MATLAB assignment

Alternative Width (in) Height

(in) Number of Bars

Bar Size

#1 12 24 3 #9 #2 15 15 6 #8 #3 10 24 4 #8 #4 10 23 3 #8 #5 11 26 5 #7 #6 12 30 6 #6 #7 12 19 3 #10 #8 10 30 8 #5

Table 2: US Rebar Size Chart

Bar Size

Unit Weight (lb/ft)

Nominal Diameter (in)

Nominal Area (in2)

#2 0.167 0.250 0.50 #3 0.376 0.375 0.11 #4 0.668 0.500 0.20 #5 1.043 0.625 0.31 #6 1.502 0.750 0.44 #7 2.044 0.875 0.60 #8 2.670 1.000 0.79 #9 3.400 1.128 1.00 #10 4.303 1.270 1.27 #11 5.313 1.410 1.56 #14 7.650 1.693 2.25 #18 13.60 2.257 4.00

Problem 2 (5 points) In your statics analysis class, you have established the following set of equilibrium equations:

0.286𝐹𝐹𝐴𝐴𝐴𝐴 − 0.428𝐹𝐹𝐴𝐴𝐴𝐴 + 0.707𝐹𝐹𝐴𝐴𝐴𝐴 = 0

−0.428𝐹𝐹𝐴𝐴𝐴𝐴 − 0.286𝐹𝐹𝐴𝐴𝐴𝐴 + 0.385𝐹𝐹𝐴𝐴𝐴𝐴 = 0

−0.857𝐹𝐹𝐴𝐴𝐴𝐴 − 0.857𝐹𝐹𝐴𝐴𝐴𝐴 − 0.923𝐹𝐹𝐴𝐴𝐴𝐴 + 0.707𝐹𝐹𝐴𝐴𝐴𝐴 = 0 You are told that 𝐹𝐹𝐴𝐴𝐴𝐴 = −1000𝑙𝑙𝑙𝑙𝑙𝑙. Use Excel to determine the value of the remaining three unknowns. In your solution, report the value of each unknown to 3 decimal places.

Figure 1. Problem 3 sketch.

Problem 3 (15 points) Vertical tanks with a conical base are often used for storing solids such as grain, salt, and gravel. The sloping sides prevent plugging as the material is withdrawn. The height of the tank is ℎ, and the height of the conical section is ℎ𝑐𝑐. The diameter of the tank is 𝐷𝐷 and the radius of the conical section is 𝑟𝑟. The angle of the conical section is 𝜃𝜃. For this example, assume that this angle is 35 𝑑𝑑𝑑𝑑𝑑𝑑𝑟𝑟𝑑𝑑𝑑𝑑𝑙𝑙. If the height of the solid in the tank is less than the height of the conical section, ℎ𝑐𝑐, then the volume is computed using the formula for the volume of a cone.

𝑉𝑉 = 1 3 𝜋𝜋𝑟𝑟2ℎ

However, if the tank is filled to a depth greater than ℎ𝑐𝑐, the volume is the sum of the conical section and the volume of the cylinder. The volume of the cylinder section is

𝑉𝑉 = 𝜋𝜋 � 𝐷𝐷 2 � 2

(ℎ − ℎ𝑐𝑐) Hence, the total volume is the sum of the two sections of the material has a depth greater than ℎ𝑐𝑐. The radius of the conical section, 𝑟𝑟, depends on the value of ℎ. If ℎ < ℎ𝑐𝑐, then 𝑟𝑟 = ℎ 𝑡𝑡𝑡𝑡𝑡𝑡(𝜃𝜃), otherwise it is just 𝐷𝐷/2. Also, we often need to know the weight of the bulk material in the tank. The bulk density includes the solid material and the air voids between the grains. For this problem, perform the following calculations:

a) Develop a table at 1 ft intervals that summarizes the volume of the tank and the weight of its

contents. As a minimum you must use the IF, MIN, and MAX functions. Assume the following parameters:

a. Total height of the tank: ℎ = 20 𝑓𝑓𝑡𝑡 b. Diameter of the cylinder: 𝐷𝐷 = 10 𝑓𝑓𝑡𝑡 c. Angle of the cone: 𝜃𝜃 = 35 𝑑𝑑𝑑𝑑𝑑𝑑𝑟𝑟𝑑𝑑𝑑𝑑𝑙𝑙. d. Bulk density of solid contents: 𝛾𝛾 = 25 𝑝𝑝𝑓𝑓𝑝𝑝.

