design of steel structure due to bending-beam steel structure
TRANSCRIPT
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STEEL & TIMBERSTEEL & TIMBERSTEEL & TIMBERSTEEL & TIMBER
DESIGNDESIGNDESIGNDESIGN
DAA 3222DAA 3222DAA 3222DAA 3222
----BEAMSBEAMSBEAMSBEAMS----
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TOPIC OUTLINE
Lateral Restraint Shear & Moment Capacity
Local Buckling & Bearing
Deflection
Design Procedures
General
Not Full Restrained
Unrestrained
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LEARNING OUTCOME
Student would be able:
To identify the degree of lateral restraint To identify the shear & moment capacity of beam
structure
structure To identify the local buckling, bearing and deflection
of beam To calculate buckling resistance, bearing capacity &
buckling moment resistance To identify the degree of lateral restraint To design of beam subjected to Lateral-Torsional
Buckling
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DEFINITION
In building construction, a beam is a
horizontal member spanning an openingand carrying a load that may be a brick orstone wall above the opening
A beam is a structural member which issubject to transverse loads
MUST be designed to withstand shear &moment
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BEAMS
Purlin carries the roof load to the trusses
Raftera slopping beam carrying the roof load to thepurlins
Lintelcarries the brick or other masonry across theopening made by a door or a window
Joist one of the closel s aced beams su ortin the
flooring of a buildingStringer one of the closely spaced beams running
parallel to the roadway and supporting the flooring of abridge( also called as secondary beam)
Floor Beam the larger beam which are perpendicularto the roadway of the bridge or perpendicular to the joistof the building
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1. Jack Rafter
2. Wall Header
3. Common Rafter
4. Hip Rafter
5. Fascia
1. Floor Joist
2. Solid Blocking
3. Beam
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Figure 2: Fascia
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Figure 3: Roof System
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Figure 4: Bridge System
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TYPES of BEAM
Simple beamsupported w/out restrained
Overhanging beamfreely supported BUT extended beyond one or bothof its supports
Continuous beam
freely supported BUT extended over three or moresupports
Fixed-end beamhaving its ends fixed against rotation
Restrained beampartially fixed at one or both ends
Cantilever beam
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Figure 7: Beam Types With References to The Method of Support
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Types of beams load1) Concentrated loads from secondary beams
& columns
2) Distributed loads from selfweight & floor slab
Classified load
BEAM LOADS
1) Dead loads from self weight, slabs, finishesetc
2) Imposed loads from people, fittings, snow on
roof3) Wind loads mainly on purlins and sheeting
rails
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Depending on distribution loading from
slab1) Two way slab-trapezoidal & triangular loads
BEAM LOADS (contd)
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LATERAL RESTRAINT
WithoutRestraint
PartialRestraint
Full LateralRestraint
Degree of lateral restraint
-Lateral torsional stability isassumed adequate
-Maybe provided by the
concrete floor whichsufficiently connected tothe beam/bracing member
-D compression by loadingmake the flange is susceptible to fail by
buckling sideway-Overall moment capacity will not be reached
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Figure 8: Deform Shape of a Full Lateral-Restrained Beam
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Figure 9: Configurations of Full-Lateral-Restrained Beam
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Figure 10: Lateral-Torsional Buckling
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Figure 11: Lateral Restraint
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Figure 12: Deform Shape of A Beam W/out Full Lateral Restraint
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DESIGN FACTORS THAT
INFLUENCE THE LATERAL
STABILITY
-The length of the member between adequate lateral restraints
-The shape of cross-section-The variation of moment along the beam-The form of end restraint provided-The manner in which the load is applied, i.e. to tension or
compression
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DESIGN PROCEDURE
(General)For Ultimate Limit State:
-shear capacity(Clause 4.4.5)shear force due the design loading must not exceed
the shear capacity, the buckling due to shear action also
- moment capacity(Clause 4.2.5.2)bending moments due to the design loading must notexceed the moment capacity. The reduction moment due
to high shear and lateral torsional buckling due toinsufficient restrained also required.
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- local buckling & bearing(Clause 4.5.2 & 4.5.3)
when loads or reactions are applied through the flange to
t e we , t e oca res stance o t e we s ou not eexceeded.
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For Serviceability Limit State:
-deflection
the deflection due to the design loading should not
exceed the limits given in Table 8, BS 5950-1:2000
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FIGURE 13: FLOW CHART OF BEAM DESIGN (GENERAL)
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SHEAR CAPACITY
REMEMBER
v
be greater than shear capacity Pv
tD
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MOMENT CAPACITY
REMEMBER
The Moment due to design load M SHOULD NOT
be greater than the moment capacity Mc
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LOCAL BUCKLING &
BEARING
Figure 14: Cases where The checking of Local Buckling & Bearing Could Be
Avoided & Could Not Be Avoided
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STIFF BEARING LENGTH
- D stiff bearing length, b1 should be taken as thelength of support that cannot deform appreciably
- Assume that the load disperses at 450 through dsection elements which are firmly fixed together.
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Figure 15: Stiff Bearing Length
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BUCKLING CAPACITY
If the flange through which the load or reaction is
applied is effectively restrained against botha) rotational relative to the web
Then, provided that d distance ae from d load or
reaction to the nearer end of the member is atleast 0.7d
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Figure 16: Buckling Capacity of An Unstiffended Web
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Figure 17: ae & Appropriate Formula For Buckling Resistance
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EXAMPLE
BEAM SUBJECTS T
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BEAM SUBJECTS To
LATERAL-TORSIONALBUCKLING
The beam w/out full lateral restrain aresusceptible to lateral torsional buckling
Generally, it need not be checked separately The ultimate moment capacity & shear capacity
should be checked before the lateral torsional
buckling D bending strength pb is dependent on the
design strength py
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FIGURE 14: FLOW CHART OF DESIGN FOR UNRESTRAINED BEAM
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General Principles of Lateral TorsionalBuckling
- Is governed by its unrestrained length and itsslenderness.
- Occurs when the bending moment M reaches theelastic critical moment Mcr.
- Idealized case, failure only occur by buckling when
orcrMM 0.1/ crMM
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Effective Length LE & Equivalent Segment
Length LLT
- Th l n h l n h h m r i l h
beam is to lateral torsional buckling.- But the susceptibility to lateral torsional buckling
may be limited by the end restraints & the
intermediate restraints
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Figure 17: A Simple Beam Without Intermediate Lateral Restraint
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Equivalent Slenderness
- Generally, for I & H section (cl. 4.3.6.7)
Buckling Moment Resistance
- Generally, for I & H section (cl. 4.3.6.4)
LT
bM
qu va en n orm omen
- For normal loading, the equivalent uniform moment factorfor lateral-torsional buckling mLT should be obtained fromTable 18 for the pattern of major axis moments over the
segment length LLT.- Purpose- to indicate one of the major parameter in
determining elastic critical moment Mcr
LTm
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GJL
EHGJEI
Lm
M ycr 2
2
11
+=
m is mLTL is either LE or LLTEIy is flexural rigidity about y-axis
G is shear constantJ is torsional constantE is modulus of elasticH is warpin section constant H=I h2/4
-The criterion of the beam to pass the lateral-torsional
buckling checking is:
LTbx mMM / cxx MM &
Mcx is the major axis moment capacity of the cross sectionMx is the maximum major axis moment in the segment
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EXAMPLE
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HAPPY ENDING