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Construction
Math 101
By Paul Bianchina
From a
minor home repair to the construction of an entire house,
virtually every construction project requires some mathematical
calculations. From calculating the square footage of a room to
more complicated figures like the area of a triangle or the
number of board feet in a piece of lumber, a calculator and a
few simple formulas are all you need.
Area
Measurements
Measuring
and calculating area takes two of the three dimensions into
account: width and length, as when measuring a floor, or width
and height, as when measuring a wall. For the following
examples, we'll use a rectangular room that is 10' wide and 12'
long and has 8' high ceilings.
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Area of the floor or ceiling: To figure the area of the room,
multiply the length by the width (10' x 12' = 120 square
feet).
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Area of the walls: The area of each wall would either be 80 square
feet (10 x 8 = 80) or 96 square feet (12 x 8 = 96). If you
need the total square footage of the walls - for figuring
paint or wallpaper for example - you can simplify the
calculation by adding all the wall lengths together first,
then multiplying by the height (10 + 12 + 10 + 12 = 44 x 8 =
352 square feet of total wall area).
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Area in square yards: There are a total of 9 square feet in a square
yard, so to calculate the number of square yards in this
room, as when ordering carpet, divide the total square
footage of the floor by 9 (120 square feet / 9 = 13.33
square yards).
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Area in square inches: There are 144 square inches in a square foot,
so to convert an area from square feet into square inches,
simply multiply by 144 (120 square feet x 144 = 17,280
square inches).
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Area of a triangle: For the area of a triangle, use this formula: .5
x the base of the triangle x the height of the triangle. If
you have a triangle - a gable end for example - that is 18
feet wide at the base and six feet high from the base to the
peak, the calculation would be as follows (.5 x 18 x 6 = 54
square feet).
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Area of a circle: To calculate the area of a circle, the formula is:
pi x radius 2 (pi = 3.1416). So, if you want to
know the area of a circle with a 22-foot diameter - which
would be an 11-foot radius - the calculation would be:
(3.1416 x 11 x 11 = 380.13 square feet).
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Circumference of a circle: To calculate the circumference of the
same circle - the total distance around it - use the
formula: pi x diameter: (3.1416 x 22 = 69.12 feet).
Cubic
Measurements
Cubic
measurements take all three dimensions into consideration -
width, length and height. This will tell you the volume of a
given area and is useful for such things as knowing how much air
is in a room when sizing an exhaust fan or the volume of a
foundation form when ordering concrete.
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Volume of a room: To calculate the number of cubic feet in the room
used in the examples above, multiply the width by the length
by the height: (10' x 12' x 8' = 960 cubic feet).
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Volume in cubic feet: There are 27 cubic feet in a cubic yard. So,
if you would like to convert cubic feet into cubic yards,
which is used for such things as dirt, gravel and concrete,
just divide the number of cubic feet by 27 to arrive at the
number of cubic yards. For example, if you have a form that
is 2' wide, 10' long, and 1 1/2' high, first figure the
cubic feet, then convert to cubic yards: (2' x 10' x 1.5' =
30 cubic feet / 27 = 1.11 cubic yards).
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Volume in cubic inches: There are 1,728 cubic inches in a cubic
foot. To convert the cubic feet in the above example into
cubic inches, you would multiply by 1,728 (30 cubic feet x
1,728 = 51,840 cubic inches).
Board
Feet
Most lumber
is sold by the board foot, which is equal to a board that is one
foot long, one foot wide, and one inch thick. If you would like
to know how many board feet are in a given piece of lumber, use
the following formula:
T x W x L /
12, where T = the thickness of the board in inches, W = the
width of the board in inches, and L = the length of the board in
feet.
For
example, suppose you would like to know how many board feet are
in a 16 foot long piece of 2 x 8 lumber. Applying the above
formula, you would have the following: 2 x 8 x 16 / 12 = 21.33,
so there are 21.33 board feet in that particular piece of
lumber.
Ceramic Tile Definitions
Tiles are a mixture of clays that are pressed into shape and
fired at high temperatures which gives the tile its hardness.
The bisque (body) of ceramic tile may then be glazed, or left
unglazed depending on its intended use.
Classifications of
Ceramic Tile
P.E.I Wear Ratings from the Porcelain Enamel Institute
Group I: Tiles that are suitable for residential bathrooms with light
foot traffic. Generally wall tile products fall into this
group. Some wall tiles can be used on the floor. Consult the
manufacturer of the tile for their recommended areas of
application.
