design of compression members · 2020. 3. 20. · columns and other compression members •the...
TRANSCRIPT
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DESIGN OF COMPRESSION MEMBERS
Sheela MalikAP (Civil)GITAM Kablana
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INTRODUCTION
• Compression members:
short or long
• Squashing of short column
• Buckling of long column
• Steel members more
susceptible to buckling
compared to RC and PSC
members
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Columns and Other Compression Members
• The strength of steel compression members is usually limited by their tendency to buckle.
• The load at which a compression • The load at which a compression member becomes unstable is the buckling load.
• The buckling load depends on the length, cross-section, and end conditions of the column and the stiffness of the material.
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ELASTIC BUCKLING OF EULER COLUMN
Assumptions:
• Material of strut - homogenous and
linearly elastic
• No imperfections (perfectly straight)
• No eccentricity of loading
• No residual stresss
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The governing differential equation is
02
2
yEI
P
dx
yd cr .
x
y
Pcr
ELASTIC BUCKLING OF EULER COLUMN
x2
2
EIPcr
Lowest value of the critical load
2
2
2
2
2
22
2
2
)/(
E
r
ErE
A
IE
A
P
cr
cr
cr
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axially loaded initially straight pin-ended column
B1f
f yA
Plastic yield defined
by ff = y
Elastic buckling ( cr )
defined by
A C
STRENGTH CURVE FOR AN IDEAL STRUT
Column fails when the compressive stress is greater than or equal to the values defined by ACB.
AC Failure by yielding (Low
c = /r
defined by 2 E / 2
B
AC Failure by yielding (Low slenderness ratios)
CB Failure by bucking ( c )
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f /fy
1.0 Elastic buckling
Plastic yield
STRENGTH CURVE FOR AN IDEAL STRUT
= (fy/cr )1/2
1.0
Strength curve in a non-dimensional form
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FACTORS AFFECTING STRENGTH OF A COLUMN IN PRACTICE:
• Effect of initial out of straightness
• Effect of eccentricity of applied
loading
• Effect of residual stress
• Effect of a strain hardening and the
absence of clearly defined yield
point
• Effect of all features taken together
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Residual stresses in flanges
Residual stressesin web
Residual Stresses
Residual stresses distribution (no applied load)
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INTRODUCTION
c
fy
Test data (x) from collapse testson practical columns
Euler curvex
x xxx
xx
x x x
x x
200
Typical column design curve
Design curve
Slenderness (/r)
x
xx
x x
x x
x xx x
100
50 100 150
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(a) Single Angle (b) Double Angle (c) Tee
Cross Section Shapes for Rolled Steel Compression Members
(d) Channel (e) Hollow Circular Section (CHS)
(f) Rectangular HollowSection (RHS)
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(b) Box Section (c) Box Section(a) Box Section
Cross Section Shapes for Built - up orfabricated Compression Members
(d) Plated I Section (e) Built - up I Section (f) Built-up Box Section
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Cross Section Limits Buckling about axis
Buckling Curve
Rolled I-Sections h/b > 1.2 : tf 40 mm
40 < tf
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7.1 DESIGN STRENGTH
Buckling Curves
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1fc
d/f
y
a
b
c
d
TABLE 7.1 IMPERFECTION FACTOR, α
Buckling Class a b c d
0.21 0.34 0.49 0.76
0
0.1
0.2
0.3
0 0.5 1 1.5 2 2.5 3Lamda
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Effective Length of Compression Members
Boundary Conditions
Schematic represen
-tation
Effective Length
At one end At the other end
Translation Rotation Translation Rotation
Restrained Restrained Free Free
2.0L
Free Restrained Restrained FreeFree Restrained Restrained Free
Free Restrained Free 1.0L
Restrained Restrained Free Restrained 1.2L
Restrained Restrained Free 0.8L
Restrained Restrained Restrained 0.65 L
Restrained
Restrained
Restrained
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• Angles under compression
– Concentric loading - Axial force
1. Local buckling
2. Flexural buckling about v-v axis
3. Torsional - Flexural buckling about u-u axis
– Eccentric loading - Axial force & bi-axial moments
BEHAVIOUR OF ANGLE COMPRESSION MEMBERS
V
V U
U
– Eccentric loading - Axial force & bi-axial moments
– Most practical case
– May fail by bi-axial bending or FTB
– (Equal 1, 2, 3 & Unequal 1, 3)
V
V U
U
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ANGLE STRUTS
Basic compressive strength curve
• Curve C of Eurocode 3 • Slenderness Ratio:
concentric loading kL/r
Single leg Connection (kl/r)eqSingle leg Connection (kl/r)eq
Equivalent normalised slenderness ratio
Where, k1, k2, k3 are constants to account for different end conditions and type of angle.
23
221
2 kkk vve
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LACED AND BATTENED COLUMNS
(a) Single Lacing (b) Double Lacing (c) Battens
Built-up column members