objectives •Provide a review of the mathematics Calculations for Road commonly used in roadway Maintenance maintenance to calculate areas, volumes, rates, and costs. •Provide examples of common roadway maintenance math problem and their solutions. Topics of discussion •USING UNITS OF MEASUREMENT •CALCULATING AREAS •CALCULATING VOLUMES •CALCULATING RATES AND COSTS •MAINTENANCE PROBLEMS CALCULATOR practice CALCULATOR PRACTICE • MULTIPLYING • ANSWERS • 3.14 X 5 • 15.7 • 4 SQUARED = • 16 • 15 X 28 X 42 = • 17,640 • Square root of 64 • 8 1 Calculator practice CALCULATOR pRACTICE • ADDING • DIVIDING • 2 + 17.2 +28.22 + 9.5 = 56.92 17/34 = • 0.5 • 14 + ½ +16 +121 = 5280/2 = • 2640 151.5 43560/4 = • 10890 • 29 + 1162.4 +7.62 = • 1/15 + ½ + 1/16 = 1199.02 0.62917 Calculator Practice Calculator practice • SUBTRACTING ANSWERS • COMBINATIONS • ANSWERS • 56 –28 = • (145 * 872)‐ 38= • 126,402 28 • 365 –65 = • 17 * 1/2000 *2000 = • 17 • 300 (pi) (2) • 41290 ‐56470 = • 3.1416 *6SQUARED = • 113.0976 ‐14880 Using units of measurement linear or length 2 Linear measurement Length measurements Field exercise LTAP INSPECTOR’S MAINT. TABLES Measuring your pace GIVEN: YOUR AVERAGE FOOT STEP • SOLUTION: COUNT THE NUMBER OF STEPS IN 100 MEASURED FEET. WANTED: DETERMINE THE LENGTH • AVERAGE STEP IS A RELAXED STEP OF THAT YOU NORMALLY REPEAT. YOUR AVERAGE FOOT STEP FOR • AVERAGE THE NUMBER OF STEPS/4 FIELD • CALCULATE YOUR AVERAGE STEP USE ON THE PROJECT. LENGTH. • MINE IS 2.52’ LAYOUT AND MARK 100 FEET ON A SIDEWALK OR ROAD. WALK THE 100 FEET FOUR TIMES WITH YOUR AVERAGE STEP Using units of measurement Subdivision area layout area 3 Area of a Circle Area of a circle • Area of a circle = pi r squared • Pi = 3.1416 • R = radius • Formulas for perimeter, area, & volume are on last page of booklet. Page 22 Using units of measurement Page 22 volume Calculating volumes 4 Using units of measurement Measurement of areas problem 1 Solution: • Given: • 3 cubic feet • Volume • 1 foot • Linear • 7’ 6” • 5 square feet • Linear • 10 miles • Area • 7.5 gallons • Linear • Wanted: What type of • volume measurement is it? • Volume, Linear, Area Using units of measurement Conversion factors problem 2 • Wanted: How many? • Given: • Solution: • 1728 • Cubic inches in a cubic • foot? • 9 • Square feet in a square yard • Cubic feet in a cubic yard. • 27 • Lineal feet in a mile • Square feet in an acre • 5280 • 43560 Using units 0f measurement FOOTBALL FIELD problem 3 Measurement conversion • Solution: Wanted: How many? • 10 yards 30 feet = ?yards • 3 sq yards • 27 sq. ft. = ? Sq. yds. • 5280 ft. = ? Miles • 1 mile • 33 feet = ? Rods • 2 rods • 6 sq. yd. = ? sq ft • 54 sq ft • 2 cu yd = ? cu ft • 54 cu ft 5 Problem 2b use your conversion factors • GIVEN: 1 FOOTBALL FIELD. • SOLUTION: • WANTED: • LENGTH IN FEET • LENGTH IN YARDS • 360 FT. • WIDTH IN YARDS • 120 YDS • LENGTH IN INCHES • 53.33 YDS • NUMBER OF ACRES • 19206.64 INCHES • 1.322 ACRES Weight measurement Measuring weight • Sixteen ounces • One pound • Two thousand pounds • One ton • Abbreviation for pound • Abbreviation for