Group II: Tiles that can be used in residential areas, but not areas with
high foot traffic, such as in kitchens, foyers, laundry rooms,
etc.
Group III: Tiles that are recommended for all residential installations
with normal foot traffic.
Group IV: Tiles that are suited for light to medium commercial applications,
such as offices, sales rooms.
Group V: Tiles used in heavy commercial traffic areas and are suited for
exterior areas, shopping centers, airports, hotel lobbies,
public walkways.
Types of Tiles
Ceramic Mosaic Tile tiles that are less than 6 inches facial area
and may be either porcelain or natural clay composition and
usually are 3/8" or less in thickness.
Quarry Tile tiles made from the extrusion process from shale or
natural clays and usually are 6 square inches or more in facial
size and can be glazed or unglazed.
Paver Tile glazed or unglazed natural clay or porcelain tiles having
a facial area of six square inches or more and made from the
dust-pressed method.
Wall Tile glazed tiles with that are designed for indoor use and are
generally non-vitreous.
Common Tile Terms
Glazed The most common style today in floor and wall tiles, as well as
for residential and commercial applications. A liquid glass is
applied to the body of the tile and fired at high temperatures.
The glazing becomes hard and non-porous resulting in a flooring
that is:
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Stain Resistant
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Scratch Resistant
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Fire Resistant
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Doesnt Fade from Sun Light
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Slip Resistant
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Easy to Clean
Shiny glazes are softer, can be scratched easier, and can be
slippery than the satin or rustic finishes.
Unglazed There is no glazing or any other coating applied to the tile.
Their color is the same on the face of the tile as it is on the
back resulting in very durable tiles that do not show the
effects of heavy traffic. The most common unglazed tiles are the
red quarry tiles or the granite looking porcelain ceramic tiles
used in heavy commercial areas.
Saltillo Tile
is a Mexican tile made of unprocessed clays.
Listello a narrow tile used to accent field tiles.
Tile Density &
Moisture Absorption
Tile Density As the weight or the density increase it becomes a
stronger tile.
Moisture Absorption Again as the density increases the amount of
moisture that a tile can absorb becomes less.
Tile
density and moisture absorption have an indirect relationship to
each other. As the density of the tile increases the moisture
absorption rate becomes less. Tile density and moisture
absorption are important to understand when selecting the tiles
for different applications.
Non-Vitreous Tiles tiles with a water absorption of 7% or greater
(wall tile). Suited for indoor use only.
Semi-Vitreous Tiles tiles with a water absorption greater than 3%,
but less than 7%. Suited for indoor use only.
Vitreous Tiles tiles with a water absorption less that 3% moisture, but
more than 0.5%. Referred to as frost resistant tiles but can not
be used in exterior areas where freeze thaw conditions could
cause tile cracking.
Impervious Tiles tiles that have less than .5% moisture
absorption (Porcelain tile). These tiles are frost proof and can
be used in exterior areas, or on the outside of building
facades.
Tile Production
Methods
Bicottura - It is an Italian word meaning "double fired". The clay body is
fired on the first pass through the kiln, and the glaze is
applied and fired on the second pass through the kiln. This
process is only being used today for decorative wall tile
products.
Monocottura It is an Italian word meaning, "single fired". The tile
passes through the firing process one time at a temperature of
2200 degrees. Monocuttura tiles have denser bodies and harder
glazes than Bicottura tiles.
White Body Tile
versus Red Body Tile
The
color of the body is determined by the color of the clay used by
the manufacturer that is available in their geographic region.
Look at the body of the tile to see if the color is red or
white. The quality of the tile is more related to the quality of
the manufacturer not the color of the body.
Wall Tile Trims
Bullnose This is the most used trim shape for wall tile installations.
Wall tile bullnose is sometimes referred to as surface cap.
It has one rounded finished edge on the tile and can be used
horizontally or vertically. For a 4" x 4" tile the industry
number would be S4449.
Corner Bullnose It has two rounded finished edges on the tile to be used
to complete the corner where the horizontal and vertical
bullnose meet. Generally you use only 2 3 pieces for a bathtub
enclosure. For a 4" x 4" tile the industry number would be
SN4449.
Stack-on Cove Base This cove base provides a coving on the bottom
and a flat edge on top to continue with more wall tile up the
wall. For a 4" x 4" tile the industry number would be A3401.
Rounded Top Cove Base This cove base has a rounded finished top like
bullnose and is used as a cove base in areas that will not have
wall tile installed above it. The industry number would be
S3419.
The
above trims are the most commonly used. There are many other
specialty trims available that will only confuse you. Your tile
installer will be able to look at your installation and know
what trims will be needed.
