Stair Design

Stairs are a challenge to design. The outdoor deck shown is 11 feet 4 inches above the concrete base ( 4 feet by 4 feet by 4 inches deep). The treads are 11 inches wide. The building code states the stairs are to be at most 30 degrees with the ground and the riser height should be between 6 inches and 8 inches. The rise must be the same for all steps. Note that building codes vary by region.
Please find the following.
1. The length of the 2 by 12 used for the stringer. Remember lumber typically comes in increments of 2 feet. Show the design (rise and run) of the stair designed. Include mathematics to show that the stairs are meeting the code of 30 degrees.
2. Where you would place the concrete base so that the stairs rest on the base and at least 3 feet is showing in front of the stairs.
3. Calculate the number of cubic yards of concrete needed for the concrete base.
4. Present at least 2 possible solutions. Explain what the advantages are to each of your 2 solutions.

Concrete Slump Test March 2010

Concrete Slump Test
Testing Concrete for Strength

Water Amount_________ (Given by the teacher)
The concrete slump test is, in essence, a method of quality control. For a particular mix being used on a construction site, the slump should be consistent. A change in slump height would demonstrate an undesired change in the ratio of the concrete ingredients. If this were to happen, the proportions of the ingredients would be adjusted to keep a concrete batch consistent. This homogeneity improves the quality and structural integrity of the cured concrete. Too much or too little water will weaken the concrete.

Goal: You will be measuring how much “slump” or sag there is in your concrete mix.

Materials Needed per pair: 1 ruler, 1 cup (18 oz)with the bottom cut out, 1 mixing bucket, 1 baggy of 2.5 lbs concrete, 1 scrap piece of OSB approximately 1 foot square, 1 graduated cylinder, and 1 stir stick.

Procedure Per Pair of Students:
1. Take your premeasured ready mix concrete that you received in the food storage baggy and pour it into the mixing bucket provided.

2. Add water to the concrete mix that is in the mixing bucket. Be sure to measure the water amount carefully. This measure is in milliliters. If your water measurement is off slightly, your results will suffer, and thus your grade.

3. Use stir stick and stir the concrete for 3 minutes or until dry spots of concrete are gone.

4. Measure, in inches to the nearest eighth inch, the vertical height of the cup and record. This height is the perpendicular height of the cup. This is the initial height of the concrete needed for #10 below.

5. Pour half the mix into the upside down cup (with the bottom cut out). Be sure cup is on the scrap piece of OSB. Tamp down the concrete by using stir stick to tamp it 25 times. Add the rest of the mix and tamp. Remember to keep the cup full to the top.

6. Scrap off excess concrete that is above the top of the cup.

7. Remove the “form” AKA cup from around the concrete carefully by lifting the cup straight up.

8. After the concrete stabilizes (stops slumping) measure the height of the concrete. The concrete will have various heights so you will need to measure the average height.

9. Find the amount of slump by taking the initial height – the ending height.

10. Record: (amount of water________ , amount of slump_______)

11. Find the average slump of all pairs of students with the same water amount in the class.
Record Average (amount of water________ , amount of slump_________)


12. Collect data from all the groups in class and record in data table below.
Water 110 120 130 140 150
Slump

13. Label the axis appropriately and graph the data on your own graph paper.


14. Write an equation for the line of best fit.


15.Explain the real life meaning of slope.


16. What type of predictions could you make from your equation


17. If you had a 60 lb bag of concrete, how much water would you need to add to give the same ratio of water to concrete mix as you initially had? Hint: You will not need your graph for this.


18. Take your cement to the designated disposal area/person. Wash all of the equipment and return equipment to teacher.



Teacher Instructions:
It is best if you pre bag the ready mix concrete. Bag 2.5 lbs in each bag. Water must be added using milliliters in the amounts of 110 ml, 120 ml, 130 ml, 140 ml, and 150 ml. Each pair of students will do one water amount or one slump test. To clarify, each pair of students will do one water amount (either 110, 120, 130, 140, 150 ml) Repeat the water amounts as needed depending on the number of groups you have.

We do one slump test per pair of students with at least 2 pairs doing each water amount. A 60 lb bag of ready mix will provide about 24 bags of concrete.

The line of best fit will predict the amount of slump per ml of water. Realize that this equation will only be useful for a specific domain. That is, a concrete mix with too little or too much water will not be a mix. The equation gives you an opportunity to discuss the concept of domain of a function. The slump test is one measure of a concrete’s strength. Once again too much or too little water will significantly weaken the concrete.

Make stepping stones with the left over experiments.

Shopping Carts February 2010

Mathematics appears in unusual places. When grocery stores are designed, an architect must calculate the space needed for storage of the shopping carts. The cart above is 39” long, 22” wide and has a nesting distance of 13.5”. Nesting distance is how much extra length a cart takes when the carts are stacked together. One cart takes up a 39” length and 2 carts take up 52.5” length. Write a length formula that would compute how much length to allow for storing the carts. Assume that there are 5 rows (nests) of carts.

LED Lighting January 2010

You probably noticed the increase use of LEDs for Christmas lighting. LEDs are beginning to be used in traditional applications for the home. EarthLED thinks that they can produce a LED “bulb” that will be equivalent to a 100 watt incandescent bulb for a suggested retail of $80. The LED will use 12 watts. An incandescent bulb sells for $1. The LED is expected to last 50,000 hours while an incandescent bulb will last 1000 hours. A kilowatt hour cost 8 cents. Prepare a cost analysis for the most used light bulb in a typical household which has an average use of 5 hours a day.

Archways November 2009

Archways are a popular feature in many construction projects. Many older archways were created using stones called keystones. In the photo above, an archway is shown with the setting of a keystone at the top of the arch.
Archeologists have unearthed a stone from an archway built many years ago. The stone is 25 inches thick. The front surface is in the approximate shape of an isosceles trapezoid. The longer base is 16 inches long and the shorter base is 12 inches long. The legs measure 24 inches. Archeologists know that typically all the other stones in the archway were congruent to the stone that was found. How many stones similar to the one described would it have taken to produce the original archway? What was the interior diameter of the archway?

Water Cistern October 2009

In Shaker communities of the past, cisterns were built to store water as shown in the photo above. They were built as a cylinder with a hemisphere on each end partially buried underground. The diameter was 10 feet. The water was collected from large barn roofs. Even today, cisterns are still used extensively. Using the Shaker design described above, calculate the size of a cistern so that it could hold all the collected water from a 90 ft by 150 ft barn roof given a 20 inch rainfall. How many gallons will your cistern hold?

Drippping Faucet September 2009

Water is one of our most valuable resources. Many times it is wasted without us even thinking about it. Suppose a faucet leaks one drop per second. How much water will be wasted by the leak in one year? How many feet of half inch water pipe would that equal? Design an experiment to find the answer.