Subject:
|
Re: Spanning large areas
|
Newsgroups:
|
lugnet.build.arch
|
Date:
|
Wed, 12 Apr 2000 03:16:09 GMT
|
Highlighted:
|
!
(details)
|
Viewed:
|
1221 times
|
| |
|
|
In lugnet.build.arch, Brad Hamilton writes:
> Most stock LEGO sets use large, thin plates to create roofs and second-story
> floors.
>
> In some cases (like Fort Legorado, 6769), they have created super-large
> plates (black in this case) to do the job.
>
> What happens when you need to span a LARGER area than this? Plates are only
> so big. Also, it is often desireable to leave the back of a building open
> to let in more light and to save on bricks. This makes the structural
> challenge of spanning the roof (or adding an extra story) all the more
> challenging.
>
> I thought I'd share some of my techniques. I'd like to hear about ideas
> you've had for solving this problem.
I've worked on a different but similar problem, but haven't had time to
finish up the write-up I started nor take accompanying pictures.
Anyway, here is the write-up in it's current state, so excuse any areas
where it still needs work:
*********************
A project I've recently begun requires load bearing beams to span
distances greater than any single piece can do - 32 and 48 studs, the
width of normal baseplates and large grey baseplates. These load
bearing beams will be used to elevate the baseplates using post and beam
construction. Additional construction will be made on top of the
baseplate and, in some cases, trains will be passing underneath.
In order to ascertain the best building technique I began a series of
experiments to evaluate the structural integrity of a variety of
constructed beams, hereafter called Cbeams. I present the results here
in the hope that they are both interesting and useful to others.
Background:
I took it as a given that a Cbeam constructed from longer pieces
would be stronger and stiffer than one constructed from shorter pieces.
However, given the number of Cbeams I need to construct and the supply
of pieces available, it will be required that they be built from shorter
pieces. So I limited myself to using bricks and beams of length 4 or
less.
I also took it as a given that thicker Cbeams would be stronger and
stiffer than thinner ones. In order to both minimize the number bricks
used and maximize the clearance between the bottom of the Cbeam and the
surface beneath I limited myself to a thickness of 3 bricks and a width
of 2 studs.
In situations where these considerations and limitations are not
applicable, these results can be extended to thicker and/or wider beams.
Method:
My test apparatus consisted of two walls, each made by stacking three
2x4 bricks, on a baseplate. Each end of a Cbeam would rest on, and be
firmly attached to, the center 4 studs of a wall, and span the distance
between the walls.
Two tests were performed several times on each Cbeam:
- pressing down on and releasing the center of the Cbeam multiple
times and observing it's stiffness.
- pressing down steadily in the center of the Cbeam with
increasing force until the beam failed.
Between tests the Cbeam was removed from the test bed and all pieces
were verified to be firmly in place.
I began by constructing Cbeams 32 studs in length, thus spanning 28
studs between the walls of the test bed.
Results:
Cbeam #1: This beam was constructed using 2x4 bricks in the standard
brick wall overlapping pattern - each brick overlapping 2 studs with
bricks in the adjacent courses. On the test bed, Cbeam #1 exhibits
considerable flexibility
Cbeam #2: This beam was constructed using 2x6 bricks in the standard
brick wall overlapping pattern, each brick overlapping 3 studs with
bricks in the adjacent course. This beam was constructed to test
whether such a beam was indeed stiffer than beam #1. The results from
the test bed confirm that it is.
Cbeam #3: This beam took its inspiration from laminated wood beam
construction (as seen on a tour of a factory that makes them, shown on
"Home Again" with Bob Villa). In this beam, the middle course of 2x4
bricks is replaced by 2 rows of 1x4 beams which are offset from each
other by 2 studs, and offset from the 2x4 bricks such that no joints
line up. This beam is even stiffer than Cbeam #2.
Cbeam #4: This is similar to Cbeam #3, except that it is the top and
bottom courses which are replaced with 1x4 beams, leaving the center
course of 2x4 bricks alone.
In the failure tests, Cbeam #3 is noticably superior to Cbeam #1.
Cbeam #3 is also superior to Cbeam #4.
Repeated tests with Cbeam #3 revealed that it always failed at the
same place near one end. I replaced two 1x4's at the failure point with
a 1x8 and retested. It now failed at the identical place at the
opposite end in multiple tests. I swapped in another 1x8 at that end
and retested. It now failed at a new place. Realizing that a beam
would always fail at it's weakest point I began analyzing why it failed
at the places it did.
Conclusions:
Between the results above, and by using variations in the pattern of
the staggered 1x4's in Cbeam #3, I determined that the weakest point of
of constructed beam was measured in how many studs had to be separated
in order to break the Cbeam into 2 pieces, with the break line always
moving in one direction as it moved from course to course.
Cbeam #1 has a stud separation value of 8.
Cbeam #2 has a stud separation value of 12.
Cbeam #3 has a stud separation value of 12.
Cbeam #4 has a stud separation value of 8.
