Stiffness (k) = (3 × E × I ) / l

Where,

E - Young's Modulus

I - Area Moment of Inertia

l - Length

S - hydraulic gradient,

v - kinematic viscosity of water,

D - Internal diameter,

Ks - Roughness coefficient,

g = 9.81 m/s

A - Area of section.

Slope at free end = ML / EI

Deflection at any section = Mx

Where,

M is the couple moment at the free end,

E is the Elastic Modulus,

I is the Area moment of Inertia,

L is the Length of the beam and

x is the position of the load.

Slope at free end = PL

Deflection at any section = Px

Where,

P is the externally applied load,

E is the Elastic Modulus,

I is the Area moment of Inertia,

L is the Length of the beam and

x is the position of the load

Slope at free end = P

Deflection at any section = P

P

Where,

P

P is the Externally applied load,

E is the Elastic Modulus,

I is the Area moment of Inertia,

L is the Length of the beam and

x is the position of the load.

Slope at free end = PL

Deflection at any section = Px

Where,

P is the externally applied load,

E is the Elastic Modulus,

I is the Area moment of Inertia,

L is the Length of the beam and

x is the position of the load

Slope at free end = Pa

Deflection at any section = Px

Deflection at any section = Pa

Where,

P is the externally applied load,

E is the Elastic Modulus,

I is the Area moment of Inertia,

Lis the Length of the beam and

x is the position of the load

a is the distance of load from one end of the support

Multiplication = ( (Value1-ft X 12) + in) X ( (Value2-ft X 12) + in) Addition = ( (Value1-ft X 12) + in) + ( (Value2-ft X 12) + in) Subtraction = ( (Value1-ft X 12) + in) - ( (Value2-ft X 12) + in) Division = ( (Value1-ft X 12) + in) / ( (Value2-ft X 12) + in)

Where,

ft - Feet

in - Inches

L=a1ta + b1tb + c1tsb +d1tad

Where,

L=Structural Number of Flexible pavement,

a1=Layer coefficient for asphalt ,

ta=Asphalt layer thickness,

b1=Layer coefficient of base,

tb=Base layer thickness ,

c1=Layer coefficient of sub-base,

tsb=Sub-base layer thickness,

d1=Layer coefficient of additional layer,

tad=Thickness of additional layer

Where,

E - Vertical Offset

g

g

L - Length of the curve

L

L

Where,

L

g

g

S - Passing Sight Distance

L

L

Where,

A - Absolute difference between g

S - Sight Distance

L

h

h

L

L

If S > L, then the first formula is used, if L > S, then the second formula is used.

Where,

A - Absolute difference between g

S - Sight Distance

L

H - Height of headlight

β - Angle of Headlight Beam

r = (g

Where,

r - Rate of change of grade

g

g

L - Length of the curve

R = 5729.58 / D

T = R * tan ( A/2 )

L = 100 * ( A/D )

LC = 2 * R *sin (A/2)

E = R ( (1/(cos (A/2) ) ) - 1 ) )

M = R ( 1 - cos (A/2) )

PC = PI - T

PT = PC + L

Where,

D = Degree of Curve, Arc Definition

1Â° = 1 Degree of Curve

2Â° = 2 Degrees of Curve

P.C. = Point of Curve

P.T. = Point of Tangent

P.I. = Point of Intersection

A = Intersection Angle, Angle between two tangents

L = Length of Curve, from P.C. to P.T.

T = Tangent Distance

E = External Distance

R = Radius

L.C. = Length of Long Chord

M = Length of Middle Ordinate

c = Length of Sub-Chord

k = Length of Arc for Sub-Chord

d = Angle of Sub-Chord

y = e

Where,

y - elevation of point of vertical tangency

e

g

g

x/L - Length of the curve

Stopping Distance =(v×t) + { v² / [2×g×(f±G)] }

Where,

g - gravity (9.8)

v - Vehicle Speed

t - perception Time

G - Grade of Road

f+G - Grade of Uphill

f-G - Grade of Downhill

Y = L − { L

Where,

Y - Tangent distance to any point on the spiral

L - Length of spiral from tangent to any point

L

R - Radius of Simple Curve

i = L² / ( 6×R×L

Where,

i - Tangent deflection angle to any point on the curve

L - Length of spiral from tangent to any point

L

R - Radius of Simple Curve

Where,

A - Area of cross section

X

Y

n - Number of points on cross section

V = ((A

Where,

L - Length between two areas

A

A

V - Eathwork Volume

L = ( 0.00047hr (fsS) ^2 ) ^ ( 1/3 )

Where,

L = Slab Length,

hr = Thickness of reinforced slab,

fs = Yield strength of steel reinforcement,

S = Steel reinforcing ratio

Volume of concrete Slab = w × l × t

Where,

l - Length

w - Width

t - Thickness

P = 9.93 ( fc^0.5 )( te^2 ) ( ( k / (19000 ( fc^0.5 )( te^3 ) ) ) ^ 0.25

Where,

fc = Concrete compressive strength,

k = Modulus of subgrade reaction,

te = Slab thickness.

w = 257.876s ( kh / E ) ^ 0.5

Where

w = Maximum Allowable Stationary Live Load,

k = Modulus of subgrade reaction,

h = Thickness of slab,

s = Allowable extreme fiber stress in tension,

E = Modulus of elasticity.

