Machines
Common values
Value
0.8–2.0 m³
Symbol
C_exc
Quantity
Excavator bucket size (standard)
Value
2.0–4.0 m³
Symbol
C_load
Quantity
Loader bucket size
Value
12–20 m³ (loose)
Symbol
C_truck
Quantity
Dump truck capacity
Value
20–50 m³/hr
Symbol
Q_pump
Quantity
Concrete pump output
Value
200–500 m²/hr
Symbol
A_compact
Quantity
Plate compactor output
Important facts
- Equipment selection depends on: material type, haul distance, project schedule, and site accessibility.
- Larger buckets/capacity ≠ faster output if cycle time increases or product spreads; balance capacity with efficiency.
- Maintenance downtime cuts productivity; budget ~5–10% for repairs/service (included in efficiency η).
- Operator skill significantly affects productivity; experienced operators outproduce inexperienced by 20–40%.
- Fuel consumption scales with load and idle time; fleet management monitors fuel/output ratio for cost control.
- Rental vs. ownership: equipment <6 months typically rented; >12 months evaluated for purchase.
- Weather (rain, extreme heat) degrades efficiency: mud slows dozer, rain halts concrete, heat increases fatigue.
- Safety: all equipment requires trained operators, daily pre-shift inspection, and maintained guards/emergency stops.
Key definitions
Excavator
Example
Komatsu PC200: 1.0 m³ bucket, used for foundation excavation, material loading.
Tracked or wheeled machine with articulated arm and bucket; digs, loads, and swings material. Common sizes: 0.8–3.5 m³.
Wheel loader
Example
CAT 950: 2.2 m³ bucket, typical for borrow pit extraction, stockpile management.
Tire-mounted machine with front bucket and articulated frame; loads, carries, and dumps material. Sizes: 1.5–5.0 m³.
Bulldozer (dozer)
Example
CAT D6: 235 kW, moves loose material, rip hardpan, grade roads.
Tracked machine with blade and ripper; pushes, levels, and cuts material. Power rated in kW; blade widths 2.5–4.5 m.
Scraper
Example
Used on large earthfill projects for efficiency; single scraper may replace loader + trucks.
Self-propelled or towed machine with cutting bowl; excavates, transports, and spreads material in one pass. Bowl capacity 10–40 m³.
Dump truck (haul unit)
Example
6-wheeler dump truck: ~18 m³, typical fleet vehicle in Philippine projects.
Truck with tilting bed for material transport; capacity 12–20 m³ (loose soil). Articulated or rigid body.
Concrete mixer (batch plant)
Example
Transit mixer: 6–8 m³ capacity, mixes during transport to site.
Stationary or mobile machine mixing portland cement, aggregates, and water into concrete. Output 1–20 m³/batch.
Concrete pump
Example
Boom pump: arm reaches ~20–40 m, typical for buildings; line pump: for tight/remote areas.
Machine forcing fresh concrete through hose to placement location; eliminates hand-carry. Output 20–60 m³/hr.
Vibrator (internal/external)
Example
Internal: 1.5–4 kg head, 50–80 Hz; external: clamps to formwork, ~70 Hz.
Handheld (internal) or form-mounted (external) device oscillating to consolidate fresh concrete and expel air voids.
Plate compactor
Example
80 kg walk-behind: 200–300 m²/hr at optimal speed/compaction layers.
Walk-behind or ride-on vibratory machine compacting granular material and asphalt. Output measured in m²/pass.
Diagrams to know
- Excavator arm reach diagram and digging pattern
- Loader trajectory (dig → swing → dump curve)
- Dozer blade push force vs. slope angle
- Truck haul route: optimal path for fuel efficiency
Must remember
Output formula: Output = C × (3600 / t_cycle) × η × F_fill. NEVER forget the 3600 (for seconds) and always apply efficiency AND fill factor. A 10% slip on any term can fail the question.
Cycle time in SECONDS; convert if given in minutes. Using 60 instead of 3600 gives 60× error. Board exams test this constantly.
Efficiency (50/60) and condition factor MULTIPLY together. 50-min-hour alone is 0.833; then apply job conditions. Never replace one with the other.
