in trusses, and in some

frizzflowerUrban and Civil

Nov 29, 2013 (3 years and 11 months ago)

92 views

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