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Construction Management
Formula Reference

Essential equations for project planning, scheduling (CPM/PERT), resource estimation, productivity analysis, equipment output, and cost control. Vital for site engineers and project managers.

πŸ‘· Productivity & Labor Estimation
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Daily Output per Worker
Output = (Shift Hours Γ— Efficiency) / Time per Unit
Estimated quantity a worker can produce in a day.

Efficiency = Decimal (e.g., 0.85 for 85%)

Time per Unit = Hours required for one unit

Common benchmarks: Bricklaying ~600-800 bricks/day; RCC shuttering ~15-20 mΒ²/day.
Manpower Requirement
Workers = (Total Quantity) / (Daily Output per Worker Γ— Duration)
Number of workers needed to complete a task within a specific timeframe.

Total Quantity = Total work units

Duration = Days available

Labor Cost Calculation
Cost = Workers Γ— Daily Rate Γ— Duration
Total direct labor cost for an activity.

Daily Rate = Wage per worker per day

Productivity Index
PI = (Actual Output / Standard Output) Γ— 100%
Measure of team efficiency compared to standard or expected performance.

PI > 100% = Better than standard

PI < 100% = Below standard

🚜 Equipment Output & Scheduling
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Excavator Cycle Time
Tc = Tscoop + Tswing + Tdump + T
Total time for one complete digging cycle.

Tc typically 15-30 seconds depending on size and soil condition.

Excavator Hourly Production
Q = (3600 / Tc) Γ— V Γ— E Γ— K
Volume of material excavated per hour.

V = Bucket capacity (mΒ³)

E = Job efficiency (cycles/hr Γ· 3600, e.g., 0.75)

K = Soil swell factor (typically 0.8 for loose to compacted)

Haul Truck Cycle Time
Ttotal = Tload + Thaul + Tdump + Treturn + Twait
Total round trip time for a dump truck.

Tload = Load time (excavator cycles Γ— bucket cycles)

Thaul = Haul distance / Speed

Number of Trucks Required
Ntrucks = Ttruck / Tload
Ratio ensuring continuous loading without truck waiting time.

Ttruck = Total truck cycle time

Tload = Time to load one truck

Round up to next integer. Add 1 buffer if high variability.
Crane Lifting Capacity Check
Rrequired = Wload + Wrigging
Ensure rated capacity at radius exceeds total lifted weight.

Wrigging = Weight of hooks, slings, spreader bars

Always consult crane load chart for specific radius and boom length. Safety margin typically 10-20%.
πŸ’° Cost Estimation & Budgeting
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Unit Rate Analysis
Rate = (Material + Labor + Equip) + Overheads + Profit
Cost per unit of work (e.g., per mΒ³ concrete).

Overheads = Site overheads (10-15%) + Office overheads (5-10%)

Profit = Contractor's margin (5-15%)

Direct vs Indirect Costs
Total Cost = Direct Cost + Indirect Cost
Separation of project-specific costs from general administrative costs.

Direct = Materials, Labor, Equipment on site

Indirect = Admin, Insurance, Utilities, Supervision

Cost Variance (CV)
CV = EV - AC
Earned Value Management metric. Negative CV indicates over budget.

EV = Earned Value (Budgeted Cost of Work Performed)

AC = Actual Cost

Schedule Variance (SV)
SV = EV - PV
Metric for schedule performance. Negative SV indicates behind schedule.

PV = Planned Value (Budgeted Cost of Work Scheduled)

Estimate at Completion (EAC)
EAC = BAC / CPI
Predicted total cost at end of project based on current performance.

BAC = Budget at Completion

CPI = Cost Performance Index = EV / AC

πŸ•ΈοΈ Network Analysis (CPM & PERT)
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Early Start (ES) & Early Finish (EF)
ES = Max(EF of all predecessors)
EF = ES + Duration
Forward pass calculation. Determines earliest possible start/finish times.

