This document provides formulas and information relevant to earthwork construction, site layout, equipment production rates, scheduling, temporary structures, worker safety, and concrete mix design and quality control. Key formulas include calculations for volume of excavation using the prismoidal method, density and specific gravity of soils, production rates for equipment like dozers and loaders, critical path method for scheduling, lateral pressure of concrete in formwork, and OSHA incident and fatality rates for safety statistics.

1. Construction Engineering Formula Sheet
Earthwork Construction and Layout
Basic Conversions
1 cubic yard = 27 cubic feet
Basic must know properties
Density of Water = 62.42 pounds per CF (pcf), 1,000 g/liter = 1,000kg/m3
Economic Haul Distance; Large Dozer up to 3000 ft; Scraper 3000 – 5000 ft; Trucks > 5000 ft
lbs of concrete/sack of cement = 94 lbs
One gallon of water = 8.34 lbs
Density = Weight (lbs) / Volume(cf)
Specific gravity = Density of material / Density of water
Density of Water = 62.4 lbs/cf or 1000 kg/cubic meter
1 liter = 1 kg
Excavation and embankment
General Trapezoidal Formula: Area = (h0/2 + h1 + h2 + …+ h(n-1) + hn/2) x w
Average end area Method = V = ((A1+A2)/2) * L
Prismoidal Method = Vp = L*(A1+4AM+A2) / 6
Pyramid Method = V = AL / 3
Borrow Pit Volumes
Conical Spoil Pile = Vol = (Ab x H) / 3; D = (7.64V / tan )1/3
; H = (D/2) tan  ;where Ab=base area;
H=pile height;D=diameter;  = angle of repose (deg)
Triangular Spoil Bank = Vol = Cross section Area x L ; B = (4V/(L x tan )1/3
; H = (B x tan ) / 2 ; V=
pile volume; B= base width ; H = pile ht; L = pile length ;  = angle of repose (deg)
Density of Water = γwater = Mw/Vw
Moisture Content (w) = Mw/Ms
Degree of Saturation (S) = Vw/Vv
Total or Wet Density of Soil (γwet) = M/V where M = Mw + Ms ; V = Vw + Vs + Va

2. Density of Solids = Ms/Vs
Specific Gravity = Gs = γsolids /γwater ; or = Ms/(Vs * γwater )
Porosity (n) = Vv/Vt ; Vv = Volume of Voids = Vw + Va ; Vt = Total Volume = Vs +Vw + Va
Void Ratio (e) = Vv/Vs
Dry Density of Soil (γdry) = Ms /V
Dry Density of Soil (γdry) = γwet / (1+w); (γdry) = (γwater*Gs) / (1+(w/S)*Gs)
(γdry)=(γwater * Gs)/(1+e)
Specific Gravity = S * e = Gs * w
Porosity (n) = e/(1+e)
Void Ratio (e) = n/(1-n)
VCompacted = VBanked (1 – SHRINKAGE)
VLoose = VBanked (1+SWELL)
Swell % = ((DB – DL) / DL) x 100 ; Swell = (DB – DL)/DL
Shrinkage % = ((DC – DB) / DL) x 100 ; Shrinkage = (DC – DB)/DL
DL = Dry Loose unit wt (pcf) ; DB = Dry Bank unit wt (pcf) ; DC = Dry compacted unit wt(pcf)
Vloose = Vc (1+Swll)/(1- Shrinkage) ; Vbank = Vc / (1-Shrinkage)
Site Layout and Control
Height of Instrument (HI) = Known elevation + Backsight (BS)
Turning Point (TP) = Height of Instrument (HI) – Foresight (FS)
Trigonometric Leveling  Elevation at unknown location = elevation at known + HI + (slope distance sin
(angle of slope)) – distance from known to unknown location
Traverse Area: Method of Coordinates; The area is A = ½ (Sum of full line products – Sum of broken line
products)
Earthwork Mass Diagrams
Rising section = cut; Falling section = fill; zero slope = moving from cut to fill or vice versa