b) Plot Volume and Weight as a function of height of solid in the tank (put height on x-axis). Set the

bounds and major gridlines such that the data series for volume and weight are superimposed on each other.

c) Suppose that you would like to know the overall height (to four decimal places) of the tank with an exact volume of 1500 ft3. Use Goal Seek to determine the overall height. In your solution, make if very clear which cells you are using for input to the Goal Seek function.

Problem 4 (10 points) Meteorological data for a water quality and hydrodynamic model of the Dead Sea in Israel/Jordan was developed for the time period 1993-2001. These data include air temperature (oC), dew point temperature (oC), wind speed (m/s) and direction (radians), cloud cover (0-10), and short wave solar radiation (W/m2). This data may be found in a text document H4.txt found on D2L For this Problem, you do not need to follow the usual Give/Find/Solution. Simply report the Table As described in Part A and the plot as described in Part B. DO NOT PRINT THE FULL DATA SET.

Part A: Using Descriptive Statistics Use Data/Data Analysis/Descriptive Statistics to give you a table with the following variables for wind speed over the entire time period as shown below.

Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count

Part B: Histogram Plot a histogram of the wind speed values showing frequency and cumulative % using the Histogram function. One way to do this is to use Data/DataAnalysis/Histogram. You must decide on the “bin” size of the wind speed and set up an area in your sheet where you outline them (You must specify your own bin size. Do not use the Excel default.). As an example, the graph in Figure 2 for air temperature used the bins: 10, 12.5, 15, 17.5, etc. A combined column cluster with a line (see under Custom graphs) was also used.

Figure 2: Histogram of air temperature in the Dead Sea between 1993 and 2001

0%

50%

100%

150%

0 10000 20000 30000 40000 50000

10 12

.5 15 17

.5 20 22

.5 25 27

.5 30 32

.5 35 37

.5 40 M

or e

Cu m

ul at

iv e

%

Fr eq

ue nc

y

Air temperature, oC

Dead Sea Air Temperature

Frequency

Cumulative %

Name _________________________________________ Last, First

Problem 1 (10 pts)

Below Avg. (5 pts) Average (7.5 pts) Excellent (10 pts) Points Problem attempted, but incorrect, poorly documented solution.

Solution has minor errors or incomplete summary of approach.

Correct answer with all general equations provided.

Problem 2 (5 pts)

Below Avg. (2.5 pts) Excellent (5 pts) Points Problem attempted, but incorrect answer or poorly organized.

Correct answers. Clear, concise organization.

Problem 3 (15 pts)

Below Avg. (6 pts) Average (9 pts) Good (12 pts) Excellent (15 pts) Points Solution has many major errors, with improper approach that is difficult to follow. No table or plot provided. Goal seek not used. No discussion provided. Incomplete solution.

Solution has notable errors or misunderstanding of approach. Table and/or plot have major error(s) Goal seek was used incorrectly or not at all. All work shown, but may be difficult to follow.

Solution has minor error(s). In general, proper approach with general equations shown. Table and/or plot have minor error(s) or goal seek may have been used incorrectly. All work shown.

Correct answer(s) including units & sig figs. Proper approach with general equations shown. Table & plot include units and labels. Goal Seek used correctly. All work shown and easy to follow.

Problem 4 (10 pts)

Below Avg. (5 pts) Average (7.5 pts) Excellent (10 pts) Points Problem attempted, but incorrect table and plot.

Only one of the following is correct: ** Descriptive statistic table ** Histogram

Both correct descriptive statistics table and histogram

General Requirements (10 pts)

Requirement Unacceptable (5 pts) Expected (10 pts)

Points

Use provided cover sheet.

If any of the requirements are missing or do not meet specification.

All format requirements met.

Header on each page (Course, Assignment, Name, page #). Single sided print copy. Each problem on a new page (single sided). Pages in correct order. One staple in the upper left corner. Final answers boxed. Solutions follow Given/Find/Solve format. Clear / Neat formatting.

Total Score

/50