STRUCTURAL DESIGN FOR ARCHITECTURE

Structural Design for Architecture

Euler formula indicates that, as would be

expected, the longer an element is the smaller

is the load which it can safely carry in

compression. For a particular element the

length which must be used in the formula is

the distance between the points at which it is

restrained against lateral movement, which is

frequently different from the total length of the

element. Another factor which is significant is

that, in real structure, the conditions of lateral

restraint are frequently different for different

planes of buckling (Fig. A2.6). In such cases the

value which is used for length in the buckling

formula must be compatible with the radius of

gyration which is used as both values must

apply to the same plane of buckling.

A number of different slenderness ratios can

normally be calculated for a particular element

depending on the conditions of lateral

restraint which are provided and on the shape

of the cross-section. Each refers to a particular

plane of buckling - the plane which is normal

to the axis from which the radius of gyration

was calculated. The highest slenderness ratio

is the one which determines the buckling

strength.

The concept of effective length

The characteristics of its end conditions affect

the critical load of a structural element. An

element which has its ends fully restrained

against rotation will carry a higher compressive

load before buckling than one whose ends are

hinged, because the buckled shape of the

fixed-ended element is more complex than

that of one with hinged ends and a greater

load is required to force the element into this

shape. An element with one end fixed and the

other end hinged has a simpler buckled shape

than the element which is fixed at both ends

and its buckling strength is therefore inter-

mediated between the other two cases.

The Euler buckling formula applies only to

compressive elements which are hinged at

both ends but it is possible to use it for

elements with different end conditions by

employing the concept of effective length. The

effective length of an element which does not

have hinged end conditions at both ends is the

Fig. A2.6 The slenderness ratio of an element depends

on the conditions of lateral restraint. Two examples are

shown here.

(a) Assuming that adequate restraint is provided at roof

level and by the intermediate floor, the slenderness ratio

of the column is based on the storey height for the assess-

ment of stability in the plane of the cross-section of the

building.

(b) The lengths on which the slenderness ratios of the

columns in this skeleton frame are based depend on the

plane of buckling under consideration. In the plane of the

wall it is the distance between the points at which lateral

movement is restrained by the cross-bracing. In the cross-

sectional plane of the building it is the height of the

256 column.

(a)

Total

length

Possible mode

of buckling Length used

in assessment

of stability

(b)

Length which determines

stability in plane normal to wall

Length which

determines

stability in

plane of wall