**Homework, reading guide and Solutions
**

**Guidelines:**

On every homework assignment please do the following.

a) On the top right corner neatly print the following, making appropriate
substitutions as appropriate.

Sally Rogers

HW 2 DUE SEPT 6, 2000

TAM 202

Section 3 at 10:10 Friday

b) STAPLE your homework in the top left corner.

c) At the top clearly acknowledge all help you got from TAs, Faculty, students,
or ANY other source (but for lecture, text and section only). Examples could
be "Mary Jones pointed out to me that I needed to draw the second FBD in problem
2." or "Nadia Chow showed me how to do problem 3 from start to finish." or "I
basically copied this solution from a tau beta sigma frat file." etc. If your
TA thinks you are taking too much from other sources he/she will tell you. In
the mean time don't violate academic integrity rules and be unclear about what
of your presentation you worked out on your own.

d) Every use of force, moment, momentum, or angular momentum balance must be associated with a clear correct free body diagram.

e) Your vector notation must be clear and correct.

f) All computer output should have your name clearly visible, as printed by the computer (e.g., title plots with your name, put your name in a comment in the first line of any .m files, etc.)

g) Every line of every calculation must me dimensionally correct. (Carry your units.)

h) Your work should be laid out neatly enough to read. Part of your job as an engineer is not just to get the right answer, but to communicate its justification clearly. So that is part of your job on the homework as well.

**Assignments: **(Check each week
for updates and changes.)

**Homework 1, due Tuesday Jan 30 at noon:**
solution grading
comments

Reading guide (Pratap and Ruina)Read "To the student" in the preface.

Read 1.1, What its all about.

Read 2.1, The notation is important. Make sure you can do sample 2.2 yourself confidently.

Read 2.2 You have to master dot products.

Read 2.3 You have to master cross products.

Problems:(download from the course text page).

Don't hand in:

1.1-9 ( know all the answers)

2.1-2.83 (don't do all of them!, but you should look at them and practice some.)

Hand these in:

1) 2.41 Projection of normal force in -j direction. Easy.

2) 2.65 Moment arm, so to speak. Easy.

3) 2.81 Various vectors defined with respect to a cube. Easy. Just a test of the basic skills.

4) 2.83 Distance of a plane to a point. A bit of a geometry challenge unless you just quote

formulas (which you shouldn't do).

Reading guide (Pratap and Ruina)Read 2.4

Review 2.1-3

Problems:(download from the course text page).1) 2.85, Forces at a point. Easy.

2) 2.91, Forces on a beam. Easy.

3) 2.93, Forces on a machine part. Easy

*) 2.84-2.92. You should be able to do all of them, don't hand in.

4) 2.78. Distance from a point to a line. Do as many different ways as possible.

5) What point on the line that goes through the points (1,2,3) and (7,12,15) is closest to the origin?

Geometry challenge.

6) What is the distance between opposite edges of a regular tetrahedron with sides of length 1.

Geometry challenge (one approach: find points on such a tetrahedron and then find a way to use

the mixed triple product to find the distance between lines).

Reading guide (Pratap and Ruina)Read about center of mass in section 2.5.

Read about free body diagrams in Chapter 3. Master fig 3.4 and box 3.3.

Read about mechanics of one body in chapter 4 intro and 4.1 (read once lightly).

Problems:(download from the course text page). Problems 1-2, and 4-9 only take a few minutes each once you know how to do them. This assignment is not especially long.

1) 2.95, Center of mass of five point masses. Easy.

2) 2.97b, Center of mass of an upside down 'U'. Easy.

3) 2.98b, Center of mass of a circular arc (calculus challenge).

4) 3.1a, Why draw a Free Body Diagram? Very easy.

Free body diagrams only in problems 5-8, no mechanics.

5) 3.2, FBD of hanging mass. Easy.

6) 3.10, FBD of disk in groove. Easy.

7) 3.18, FBD of block on wheel with force. Easy.

8) 3.39, FBD of hanging shelf in 3D. Not hard.

Course rule: You must draw a free body diagram for any use of force or moment balance.

This applies to problems 9-11 below.

9) 4.2, n hanging masses. Easy.

10) 4.4, mass hanging by 2 strings. Not hard. Do carefully, thoroughly, and neatly.

11) 4.3, zero length spring and rod. Interesting.

Reading guide (Pratap and Ruina)Read 4 intro and 4.1 on mechanics carefully.

Read 4.2 on trusses

Read If you like trusses and theory look at 4.3 (not emphasized in HW and tests)

Problems:download non-book problems here1) 4.23, mass hanging from strings: a) 1D, b) 2D, c) 3D. Easy.

2) minimum coefficient of friction to drive a front-wheel drive car up hill (click above). Some time and thought.

3) 4.25, 3D hanging shelf. Takes some thought and time.

4) zero force members (click above). Easy.

5) symmetric 9 bar truss (click above). Not hard.

6) a truss with no closed triangles. A little tricky. Extra credit challenge.

