Linear Measure OBJECTIVES. After completing this chapter, the student should be able to: read a U.S. customary scale accurately to within 1/16 inch.

Transcription

1 CHAPTER 9 Linear Measure OBJECTIVES After completing this chapter, the student should be able to: read a U.S. customary scale accurately to within 1/16 inch. read a metric scale to the nearest millimeter. perform basic operations with linear measure.

2 GLOSSARY OF TERMS metric system a system of measurement based on 10 (often called the SI system). nominal dimensions the dimensions of a product before allowances or adjustments are made. The sizes of many construction materials are identified by their nominal dimensions. For example, nominal dimensions of lumber are the dimensions of lumber before it is dried and planed or the dimensions of masonry units include the mortar joints as well. perimeter the distance around the outside of a shape. scale the system of graduating a measuring device, such as a ruler, into units and fractional parts of those units. U.S. customary system the system of measurements used in America based on inches, feet, quarts, gallons, pounds, and so on. 125

3 126 SECTION 3 Construction Math The ability to measure distances and work mathematically with linear measure is fundamental to construction. Nearly every piece that is assembled into a house must be measured to fit. Major assemblies are made up of many small parts, and so it is necessary for a construction worker to be able to plan the size of those assemblies. To estimate the cost of building a house, it is vital for a construction worker to be able to perform mathematical operations with the linear measure of the parts. READING A U.S. CUSTOMARY SCALE Most measurements of distances in the U.S. construction industry are done in feet and inches units of measure in the U.S. customary system. It is nearly impossible to work in the building trades without being able to read a foot-and-inch scale, such as that found on a tape measure or ruler. A scale is the system of graduating a measuring device, such as a ruler, into units and fractional parts of those units. The major units of measure are the yard, foot, inch, and fractions of an inch (Fig. 9 1). There are 3 feet in a yard and 12 inches in a foot. Each inch can be divided into fractional parts of an inch. If an inch is divided in two, the parts are halves of an inch. Each of the two halves can be divided in two, making four quarters of an inch. If the quarters are divided in two, the parts are eighths. If the eighths are divided in two, the parts are sixteenths of an inch. The marks on a U.S. customary scale are called graduations. If the scale is graduated in sixteenths, there are five sizes of graduation marks. The wholeinch marks are the longest; the half-inch marks are the next longest; quarter-inch marks are next; 3 FT. 1 inches inches inches YD. 12 IN. inches IN. 1 FT. inches 1 2 FRACTIONS OF AN INCH FIGURE 9-1

4 CHAPTER 9 Linear Measure 127 HALF-INCH MARKS 1/ 2 2 / / 4 2 / 4 3 / 4 4 / 4 1 THE SHORTEST MARKS AND EVERY MARK THAT IS LONGER REPRESENTS SIXTEENTHS. 5 1 / 2 INCHES QUARTER-INCH MARKS / 8 2 / 8 3 / 8 4 / 8 5 / 8 6 / 8 7 / 8 8 / 8 FIGURE / 4 INCHES SIXTEENTH-INCH MARKS then there are the eighths, and the smallest are the sixteenth-inch marks (Fig. 9 2). To read the value of a fractional-inch graduation, first see the length of the mark to determine if it is halves, quarters, eighths, sixteenths, and so on. Then count the number of marks that are that big or bigger than the last whole-inch mark (Fig. 9 3) / 16 INCHES Write the dimensions shown by the circled numbers in Figure FIGURE 9-3 inches NOMINAL DIMENSIONS Many things in construction are sized by their nominal dimensions. Those are the dimensions of the product before any allowances or adjustments are made. A typical concrete block is 8 inches 3 8 inches 3 16 inches nominal. The actual dimensions of that block are inches inches inches, leaving room for 3/8-inch mortar joints. The following are the nominal dimensions of some common lumber sizes: FIGURE 9-4 Nominal Actual /4 3 3½ /4 3 5½ ½ 3 3½ ½ 3 5½ ½ 3 7¼ ½ 3 9¼