ES starts at 0 (or 1) for first activity.

Late Start (LS) & Late Finish (LF)
LF = Min(LS of all successors)
LS = LF - Duration
Backward pass calculation. Determines latest allowable start/finish times without delaying project.

LF of last activity equals its EF (project duration).

Total Float (TF)
TF = LS - ES = LF - EF
Amount of time an activity can be delayed without delaying the project completion date.

TF = 0 = Critical Activity

Free Float (FF)
FF = Min(ES of successors) - EF
Time an activity can be delayed without delaying the early start of any immediate successor.
Critical Path Determination
Path where TF = 0 for all activities
Longest path through the network diagram. Determines minimum project duration.
Any delay on critical path delays entire project.
PERT Expected Time (te)
te = (O + 4M + P) / 6
Weighted average of Optimistic (O), Most Likely (M), and Pessimistic (P) times.

O, M, P = Time estimates in days/hours

PERT Standard Deviation (Οƒ)
Οƒ = (P - O) / 6
Measure of uncertainty in activity duration.
Project Variance & Probability
Οƒp = √(Ξ£ ΟƒiΒ²) for critical path activities
Standard deviation of the entire project. Used with Z-score for probability of meeting deadline.

Z = (Deadline - te,project) / Οƒp

βš–οΈ Resource Leveling & Crashing
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Cost Slope (Crash Cost)
Slope = (Crash Cost - Normal Cost) / (Normal Time - Crash Time)
Additional cost incurred per unit of time saved by crashing an activity.

Used to select which activity to crash first (lowest slope).

Activity Float Utilization
Utilized Float = Available Float - Required Shift
Remaining float after shifting an activity to balance resources.
Resource Histogram Peak
Peak Demand = Max(Sum of overlapping activities)
Maximum number of workers/equipment required at any single point in time.
Goal of leveling is to minimize peak demand while keeping project duration constant.
Optimum Project Cost
Total Cost = Direct Cost + (Indirect Cost Γ— Duration)
Finding the duration where sum of direct (increases with crashing) and indirect (decreases with duration) costs is minimum.
Derivative d(Total)/d(Duration) = 0 gives optimum point.
🧱 Material Quantities & Waste
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Dry Volume to Wet Volume
Vdry = Vwet Γ— 1.54
Factor to account for voids in sand and aggregates when converting wet concrete volume to dry material volume.

1.54 is typical for RCC. Use 1.50 for plain concrete.

Reinforcement Weight
W = (DΒ² Γ— L) / 162
Quick formula for steel bar weight in kg, where D is diameter in mm and L is length in meters.

Derived from ρ = 7850 kg/m³

Material with Waste Factor
Order Qty = Net Qty Γ— (1 + Waste %)
Adjustment for spillage, breakage, cutting losses.

Typical waste: Concrete 5-10%, Steel 3-5%, Bricks 5%, Paint 10-15%

Mix Proportion Volume
Vol Cement = (1 / Ξ£Parts) Γ— Vdry
Volume of cement required for a given mix ratio (e.g., 1:2:4).

For 1:2:4: Vol Cement = (1/7) Γ— Vdry

πŸ›‘οΈ Safety Metrics & Compliance
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Lost Time Injury Frequency Rate (LTIFR)
LTIFR = (LTI Count Γ— 1,000,000) / Total Man-Hours
Standard safety metric indicating injuries resulting in lost work time per million hours worked.
Total Recordable Incident Rate (TRIR)
TRIR = (Total Incidents Γ— 200,000) / Total Man-Hours
Measures all recordable incidents (medical treatment, restricted duty, lost time) per 100 full-time employees.

200,000 represents hours worked by 100 employees in a year.

Scaffold Load Capacity
Load = Dead Load + Live Load + Wind Load
Total load check for scaffolding stability.

Check against design safe working load (SWL).

Live load typically 2 kN/mΒ² for general access, higher for heavy work.