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)