University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Eureka Museum, Ballarat
1/16
Tension members occur
in trusses, and in some
special structures
Load is usually self

aligning
Efficient use of material
Stress = Force / Area
The connections are the
hardest part
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
For short piers,
Stress = Force / Area
Slender columns,
Uni swimming pool
Squat brick piers
2/16
Load is seldom exactly axial
For long columns,
buckling
becomes a problem
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Member will only fail in true compression
(by squashing)

if fairly short
short column
Otherwise will buckle before full
compressive strength reached
long column
3/16
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Horizontal load
x
height
W
P
e
R = W + P
M
OTM = Pe
4/16
y
H
R = W
M
OTM = Hy
W
R = H
Load
x
eccentricty
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
The average
compressive stress =
Force / Area
But it isn’t uniform
across the section
Stresses can be
superimposed
P
P
e
= compressive stress
= tensile stress
M
Stress diagrams
P only
M only
5/16
P and M
added
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Stress due to vertical load is P / A, all
compression
Stress due to OTM is M / Z, tension one
side and compression on the other
Is the tension part big enough to overcome
the compression?
What happens if it is?
6/16
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
If eccentricity is
small,
P/A
is bigger
than
P
e
/Z
P and M
added
7/16
P only
Smaller
M only
P and M
added
P/A
Pe/Z
P only
Larger
M only
Tension
P/A
Pe/Z
If eccentricity is larger,
P
e
/Z
increases
Concrete doesn’t
stick to dirt
—
tension can’t develop!
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
For a rectangular pier
—
Reaction within middle third, no tension
Reaction outside middle third, tension tries
to develop
8/16
Within middle third
Limit
Outside middle third
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
The overturning
effect is similar to
eccentric loading
We treat them
similarly
There is only the
weight of the pier
itself to provide
compression
y
H
W
R = W
M
OTM = Hy
9/16
R = H
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Extra load helps to increase
the compression effect, and
counteract tension
Pinnacles add load
10/16
Stress diagrams
= compression
= tension
P
H
y
Some
tension
occurs
H
2P
Extra
load
avoids
tension
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Will it sink? (Can the material stand the
maximum compressive stress?)
11/16
Will it overturn?
Reaction within the middle third
—
factor of safety against overturning
> 3
Reaction outside middle third
—
factor of safety inadequate 1

3
Reaction outside base
—
no factor of safety
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
A slender column buckles before it squashes
A slender column
looks
slender
We can quantify slenderness by a ratio
—
The slenderness ratio is
L/B
or
L/
r
, where
The minimum breadth,
B
,
or the radius of gyration,

r
The effective length,
L
12/16
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
For timber and concrete
—
limit for
L/B
is
about 20 to 30
For steel, limit of
L/
r
is about 180
At these limits, the capacity is very low: for
efficient use of material, the ratios should
be lower
Note

effective length
(depends on end

conditions)
13/16
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
The buckling stress increases with
E
(so steel is better than aluminium)
The buckling stress reduces with
(L/
r
)
2
(so a section with a bigger
r
is better)
14/16
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
L/
r
may be different in each direction
the smaller
r
is the critical one
Can we support the column to reduce
L
?
Can we use a section with a bigger
r
in
both directions?
15/16
University of Sydney
–
Building Principles
Axial Forces
Peter Smith& Mike Rosenman
Tubular sections are stiff all ways
Wide

flange
H

beams
better than
I

beams
Squarish timber posts rather than
rectangular
= better sections for columns
16/16
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