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Calc. No.
CALCULATION SHEET
Project No.
Project Title:
Calc. By
Date
Rev.
Subject:
Steel beam capacity calculation in accordance with the "Manual of Steel Construction" Load and Resistance Factor Design" (LRFD)
Beam Design for Flexure and Lateral-Tortional Buckling.
Section properties
Braced length
Section
L
b
=
150
in
A =
in
2
beam cross-sectional area
L
b
- distance between points braced against lateral
I
y
=
in
4
moment of inertia about Y axis
displacementof the compression flange or between
S
x
=
in
3
elastic section modulus - major axis
points braced to prevent twist of the cross section.
r
y
=
in
radius of gyration about minor axis
(This parameter can not be mdoified in the Demo Version)
J =
in
4
tortional constant
C
w
=
in
6
warping constant
Z
x
=
in
3
Steel properties
E =
ksi
modulus of elasticity of steel
per Manual of Steel Construcion (LRFD)
G =
ksi
shear modulus of elasticity of steel
Chapter F Section 2.a
F
y
=
ksi
minimum yield stress of the type of steel being used
F
yf
=
ksi
yield stress of flange
F
yw
=
ksi
yield stress of web
F
r
=
ksi
compressive residual stress in flange for rolled shapes F
r
= 10 ksi, for welded shapes F
r
= 16.5 ksi
C
b
=
bending coefficient dependent upon moment gradient C
b
is permitted to be conservatively taken as 1.0
f
b
=
resistance factor for flexure
Yielding flexural design strength
per Manual of Steel Construcion (LRFD)
M
p
=
F
y
* Z
x
=
kip-ft
plastic section moment < 1.5 M
y
Chapter F Section 1.
1.5*M
y
= F
y
* S
x
=
kip-ft
M
n
= M
p
=
kip-ft
f
b
* M
n
=
kip-ft
Yielding flexural design bending moment
Lateral - torsional Buckling
per Manual of Steel Construcion (LRFD)
L
r
- limiting laterally unbraced length
Chapter F
L
p
=
1.76*r
y
*sqrt(E/F
yf
) =
in
Eq. F1-4
for I shaped members and channels
F
L
=
smaller of (F
yf
- F
r
) or F
yw
F
L
=
ksi
M
r
=
F
L
* S
x
=
kip-ft
Eq. F1-7
X
1
=
(
p
/S
x
)*sqrt(EGJA/2) =
ksi
Eq. F1-8
X
2
=
4*(C
w
/I
y
)*(S
x
/GJ)
2
=
ksi
-2
Eq. F1-9
L
r
=
(r
y
*X
1
/F
L
)*sqrt(1+sqrt(1+X
2
*F
L
2
)) =
in
Eq. F1-6
for L
b
< L
r
Chapter F Section 2.a applies
M
n
=
C
b
*[M
p
-(M
p
-M
r
)*(L
b
-L
p
)/(L
r
-L
p
)] =
Eq. F1-2
f
b
* M
n
=
for L
b
> L
r
Chapter F Section 2.b applies
M
n
=
M
cr
M
cr
=
C
b
*S
x
*X
1
*sqrt(2)/(L
b
/r
y
)*sqrt(1+X
1
2
*X
2
/(2*(L
b
/r
y
)
2
)
M
cr
=
f
b
* M
n
=
References:
Manual of Steel Construction - American Institute of Steel Construction Inc., 2005
