Civil Engineering Formulas Cheat Sheet, Cheat Sheet of Civil Engineering

Download Civil Engineering Formulas Cheat Sheet and more Cheat Sheet Civil Engineering in PDF only on Docsity!

CIVIL ENGINEERING 163

Transportation Models See INDUSTRIAL ENGINEERING for optimization models and methods, including queueing theory.

 >   ]– ’ “_

DENSITY k (veh/mi)

SPEED v (mph)

DENSITY k (veh/mi)

VOLUME q (veh/hr)

CAPACITY

VOLUME q (veh/hr)

SPEED v (mph) CAPACITY

Vertical Curves: Sight Distance Related to Curve Length

S ≤ L S > L

Crest Vertical Curve General equation:

h 1 = 3.50 ft and h 2 = 2.0 ft:

L =

2 2 100( 2 1 2 2 )

A S

h + h

L =

2

2,

A S

L = 2 S −

2 200 h 1 (^) h 2 A

L = 2 S −

2, A

Sag Vertical Curve (based on standard headlight criteria)

L =

2

400 3.

A S

+ S

L = 2 S −

400 3.5 S A

Sag Vertical Curve (based on riding comfort)

L =

2

AV

L =

2

A S

h h C

L = 2 S − 1 2

800 2

h h C A

−

Sag Vertical Curve (based on adequate sight distance under an overhead structure to see an object beyond a sag vertical curve) C = vertical clearance for overhead structure (overpass) located within 200 feet of the midpoint of the curve

Standard Criteria:

Horizontal Curves

Side friction factor (based on superelevation)

2

15

V e f R

• =

Spiral Transition Length L (^) s =

3.15 V^3

R C

C = rate of increase of lateral acceleration [use 1 ft/sec^3 unless otherwise stated]

Sight Distance (to see around obstruction)

HSO = R

1 cos

S R

−

HSO = Horizontal sight line offset

[ ( )]

CIVIL ENGINEERING 165

Vertical Curve Formulas

TANGENT OFFSET

BACK TANGENT

VERTICAL CURVE FORMULAS NOT TO SCALE

DATUM

FORWARD TANGENT

L

x y E g 2

g^1

YPVC

PVC

PVT

PVI

L = Length of Curve (horizontal) g 2 = Grade of Forward Tangent

PVC = Point of Vertical Curvature a = Parabola Constant

PVI = Point of Vertical Intersection y = Tangent Offset

PVT = Point of Vertical Tangency E = Tangent Offset at PVI

g 1 = Grade of Back Tangent r = Rate of Change of Grade

x = Horizontal Distance from PVC to Point on Curve

xm = Horizontal Distance to Min/Max Elevation on Curve = a

g g g

g L 2

1 1 2

Tangent Elevation = Y PVC + g 1 x and = Y PVI + g 2 ( x – L/ 2)

Curve Elevation = Y PVC + g 1 x + ax^2 = Y PVC + g 1 x + [( g 2 – g 1 ) / (2 L )] x^2

y ax a (^) L

g g E a L^ r (^) L

g g 2 2

2 2 1 2 = = -^ = b^ l = 2 -^1

EARTHWORK FORMULAS

Average End Area Formula, V = L(A 1 + A 2 ) / 2

Prismoidal Formula, V = L (A 1 + 4A (^) m + A 2 ) / 6,

where A (^) m = area of mid-section, and

L = distance between A 1 and A 2

Pyramid or Cone, V = h (Area of Base) / 3

AREA FORMULAS

Area by Coordinates: Area = [X (^) A (Y (^) B – Y (^) N ) + X (^) B (Y (^) C – Y (^) A ) + X (^) C (Y (^) D – Y (^) B ) + ... + X (^) N (Y (^) A – Y (^) N – 1 )] / 2

Trapezoidal Rule: Area = w h h h h h h 2

n n 1 2 3 4 f 1

c (^) + + + + + (^) - m (^) w = common interval

Simpson’s 1 / 3 Rule: Area = w h 2 h 4 h h 3 , , , , k k

n k k

n 1 n 3 5

2 2 4

1 = + + + = f f

• = -

e! o e! o H n must be odd number of measurements

w = common interval

Vertical Curve Offsets Parabolic Equations

2

x

L

A

Y = y = ax

2

+ bx +c

A = ∣ G1 – G2∣ *A is in percent form. Where y = roadway elevation at

distance x from the PVC.

K

A

L

G G

a

L

= ; b = G 1 ; c = ELEVPVC

xhl = K × G 1 *keep in mind that you must use

either station/% or ft/decimal for

x/Gi.

4. Regression Equation?
5. Size within Data Extremes?
6. Number of Data Points?
7. Compatible with ITE Land Use Code?

A B

Collect Local Data

Source: ITE Trip Generation Handbook , 2nd Edition

Yes

Yes

Yes

No

No

1 or 2 3- 3-

6 +

No

Selection of ITE

Rates/Equations,

or Collection of

Local Data

16

If number of data points between 3 and 5, analysts are encouraged to collect local data, but can proceed to Step 4.

5. Standard Deviation  110 percent?
   6. Data Cluster Okay?

Use Weighted Average Rate

Collect Local Data

A

Yes

No

No

Yes

17

Figure 3. Source: ITE Trip Generation Handbook , 2 nd^ Edition

Selection of ITE Rates/

Equations, or Collection of Local

Data (cont.)

7. 20 or More Data Points?

Use Regression Equation

8a. R^2 0.75? And Within Cluster?

 8B. Std Dev^ 110%? And Within Cluster?



If 8A is yes & 8B is yes

If 8A is yes & 8B is no

If 8A is no & 8B is yes

If 8A is no & 8B is no

Choose Line at Cluster

Use Weighted Average Rate

Use Regression Equation

Collect Local Data

B

Yes

No

18

Figure 3.

Source: ITE Trip Generation Handbook , 2nd Edition

Selection of ITE Rates/

Equations, or Collection

of Local Data (cont.)