This confirms the empirical results above that Cbeam #3 is stronger
than Cbeam's #1 and #4, and also that Cbeam #2 is stronger than Cbeam
#1. It is interesting to note that while Cbeam's #2 and #3 have the
same strength, Cbeam #3 is stiffer than Cbeam #2.
With a quantitative measure now in hand it is possible to design
Cbeams to maximize the minimum stud separation value needed to divide it
into 2 pieces, thus maximizing it's strength.
Other testing revealed an important principle to bear in mind when
designing Cbeams using other size pieces and configurations.
Try this: Build Cbeam #5 from two 1x6's sandwiched between two
2x2's, such that the 1x6's protrude 4 studs in opposite directions and
the 2x2's are vertically aligned with each other. This Cbeam has
*amazing* stiffness and strength on the test bed. Removing either 2x2
results in a next to worthless Cbeam. Extending the length of the Cbeam
with more 1x6's and 2x2's also results in poor strength, unless
additional courses are added. How many? - the total number of courses
should be 1 more than the number 1x6's used in the main course.
The investigation of this lead me to realize that this design, and
indeed the design of Cbeam #3, was employing the age old principle of
the arch. Extending the number of courses allowed much of the force
being applied to the top center to be directed sideways and transfered
to the supporting walls. Switching the point of the load from the
center to slightly off center (ie. off the "keystone" brick) results in
noticably less force needed to cause the Cbeam to fail since the load on
the longer portion is not transfered as efficiently to the wall on that
end.
Practice:
For the posts in my post and beam construction I settled on a plus
shaped cross section, made from one 2x4 and two 1x2 bricks per layer.
This gives good side-to-side stability and strength. Posts are placed
under Cbeams such that the outside edges of the posts are flush with
the outside edges of the Cbeams.
My Cbeams are constructed such that in the middle layer, 2 rows of
1xn's, one row extends 1 stud beyond the ends of the top and bottom
layers and the other row extends 2 studs beyond. Each row is the same
total length and makes a mirror image overhang on the opposite end.
This construction technique allows 4 beams to converge on a single
post without getting in each others way. Additional bricks are used to
lock the Cbeams together, completing the top and bottom courses.
It is desirable to have half the width of each Cbeam (1 stud) extend
beyond the edge of the baseplate for 2 reasons:
First, it allows adjacent raised baseplates to share the Cbeam,
rather than each having its' own. This reduces the brick requirements.
Second, the exposed row serves as the building surface for a lip to
hold the baseplate in position. Depending on the requirements of the
particular construction this lip can be built from either 1xn beams, 1xn
plates, or a mixture. Using 1xn beams allows the baseplate to float
free and be easily lifted when required. Using 1xn plates allows
anchoring the baseplate to the lip with additional pieces spanning the
joint between the lip and baseplate.
Cbeams long enough to support the entire length of a large grey
baseplate exhibit too much flexibility under my constraints, so I
switched to Cbeams 23 studs long and additional posts. This arrangement
also increases the Cbeam area which can efficiently transfer its' load
to a post.
Why 23 studs?
My Cbeams to support large grey baseplates are constructed as
follows:
- one center row contains, in order, beams of length 6, 4, 8, and 4.
- the other center row is in the reverse order: 4, 8, 4, and 6.
- the 1x8's overlap by 3 studs, making the whole layer 23 studs long.
- the top row contains, in order, bricks of length 2,4,3,(gap),3,4,2.
- the bottom row contains, in order, bricks of length 6,3,(gap),3,6.
The additional 2 stud span required to create this lip is easily
enacted by topping the center post on each side with a 2x6 rather than a
2x4.
To further support the surface of large grey baseplates, half arches
are added at the mid-point of the Cbeams using the 1 stud gap in the top
and bottom courses as anchor points for 1x4's oriented 90 degrees to the
length of the Cbeam. Using four 1x4's gives a 6 stud long half arch.
For side to side strength, these half arches can be extended until they
can be joined with the half arch from the other side using 2x4 bricks.
*******************************
BTW, my project is a 4'x8' LEGO moonscape with a mining colony.
Brian
|
|
Message has 1 Reply:
 | | Re: Spanning large areas
|
| That's a pretty interesting discussion! I suspect that your beams would be much stronger if you used the 1/3 high bricks instead of the standard 1 brick high. I have noticed that the 1/3 size bricks bind considerably more tightly than the full size (...) (24 years ago, 12-Apr-00, to lugnet.build.arch)
|
Message is in Reply To:
| | Spanning large areas
|
| Most stock LEGO sets use large, thin plates to create roofs and second-story floors. In some cases (like Fort Legorado, 6769), they have created super-large plates (black in this case) to do the job. What happens when you need to span a LARGER area (...) (24 years ago, 8-Apr-00, to lugnet.build.arch)
|
10 Messages in This Thread:
 
 
- Entire Thread on One Page:
- Nested:
All | Brief | Compact | Dots
Linear:
All | Brief | Compact
This Message and its Replies on One Page:
- Nested:
All | Brief | Compact | Dots
Linear:
All | Brief | Compact
|
|
|
|
