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Diseño de Estructuras de Acero. Diseño de elementos sometidos a carga axial.
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Design of Steel Structures
Design of Axial Members
Naveed Anwar, Buddhi Sharma
ACECOMS, AIT
Co-sponsored by:
Siam Yamato Steel Co., Ltd.
ACECOMS: Design of Steel Structures -
Axial Members: Strut-Tie
Tension Members
Compression Members
Axial Members
ACECOMS: Design of Steel Structures -
Cross-section Shapes
• Shapes used for this Seminar and SYSSoftware
– Wide Flange, W = H
– Narrow Flange, S, M = I
– Tees, WT, TH = T
– Angles
• Equal Angle Single: L, EL
• Unequal Angle Single : UL
• Double Angle : ELL, ULLS, ULLL
– Built-up Channels
• Back to Back: CCI
• Box : CCB
ACECOMS: Design of Steel Structures -
Tension Members
• Common Usage
– Tie Rods, Sag Rods
– Tension Members in Trusses
– Tension Members in Bracing
• Critical Considerations
– Tensile stresses
– Effective Area
– Yield Strength, Fy
– Ultimate Strength, Fu
– Connections
Tension Members
ACECOMS: Design of Steel Structures -
Basic Governing Equations
gyt AFP 6.0
eut AFP 5.0
Smaller of the following Capacities
Pt = Capacity in Tension
Fy = Yield strength of steel
Fu = Ultimate strength of steel
Ag = Gross cross-section area
Ae = Effective area in tension
An = Net cross-section area
U = Area reduction factor
x = Distance between centroid
and shear plane of connection
L = Length of connection
ne AUA
L
xU
1
Where
ACECOMS: Design of Steel Structures -
Overall Design Process
Pt, Fy,, Fu , L Compute Ag1 Determine U
Compute Ae
Compute Ag2
Accept Section
Design OK
Select
Section
Determine K
Kl/r < 300
Compute KL/r
max2
1
g
g
g A
AA
U
AA e
g 2
y
tg
F
PA
6.01
u
te
F
PA
5.0
Tension Members
Apply Net Area
Correction
ACECOMS: Design of Steel Structures -
Overall Design Process
1. Compute Ag1 based on Yield Criteria (Fy)
2. Compute Ae based on Fracture Criteria (Fu)
3. Select Area Reduction Factor, U
Based on connection type etc ( U = 0.75 - 1.0)
4. Compute Ag2 based on Ae from step 3
5. Select section to satisfy higher of Ag1 and Ag2
6. Check for other end connection requirements
Tension Members
ACECOMS: Design of Steel Structures -
Net Effective Area, Ae
• Why Net Effective Area?
To account for efficiency of end connections
Shear lag effect caused by partial connection and
uneven stress distribution
Many other factors that affect connection strength
• How to Calculate?
Tension Members
For Bolted and Riveted Connections, Ae = U An
For Welded Connections, Ae = U Ag
AgAnAg = Gross Area
An = Net area after holes
Ae = Effective Area
ACECOMS: Design of Steel Structures -
General Effective Area Factor, U
L
X X
X
X
connectiontheofLengthL
planesheartheandAreaconnectedthe
ofCentroidBetweenceDisx
L
xU
tan
1
X
ACECOMS: Design of Steel Structures -
WF Bf/ d>2/3
Ae
=0.75 An
Single or Double
Angle
Ae
=0.85 An
WT Bf/ d>2/3
Ae=0.90A
n
WF Bf/ d<2/3
Ae=0.85A
n
WF Bf/ d<2/3
Ae=0.75A
n
Single or Double
Angle
Ae
=0.75 An
Bar or Plate
Ae =An
WF Bf/ d>2/3
Ae=0.9A
n
Effective Area Factor, U
Tension Members
Typical Values of U for various cases
ACECOMS: Design of Steel Structures -
Area Reduction Factors
Special Cases for Welded Connections
A - For any H, I, T connected by transverse welds alone
U = 1.0, Ae = area of connected element
B - For plates and bars connected by longitudinal welds
alone, values of U depending upon the relative length of
the weld and their spacing
U=1.0 for l >= 2w
U=0.87 for 1.5 =< l < 2w
U=1.0 for w =< l < 1.5w
Tension Members
w
L
Only Transverse Weld
w
L
Only Logtudinal Weld
ACECOMS: Design of Steel Structures -
Axial Members: Strut-Tie
Tension Members
Compression Members
Axial Members
ACECOMS: Design of Steel Structures -
Compression Members
• Common Usage
– Struts
– Compression Members in Trusses
