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CIVN 3030A: Civil Engineering Theory (III)
LT 06: Resistance of steel beams and plate girders
Presenter: Dr Matongo Kabani
Module Content
Overview of module
Lecture 6: Resistance of steel beams and plate girders
V Resistance of laterally restrained beams
V Resistance of laterally unrestrained beams
V Shear resistance
V Bearing capacity under concentrated loads
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Learning Outcomes
On completion of this module, students should be able to:
V Understand different modes of failure for beams and plate girders
V Shear resistance for beams and plate girders
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LT 6: Resistance of steel beams and plate girders
Introduction
Beams are structural members which transfer the transverse loads
they carry to the supports by bending and shear actions. Beam crosssections may take many different forms, with the most common
being hot rolled parallel and taper flange sections. The capacity of
a beam can be increased by adding sections to it to form compound
sections.
The most common compound sections are crane girders which can
be readily obtained in South Africa. Other custom made sections
such as plate girders, tapered beams and castellated beam can be
fabricated readily
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LT 6: Resistance of steel beams and plate girders
Introduction
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LT 6: Resistance of steel beams and plate girders
Introduction
The design of beams involves an analysis to determine the maximum
factored applied moments and shear and compare with factored resistance. The moment resistance depends on the controlling limit
states such as local buckling, lateral torsional buckling, the elastic
or plastic capacity.
Local buckling can significantly reduce a section’s load carrying capacity. Local buckling happens because part of a beam will be
subjected to flexural induced compression. The likelyhood of local buckling happening is determined through section classifications
similar to what was done for compression members.
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LT 6: Resistance of steel beams and plate girders
Steel beam failure modes
The moment resistance of a beam is governed by the following failure
modes:
V Local buckling of compression flange
V Local buckling of the compression region of the web
V Full yielding of cross-section leading to plastic hinge formation.
V Lateral-torsional buckling (LTB) of compression flange of the
beam.
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LT 6: Resistance of steel beams and plate girders
Steel beam failure modes
V Whether in the elastic or plastic material range, the crosssectional resistance and rotation capacity are limited by the effects
of local buckling;
V Local buckling checks are done through crosssection classification;
V The classifications put steel sections into Class 1, Class 2, Class
3 and Class 4.
The global failure modes of beams such as yielding or cross-section
or lateral torsional buckling of compression flange depend on whether
the compression flange has continuous lateral restraint or not.
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LT 6: Resistance of steel beams and plate girders
Continuously laterally supported beams
Continuous restraint of compression flange can be provided by a slab
as in the case of composite construction.
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LT 6: Resistance of steel beams and plate girders
Continuously laterally supported beams
Continuous restraint of compression flange can be provided by a slab
as in the case of composite construction.
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LT 6: Resistance of steel beams and plate girders
Continuously laterally supported beams
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LT 6: Resistance of steel beams and plate girders
Beams that are not continuously laterally supported
This instability also known as lateral torsional or flexural torsional
buckling is caused by the instability in compression moving laterally
while the tension part prevents the lateral movement thus causing a
twist. Lateral torsional buckling is a key design consideration consideration for beams. Slender beams under moments without lateral
restraints will fail through this lateral torsional buckling. However
if lateral restraints are provided, the beam can fail through inelastic
buckling or material yielding if the slenderness ratios of flanges and
webs do not permit local buckling to occur first.
Lateral restraints in beams used in composite construction may be
provided by the concrete deck. However, such beams by still be
vulnerable to buckling during construction.
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LT 6: Resistance of steel beams and plate girders
Beams that are not continuously laterally supported
Lateral torsional mode
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LT 6: Resistance of steel beams and plate girders
Beams that are not continuously laterally supported
The areas where lateral torsional buckling can occur are shown below.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of beams and girders
For short span beams or those carrying concentrated loads, shear
capacity becomes the dominant design consideration.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of beams and girders
However, in most cases, the bending effects are dominant and in
general beams and girders will be designed for flexural resistance
and then checked for shear. Shear in plate girders is carried by the
webs and therefore greatly influenced by the slenderness of the web.
The capacity of an unstiffened web of an I-beam or plate girder
progressively reduced as web slenderness increases. The web failure
can be grouped into the following:
V Plastic yielding which occurs for class 1 and class 2 sections
(compact sections)
V Inelastic buckling of the web in beams and girders in sections
where these are class 3 (noncompact).
V Elastic buckling for slender webs which overs sections in class
4
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LT 6: Resistance of steel beams and plate girders
Shear resistance of unstiffened webs
Web yielding: Webs that are in class 1 and 2 fail through material
yielding as this occurs at a lower stress than critical buckling stress.
The web in an I section will be elastic until and as the stress is
increased, plastification will increase until the whole web has yielded.
Figure 1: Web failure through yielding
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LT 6: Resistance of steel beams and plate girders
Shear resistance of unstiffened webs
Web buckling: Plate girders usually have deep thin webs prone to
buckling. When a web panel shown below is subjected to increasing
shear, the principle compression along diagonal will reach a critical
value and eventually lead to plate buckling.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of unstiffened beams
The buckling of web under shear loads can be increased through the
following:
V Reducing the depth to thickness ratio of the web.
V Providing web stiffeners to form panels that increase shear resistance. The critical elastic buckling can be significantly increased by using either transverse stiffeners.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of unstiffened beams
Figure 2: Shear strength and web slenderness for unstiffened beams
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LT 6: Resistance of steel beams and plate girders
Shear resistance of stiffened beams
The shear and bearing capacity of beams can be significantly increased through addition of stiffeners to the web.
Figure 3: Stiffened girders
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LT 6: Resistance of steel beams and plate girders
Shear resistance of stiffened webs
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LT 6: Resistance of steel beams and plate girders
Shear resistance of stiffened webs
Figure 4: Plate girder stiffeners)
Stiffeners are classified based on their role as follows:
V Bearing stiffener: These are placed in pairs where at supports
and areas where there are high concentrated forces.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of stiffened webs
Stiffeners are classified based on their role as follows:
V Intermediate transverse stiffener: These are provided to increase shear strength by increasing buckling stress of the web
and may be provided as pairs on opposite sides of webs or only
on one side.
V Torsional stiffeners: These are provided at supports to restrain
against torsional effects.
V Longitudinal stiffeners: They are provided to increase buckling resistance of the web.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of stiffened webs
The length of the zones with stiffeners depends on the spread of the
load and the shear force diagram.
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LT 6: Resistance of steel beams and plate girders
Shear resistance of stiffened webs
In general the shear resistance for a stiffened beam is shown below.
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LT 6: Resistance of steel beams and plate girders
Lecture Summary
V The main failure modes for beams include local buckling of
compression flange, local buckling of web, yielding of crosssection or lateral torsional buckling.
V Beams under transverse loads can fail through lateral torsional
buckling. This failure mode can be prevented by providing restraints to the compression flange
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