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House Hunters |
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Here's a preliminary home inspection checklist for
home buyers. You see so many homes it's difficult to
remember all of the details; take this home
inspection checklist with you when you go house
hunting to keep track of details to help you
evaluate the homes on your short list.
This checklist is not a substitute for a home
inspection conducted by a Licensed Professional
Engineer (P.E.) but can also be used to bring areas
of concern to the attention of your home inspection
engineer. |
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Caution |
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Address_______________________________________________
Asking Price______________________Taxes_________________
Bid Price (My Offer)________________ Lot
Size_______________
School
District__________________________________________
Year Built_____________House
Style_______________________
No. Of Bedrooms_____ No. Of Bathrooms_____ Sq.
Ft._________
Amenities______________________________________________
Real Estate Agent's
Name_________________________________
Real Estate Agent's Tel No._____________FAX
No.____________
Date________Comments_________________________________
______________________________________________________ |
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EXTERIOR
Land Grading
Satisfactory___ Low Spots___ Needs Regrading___
Landscaping
Good___ Fair___ Poor___ Privacy Good___ Fair___ Poor___
Driveway
Good___ Fair___ Poor___ Walkways Good___ Fair___ Poor___
Garage Good___ Fair___ Poor___ Attached___ Detached ___ No.
Cars___
Decks Good___ Fair___ Poor___ Patios Good___ Fair___ Poor___
Porches Good___ Fair___ Poor___
Retaining Walls
Good___ Fair___ Poor___
Roof (Type)
Asphalt Shingles___ Slate___ Tile___ Cedar___ Other___
Roof (Condition)
Good___ Fair___ Poor___ Sags___
Roof Leaders & Gutters
Good___ Fair___ Poor___
Chimney
Good___ Fair___ Poor___ Not
Plumb___
Exterior Facades (Type)
Wood Siding___ Aluminum Siding___ Vinyl Siding___
Stucco___ Stone___ Brick___
Wood Shingles___ Asbestos Cement Shingles___
Exterior Facades
(Condition) Good___
Fair___ Poor___ Bulges___
Exterior Trim
Good___ Fair___ Poor___
Windows (Type)
Single Glazed___ Double Glazed___
Windows (Condition)
Good___ Fair___ Poor___
Exterior Doors
Good___ Fair___ Poor___
Comments
_______________________________________________________
INTERIOR
Ceilings (Type)
Sheetrock___ Plaster___ Paneling___ Acoustic Tiles___ Tin ___
Ceilings (Condition)
Good___ Fair___
Poor___ Evidence Of Water Damage___
Cracks___ Peeling Paint___
Needs Repainting___
Walls (Type)
Sheetrock___ Plaster___ Paneling___ Wallpaper___
Walls (Condition)
Good___ Fair___ Poor___
Cracks___ Peeling Paint___
Needs Repainting___ Needs
Removal Of Wallpaper___
Needs Removal Of Paneling___
Evidence Of Water Damage_____________
Floors (Type)
Hardwood___ Ceramic Tile___ Marble Tile___ Vinyl___ Carpet___
Slate___ Other___
Floors (Condition)
Good___ Fair___ Poor___ Squeaks___ Unlevel___
Closets Adequate___ Inadequate___
Window Treatments
Included___ Not Included___ Good___ Fair___ Poor___
Built-In Furniture
Included___ Not Included___
Good___ Fair___ Poor___
Ceiling Fixtures
Included___ Not Included___ Good___ Fair___ Poor___
Doors Good___ Fair___ Poor___
Source Of Heat In Each
Room
Yes___ No___
Source Of Air-Conditioning
In Each Room
Yes___
No___
Comments
_____________________________________________________
_______________________________________________________________
KITCHEN
General Condition
Good___ Fair___ Poor___ Needs Remodeling ___
Appliances
Good___ Fair___ Poor___ Exclusions ______________________
Cabinets & Counters
Adequate___ Inadequate___ Good___ Fair___ Poor___
Pantry Space
Good___ Fair___ Poor___ Eat
In Kitchen ___
Comments
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BATHROOMS
Number Full___ Half___ Condition Good___ Fair___ Poor___ Remodel
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Fixtures
Good___ Fair___ Poor___ Faucets Good___ Fair___ Poor___
Cabinets
Good___ Fair___ Poor___
Jacuzzi___ Steam Shower___
Wall Tile
Good___ Fair___ Poor___
Fiberglass Enclosures
Good___ Fair___ Poor___ Re-tile___
Comments
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LAUNDRY
Condition
Good___ Fair___ Poor___
Exclusions______________________
