ALLOWABLE STRESS DESIGN FLOWCHART
FOR
AISC MANUAL OF STEEL CONSTRUCTION, NINTH EDITION
APPENDIX A
ALLOWABLE NORMAL STRESS CALCULATION
SHEN-YEH CHEN, PH.D.
Aug, 1995
All Rights Reserved. No part of this book may be reproduced for commercial purpose, in any form or by any
means, without permission in writing from the author.
1
DISCLAIMER AND COPYRIGHT NOTICE
The author makes no warranty of any kind, expressed or implied, with regard to any text, the algorithms and the program contained in this
book. The author shall not be reliable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing,
performance, or use of this text, algorithms and programs.
You may distribute this documentation for educational purpose, provided that none of the text in this documentation has been modified or
deleted. This includes, but not limited to, cover page, disclaimer and copyright notice and all remaining pages. For commercial usage of this
documentation, the reader should contact the author directly for details. If you use any information in this documentation, you need to refer to this
documentation, or the following reference
S-Y. Chen, December 1997, Using Genetic Algorithms for the Optimal Design of Structural Systems, Dissertation for Doctor of Philosophy,
Department of Civil Engineering, Arizona State University.
2
BENDING : I & CHANNEL : X-AXIS
lb ≤ Lc
Hybrid Girder or Fy ≥ 65ksi
NOT Hybrid, and Fy ≤ 65ksi
bf
95
>
2∗ t f
F
bf
95
>
2∗ t f
Fy
⇒ slender section (1)
bf
95
≤
2∗ t f
Fy
⇒ Fb = 0.6∗ Fy
(F1-5)
⇒ slender section (1)
y
b
65
95
< f ≤
t
∗
2
f
Fy
Fy
⇒ Fb = Fy ∗[0.79 − 0.002∗
Built-Up
NOT Built-Up
bf
2∗ t f
d
satisfies Eqn(1)
tw
∗
Fy
kc
(F1-4)
]
⇒ Fb = Fy ∗[0.79 − 0.002∗
bf
2∗ t f
∗ Fy ]
(F1-3)
bf
65
≤
2∗ t f
Fy
d
NOT satisfies Eqn(1)
tw
⇒ Fb = 0.6∗ Fy *(NOTE)
(F1-5)
d
satisfies Eqn(1)
tw
⇒ Fb = 0.66∗ Fy
(F1-1)
d
NOT satisfies Eqn(1)
tw
⇒ Fb = 0.6∗ Fy *(NOTE)
(F1-5)
⎛
f
f ⎞⎞
640 ⎛
d
⎜ for a ≤ 016
. :
. − 3.74∗ a ⎟⎟ ⎟
≤
∗ ⎜⎜10
Fy
tw
Fy ⎠ ⎟
⎜
Fy ⎝
4.05 ⎞
h
⎛
⎟
⎜
⎜ IF : > 70 ⇒ k c =
0.46 ⎟
⎟
⎜
f
257
d
tw
⎛⎜ h ⎞⎟
⎟
(F1-4)
Eqn(1) : ⎜ for a > 016
. :
kc : ⎜
≤
⎟
⎝ tw ⎠
⎜
⎟
Fy
tw
Fy
⎟
⎜
⎜
⎟
⎟
⎜
.
⎝ ELSE : ⇒ k c = 10
⎠
⎟
⎜ f a = 0, if member is in tension
⎟
⎜ Fy
⎠
⎝
*(NOTE) : Slender section design is required only for compression elements.
3
(TBL B5.1)
(B5.2)
lb > L c
bf
95
>
2∗ t f
Fy
bf
95
≤
2∗ t f
Fy
⇒ slender section (1)
I sections
⇒ tahe the maximum of (a) & (b)
Channel
⇒ use (b)
2
⎞
⎛
⎡
⎛⎜ lb ⎞⎟ ⎤
⎟
⎜
F
∗
3
3
⎢
y ⎝ r ⎠ ⎥
T
⎟
⎜ (a ) for 120∗10 ∗ Cb ≤ lb ≤ 510∗10 ∗ Cb ⇒ F = ⎢ 2 −
⎥
F
F
0
6
.
∗
≤
∗
b
y
y
3∗
⎟
⎜
Fy
rT
Fy
⎢ 3 1530∗10 Cb ⎥
⎟
⎜
⎢⎣
⎥⎦
⎟
⎜
3
3
⎟
⎜
lb
510∗10 ∗ Cb
170∗10 ∗ Cb
⎟
⎜
F
for
0
6
.
>
⇒ Fb =
≤
∗
y
2
rT
Fy
⎟
⎜
⎛⎜ lb ⎞⎟
⎟
⎜
⎝ rT ⎠
⎟
⎜
lb
12∗103 ∗ Cb
⎟
⎜
≤ 0.6∗ Fy
⇒ Fb =
⎟
⎜ (b ) for any r
d
lb ∗ A
T
⎟
⎜
f
⎟
⎜
⎠
⎝
h∗ t w 3
2 − 36
≅
A f + Aw 6
Iy
rT =
Iy
2
A f + Aw 6
LC = min (
76 * b f
Fy
,
20000
)
( d A )* Fy
f
2
⎞⎟ + 0.3∗ ⎛⎜ M1
⎞⎟ ≤ 2.3
Cb = 175
. + 105
. ∗ ⎛⎜ M1
M2 ⎠
M2 ⎠
⎝
⎝
M1
≤ 1 ; ⎛⎜ M1 M ⎞⎟ > 0 , if M1 & M 2 cause reverse curvature ; otherwise, ⎛⎜ M1 M ⎞⎟ < 0
⎝
⎝
2⎠
2⎠
M2
(1) Cb can be conservatively taken as 10
.
