Technical
The value of (Mp − Mpr)/Mpw where the shear force is half the
shear resistance of the web is 0.134. The reduction in plastic
bending resistance of the section is therefore about 13% of
the plastic bending resistance of the web. For a 400 mm deep
I section with 180 mm wide flanges 15 mm thick and an 8 mm
thick web, the reduction in the full plastic bending resistance is
only 3% under a shear force of half the shear resistance of the
web. Figure 3 shows the relationship between plastic resistance
moment and the ratio of shear force to shear resistance of the
web for the I section discussed.
If bending about the minor axis of an I section is considered
the behaviour is similar to a rectangular section and the shear
stress is distributed parabolically over the width of the flanges
and the bending stress distribution is also non-linear. The
reduced bending resistance is given by Horne and Morris as:
Mpr = Mp1 – 0.45(τw/τy)2
where τw is the shear stress calculated on the area of the
flanges. If the shear force on the section is half the shear
resistance of the flanges then the reduced resistance moment
is about 89% of the full plastic resistance moment ie as found
earlier.
Results of tests and design rules
Despite the foregoing analysis, the results of tests and also
of advanced theory shows that there is no reduction in the
resistance moment due to the presence of shear unless the
shear force approaches the shear resistance of the section. This
is because the portions of a beam section which are subject to
both high shear and high bending stresses are limited in extent
and are surrounded by elastic zones so plastic flow is largely
prevented. The locations in a structure where both bending and
shear may be significant are limited: the root of a cantilever and
at the central support of a two–span beam are two possible
locations.
The design rules in BS 5950-1:2000 and BS EN 1993-1-1 adopt
a safe approach to the effect of shear force on the resistance
moment and allow the full plastic resistance moment to be
used in conjunction with a shear force of up to half the shear
resistance of a beam. In fact BS 5950 was slightly more generous
than EC3 and no reduction in bending resistance was required for
shear force up to 60% of the shear resistance. The contribution of
the shear area of the section to the bending resistance is reduced
when the shear force on the section exceeds half the shear
resistance. Figure 4 shows the percentage reduction in resistance
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Figure 2 Effect of shear force on plastic moment of resistance
of an I section
Figure 3 Reduction in plastic resistance moment for increasing ratio of
shear force to shear resistance
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/Member_design#Shear
/Design#BS_5950
/Design_codes_and_standards#General_rules_and_rules_for_buildings
/Design_codes_and_standards#Eurocode_3_-_Steel_structures
