Topic 8 - steel columns
Transcript of Topic 8 - steel columns
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Topic 8 Columns Design
Prof Dr Shahrin Mohammad
Structural Steel and Timber Design SAB3233
Structural Steel Design
Topic 1 -‐ Overview
Topic 4 – Design of steel structures (BS EN 1993)
Topic 3 –AcKons on
Structures (BS EN 1991)
Topic 5 – Cross-‐secKon
classificaKon
Topic 2 -‐ Basis of Structural Design (BS EN 1990)
Topic 6 – Laterally restrained beams
Topic 7 – Laterally unrestrained beams
Topic 8 – Columns Design
Topic 9 – Trusses
Topic 10 -‐ ConnecKons
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Columns subjected to axial load
Prof Dr Shahrin Mohammad
Structural Steel and Timber Design SAB3233
Mx,t My,t
x
y
Mx,b
My,b Squashing, normally occurs in short column
Overall flexural buckling
Torsional buckling
Local buckling
NEd NEd NEd NEd NEd
NEd = Design value of compression force
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! compression members subject to § axial compression only § no bending
! however in pracKcally real columns are subject to § eccentriciKes of axial loads § transverse forces
! the treatment disKnguishes between § stocky columns, and § slender columns
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Stocky columns The characterisKcs of stocky columns are
• very low slenderness • unaffected by overall buckling
The compressive strength of stocky columns is
• dictated by the cross-‐secKon • a funcKon of the secKon classificaKon
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Slender Steel Columns
Slender columns present a quasi elasKc buckling behaviour
Euler criKcal stress λ = Lcr / r, where r is radius of gyraKon
Lcr is the buckling length
2
2
λπ
σE
cr =
Failure by yielding
Failure by buckling
Euler buckling curve
λ
σ
fy
λ1
Euler buckling curve and modes
of failure
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Behaviour of real steel columns
q columns of medium slenderness are very sensiKve to the effects of imperfecKons
q inelasKc buckling occurs before the Euler buckling load due to various imperfecKons § iniKal out-‐of-‐straightness § residual stresses § eccentricity of axial applied loads § strain-‐hardening
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Effects of imperfecKons
• structural imperfecKons most important for intermediated columns
• this represents most pracKcal columns
• lower bound curve is obtained from a staKsKcal analysis of test results
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Effect of imperfecKons in relaKon to slenderness
Slender column ⚈ largely unaffected by imperfecKons ⚈ ulKmate failure load ≈ Euler load (Ncr) ⚈ independent of the yield stress
Intermmediate column ⚈ imperfecKons important ⚈ failure load less than Euler load ⚈ out-‐of-‐straightness and residual stresses are the most significant imperfecKons
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Residual stresses pa_erns
Typical residual stress pa_ern
y
y
y
0 , 3 f
0 , 2 f
0 , 2 f
∼
∼
∼ compression
tension
compression
+ =
σ R N / A σ n f y < σ n f y
f y
o r =
reaching
CombinaKon with axial stresses
• combined with axial stresses cause yielding • effecKve area reduced
Modify
IniKal out-‐of-‐straightness
! induces bending moments
Yielded zones
Combined effect of imperfec0ons and axial load
! bending stress σB ! residual stress, σR ! applied axial stress, NEd/A
+ +
P / A σ R
=
σ B σ max
NEd
NEd
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Buckling resistance in axial compression
The design buckling resistance of a compression member
Nb.Rd = χAfyγM1
1.
M
yeff
Rdb
fAN
γχ=
for Class 1, 2 and 3 cross secKon
for Class 4 cross secKon
where χ a reducKon factor and is related to the reference slenderness Buckling curves plo_ed as χ versus reference slenderness raKo
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European buckling curves (Cl 6.3.1.2)
Ncr is the elastic critical force for the relevant buckling mode based on the gross cross sectional properties.
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European buckling curves
Based on experiment more than 1000 tests secKon Range of slenderness raKos between 55 and 160
• Based on a half sine-‐wave geometric imperfecKon = L/1000
• residual stresses related to secKon type
• 4 curves apply to different cross-‐secKon types corresponding to different values of the imperfecKon factor α
Modify
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ImperfecKon factor a
• α depends on § the shape of the column cross-‐secKon § the direcKon of buckling (y or z axis) § the fabricaKon process (hot-‐rolled, welded or cold-‐formed
• imperfecKon factors given in Table 6.1
Non dimensional slenderness, ___λ
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SelecKon of appropriate buckling curve
Table 6.2 helps with the selection of the appropriate buckling curve
Modify
Example 1 : Design of an axially loaded column
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Columns subjected to combined
bending and axial load
Prof Dr Shahrin Mohammad
Structural Steel and Timber Design SAB3233
Mz,t
y
z
My,t Mz,t
My,b
Mz,b
y
z
My,t Mz,t
My,b
Mz,b
y
z Pin
connecKon Pin
connecKon Pin
connecKon
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Mz,t
y
z
My,t Mz,t
My,b
Mz,b
y
z
My,t Mz,t
My,b
y
z Mz,b
My,b
Mz,b
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simple construcKon
‘Simple construcKon’ is commonly used for the design of mulK-‐storey buildings
• Beams are designed as simply supported
• Columns are designed for nominal moments arising from the eccentricity at the beam-‐to-‐column connecKon.
NEd
Nb,z,Rd
+My,Ed
Mb,Rd
+1.5 Mz,Ed
Mc,z,Rd
≤1
The moment components are small for simple construcKon, the interacKon factors can be conservaKvely simplified to :
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Example 1 : Design of column with combined bending and axial load
Thank You