in trusses, and in some

Πολεοδομικά Έργα

29 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

104 εμφανίσεις

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

-
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

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

x

height

W

P

e

R = W + P

M

OTM = Pe

4/16

y

H

R = W

M

OTM = Hy

W

R = H

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

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

7/16

P only

Smaller

M only

P and M

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

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

the compression effect, and
counteract tension

10/16

Stress diagrams

= compression

= tension

P

H

y

Some
tension
occurs

H

2P

Extra
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

-

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

B
,

-

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

For steel, limit of
L/
r

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