lab #10 worksheet
----------------

- make a new folder for week 10

- files for this week:

  w1setup.m  w10solve.m  w10mytruss0.m

- start matlab & change to the
  week 10 folder

KEY ACTIVITY:  design a 2D wooden
bell tower & begin to understand
why 3D structural engineers should
get paid the big bucks.


warm-up
-------

rerun the triangle example from class.
try to understand what goes on in the 
sequence:

w10mytruss0
w10setup
w10solve

type out the following variables:

nodes, join, loads
Nnodes, Nstrut

struts, Xstrut, Ystrut, length, angles
loadA, loadR

join2, matrix, vector, solution

compare "solution" to the result of
"sol=-matrix\vector".


DESIGN #0
---------

make a new "mytruss" file that corresponds
to the 11 march image on the class webpage.
count the # of unknowns & equations.

a)  type in the node coordinates.  run "w10setup"
to check the placement & numbering (it will 
give an error, but the blue dots will be plotted).

b)  type in the join matrix.  running "w10setup"
occasionally will give you a check.

c)  type in the load matrix for 100% of the 
load at the top.  for example, if the top is
node 27:

loads = zeros(size(nodes));
loads(27,:) = [0 -100];

d)  not unexpectedly, "w10solve" dies horribly.
there are too many unknowns (Nstrut+3=17) for the
number of equations (2*Nnodes=16).

e)  set "join(6,7)=0" in your "mytruss" file, now 
"w10solve" is happy.

note that a lot of the internal struts are
not doing anything!  this is not a great 
design!  (not that i knew this yesterday.)


DESIGN #1
---------

design a wooden bell tower.  the very heavy
bell is to be at least units above the ground
(load = -100% downward), but there are constraints.

a)  regular strut lengths can be no longer than 
2 units (CHANGED).  "ground struts", that is, 
struts along the ground, are not restricted to 
length & do not count in part d) below.

b)  the lateral "footprint" of the tower is no 
more than 6 units, the height must be no more
than 10 units.

c)  you are allowed to use up to 4 struts with
extra length -- 6 units (CHANGED) -- but these 
are steel cables & hence must be under tension!

d)  calculate:

total length of all struts ($cost of tower).
the max |force| on the regular struts.
the max |force| on the special cables.

your evaluation will be partially based on these
figures & the architectural style.

building tips:  your biggest problem will be
getting the 

# of struts + 3 = 2 * # of nodes

also, you will need to build a stable structure.
the solve routine will give really weird numbers
if your truss doesn't make sense.  these numbers
will not be right.

define node 1 and 2 to be your support nodes.

WARNING:  design your tower from the ground up.
don't build the whole thing in one shot, you'll
like get "inf's".  build a base, then run the 
solve (be sure to give a load!) to check for 
good design.  continue building up.

(ps:  i actually built one of mine from the
top down.  also useful was defining node 3 to 
be the bell node with load.)


DESIGN #2
---------

take your tower from design #1 and subject it
to a lateral wind load (as well as the bell).  
assume the total lateral wind force is the 
same as the bell (100%), but it should be fairly
distributed at all exposed nodes.  note:  those
long cables do not shield the tower from the wind.
(i will discuss this in class on WED.)

if your tower is asymmetric, you should check the
wind loading from both sides.