Comments_____________________________________________________
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ATTIC
Type
Walk-up___ Access Via Hatch___
Room For Storage___
Insulation
Adequate___ Inadequate___
Ventilation
Adequate___ Inadequate___
Evidence Of Past Water
Intrusion No___ Yes
(Location)_______________
Roof Structure
Good___ Fair___ Poor___ Cracked Structure___ Sags___
Comments
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BASEMENT
Type Full___ Partial___ Crawl___ Room For Storage___
Foundation Walls
Good___ Fair___ Poor___ Cracks___ Bulges___
Basement Structure
Good___ Fair___ Poor___ Cracked Structure___
Sags___ Water/Insect
Damage___
Evidence Of Past Water
Intrusion No___ Yes
(Location)_______________
Sump Pump___ Dehumidifier___
Comments
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ELECTRICAL SYSTEM
Service To House
Overhead___ Underground___
Amperage
30___ 60___ 100___ 125___ 150___ 200___
Voltage 110___ 110/220___ Service Panel
Circuit
Breakers___ Fuses___
Electrical Outlets
Adequate___ Inadequate___
Lighting
Good___ Fair___ Poor___
Exclusions ________________________
Comments
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PLUMBING
SYSTEM
Source Of Water
Municipal___ Community___
Private Well___
Private Well Pump,
Pressure Tank Good___
Fair___ Poor___
Water Pressure
Adequate___ Inadequate___
Domestic Hot Water Source
Separate Tank___ Oil Fired___ Gas Fired___
Electric___ Integral With
Space Heating System___
Domestic Hot Water
Condition Good___
Fair___ Poor___ Aged___
Water Pipes
Copper___ Brass___ Steel___ Lead___ Plastic___
Water Pipe Condition
Good___ Fair___ Poor___ Leaks___ Asbestos___
Drainage, Waste, Vent
Pipes Copper___ Cast
Iron___ Steel___ Plastic___
Drainage, Waste, Vent Pipe
Condition Good___
Fair___ Poor___
Sanitary Waste Disposal
Municipal___ Community___ Private___
Comments
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HEATING
SYSTEM
System Type
Steam___ Warm Air___ Hot Water___ Hydroaire___
Heat Pump___ Electric
Resistance Heaters___
System Fuel
Oil___ Natural Gas___ Propane Gas___ Electric___
System Condition
Good___ Fair___ Poor___ Aged___
Number Of Systems/Zones
1___ 2___ 3___ 4___ 5___ 6___ Other___
Oil Tank
Visible___ Buried___
Piping/Duct Condition
Good___ Fair___ Poor___ Leaks___
Duct Condition
Good___ Fair___ Poor___
Evidence Of Asbestos
Insulation On Pipes/Ducts
Yes___ No___
Heating Source
Radiators___ Heating Baseboards___ Heating Registers___
Fireplaces
Masonry___ Prefabricated___ Good___ Fair___ Poor___
Comments
____________________________________________________
______________________________________________________________
AIR-CONDITIONING
System Type
Central___ Window/Wall Units___
System Condition
Good___ Fair___ Poor___ Aged___
Number Of Systems/Zones
1___ 2___ 3___ 4___ 5___ 6___ Other___
Duct Condition
Good___ Fair___ Poor___ Asbestos___
Comments
____________________________________________________
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Compound Miter Saw Adjustments
for Crown Moulding |
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Wall Intersection Angle |
Crown Moulding with
52° and 38° Edges |
Crown Moulding with
45° and 45° Edges |
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Miter Adjustment |
Bevel Adjustment |
Miter Adjustment |
Bevel Adjustment |
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85° |
33.90 |
35.52 |
37.66 |
31.42 |
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86° |
33.43 |
35.19 |
37.17 |
31.14 |
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87° |
32.97 |
34.86 |
36.69 |
30.86 |
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88° |
32.52 |
34.53 |
36.21 |
30.57 |
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89° |
32.07 |
34.20 |
35.74 |
30.29 |
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90° |
31.62 |
33.86 |
35.26 |
30.00 |
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91° |
31.17 |
33.53 |
34.79 |
29.71 |
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92° |
30.73 |
33.19 |
34.33 |
29.42 |
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93° |
30.30 |
32.85 |
33.86 |
29.13 |
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94° |
29.86 |
32.51 |
33.40 |
28.83 |
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95° |
29.43 |
32.17 |
32.94 |
28.54 |
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