Volume of concrete Footer = [ (ow × ol) − (iw × il) ] × t

Where,

ol - Outside Length

ow - Outside Width

il - Inside Length

iw - Inside Width

t - Thickness

Radius = diameter/24 cubic yards = (height*(radius)

Footing Pours = ( Diameter * ( Width / 12 ) ) * ( Depth / 12 ) / 27 );

Concrete Volume = [( 22/7 )r

Cubic Yards to be filled = (L * W * 0.32 / 27);

For size = 12inch

Cubic Yards to be filled = (L * W * 0.51 / 27);

Single Stepping Stone = (Π X r

Where,

h = Depth in inches

r = d / 2

d = Diameter in inches

Single Stepping Stone = (l X b X h) / 324

Where,

l = Length in feet

b = Width in feet

h = Depth in inches

Single Stepping Stone = (l X b X h) / 648

Where,

l = Length in feet

b = Width in feet

h = Depth in inches

Cement = Volume × 320

Sharp Sand= Volume × 600

Gravel = Volume× 1200

Water = Volume × 176

C = L × W × T × R

Circle,

C = π × (M/2)

Footing,

C = L × W × D × R

Circular column,

C = π × (M/2)

Where,

C = Total Cost Of Concrete Driveways

L = Length(yard)

W = Width(yard)

T = Thickness(yard)

R = Cost

D = Depth(yard)

M=Diameter(yard)

Safe Speed for Horizontal curve ( V > 50mph ) = ( ( ( -0.03 × r ) + ( √ (((.03 × r) × (.03 × r)) + ((4 × r) × ((15 × (e / 100)) + 3.6))))) / 2)

If Safe speed of horizontal curve less than 50 mph

Safe Speed for Horizontal curve ( V < 50mph ) = ((( -.015 × rhname ) + ( √ ((( .015 × rhname ) × ( .015 × rhname )) + ((4 × rhname) × (( 15 × ( ehname / 100 )) + 2.85 ))))) / 2);

Where,

r = Radius of Horizontal Curve(ft)

e = Superelevation

f = ( u × m × g × sin(a) ) + ( m × g × cos(a) )

v = √ (((( u × m × g × sin(a) ) + ( m × g × cos(a) )) × r ) / m )

Where,

t = Static Friction

u = Static Friction's Coefficient

m = Mass of Vehicle (kg)

g = Gravity Accelaration

r = Radius (m)

f = Total Net Force

v = Maximum Speed

a = Slope of the Road

P = 2 × (l+b)

Where,

A = Drive way Area

P = Drive way Perimeter

l = Length

b = width

Slope = ( Rise / Run ) × 100

Angle = tan

Angle = tan

Roof Pitch = ( Rise /(Run/12) )

Slope = ( S / N ) × 100

Angle = tan

Where,

S = Rise (inches)

N = Run (inches)

Roof Pitch = Rise / ( Run/ 12 )

Slope = ( Rise / Run) × 100

t = r × tan(i / 2)

e = ( r / cos(i / 2)) -r

c = 2 × r × sin(i / 2)

m = r - (r (cos(i / 2)))

d = 5729.58 / r

Where,

i = Deflection Angle

l = Length of Curve

r = Radius

t = Length of Tangent

e = External Distance

c = Length of Long Chord

m = Middle Ordinate

d = Degree of Curve Approximate

Where,

T = Total Unit Weight in kN/m³

S = Total Unit Weight in lb/ft³

Where,

V = Volume of Trapezoid Footing

h = Height of Trapezoidal

A1 = Area of the Lower Shape

A2 = Area of the Upper Shape

A1 = m x n (Lower Height x Lower Breadth)

A2 = o x p (Upper Height x Upper Breadth)

Where,

W = Width(ft)

L = Length(ft)

H =Thickness(inch)

Where,

l = Length(ft)

f = Flag Thickness(inch)

g = Gutter Width(inch)

h = Curb Height(inch)

Where,

c = Concrete Yardage

n = Number of stairs

t = Tread(inch)

r = Riser(inch)

w = Width(ft)

T = M + N + O

X = (M / T) x V

Y = (N / T) x V

Z = (O / T) x V

Where,

H = Height of Concrete

W = Width of Concrete

B = Breadth of Concrete

M = Cement Ratio

N = Sand Ratio

O = Coarse Ratio

V = Volume of Concrete

T = Total Ratio of ingredients

X = Cement Quantity

Y = Sand Quantity

Z = Coarse Quantity

X = V x 1.54

C = X x (M / G)

S = X x (N / G)

Where,

T = Plastering Thickness

V = Volume of Cement Mortar

A = Area of Plastering

M = Ratio of Plastering Cement

N = Ratio of Plastering Sand

C = Cement Required (1 Part)

S = Sand Required (5 Part)

X = 35% Sand Bulkage

G = Total ratio (M+N )

Skirting Tiles Area = Perimeter of Room x Skirting Tiles Height

Area of Room = Room length x Room Breadth

Total Area to be Laid = Area of Room + Skirting Tiles Area

Area of Tiles = Tiles length + Tiles Breadth

Number of Tiles We Need = (Total Area to be Laid / Area of Tiles) x Tiles Wastage%