( 2) when there is moment greater than M1 or M 2 ⇒ Cb = 10
.
(3) Cb should be taken as 10
. , for frame BRACED AGAINST sidesway.
4
(F1-6) & (F1-7) & (F1-8)
BENDING : I & SOLID ROUND & SOLID RECTANGULAR & SQUARE BAR : Y-AXIS
I SECTION :
Fy > 65ksi
⇒ Fb = 0.6∗ Fy
Fy ≤ 65ksi
bf
95
>
2∗ t f
Fy
b
65
95
< f ≤
∗
2
t
f
Fy
Fy
bf
65
≤
2∗ t f
Fy
(F2-2)
⇒ slender section (1)
.
− 0.005∗
⇒ Fb = Fy ∗[1075
bf
2∗ t f
⇒ Fb = 0.75∗ Fy
∗ Fy ]
(F2-3)
(F2-1)
SOLID ROUND & SOLID RECTANGULAR & SQUARE BAR :
⇒ Fb = 0.75∗ Fy
(F2-1)
5
BENDING : BOX & RECTANGULAR TUBE & CIRCULAR TUBE
BOX AND RECTANGULAR TUBE
d < 6 * bf
bf
d
95
For Compact Section :
& lb ≤ Lc &
satisfies eqn1 &
≤
2∗ t f
t f < 2 * tw
tw
Fy
⇒ Fb = 0.66∗ Fy
(F3.1)
(F3-1)
⎛d
bf
bf
119
95 ⎞⎟
or ⎜⎜ does NOT satisfy eqn1 &
or d > 6 * b f
>
>
2∗ t f
2*tf
Fy ⎟⎠
Fy
⎝ tw
⇒ slender section (2)
For Slender Section :
All Other Sections (non-compact) :
⇒ Fb = 0.6∗ Fy
(F3.2)
(F3-3)
CIRCULAR TUBE (???)
D 3300
d
For Compact Section :
≤
& lb ≤ Lc &
satisfies eqn1
tw
t
Fy
⇒ Fb = 0.66∗ Fy
All Other Sections (non-compact) :
⇒ slender section (2)
LC = (1950 + 1200
M1 b f
)*
M 2 Fy
(F3-2)
BENDING : ALL OTHER SECTIONS : Y-AXIS (1978) (???)
⇒ Fb = 0.60∗ Fy
6
BENDING OF SLENDER SECTION
⇒ Fb = 0.6∗ Fy * QS * Qa
kc :
4.05 ⎞
h
⎛
⎜ IF : > 70 ⇒ k c =
0.46 ⎟
tw
⎛⎜ h ⎞⎟ ⎟
⎜
⎝ tw ⎠ ⎟
⎜
⎟
⎜
.
⎠
⎝ ELSE : ⇒ k c = 10
Slender Section (1) : (Unstiffened element)
Qa = 1
bf
bf
95
195
Fy
<
≤
⇒ Q S = 1293
.
− 0.00309 *
*
kc
2*tf
2*tf
Fy
Fy
kc
kc
bf
26200
195
⇒ QS =
<
2
2*tf
Fy
⎞
⎛bf
Fy
kc
k c * ⎜⎝ 2 * t f ⎟⎠
(A-B5-3)
(A-B5-4)
Slender Section (2) : (Stiffened element)
QS = 1
With uniform thickness :
⎡
⎤
⎢
⎥
253 * t f
50.3
⎢1 −
⎥ ≤ 10
⇒ Qa =
.
fa + fb ⎢ ⎛ bf ⎞
⎥
⎢⎣ ⎜⎝ t f ⎟⎠ * f a + f b ⎥⎦
7
(A-B5-7)
AXIAL COMPRESSION
For slender section
⇒ slender section (1) or (2) ⇒ Find QS , Qa ⇒ Q = QS * Qa (see BENDING OF SLENDER SECTION)
S e ≤ CC
⎡
Se2 ⎤
Q ⋅ ⎢1 −
⋅ Fy
2 ⎥
⎣ 2 ⋅ CC ⎦
⇒ Fa =
Se3
5 3⋅ Se
+
−
3 8 ⋅ CC 8 ⋅ CC 3
(E2-1)
S e > CC
12 ⋅ π 2 ⋅ E
⇒ Fa =
23 ⋅ S e 2
(E2-2)
where
CC =
2⋅π 2 ⋅ E
Q ⋅ Fy
Se =
K ⋅l
r
For compact and non-compact section
S e ≤ CC
2
⎡
Se ⎤
1
⋅ Fy
−
⎢
2⎥
2 ⋅ CC ⎦
⎣
⇒ Fa =
3
S
5 3 ⋅ Se
+
− e 3
3 8 ⋅ CC 8 ⋅ CC
(E2-1)
S e > CC
⇒ Fa =
12 ⋅ π 2 ⋅ E
23 ⋅ S e 2
(E2-2)
where
2⋅π 2 ⋅ E
Fy
CC =
Se =
K ⋅l
r
*(NOTE) : Both x (major) and y (minor) buckling mode should be check, and pick the smaller one
AXIAL TENSION
Ft = min( 0.6 ⋅ Fy , 0.5 ⋅ Fu )
8
