STRUCTURAL DESIGN FOR ARCHITECTURE

Equation (A2.3) is called the elastic bending
formula. It is only valid if the peak stress is
within in the elastic range. It is one of the
most important relationships in the theory of
structures and it is used, in a variety of forms,
in the design calculations of all structural
elements which are subjected to bending-type
loads.
For the purpose of calculating the maximum
bending stress, which occurs at the extreme
fibres of the cross-section, equation (A2.3) is
frequently written in the form,

fbymax= M/Z (A2.4)

where: Z = I/ymax

Z is called the modulus of the cross-section.
(It is often referred to as the 'section modulus';
sometimes the term 'elastic modulus' is used
and this is unfortunate because it leads to
confusion with the term modulus of elasticity.)
If the cross-section of an element is not
symmetrical about the axis through its
centroid the maximum stresses in tension and
compression are different. Where this occurs
two section moduli are quoted for the cross-
section, one for each value of ymax.

A2.3.3.2 Calculation of shear stress
Shear stress acts on the cross-sectional
planes of bending elements due to the
presence of shear force. The distribution of
shear stress within a cross-section is not
uniform (the pattern of distribution depends
on the shape of the cross-section) but
normally only the average value of shear
stress is calculated.

average shear stress = shear force/area of
cross-section which
resists shear

v = V/Av (A2.5)

In the case of a rectangular cross-section the
area which resists shear is the total area of the
cross-section. For I- and box-sections the area
of the web only is used.

A2.3.3.3 Approximate sizing of bending-type

elements

Bending-type elements are subjected to both

bending and shear stress and the size of cross

section which is adopted must be such that

neither is excessively large. Normally, the

bending strength criterion is used for initial

selection of the cross-section size and the

chosen section is then checked to ensure that

it will be satisfactory in respect of shear.

Appendix 2

Fig. A2.2 Stresses in compression elements.

(a) If the element is straight and perfectly aligned with the

load the stress in each cross-section is axial.

(b) If the element has a slight curvature the eccentricity

which is present gives rise to bending stress and the total

stress is a combination of this and axial stress. 251

Bending stress due

to eccentricity

Axial stress due to

compressive load

Combined

stress

Maximum

stress

Axial

stress