Beams and Columns
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4 | 5
When building clay trees and
animals with large versus small clay trunks or legs, your students find
a number of differences. Have them bring in pictures of actual large and
small trees and animals to look for similar differences.
If the more open-ended activity is done in a center as suggested above,
it is best to have students write about their experience. Have them respond
to some of the questions on the previous page.
For the demonstration part of this activity, ask your students what they
observed when looking at the large and small clay beams. Which was stiffer?
Which was stronger? Which bent over the fastest? Ask them why they think
the clay beams behaved differently on the two scales.
Ask them how much more clay there is in the big beam (64 times as much).
Ask them how much more the big beam weighs (64 times the weight). Ask them
how much greater the area of the base (or cross-sectional area) is for the
big beam (16 times the area). Ask them how much stronger the big beam is
(16 times as strong). Then ask if this helps explain why things were different
on the two scales.
The linear dimensions of the big clay beams are 4 times that of the small
clay beams. They are 4 times as long, 4 times as wide, and 4 times as thick.
This means that the volume of the big beam is 4 X 4 X 4 = 64 times the volume
of the small beam. This means 64 times as much clay which is 64 times as
The area of the big beam is 4 X 4 = 16 times the area of the small beam.
Since strength depends on the area of the cross-section of a beam or column,
the big clay beam is 16 times as strong as the little clay beam. The increase
of the volume (64 times) of the big clay beam over the little clay beam
is 4 times as great as the increase of area (16 times). This means that
the increase in weight of the big beam over the little beam is 4 times as
great as the increase in strength. The big beam cannot easily support its
own weight and collapses and bends much more than the small beam.