University of Sydney –Building Principles AXIAL FORCES

Peter Smith& Mike Rosenman

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

Eureka Museum, Ballarat

University of Sydney –Building Principles AXIAL FORCES

Peter Smith& Mike Rosenman

For short piers,

Stress = Force / Area

For long columns,

buckling becomes a problem

Load is seldom exactly axial

Slender columns, Uni swimming pool

Squat brick piers

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

University of Sydney –Building Principles AXIAL FORCES

Peter Smith& Mike Rosenman

Horizontal load x height Load x eccentricity

y

H

W

P

e

R = WR = W + PM M

OTM = Hy OTM = PeW

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

Elevation

P

Plan

Stress diagrams

P

e

b

d

= compressive stress

= tensile stress

M

P only M only P and Madded

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?

University of Sydney –Building Principles AXIAL FORCES

Peter Smith& Mike Rosenman

If eccentricity is small, P/A is bigger than Pe/Z

If eccentricity is larger, Pe/Z increases

Concrete doesn’t stick to dirt — tension can’t develop!

P only LargerM only

P and Madded

P only SmallerM only

P and Madded

Tension

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

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 = WM

OTM = Hy

University of Sydney –Building Principles AXIAL FORCES

Peter Smith& Mike Rosenman

Extra load helps to increase the compression effect, and counteract tension

2P

Elevation

P

Plan

H H

y

= compression

= tension

Stress diagrams

Some tension occurs

Extra load

avoids tension

Pinnacles add load

University of Sydney –Building Principles AXIAL FORCES

Peter Smith& Mike Rosenman

Will it sink? (Can the material stand the maximum compressive stress?)

Will it overturn? Reaction within the middle third — factor of

safety against overturning usually between 2 and 3

Reaction outside middle third — factor of safety inadequate

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 minimum breadth, B, or the radius of gyration,

- r

The effective length, L

The slenderness ratio is L/B or L/r

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)

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)

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?

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