Civil Engineering Formulas

Accident analysis

- Rate at segment

- Rate at intersection

- Severity ratio

Stopping Sight Distance (SSD)

Parabolic Summit Curve

L>S

L

Parabolic Sag Curve

L>S

L

Underpass Sight Distance

- Design speed

Horizontal Curve

Design of Horizontal Curve

Minimum radius of curvature

- prevent skidding

Design of Pavement

- Rigid pavement without dowels

- Rigid pavement with dowels

- Flexible pavement

- Thickness of pavement in terms of expansion

- Stiffness factor of pavement

Railroad engineering

Frog angle, heel spread, heel length, toe lenth

- Frog number

- Total length of the turnout

Ports and Harbor

HWL, RWL, MLLW, LWL

- Gravity type

- Sheet pile type

Design of Horizontal Curve

- Minimum radius of curvature

- Centrifugal ratio or impact factor

Power to move a vehicle

Design of Pavement

- Rigid pavement without dowels

- Rigid pavement with dowels

- Flexible pavement

- Thickness of pavement in terms

of expansion pressure

- Stiffness factor of pavement

Accident rate for 100 million

vehicles per miles of travel in a

segment of a highway

Accident rate per million entering

vehicles in an intersection

Severity Ratio

Flow of Vehicles

Differential Calculus

- Slope of a curve

- Angle of a curve

- Rate of change

- Curvature

- Radius of curvature

- Maxima and minima: rate of change

Common maxima and minima

Intergral Calculus

Length of Arc

- Rectangular coordinates

- Polar coordinates

Plane Area

- Rectangular coordinates

- Polar coordinates

Solids of Revolution

- Volume

- Surface area

- Volume generated from oblique line

Volume using x-y-z plane

Centroid

- Plane area

- Volume

- Centroid of parabolic segment & spandrel

Moment of Inertia

- About x-axis

- About y-axis

- Polar moment of inertia

- Product of inertia

Fundamentals of Counting

Permutations

- n different things taken r at a time

- n things, q are alike, r are alike (identical)

- n different objects in a circle

- repetition is allowed

- repetition is not allowed

Combination

- n things taken r at a time

- n obhect taken one, two, three

Pascal's Triangle

Probability

Complement Rule

Multiplication Rule

General Addition Rule

Addition for mutually exclusive

Inequality

Conditional Property

A given that B

B takes A

Measure of Natural Tendency

- Mean: grouped data (non age problems and age problems)

- Median: grouped data

- Mode: grouped data

Standard Deviation

- Population standard deviation

- Sample standard deviation

Coefficient of Linear Correlation

or Pearson's r

Variance

Mean/Average Deviation

Fractiles

- Range

- Quartiles

- Interquartile Range

Normal Distribution

z-score

Exponential Distribution

- P of left

- P of right

- P in between

Discrete Probability Distributions

- Binomial probability distribution

- Geometric probability distribution

- Poisson probability distribution

Special Products and Factoring

Quadratic Equation

- Roots

- Sum of Roots

- Product of Roots

- (3) Discriminant conditions

- Two roots/perfect square roots/one real solution

Binomial Theorem

Possible questions:

- Numerical coefficient of the rth term

- Middle term

- Term involving xc

- Constant term

- Sum of the coefficient of variables

- Sum of the exponents

Progression

- Arithmetic: Mean

- Geometric: Mean

- Infinite Geometric

- Harmonic: Mean

Word Problems

- Age Problems

- Motion Problems

- Work Problems

- Clock Problems

Note: In 12 hours, 11 times the hour hand and minute hand are together.

