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02/09/05

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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.

  • 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).
  • 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).
  • 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).
  • 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).
  • 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).
  • 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).
  • 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.

  • 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).
  • 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).
  • 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 it’s hardness. The bisque (body) of ceramic tile may then be glazed, or left unglazed depending on it’s 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:

·         Stain Resistant

·         Scratch Resistant

·         Fire Resistant

·         Doesn’t Fade from Sun Light

·         Slip Resistant

·         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.

 


House Hunters

 

 

 

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.

 

 

 

 

Caution

 

 

 

 

 

 

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_________________________________

______________________________________________________

 

 

 

         

 

 

 

 

 

 

 

 

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 ___________________________________________________

_____________________________________________________________

_____________________________________________________________

BATHROOMS

Number Full___ Half___ Condition Good___ Fair___ Poor___ Remodel ___

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 ___________________________________________________

_____________________________________________________________

LAUNDRY

Condition Good___ Fair___ Poor___ Exclusions______________________

Comments_____________________________________________________

______________________________________________________________

 

 

 

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 ___________________________________________________

_____________________________________________________________

_____________________________________________________________

 

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 ___________________________________________________

_____________________________________________________________

_____________________________________________________________

 

 

 

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 ______________________________________________________

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 ______________________________________________________

 

 

 

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 ____________________________________________________


Compound Miter Saw Adjustments
for Crown Moulding

Wall Intersection Angle

Crown Moulding with
52° and 38° Edges

Crown Moulding with
45° and 45° Edges

Miter Adjustment

Bevel Adjustment

Miter Adjustment

Bevel Adjustment

85°

33.90

35.52

37.66

31.42

86°

33.43

35.19

37.17

31.14

87°

32.97

34.86

36.69

30.86

88°

32.52

34.53

36.21

30.57

89°

32.07

34.20

35.74

30.29

90°

31.62

33.86

35.26

30.00

91°

31.17

33.53

34.79

29.71

92°

30.73

33.19

34.33

29.42

93°

30.30

32.85

33.86

29.13

94°

29.86

32.51

33.40

28.83

95°

29.43

32.17

32.94

28.54

 

 

 

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This site was last updated 02/03/05

Attention: California State Law requires me to notify all customers that I am not a Licensed Contractor, this has no reflection on the quality of work or performance.

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