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Steel Designers' Manual - 6th Edition (2003)
292 Introduction to manual and computer analysis
Fig. 9.4 Monosymmetric section subjected to bending
• Bending about a principal axis in which no displacement perpendicular to the
plane of the applied moment results.
• The plane of the applied moment passes through the shear centre of the cross
section.
When a cross section is subjected to an axial load and a moment such that no
twisting occurs, the stresses may be determined by resolving the moment into components
Muu and Mvv about the principal axes uu and vv and combining the resulting
longitudinal stresses with those resulting from axial loading:
P Muu v Mvv u
fuv
, =± ± ±
(9.5)
A Iuu
Ivv
For a section having two axes of symmetry (see Fig. 9.2) this simplifies to
P Mxx y Myy x
fxy
, =± ± ±
A I I
xx
yy
Pure bending does not cause the section to twist. When the shear force is applied
eccentrically in relation to the shear centre of the cross section, the section twists
and initially plane sections no longer remain plane. The response is complex and
consists of a twist and a deflection with components in and perpendicular to the
plane of the applied moment. This is not discussed in this chapter. A simplified
method of calculating the elastic response of cross sections subjected to twisting
moments is given in an SCI publication. 2
9.3.3 Elastic analysis of line elements subject to shear
Pure bending discussed in the preceding section implies that the shear force applied
on the section is zero. Application of transverse loads on a line element will, in
general, cause a bending moment which varies along its length, and hence a shear
force which also varies along the length is generated.
y