- Digit Problems

- Mixture Problems

Motion in a circle or any closed circuit

- same direction

- opposite direction

Walli's Formula

Fibonacci Numbers

Remainder Theorem

-degree of remainder

Factor Theorem

x-r is a factor of f(x)

Fraction of polynomials

Improper Fraction

- long division

- synthetic division

Proper Fraction

- partial fraction

Relationship of Angles

- Complement

- Supplement

- Explement

- Coterminal

Sine Law and Cosine Law

Trigonometric Identities

- Reciprocal Relations

- Quotient Relations

- Co-function Identitues

- Squared Identities

- Sum & Diff. of Angles Identities

- Double Angles Identities

- Half Angle

- Squares

Other identities (ver, cover, haver, hacover, ex)

- Versine

- Coversine

- Haversine

- Exsecant

Length of Chord

C=2Rsin(I/2)

Properties of Trigonometric Functions

- Sine function

- Cosine function

- Tangent function

- Amplitude

- Period

- Frequency

- Horizontal Shift

- Vertical Shit

Area of Triangle

- Given the base and altitude

- Given two sides and included angle

- Given three sides (Heron's Formula)

- Given three angles and one side

Centers of Triangle (Definition)

- Incircle

- Circumcircle

- Orthocenter: altitude line

- Centroid: median of a triangle

- Euler line

Area of Centers of Triangle

- Incircle (Circle inscribed in a triangle)

- Circumcircle (Circle circumscribing a triangle)

- Excircle (Escribed circle)

Spherical Triangles

- Napier's Circle

- Sine and cosine law

- Area

- Volume

- Nautical mile

Triangles

- Sine Law

- Cosine Law

Common Quadrilaterals

- Square

- Recangle

- Parralelogram

- Rhombus

Trapezoid

- Length dividing two areas

General Quadrilateral

- Cyclic Quadrilateral (sum of opposite angles)

- Ptolemy's Theorem

- Non-cyclic Quadrilateral

- Circle circumscribed about a Quadrilateral

- Circle inscribed in a Quadrilateral

Circles

- radius, diameter, chord, secant, tangent, arc

- external and internal tangent between two circles

- concentric circles

- two chords rule, two secants rule, secant-tangent rule

Ellipse

Centers of Triangle

Triangle-Circle Relationship

ex-in circle

Polygon

- Sum of interior angles

- Sum of exterior angles

- No. of diagonals

- Polygon names:

Regular - same side and same angle

Prefix - depends on number

Suffix - 2D (gon), 3D (hedron)

n-sided Polygon

Cavalieri's Theorem

V=AH

LA=Pe

SA=LA+2A

Prism/Cylinder, Pointed Soilds

- General Volume and Lateral Area

- Pointed Solid: Lateral Area of Cone and Pyramid

Special Solids

- Truncated Prism or Cylinder

- Frustum of Cone or Pyramid

- Prismatoid

Similar Solids

(V/Vtotal)=(h/htotal)^3

Spherical Solids

- Sphere

- Spheroid

- Prolate Spheroid

- Oblate Spheroid

Spherical Lune, Wedge, Zone, Sector, Segment

Spherical Polygon

A=(R^2)(E)

V=(1/3)(R^3)(E)

E=(sum of given angles) - (n-2)(180)

Pappuss Theorem

- 1st and 2nd proposition

Simple Interest, Compound Interest, Continuous Compounding Interest

Annuity, Perpetuity, Capitalized Cost

Annuity Due

Capital Recovery Factor

Depreciation

- Straight line

- Sinking fund

- Sum of the year digit

- Declining balance

- Double declining balance

- Service output method

Inflation, rate of return

- Inflation

- Rate of return

MACRS

Others

- Break-even analysis

- Benefit-cost ratio

- Rate of return

- Recovery period

- Payout period

- Bond

- Stock: constant annual dividend, dividend with constant growth rate

- Comparing Alternatives

Measurement Corrections

- Due to long/short measurement: measure; layout

- Due to temperature

- Due to pull: normal tension

- Due to sag

- Due to slope

Probable Errors

- Single

- Mean

Stadia Measurement

- Horizontal

- Inclined

Effect of Curvature and Refraction

Leveling

- Inclined upward

- Inclined downward

- Total error

Reduction to Sea lLevel

Substense Bar

Closed Traverse

- Error of closure

- Relative error/precision

- Missing Data Problems

Area of Irregular Boundaries

- Trapezoidal Rule

- Simpson's Rule 1/3

Double Meridian Distance Method (DMD)

Double Parallel Distance Metterm-21hod (DMD)

Earthworks

- End area

- Prismoidal: correction

- Truncated

Parabolic Curve Figure

Parabolic Curve

- Symmetrical

- Unsymmetrical