3. Estimating Quantities and Cost
Quantity take-off methods
Trenching: Be careful to fully understand what the dimensions represent, Use horizontal In-In and Vertical
Out-Out
Estimating # bricks in wall : net wall (sf) = Gross surface Area of Wall (sf) – Area of open surface (sf)
 then find surface area of brick with mortar (sf)  (net wall / SA of one brick) x # rows = bricks in
wall
Volume of mortar per brick = (mortar thickness)(brick width)(length + height + mortar thickness)
Board feet = Thickness(in) x Width (in) x Length (in) / 144
Rebar = When finding the number of rebar bars in wall = # rebar = (the length of wall / spacing of bars) +
1
Engineering economics
Present/Future Value: F= P(1+i)
n
or P = F/ (1+i)
n
; i= (F/P)
1/n
– 1
Series Payment : P=A[(1+i)
n
- 1]/[I (1+i)
n
] ; F=A[(1+i)
n
- 1]/[i]
Future/Present Value and Arithmetic gradient: F=G/i[((1+i)
n
- 1)/i)-n] ; P=G(i(1+i)
n
- iN - 1)/(i2
(1+i)n
]
Depreciation:
Straight Line Method : Dn = (Initial Cost – Salvage Value)/ N
Sum of the years Digit Method: Dn = (n2 + n)/ 2
Declining balance Method: Dn = 2 x (1/n)
Construction Operations and Methods
Lifting and Rigging
Solve for Center of Gravity: Ax = (A1)(x1) + (A2)(x2) + … + (An)(xn) ; where A= Total Area
x = distance to the CoG in the x direction, A1 and A2 = Area/Volume or Mass; x1 and x2 = distance to the CoG

4. Crane selection erection and stability
Crane Stability: Factor of Safety against toppling = Resisting moment / Toppling moment
Toppling Moment = (Weight of Load(WL)) x (Distance from toppling pt to Load)(LL) + Weight of
boom(WB) x Distance to Center of Boom(LB)
Resisting Moment = = (Weight of Counter Weight (WC)) x (Distance from toppling pt to
Counterweight)(LC) + Weight of Crane Body(WG) x Distance to Center of Crane Body(LG)

5. Equipment Production
Dozer: Total Time = Q / (P x N) : Q = Quantity of material to be moved; P = hourly production rate per
dozer; N = Number of Dozers
Grader: Total Time = (P x D) / (S x E): P= number of passes required; D = distance traveled in each pass,
in miles or feet; S = speed of grader, in mph or fpm (multiply mph by 88 to convert to fpm; E = efficiency
factor
Scraper: Total time (hours) = Q / P x N  Q = total volume to move(BCY), P = hourly production rate
(BCY/hr), N = number of scrapers
Loader: Maximum production rate (LCY per hour) = heaped bucket capacity x bucket fill factor x 60
minutes/ loader cycle time (min)
Net production rate (LCY per hour) = maximum production rate (LCY per hour) x efficiency factor
Excavator: q = ((3600 sec/hour x B x E x P)/ C) x Volume Correction  q = Volume of soil excavated and
dumped in a truck by the excavator (CY/hr), B = Bucket struck capacity (CY), E = Bucket efficiency factor, P
= Productivity factor, C = Cycle time for 90 degree angle and optimum depth
Compactor: Production (CCY per hour) = (16.3 x W x S x L x E) / N  W = compacted width per pass (in
feet), S = compactor speed(mph), L= compacted lift thickness(in), E = efficiency, N = number of passes
required
Compactor: Compactors required = FD x SCF / CP  FD = amount of fill delivered (LCY per hour), SCF =
soil conversion factor (LCY:BCY), CP = compactor production (CCY per hour)
Dump Truck: Number of trucks required = 1 + truck cycle time (minutes) / loader cycle time (minutes)
Scheduling
CPM Network Analysis
Total Float(TF) = Late Finish(LF) – Early Finish(EF) ;
TF = LF – (Early Start(ES)) + Duration(D)) = LF – ES – D
Total Float (TF) = Late Start (LS) – Early Start (ES)
TF = LS – ES = LS – (EF – D) = LS – EF + D
Total Float (TF) = Free Float (FF) + Independent Float (IF)
Free Float = Early Start of successor – Early Finish of Activity
Independent Float = Early start of successor – Late finish of predecessor – duration of Activity
Forward pass  Early start + Duration = Early Finish :
Backward pass  Late Finish – Duration = Late Start
Early Finish = Early Start + Duration ; Early Start = Early Finish – Duration