tons • lb. • Symbol for pound • T. • # Converting pounds to tons Pounds to tons problem 4 • Given: 56000 lbs. Solution: 56000/2000= • Wanted: Convert pounds to tons 28 Tons 6 Converting tons to pounds Conversion factors problem 5 • Given: • Answer: • 23 tons • Wanted: Convert to pounds • 46,000 lbs. Weight measurement Liquid Measurement Problem 6 Problem 7 • • Given: • Solution: GIVEN: • SOLUTION: • A TANK HAS A CAPACITY OF • 15,000 lbs. • 7.5 tons 940 CUBIC FEET. • 18,500 lbs. • 9.25 tons • 7031.2 Gallons • WANTED: • 3.5 tons • 7000 lbs. • How many gallons of ashpalt • 17 tons • 34,000 lbs. can be placed in the tank? • Wanted: Convert tons to lbs and lbs to tons Concrete sidewalk problem 7 Concrete sidewalk Concrete sidewalk problem problem 8 Calculating quantity of concrete order for sidewalk Asphalt emulsion coverage Problem 8 Problem 9 • Given: 4” Sidewalk 5 feet wide, • Solution: length 100 feet • 4”/12”/ft X 5 ft x 100 ft./27 • Wanted: Calculate the quantity cubic feet/ yard. of ready mix concrete for 100 linear feet of sidewalk in cubic yards you need to order. • 6.17 cubic yards • How much would you order? Highway Maintenance Tables Applications – lineal feet covered by 1000 gal tank of emulsion Asphalt emulsion 1000 gal coverage Problem 9 • GIVEN: • SOLUTION: • .35 gal/sqyd • 22 feet wide • 1169 ft • WANTED: • Calculating “Lineal feet covered by a 1000 – gallon Tank • Lineal Coverage = 1000gal x (syd/gal) x (1/road width ft.) x (9sft/sqyd) 8 Rates of application Gallons of Asphalt required per mile for various rates of application Rates of application Problem 10 • Given: • Answer • Appl rate = 0.40 gal/sqyd • 5632 gal • Road width = 24 ft • Wanted: Gallons of Asphalt per mile = • (gal/sqyd) x rd. width x 1 (sqyd/9sqft) x 5280 ft/mile Rates of application Tons of aggregate per mile 9 Tons of aggregates required per mile for various rates of application Tons of aggregate per mile problem 11 • Given: • Answer • 300 #/sqyd, 16 ft wide • Wanted: How man tons of aggregate per mile? • 1408tons • Solution: • Tons/mile=(lbs/sqyd)x(rd width)x (1sqyd/9sqft)x(5280ft/mile)x1ton/2000 lbs Tons of aggregate per mile cubic Yards per 100 lineal feet Cubic yards of material required per 100 lineal feet cubic Yards per 100 lineal feet Problem 12 • Given: Road Width = 24 ft, • Answer • depth of gravel 6” • Wanted:How many cubic yard/100 lineal feet? • Solution: • 44.44 cuyds • Cubic yds/100 ft=depth x (yd/36in) x road width x 100 ft x (1 sqyd/9 sqft) 10 Pounds of aggregate cubic Yards per 100 lineal feet per square yard Pounds of aggregate required per square yard Pounds of aggregate Problem 13 per square yard • Given: 8 inches compacted depth • Answer and 3200 #/cubic yd. • 711 # • Wanted: How many pounds of aggregate per square yard? • Solution :#/sq yd = depth x (1yd/36 in) x (lbs/cu yd) Compacted weights Trap rock of various materials • form of igneous rock that tends to form polygonal vertical fractures 11 Weights of different rock products Conversion factors • Limestone • Pea gravel Shale • Sand Conversion factors Questions ??????? 12.