Reading guide (Pratap and Ruina)Read 4.4 on internal forces

Problems:download here. (typo in 4b: density is lbm/ft^3 NOT lbm/ft^2)

All problems in file above.1) Internal forces in a bent rod, two ways.

2) Tension in a telephone pole.

3) Lightest cable to hang a 10 pound weight one mile

4) Shear and bending moment diagrams for two beams.

Reading guide (Pratap and Ruina)Read 4.5 on springs

Review all else

Section 4.6 is delayed one lecture,

All of this HW could be on prelim.

Problems:download here1) three springs, find force

2) springs in parallel find the deflection

3) springs in series find the force

4) sign held by 6 bars

5) 4.17, pulley on a ramp

Reading guide (Pratap and Ruina)Read 4.6

Problems:download1) pipe wrench

2) bike goes forward or backward?

**Homework 8, due Tuesday March 26 at noon: **Solutions** **grading
comments**
**(automatic extension to Thursday March 28 at 9 AM to all but Eric)

Reading guideRead Pratap and Ruina section 4.5, esp pgs 168-170

Read Beer and Johnston 1.1-9 (mostly review of lab material)

Read Beer and Johnston 2.1-7 (mostly review of lab material)

Problems:from Beer and Johnston (note, even # probs have answers (of sorts) in back of book). Many problems this week, but mostly quickies.1) 1.2, def of stress, simple

2) 1.20, stress in truss, not hard

3) 1.23, stress in rod in tow cart, basic statics and easy stress

4) 1.36, normal and shear on crooked plane, easy

5) 1.46, shear in glue, easy

6) 2.2, a wire can't stretch too much, easy

7) 2.28, an upside down paraboloid squishes, calculus needed, about as hard as the long hanging wire problem.

Reading guide (Beer and Johnston)Read 2.9-10

Read 2.10-11, 2.14

Read but don't fester over 2.12, 13, 15-19

Problems:1) 2.34, parallel alum & brass strips, easy.

2) 2.38, brass and steel (4 springs in series), neither trivial nor hard.

3) 2.48, lever constrained by two rods, straightforward.

4) 2.64, heating of brass and alum in series with gap, takes some care.

5) 2.66, tension test thinning, trivial.

6) 2. 68, angle change of diagonal line tension test, easy.

7) 2. 86, shear of rubber layer, easy.

Reading guide (Beer and Johnston)Read 3.1-6

Read 3.7-8, but not too seriously

Problems:(download from the course text page).1) 3.2, basic torsion stress formula plug in (easy, really)

2) 3.6b, slight elaboration of above, multiple power take offs.

3) 3.24, angle of twist, formula plug in (easy, really)

4) 3.38, two shafts in series connected by gears (takes a little thought)

5) 3.50b, Statically indeterminate torsion problem (takes a little thought)

Reading guide (Beer and Johnston)Read 4.1-5 and 4.7

Read A1.5 (pp 690-699, understand ex A.06 perfectly)

Problems:1) 4.2, stress in a beam w/ cylindrical holes (not hard, need to know appendix A,

also see inside back cover).

2) 4.10, stress in an H beam. Plug and chug (not hard).

3) 4.20, but replace bar with wood "2by4" (1.5 in X 3.5 in) with modulus

E= 2*10^6 PSI and load of 2000 lb in. Comment on the relation between

your answers to parts (a) and (b). (Not hard.)

4) 4.26, cut the best rectangular beam out of a round log.

Compare your answers for parts (a) and (b). (Not hard once you are good at calculus.)

5) 4.46, reinforced concrete beam (not pre-stressed). (A bit of work. see sample 4.4).

Reading guide (Beer and Johnston)Read 5.1-5.6

Read 5.11

Problems:1) 5.22, shear in T beam. Straightforward but work.

2) 5.14, I beam. Also compare with VQ/It. See page 707.

3) 5.58, bending, shear & tension. Not hard.

4) 5.66, everything combined. If you master this you are in good shape. Some work.

Reading guide (Beer and Johnston)Read 7.3-4 (review of V, M diagrams)

Read 8.1-4 on deflection of beams

Problems:1) 8.2, cantilever with couple at end, the easiest possible beam deflection problem.

2) 8.4&8.8,cantilever with uniform loading, the next easiest (after 8.1 from lecture).

3) 8.16, overhanging simply supported beam (see sample 8.1)

4) Harder: Imagine supporting a weight midway between two walls using a beam

of given material and cross section. One way to do this is with a cantilever.

Another is with a beam that goes from one wall to the other, clamped (welded) at both

ends. How much smaller is the deflection of one than the other? That is,

compare problems 8.1 and 8.56 (but with twice the length in 8.56). Challenge:

can you see a way to get this ratio by mental calculations only? If so, present your

argument. (See sample 8.3 as an example of a statically indeterminate beam).

Reading guide (Beer and Johnston)Read 6.1-4,

Read 11.1-4, especially 11.2 and 11.3

Problems: (Donothand in. Solutions will be posted. Topics might be on final exam.)1) 6.6, 6.10, 6.30

2) 6.44

3) 11.1 (answer is kL)

4) 11.24

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