Fleet matching: N = T_cycle / T_load. ROUND UP (6.2 trucks → 7). Under-matching starves loader (production loss > cost of extra truck).
Swell multiplier is (1 + S_swell), NOT (1 − S_swell). 25% swell = ×1.25. Forgetting the '+1' is the #1 exam mistake.
Shrinkage formula: V_bank = V_compacted / (1 − S_shrinkage). To get 800 m³ compacted fill at 10% shrinkage, need 800/0.9 = 889 m³ bank. Inverse of swell logic.
Fresh concrete lateral pressure on formwork is NOT just γ_c·h. Pour rate and temperature matter. Underestimating pressure → formwork failure → catastrophic (and exam highlight).
Concrete design strength is 28-day (ACI 318). At 7 days ~70%, at 1 day ~25%. Early loading before strength gain causes cracking/failure.
Truck cycle time = load + haul + dump + return. Forgetting return time (often 40–60% of haul) throws off fleet matching by 30%.
Formwork must be designed and braced per site conditions. Formwork failures are leading construction accidents in the Philippines; PRC exam expects awareness of NSCP 2015 requirements.
Last minute tips
Double-check units and conversion factors
Cycle time in seconds? Use 3600. In minutes? Divide by 60 first, then apply 3600 or use 1/t_minutes. Efficiency as decimal (0.83)? Yes. As percentage (83%)? Convert. A unit error drops the entire calculation.
Swell and shrinkage direction: always ask 'which way is volume going?'
Bank → Loose (swell UP): multiply by (1+S). Bank → Compacted (shrinkage DOWN): divide by (1−S). Draw an arrow if confused. If exam gives loose volume and asks for bank, invert the formula.
Fleet matching: if N is fractional, round UP
6.2 trucks → 7. Under-matching (rounding down) causes loader idle time, which is more costly than one extra truck queuing. Examiners test this logical trade-off.
Formwork/falsework: formwork collapse is a PRC exam favorite
Know that lateral concrete pressure depends on height, pour rate, and temperature. NSCP 2015 requires engineered design. A superficial 'formwork = temporary' answer scores zero; examiners expect awareness of design requirements and failure risks.
Read the problem statement carefully for efficiency clues
Look for 'works 50 minutes per hour,' 'poor site conditions,' 'experienced crew,' or 'rainy season.' These affect η directly. Missing one word (e.g., 'and') can change efficiency from 0.83 to 0.70. Highlight these in the problem text immediately.
Comparison tables
Swell vs. Shrinkage — Common Confusion
| Aspect | Swell (Excavation) | Shrinkage (Compaction) |
|---|---|---|
| Definition | Volume INCREASES when soil is dug and loosened | Volume DECREASES when loose soil is compacted in-place |
| Direction | Bank → Loose (multiply by 1 + swell %) | Compacted < Bank (divide by 1 − shrinkage %) |
| Formula | V_loose = V_bank × (1 + S_swell) | V_bank = V_compacted ÷ (1 − S_shrinkage) |
| Typical Range | 15–50% (clay ~30%, sand ~20%, rock ~50%) | 8–15% for fill (depends on compaction effort) |
| Haul Impact | Increases truck volume needed; 100 m³ bank → 125 m³ haul at 25% swell | N/A for haul; only affects volume required from source |
| Fill Impact | N/A for fill; haul volume is converted to compacted fill | If fill needs 800 m³ compacted, must excavate 889 m³ bank at 10% shrinkage |
| Exam Trap | Using shrinkage factor (1−S) instead of (1+S); confusing with shrinkage | Using swell factor (1+S) instead of (1−S); confusing with swell |
Fleet Matching Scenarios — Truck Count Decision
| Cycle Time (min) | Load Time (min) | Calculated N | Recommendation | Risk if Under/Over | |
|---|---|---|---|---|---|
| Scenario A: 24 min / 4 min | 24 | 4 | 6.0 | Exactly 6 trucks | Under (5): Loader idle. Over (7): Queuing, extra cost |
| Scenario B: 30 min / 5 min | 30 | 5 | 6.0 | Exactly 6 trucks | Same as A |
| Scenario C: 25 min / 4 min | 25 | 4 | 6.25 | Round UP → 7 trucks | Under (6): Loader idle ~4 min/cycle. Over (7): 1 truck queues; acceptable |