5 128 SECTION 3 Construction Math COMBINING FEET AND INCHES It is frequently necessary to work with dimensions of feet and inches combined. To combine them, start by converting everything to inches. Multiply the number of feet by 12 and add the inches. EXAMPLE 1 Express 5 feet 4 inches as inches. Multiply the number of feet by Add the inches in. When you finish your calculations, you should express the answer in terms of feet and inches. To convert inches to feet and inches, divide by 12 to find the number of whole feet. The remainder is the number of inches in addition to the whole feet. EXAMPLE 2 Express 131 inches as feet and inches. Divide the number of inches by R11 12) in ft. 11 in. Convert the following to inches: 6. 1 ft. 4 in ft. 7 in ft. 1 in ft. 6 in ft. 9 in ft. 3 in. 1 1 ft. 2 in ft. 4 in. 1 2 ft. 5 in ft. 5 in. 1 3 ft. 6 in. Solve the following problems: 21. What is the width of the wall space without the door in Figure 9 5? 22. A piece of PVC pipe 2 feet 3 inches long is cut from a 10-foot 0-inch piece. How much pipe is left? 23. A furnace flue is made from four pieces of pipe. After they are fitted together, each piece of flue pipe is 1 foot 10½ inches long. What is the total length of the flue? 24. A wiring job requires 43 feet 3 inches of electrical metallic tubing (EMT). If the EMT is available in 10-foot lengths, how many pieces are needed, and how much must be cut off the last piece? 25. The control wire for a gas burner runs 6 inches, 2 feet 4 inches, 6 feet 9 inches, 12 feet 2 inches, and 10 inches. What is the total length of the control wire? 26. In Figure 9 6, how many feet and inches is it from the left end of the building to the centerline of the window? 27. In Figure 9 6, what is the width of bedroom 1? Convert the following to feet and inches: in in in in in. Add or subtract the following, and express the result in feet and inches: ft. 6 in. 1 4 ft. 3 in ft. 7 in ft. 8 in. FIGURE 9-5 8' 4" 2' 6"

6 CHAPTER 9 Linear Measure 129 BEDROOM 1 BEDROOM 2 BATHROOM 6" 4" 12' 6" 6' 4" 6' 4" 5' 10" C L (CENTERLINE) FIGURE In Figure 9 6, what is the total width of the outside of the house in feet and inches? 29. A duct must be 9 feet 5½ inches long. When the sections of duct are assembled, they are each 1 foot 10½ inches long. How many pieces are needed, and how much must be cut off the last piece? 30. Support straps for a duct are each 1 foot 2 inches long. How many straps can be cut from a 50-foot roll of metal? METRIC SYSTEM The metric system is a decimal system. That is, it is based on dividing units of measure by 10 or multiplying them by 10. The base unit for linear measure in the metric system is the meter. A meter is slightly longer than your leg. To work with metric units you need to know the most common metric prefixes. For units larger than a meter: 10 meters 5 1 dekameter (about the width of a small house) 10 dekameters or 100 meters 5 1 hectometer (about the length of a football field) 10 hectometers or 1,000 meters 5 1 kilometer (a little more than one-half mile) For units smaller than a meter: One-tenth of a meter 5 1 decimeter (the length of a child s crayon) One-tenth of a decimeter or one-hundredth of a meter 5 1 centimeter (the thickness of a pencil) One-tenth of a centimeter or one-thousandth of a meter 5 1 millimeter (about the thickness of a dime) The metric system is not frequently used by the construction industry in the United States, but some materials and parts are built for the world market, which uses metric dimensions. Match the item from the left column with the metric dimension in the right column. Item Metric Dimension 31. Thickness of plywood 20 mm 32. New coil of cable 100 M 33. Uncut length of plastic pipe 3 M 34. Length of a large housing 1.1 km development 35. Width of a wood beam 22 cm PERIMETER MEASURE The distance around the outside of a shape is its perimeter. We could find the perimeter of a square or a rectangle by adding the lengths of all four sides. A rectangle is a four-sided shape in which the opposite sides are of equal length (Fig. 9 7). The perimeter (P) of a rectangle can be calculated by multiplying 2 3 the length (l) and 2 3 the width (w) and adding the two products together. This formula is written as P 5 2l 1 2w. Since a square is

7 130 SECTION 3 Construction Math RECTANGLE RADIUS (r ) LENGTH (l ) WIDTH (w ) WIDTH (w ) LENGTH (l ) C 5 2πr C π 3 r OR USE π C 5 πd C 5 π 3 D DIAMETER (D) PERIMETER 5 LENGTH 1 WIDTH 1 LENGTH 1 WIDTH OR P 5 2l 1 2w FIGURE 9 8 Circumference of a circle. SQUARE center. To find the circumference of a circle, we use a certain number represented by the Greek letter p, pronounced pie. p is equal to or The circumference of a circle is found by multiplying p 3 the diameter of the circle. This formula is written as C 5 pd. PERIMETER 5 SIDE 1 SIDE 1 SIDE 1 SIDE OR P 5 4s FIGURE 9 7 Perimeters of squares and rectangles. a rectangle with four equal sides, you can find its perimeter by multiplying 4 3 the length of one side (s). This is written as P 5 4s. The perimeter of a circle is called the circumference, known as C (Fig. 9 8). The diameter (D) of a circle is the distance across a circle through its Solve the following problems: 36. What is the perimeter of a house that is 28 feet wide and 40 feet long? 37. What is the perimeter of a square room that is 14 feet on each side? 38. How wide must insulation be to wrap around an 8-inch square duct? 39. How wide must insulation be to wrap around an 8-inch-diameter round duct? 40. What is the perimeter of a rectangular building lot that is 80 feet wide and 140 feet deep?