Warm-up

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

•

cross-sectional

•

rectangular

•

Square

•

circular

•

triangular

Column Strength

•

Columns

are vertical structural elements that carry

compressive

loads

and come in a variety of

cross-sectional

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

cross-sectional

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

cross-sectional 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

cross-sectional 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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