NSC 29
April 18
Figure 4 Reduction in resistance moment due to shear
AD 417:
Resistance of
sections to
combined shear
and bending
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Technical / Advisory Desk
moment according to both EC3 and BS 5950 for the 400 mm
deep beam. The difference in the treatment is insignificant.
The reduction in minor axis bending resistance when the
section is subject to a shear force is also shown in Figure 4,
labelled Rectangular Section. Unlike the I section, the bending
resistance reduces significantly under high shear and reduces to
zero when the shear force reaches the shear resistance because
the maximum shear stress of fy/√3 is present over the full extent
of the flanges. This effect also applies to rectangular sections. For
a Tee section, the stem of the Tee provides the shear resistance
but also develops longitudinal stresses to provide the bending
resistance. These stresses are reduced in the presence of shear in
a similar way to those in a rectangular section.
References
1 Sir John Baker, M R Horne and J Heyman, The Steel Skeleton,
Volume Two, Plastic behaviour & design, 1956, Cambridge
University Press
2 M R Horne, Plastic theory of structures, 1979, Pergamon Press
3 M R Horne and L J Morris, Plastic design of low resistance rise
frames, 1981, Granada Publishing
This Advisory Desk note reminds designers that the form
of the section has a significant impact on the reduction of
bending resistance under high shear.
Clause 6.2.8 of BS EN 1993-1-1:2005 deals with the
resistance of cross sections to combined bending and shear
and first of all states:
(1) Where the shear force is present allowance should be
made for its effect on the moment resistance.
It then goes on to say:
(2) Where the shear force is less than half the plastic
shear resistance its effect on the moment resistance may be
neglected except where shear buckling reduces the section
resistance, see EN 1993-1-5.
(3) Otherwise the reduced moment resistance should
be taken as the design resistance of the cross-section,
calculated using a reduced yield strength … for the shear
area.
The reduced yield strength depends on the ratio of
design shear force to the shear resistance of the section.
For an I section, the shear area approximates to the area
of the web and the flanges still provide their full resistance
moment so the reduction in bending resistance may not
be more than about 20% when the design shear force
equals the shear resistance. For a rectangular section, the
full section forms the shear area so the bending resistance
reduces to zero under the same circumstances. A Tee section
would also behave in a similar way.
Contact: Dr Richard Henderson
Tel: 01344 636555
Email: advisory@steel-sci.com
/Member_design#Bending_and_shear
/Steel_material_properties#Yield_strength
/www.rainhamsteel.co.uk
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