– Compression Members in Bracing
– Columns without significant Moment
• Critical Considerations
– Axial Stresses
– Axial- Flexural Buckling
– Flexural-Torsional Buckling
– Local Buckling
– Effective Length, kL and Slenderness Ratio, kL/r
Compression Members
ACECOMS: Design of Steel Structures -
Compression: Influencing Factors
– Grade of Steel
Stress-strain relations
Yield stress
– Manufacturing method - Residual Stresses
Hot rolled shape
Welded buil-up shape
Using flame-cut plates
Using universal mill plates
Cold-straightened shape
Rotorizing ( continuous straightening )
Gag ( point ) straightening
Compression Members
ACECOMS: Design of Steel Structures -
Compression: Influencing Factors
– Size and Properties of section ( Ag, rx, ry )
– Cross section geometry ( W, H, C,WT etc )
– Bending axis (Major or minor)
– Initial out-of-straightness
Maximum value
Distribution along column length
– Framing and End support conditions
Without sway, pinned or otherwise
With sway, pinned or otherwise
Restrained ends, with or without sway
Unsupported Member Length
Compression Members
ACECOMS: Design of Steel Structures -
Basic Strength Equation
'
asaa FQQF
aF
aQ
sQ
= Permissible stress as determined by bend buckling
criteria (based on basic equations without Qa ad Qs)
= Effective area correction factor
= Stress reduction factor based on width-thickness ratio
ga AFP P = Axial Capacity of Member
Fa = Permissible stress
Ag = Gross cross-section Area
Compression Members
ACECOMS: Design of Steel Structures -
Basic Strength Equation
gasa AFQQP'
Compression Members
Permissible stress as determined
by bend buckling criteria
ACECOMS: Design of Steel Structures -
Determination of Fa
For compression members, the critical (ultimate) stress,
including the effect of Residual Stresses, Initial Imperfections
and other non-linear factors is given by the general equation:
2
/
2
11
c
ycrC
rkLFF
c
v
ccr
a
Cr
kLfor
r
kLfor
FOS
F
EC
FOS
FF
92.1
067.1
2,
'
For AISC/ASD
ACECOMS: Design of Steel Structures -
Determination of Fa’
Fy
ECc
2
3
2
'
/
8
1/
8
3
3
5
/
2
11
cc
c
y
a
C
rKL
C
rKL
C
rKLF
F
Compression Members
2
2'
23
12
r
KL
EFa
r
KLCact .max
Cact >= Cc
Slender
Y
• Takes into account Section
Size, Length, End
Conditions etc.
• Main Problem is the
Effective Length Factor “K”
ACECOMS: Design of Steel Structures -
Effective Length Factor, K
• To account for “Axial-Flexural Buckling”
• Indicates the “total bent” length of column between
inflection points
• Can vary from 0.5 to Infinity
• Most common range 0.75 to 2.0
0.5 1.02.0
0.5 - 1.0 1.0 -
Compression Members
ACECOMS: Design of Steel Structures -
K Factor Examples
Model Example Factor
1.0
0.85
0.7
2.0
1.0
Compression Members
ACECOMS: Design of Steel Structures -
Determination of K
• Isolated Members
Fix Pin Free
Fix 0.5 0.8 2.0
Pin 0.8 1.0 Unstable
Free 2.0 Unstable UnstableBott
om
En
d
Top End
Compression Members
ACECOMS: Design of Steel Structures -
Determination of K
• Members Part of Framed Structure
IncreasesKIncreaseGGK
BeamsLEI
ColumnsLEIG C
,
)/(
)/(
2120
20
mm
m GforGG
K
2)1(9.0 mm GforGK
0.105.085.0
0.1)(05.07.0
m
BT
Gk
GGK
Unbraced
Frames
Braced
Frames
(smaller of)
BTm
B
T
GandGofMinimumG
EndBottomG
EndTopG
Compression Members
ACECOMS: Design of Steel Structures -
Basic Strength Equation
Compression Members
gasa AFQQP'
Stress reduction factor based on width-thickness ratio
To account for Local Buckling of Un-Stiffened Plates
ACECOMS: Design of Steel Structures -
• Accounts for “Local Plate Buckling”
• Governed by “Thinnest” (max b/t)
Un-stiffened element
Stress Reduction Factor, Qs
K = Factor based plate boundary
E = Modulus of Elasticity
b = Width of plate
t = Thickness of plate
m = Poison Ratio = 0.3
2
2
2
112
t
b
EKPcr
m
2/
9.0,
tb
KEPor cr
The codes use various limits on (b/t ) to specify some empirical
