Warmup
The Riddler has left a clue for Batman to follow at the scene of
each crime. These are the clues that Batman has found:
•
(1) There is a 1 in the thousands place.
•
(2) The digit in the tens place is 9 times the digit in the
thousands place.
•
(3) Multiply the digit in the thousands place by 2.
•
(4) The digit in the ones place is a hand without a thumb.
•
(5) The digit in the hundreds is 2 less than the number in the
tens. Solve the riddle to find the number and help Batman
stop the Riddler.
2794
Column Strength
Objectives
Students will:
•
Identify columns in structures and to explore the behavior of different shapes of
columns, i.e. round, square, and triangular
•
Distinguish between columns and beams
•
Understand the concept of a cross section
•
Understand the concept of strength in relation to a structural element, and to
distinguish strength from stiffness
•
Construct and test a hypothesis on which of 3 column shapes is strongest
•
Observe through experimentation how a column collapses
•
Collect data, organize it in a table, and express results in correct units
•
Divide tasks and cooperate to meet the goals of the group
•
Make joint decisions on which column shape to test and how to phrase their
hypothesis
•
Reach a joint conclusion on column behavior through discussion of their results
Column Strength  Vocabulary
•
Columns
•
compressive loads
•
crosssectional
•
rectangular
•
Square
•
circular
•
triangular
Column Strength
•
Columns
are vertical structural elements that carry
compressive
loads
and come in a variety of
crosssectional
shapes, including
rectangular
,
square
,
circular
and
triangular
. They may be hollow
or solid. They may be “short” or “long.”
•
The difference between a
beam
and a
column
is its orientation and
the way it carries load in a structure. If it is
horizontal
and carries
loads in bending (
tension
and
compression
), we call it a
beam
; if it is
vertical
and carries loads in
compression
, we call it a
column
.
•
The
crosssectional
shape of a
column
is one factor that affects its
stiffness
and its strength.
Column Strength
•
Stiffness
is the ability of the
column
to resist bending under loads.
•
Strength is a measure of how much
vertical load
a
column
can
support without failing. (Related concepts:
live load
,
dead load
.)
•
A
column
loaded vertically will eventually fail by
buckling
—
bending
out sideways under a
compressive
load—or
crushing
.
•
A
column
is stiffer if its material is further away from the
central
vertical axis
. Thus the ideal shape for a column is a
cylinder
. A
cylindrical
shape, however,
is not
always practical. It is used in
concrete, but not commonly in steel, because it is difficult to connect
beams to a
cylindrical
column.
Column Strength
A column can fail in one of two ways,
crushing
or
buckling
.
Crushing
occurs when the
maximum strength of the material (in this
case, the paper) has been reached and the
material collapses under additional load.
Buckling
occurs when the column becomes
unstable due to its slenderness, bends out of
plane of the vertical axis and falls down.
Buckling occurs before the column has
achieved the limiting strength of the material,
and thus occurs under less load than crushing.
Column Strength
Are there any columns in this school building?
Where?
What are the columns made of?
Concrete, steel, masonry, etc.
Are all of the columns in this building visible?
Are there structures in your body that work like columns?
What are they?
What would happen if they weren’t strong enough to do their
job?
Column Strength
What shapes can columns have?
Does the shape make a difference in how strong the column is?
Why
?”
Column Strength
Short columns tend to fail by crushing (a
strength failure). Short columns are
defined as columns in which the least
crosssectional dimension (i.e. the
diameter in a round column) is large
compared to the height of the column.
These columns are stout and stocky
looking, thus the term “short.” The
proportions of a short column results in a
stability that allows the column to
continue carrying load until the material
the column is made of crushes.
Column Strength
Long columns tend to fail by buckling,
which is an instability failure rather than a
strength failure. Long columns are
defined as columns in which the least
crosssectional dimension is small
compared to the height of the column.
These columns are tall and slender, thus
the term “long.” Because of their
proportions, long columns tend to become
unstable before they achieve the limiting
load of the material. Buckling occurs
when the column bends out of plane from
the vertical axis.
Column Strength
Factors that influence the buckling load of a column include the
length of the column, the stiffness of the column, the amount of
material used in a cross section and the way the material is
distributed. Of these factors, the length of the column is the most
critical. Generally, the load carrying capacity of a column varies
inversely as the square of its length.
Column Strength  Challenge
Imagine that you are architects and structural engineers. The
Board of Education has asked you to design a new building to
house his school. You plan to have a gym on the roof, and you
don’t want the building to collapse from the weight of all the
exercise equipment you plan to install, not to mention the
rooftop swimming pool.
One thing you’ll have to think about is how to design the
columns that support the building. Think about all the forces
that will act upon them, and try to figure out which of the 3
possible columns shapes will support the most weight without
collapsing. Don’t just guess! Use everything you know about
structures and your best thinking skills.
Column Type
Total weight held
(grams)
Total weight of
column
Effciency = weight
held/column weight
C1
C2
C3
C4 half height
S1
S2
S3
S4 half height
T1
T2
T3
T4 half height
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