6. Activity Time Analysis
Expected Duration of activity = (a + 4b + c) / 6  where a = optimistic estimate; b = most likely
Estimate; c = pessimistic estimate
Time Cost Trade off
Cost Slope = (crash cost – normal cost) / (normal time – crash time)
Material Quality Control and Production
Concrete Mix Design
Water / Cement Ratio = Weight of Water (lbs) / Weight of Cement (lbs)
Air Content (%) = Volume of Air (cf) / Total Volume of Concrete (cf)
Volume of material (cf) = Weight of material (lbs) / ( 62.4 x specific gravity of material)
Volume = Weight of material (lbs) / density of material (lbs/cf)
Temporary Structures
Construction Loads
As per ASCE 37-02,
Cp = Lo (.25 + 15/sqrt(AI))  Cp = reduced design uniformly distributed Personnel and Equipment load per
sf, Lo = is the unreduced uniformly distributed P&E per sf; AI = is the influence area, sf
P&E on slope roof; R = 1.2 –0.5F  where F = slope of the roof (in/ft); R = Reduction Factor (.6 < R < 1.0)
Formwork
Lateral pressure of concrete(p) = wh or ρgh  p = lateral pressure, lb/ft2
; w = unit weight of concrete,
lb/ft3
; ρ = density of concrete (kg/m3
); g = gravitational constant, 9.81 N/kg ; h = depth of fluid or plastic
concrete from top of placement to point of consideration in form, ft(m).
ACI Lateral pressure equations:
Columns: For slump 7in or less to depth of 4ft or less: pmax = CwCc[150 + 9000 R/T]
Walls: rate of placement (R) less than 7ft/h and height not exceeding 14 ft: pmax = CwCc[150 + 9000 R/T]
Walls: R is 7ft/hr to 15ft/hr and height not exceeding 14 ft: pmax = CwCc[150 + 43,400/T +2800R/T]
R = rate of placement(ft/hr), T = temperature of concrete during placing, o
F, Cw = unit weight coefficient, Cc
= chemistry coefficient

7. Shoring and Reshoring
Use ACI SP-4 Formwork for concrete
Concrete maturity and early strength evaluation
Bracing
P = (H x h1 x L1) / (h2 x L2)  P = strut load per foot of form (lb/ft)(kN/m) ;
H = lateral load at top of form ( lb/ft ) (kN/m) ; h1 = height of form (ft)(m) ;
H2 = height of top of strut (ft)(m) ; L1 = length of strut (ft) (m) ;
L2 = horizontal distance from form to bottom of strut (ft) (m)
Pressure applied to wall due to wind ; P = .00256 Vc2
 Vc = Wind Velocity
Anchorage
The force required to pull the concrete apart = Force (lbs) = material cohesion (lbs/in2
) x Surface Area of
failure
Surface Area of a Cone = pi x r x sqrt (r2
+ h2
)
Volume of the Cone = 1/3 (pi x r2
x h)
Cofferdam (systems for temporary excavation support)
F1 = wh1
2
/ 2 ; F2 = wh2
2
/ 2 ; w = unit weight of water ; h1 = outside water height ; h2 = inside water
height
F1 = outside hydrostatic force ; F2 = inside hydrostatic force ; F3 = water
buoyancy force
If h1 = 2 h2, then F1 = 4 F2 and F3 = ¾ F1

8. Worker Health, Safety, and Environment
Safety Statistics (e.g., incident rate, EMR)
OSHA Incident Rate = (# of Injuries & Illness * 200,000) / Total hrs all employees
Fatal Accident Rate = (# of Fatalities * 108
) / Total hrs all employees
Fatality Rate = (# of Fatalities / yr) / (Total # people exposed)