STRUCTURAL DESIGN FOR ARCHITECTURE

Structural Design for Architecture

If the size of cross-section does not vary along

the length of an element the magnitude of the

stress is the same at all locations.

The size of cross-section which is required

for a particular tensile element is calculated

from the following variation of the above

equation:

Areq = P/fatp (A2.2)

where:Areq = area of cross-section required

P = applied axial load

fatp = maximum permissible axial

tensile stress

The area of cross-section which is required in

practice is normally slightly larger than that

given by (A2.2) due to complications with the

end connection.^1 In particular, the need to

allow for the effect of stress concentrations

around fastening elements, such as bolts and

screws, and for any eccentricity which may be

present in the connection (such as might occur

where a steel angle element is connected

through one leg only) normally require that a

slightly larger cross-section be adopted than is

given by equation (A2.2). For the purpose of

approximate element sizing the adoption of

the very crude device of simply increasing the

size of the cross-section calculated from

equation (A2.2) by 15% will normally give a

satisfactory result.

A2.3.3 Elements subjected to bending

A2.3.3.1 Calculation of bending stress

Bending stress occurs in an element if the

external loads cause bending moment to act

on its cross-sections. The magnitude of the

bending stress varies within each cross-section

from peak values in tension and compression

in the extreme fibres on opposite sides of the

cross-section, to a minimum stress in the

1 The making of satisfactory tensile connections is one of

the classic problems of structural engineering. See

Gordon, |. E., Structures, Harmondsworth, 1978,

250 Section 2 for a discussion of this.

Fig. A2.1 Distribution of bending stress. Where bending-

type load is present the resulting bending stress on each

cross-section varies from maximum tension on one side to

maximum compression on the other.

centre (at the centroid) where the stress

changes from compression to tension (Fig.

A2.1). It will normally also vary between cross-

sections due to variation in the bending

moment along the length of the element.

The magnitude of bending stress at any

point in an element depends on the following

four factors: the bending moment at the cross-

section in which the point is situated; the size

of the cross-section; the shape of the cross-

section; and the location of the point within

the cross-section. The relationship between

these parameters is,

fby = My/I (A2.3)

where fby = bending stress at a distance y

from the neutral axis of the cross-

section (the axis through the

centroid)

M = bending moment at the cross-

section

I = the second moment of area of the

cross-section about the axis

through its centroid; this depends

on both the size and the shape of

the cross-section.

This relationship allows the bending stress at

any location in any element cross-section to be

calculated from the bending moment at that

cross-section. It is equivalent to the axial

stress formula fa = P/A.

Neutral axis

High compressive stress

High tensile stress