| Scenario D: 20 min / 5 min | 20 | 5 | 4.0 | Exactly 4 trucks | Under (3): Heavy idle. Over (5): Significant queuing |
| Scenario E: Long haul: 45 min / 3 min | 45 | 3 | 15.0 | 15 trucks (or consider another loader) | Under (12): Loader idle. Over (15): All trucks busy, minimal queuing |
Efficiency Factor (η) — Composition & Impact
| Component | Typical Value | Effect on Output | Example |
|---|---|---|---|
| 50-minute hour | 50/60 = 0.833 | −16.7% from ideal | Breaks, crew coordination, minor delays |
| Good site conditions | 0.90 | −10% from 100% | Level ground, organized layout, experienced crew |
| Fair site conditions | 0.80 | −20% from 100% | Muddy access, some congestion, average crew |
| Poor site conditions | 0.70 | −30% from 100% | Difficult terrain, weather, inexperienced crew |
| Combined typical | 0.833 × 0.85 = 0.708 | −29.2% from ideal | 50-min-hour × fair site = realistic field output |
| Worst case | 0.833 × 0.65 = 0.542 | −45.8% from ideal | 50-min-hour × poor site = sluggish operation |
Concrete Operations — Key Timeline & Milestones
| Stage | Time/Duration | Action | Critical Notes |
|---|---|---|---|
| Batching | 5–8 min/batch | Charge, mix, discharge | Ensure water/cement ratio correct (per ACI 318) |
| Transport | 5–20 min (on-site haul) | Truck mixer or pump delivery | Prevent segregation; keep slump within spec |
| Placement | Varies (pump speed, access) | Pour into formwork | Uniformly distribute; avoid drop >1.5 m (ACI 318) |
| Consolidation (vibration) | 10–30 sec/zone | Internal or external vibration | Remove air; improves strength & appearance |
| Initial set | ~90 min (standard) | Concrete begins to lose workability | Finish surface work must be done before this |
| Final set | ~24 hours | Concrete hardens; support load marginal | Forms not stripped; further curing required |
| Curing (moist) | Minimum 7 days | Keep surface wet, cover with plastic/burlap | ACI 318 mandatory; improves strength ~20% |
| Design strength | 28 days (reference age) | Standard test age; strength plateau | ACI 318 basis for strength acceptance |
Diagrams
Equipment Productivity Calculation — Decision Tree
Step-by-step flowchart for calculating equipment productivity. Emphasizes the critical decision on cycle time units (seconds) and the multiplication of all factors. Helps students avoid the #1 mistake (using 60 instead of 3600).
Earthwork Volume Conversions — Swell & Shrinkage Logic
Visual decision tree for converting between bank, loose, and compacted volumes. Highlights the two main paths (multiply for swell, divide for shrinkage) and prevents the common exam mistake of confusing the operations.
Equipment Productivity Formula Tree — All Components
Mind map breaking down all components of the productivity formula. Shows how capacity, frequency, and efficiency combine multiplicatively. Useful for reviewing all terms before an exam.
Fleet Matching — Truck Count Optimization
Flowchart for fleet matching logic. Critical rule: always round UP to keep the loader busy. Includes decision point for site feasibility when fleet size is large. Prevents under-matching errors.
Concrete Operations Timeline — From Batching to Strength
Timeline of concrete operations from batching to design strength. Emphasizes the ACI 318 milestones: 7-day curing minimum, 28-day design strength reference, and the initial/final set times. Essential for understanding when formwork can be stripped and when design loads can be applied.
Typical Equipment Efficiency Breakdown (Fair Site)
Pie chart showing how efficiency compounds. Even at fair site conditions (80% factor), the realistic combined efficiency is only ~67% when accounting for the 50-minute hour. Illustrates why theoretical output and field output differ significantly.