values of stress reduction factor in terms of Fy to take into
account post-buckling strength of un-stiffened elements
Compression Members
ACECOMS: Design of Steel Structures -
Stress Reduction Factor, Qs
y
yy
y
s
Ffor
FFforF
Q155
t
b
(b/t)F
15,500
155
t
b76
t
b 00447.0340.1
2
y
y
yy
y
s
Ffor
FFforF
Q195
t
b
(b/t)F
20,000
195
t
b95
t
b 00437.0415.1
2
y
y
yy
y
s
Ffor
FFforF
Q176
t
b
(b/t)F
20,000
176
t
b127
t
b 00715.0908.1
2
y
For stems of tees
For projecting
elements of
compression flanges
of columns and beams
For single angles
Compression Members
ACECOMS: Design of Steel Structures -
Qa for Fy = 2400 Ksc (34 ksi)
3.26t
b
(b/t)
446.7
3.26t
b9.12
t
b 026.0340.1
2for
for
Qs
1.33t
b
(b/t)
576.4
1.33t
b1.16
t
b 0257.415.1
2for
for
Qs
9.29t
b
(b/t)
576.4
9.29t
b6.21
t
b 0421.0908.1
2for
for
QsFor stems of tees
For projecting
elements of
compression flanges
of columns and beams
For single angles
Compression Members
ACECOMS: Design of Steel Structures -
Basic Strength Equation
Compression Members
gasa AFQQP'
Effective area correction factor to
account for Non-Linear Stress Distribution on Stiffened Elements
ACECOMS: Design of Steel Structures -
Effective Area Factor, Qa
• To account for “Non-uniform, Non-linear, Post-buckling
Stress Distribution” or “Karman” effect
• Governed by “Thinnest” (max. b/t) stiffened element
• Effective Area, Ae
– for “Un-stiffened” elements of the section, be = b
– for “Stiffened” elements, be must be computed
g
ea
A
A
AreaGross
AreaEffectiveQ
Compression Members
tbA ee
ACECOMS: Design of Steel Structures -
Effective Area Factor, Qa
Compression Members
Non-linear Compressive Stress
Distribution in Stiffened Elements
Stiffened
Element
Un-Stiffened
Element
be = 1
be/2
ACECOMS: Design of Steel Structures -
Effective Plate Width, be
Compression Members
bftbf
tbe
)/(
9.641
326
bftbf
tbe
)/(
2.571
326
For flanges of rectangular box sections
Other uniformly compressed stiffened elements
f = P/Ag for columns (in ksi)
f = M/Sx for beams (approx.) (in ksi)
ACECOMS: Design of Steel Structures -
Effective Area Factor, Qa
• Example:
Compression Members
b e2
2
b e2
2
b2 t2
t1
b1
2211
2211
2
2
tbtb
tbtbQ e
a
ACECOMS: Design of Steel Structures -
Design Steps
1. Assume a trial section by judgement and experience or by
using design aids
2. Assume Qa=1.0 for first trial
3. Compute Qs based on the specification formula
4. Compute the critical slenderness ratio Cc
5. Assume or compute the Kx and Ky by using alignment chart
or equations.
6. Compute Cact , the highest KL/r
7. Compute Fa based on Cc and Cact
Compression Members
ACECOMS: Design of Steel Structures -
Design Steps
8. Revise the value for Qa by using new value for Fa .
If the new Qa is same as assumed then accept Fa (Go to
next step) otherwise revise the Fa ( Go back to step 4 ).
Repeat the procedure until the desired accuracy is obtained.
9. Compute the capacity based on gross area and the Fa
computed from step 8
10. If the section capacity is more than or equal to the required
capacity accept the section otherwise try new section and
repeat the whole calculation until suitable section is found
Compression Members
ACECOMS: Design of Steel Structures -
Compute Fa
Overall Design Process
P, W, Fy, LSelect
SectionDetermine K
Assume Qa,
Compute Qs
Compute Cc
Compute Cact
Compute Fa
Compute Qa2Qa2 ~ QaCompute Pn
Pn > PAccept Section
Design OKQa2= Qa
Compression Members
ACECOMS: Design of Steel Structures -
The Stress Ratio Components
0.1 bybxa RRRR
a
aa
F
fR
'
asaa
g
a
FQQF
A
Pf
ACECOMS: Design of Steel Structures -
Unsymmetrical Sections
• Special Considerations for
• Angle, Double Angle, Tee, Zee etc
• Covered by special methods and specifications
Compression Members
ACECOMS: Design of Steel Structures - Compression Members