STRUCTURAL DESIGN FOR ARCHITECTURE

Structural Design for Architecture

Initial selection of section size can be based

on the following version of the elastic bending

formula:

Zreq = M/fbp (A2.6)

where: Zreq = required modulus of section

M = maximum applied bending

moment

fbp = permissible bending stress

A2.3.4 Sizing of elements subjected to axial

compression

Compression elements are the most problem-

atic to size due to the need to allow for the

phenomenon of buckling. Compressive forces

are inherently unstable because if any eccen-

tricity is present in a compressive system the

action of the forces causes the amount of

eccentricity to increase. For example, in Fig.

A2.2 the internal forces in a simple compres-

sive element are exposed by use of the device

of the imaginary cut. It can be seen from (a)

that the internal force is one of pure axial

compression if the element is perfectly

straight; an axial stress is produced which is

evenly distributed across the cross-section and

the system is in a state of equilibrium. It is,

however, potentially unstable.

If the element is given slight curvature, as in

(b), which might occur due to the presence of a

small lateral disturbance, a couple is produced

by the misalignment of the internal axial

forces. This causes a bending moment to act

on each cross-section. The bending strain

which the curvature generates produces

bending stress which resists the bending

moment and which tends to restore the

element to its original straight condition.

Unlike in a beam, however, the bending

moment and the bending stress which occur

when curvature is introduced into a compres-

sive element are not directly related. The

bending moment is dependent solely on the

magnitude of the applied compressive force

and the amount of eccentricity which is

present. The bending stress is determined by

the bending strain (dependent on the amount

of curvature which has developed) and on the

Fig. A2.3 Stability of a 'perfect' strut (i.e. a compression

element which is straight initially and perfectly aligned

with the load). The condition with respect to stability

depends on the level of applied axial load. If this is small,

as in the first diagram, the strut is stable and will return to

the original condition following a disturbance. If the axial

load is high the strut is unstable and will buckle if

disturbed. The third diagram depicts the situation when

the 'critical' level of load, which occurs at the transition

between these two load ranges, is applied. When the criti-

cal load is applied the strut remains in the displaced

252 position following a disturbance.

Axially

loaded

strut

Stable state

Unstable state

Critical state

P large

P small

P critical Strut remains

in disturbed

position

Buckling

failure

Strut returns

to original

state

Disturbing

force

removed