Homework 1

Due: Wednesday, 1/23, by 5:00 PM.

You may turn your assignment in during class Friday or into the CEE3202 mailbox on the 1st floor of Dillman Hall by Noon.  

No late assignments will be graded.

Make sure that your answers are clearly indicated and supported by work that is presented in a clear and logical (and legible) manner. 

The calculations that produce your answer are worth many more points than the answers themselves.  Do your own work.

Incomplete homework assignments will not receive any credit.

It is recommended that you use a basic or simple scientific calculator for all homework assignments. 

Course Text Chapter 3

1) Text problem 3.2

2) Text problem 3.5

3) Text problem 3.9

4) Text problem 3.14

5) Text problem 3.15

6) Text problem 3.32

7) Stretch problem (stretch problems ask for more effort and time than the average exam problem; use of computer aided computation and visualization tools are encouraged on stretch problems)

Statics and calculus:

     MTU finally comes to its senses, rectifying its glaring lack of on-campus statues honoring Star Trek DS9 actor Avery Brooks, by commissioning a glorious 5,000 kg statue to be placed on a 9 m swept-circular base pedestal to located in front of the MUB (see attached diagram).  The architect has provided an equation that defines the radius of the base as a function of height as it rises up to meet Captain Sisko (see diagram).  The density of the base material is given as 2,500 kg/m³. 

Find and plot a function for the internal axial force due to the weight of the statue and the self-weight of the pedestal.  Also find and plot a function that gives us the axial stress within the base as a function of height above the ground due to the same loads.  Your answers to this problem will include two equations (one for force and one for stress), as well as their plots over the domain of y = [0,9m].

Hints:

a.) The force due to the weight of Captain Sisko is pretty trivial to find (since it is a constant with respect to height), but the internal force due to the self-weight of the base pedestal is dependent on height and will require an integral to calculate.

b.) The total force you find ought to be highest at the base.  The stress might not be.

c.) Mass and weight are not the same thing. 

d.) Programs like Matlab, Mathematica, MathCAD, and even Excel generate very accurate and easy to grade printable graphs... just saying...

e.) A dummy variable (some variable that represents height that is not y) might be helpful when you are attempting to calculate the internal force as a function of y.

f.) While this example is, admittedly, a bit absurd, computing axial stresses in irregularly shaped structures (e.g., foundations, dams, retaining walls, etc.) is an important skill as is application of calculus to solve problems with continuously changing parameters, something we will do a lot of this semester.