Civil Engineering & Architecture Math

Area:

  • Rectangle:  A = bh

  • Parallelogram:  A = bh

  • Triangle:  A =  1/2 bh

  • Circle:  A = πr2

  • Cone:  A =  π x Diameter x Length ÷ 2

  • Sphere:  A = π x Diameter2

Volume:

  • Cylinder = πr2h

  • Rectangular Solid = whd

  • Pyramid = 1/3 x (Area of Base) x (Height)

  • Cone =  1/3 x (Area of Base) x (Height)

  • Sphere = 4πr3  / 3

  • 1 Cubic inch = 1.804 Fluid Ounces

  • Right Tri. Prism = 1/2 Base x Height

Surface Area:

  • Total Surface Area = Sum of all Exterior Surfaces

  • Prism = 2(wd + wh + dh)

  • Cylinder = 2πrh + 2πr2

  • Cone = πr2 + πrs

  • Sphere = 4πr2

Circumference:  C = πD

Mass = Volume x Density

Trigonometry:

  • Right Triangles

    • SOHCAHTOA

  • θ = angle

  • sin θ= opposite / hypotenuse

  • cos θ= adjacent / hypotenuse

  • tan θ= opposite / adjacent

Pythagorean Theorem:

Right Triangles

a2 + b2 = c2

Conversion:

  • Decimal Inches to Millimeters, multiply by 25.4

    2 in x 25.4 = 51mm
    .75 x 25.4 = 19mm

  • Millimeters to Decimal Inches, divide by 25.4

    75mm ÷ 25.4 = 2.95 in

    10mm  ÷ 25.4 = .39 in

Physics:

  • Density = mass/Volume; D = m/V

  • Total Distance =  average velocity/time; d=vt

  • Momentum = Mass * Velocity; p=mv

  • Work = Force * Distance; W=Fd

  • Power = Work / Time; P=W/t

  • Energy Transfer = Mass * Specific Heat * Change in temp.
    q=mc/\T

Unit 4 - Site Planning

Site Grading

  • Plasticity Index (Pl) = Liquid Limit (LL) - Plastic Limit (PL)

  • Pl = LL - PL

Calculating Rainfall (Storm Water)Amounts:

  • Q = CiA
  • Q = peak runoff rate in cubic feet per second
  • i = rainfall intensity in inches per hour
  • A = drainage area in acres
  • C = runoff coefficient
  • 1 Acre = 43,560sqft

Weighted "C" Value

Cw = C1A1 + C2A2 / A1 + A2

Reduction in Q = Pre-Development Q - Post Development Q

Water Supply:

  • Required Pressure = 40psi
  • 1psi = 2.31' of water
  • 1 mile = 5,280'
     
  • Static Water Head = WSEL at Tower - Elevation water supply at discharge point
  • Static Water Pressure = Static Water Head * (psi/2.31')
  • Actual Head = Static Head - Head Loss
  • Actual Pressure = street pressure - static difference - head loss
     
  • Calculate the equivalent length of the fittings:
  • Calculate total length of pipe:
  • Select Hazen-Williams coefficient:
     
  • Head Loss:

hf = 10.44 * L * Q1.85
          C1.85 * d4.8655

  • hf is head loss due to friction, feet
  • L is the length of pipe, feet
  • Q is the flowrate of water through the pipe, gpm
  • C is the Hazen-Williams coefficient
  • d is the diameter of the pipe, inches

Waste Water Management:

  • Total Daily Wastewater Flow = Flowrate per customer x number of customers + flowrate per employee x number of employees
     
  • Septic Tank Sizing & Layout:
     Hydraulic detention time = liquid volume ÷ flowrate
     
  • Total volume = liquid volume ÷ [1-scum / solids volume as a fraction]
     
  • Liquid volume = (hydraulic detention time) * (wastewater flow rate)
     
  • Total volume = Liquid Volume ÷ [1-scum/solids volume as a fraction]
     
  • Infiltration Field Sizing & Layout:
    Infiltration Area = trench area = wastewater flow rate / hydraulic loading rate
     
  • Trench Length = infiltration area / trench width

Unit 5 - Architecture

Heat Gain or Loss:

  • Q = A U /\T

  • Q = Total cooling/heating load in BTU/hr

  • A = Area under investigation in ft. sq.

  • U = Coefficient of heat conductivity in BTU/ hr.ft.sq.0F

  • /\T = Difference in temperature between outside and inside conditions in 0F

  • U = 1/R

Unit 6 - Structural Engineering:

Structural Analysis:

Beam Load Calculation:

Beam Load(w) = Tributary Width * (Design Load)
w = tributary width * (DL + LL)

Design Load = DL + LL
DL = Dead Load
LL = Live Load
w = Beam Load
Tributary Width = length of beam on either side of beam / 2

Girder Load Calculation:

Girder Load(w) = Tributary Width * (Design Load)
w = tributary width * (DL + LL)

Identify Girder that carries maximum load
Design Load = DL + LL
DL = Dead Load
LL = Live Load
w = Girder Load
Tributary Width = length of beam on either side of girder / 2

Beam Deflection - limited to L/360 (L = Length of beam in inches)

Calculating End Reactions = wL / 2 (for symmetrically loaded beam)

Calculating Maximum Moment = wL2 / 8 (for symmetrically loaded beam)

Calculating Maximum Moment = wL2 / 8 + Pa (with 2 applied forces)

L = Length of Beam
W = Beam Load
P = Applied Load
a = location of load from end support
P1 = load distance from support A
P2 = load distance from support B

Calculating Shear = wL / 2 + P (with 2 applied forces)

L = Length of Beam
W = Beam Load
P = Applied Load
P1 = load distance from support A
P2 = load distance from support B
   

Calculating Footing Size:

Pressure = Load / Area   or  q = P /A
q = pressure or allowable Bearing Capacity of soil
qnet = Soil Capacity Available
P = total column load
A = Area

1.  Weight of Footing
     Weight of Footing = footing thickness x 150 lb/ft2   (Cement = 150 lb/ft2 )

2.  Deduct the weight of the footing
      qnet = q - weight of footing = Soil Capacity Available

3.  Total Load of Column = DL + LL + Column Height (Column Load)
      (Column Size:  W14 x 65   14 = widh of beam;  65 = lbs/ft)

4.  q = P/A

5.  Rearrange formula to find Area

6.  A = P / qnet

7.  Square Root of Area

Beam Calculations:

Beam = 16'
Limit Deflection - L/360

Convert feet to inches because L must be in inches.

16’ x 12 in/ft   =  0.533”
       360

Actual Deflection ∆ = 0.5159” must be less than 0.533”

NOTE: If deflection is more than 0.533”, you can not use the beam.