Mathcad - AISC Torsional Design LRFD AND ASD (Pinned - Pinned)

12 Pages·2008·0.09 MB·English

AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 1
ASD (Pinned - Pinned) Case.xmcd
1.0 TORSIONAL MEMBER (BI-AXIAL BENDING) PINNED-PINNED CASE)
Thu Dec 18 7:32:17 PM 2008
e := Eccentricity of Loads About Neutral X-Axis in Inches (This is
x
0 assumed to be the same for all Loads)
e := Eccentricity of Loads About Neutral Y-Axis in Inches (This is
y
3 assumed to be the same for all Loads)
Thu Dec 18 7:32:45 PM 2008
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 2
ASD (Pinned - Pinned) Case.xmcd
Refers to External Loads
Refers to External Loads
Section's Bending
Capacity Determinant
Section's Shear Capacity
Determinant
Design Philosophy (Load Combinations
and Resistance Factors Determinant)
1
Design Safety Factor
Thu Dec 18 7:33:04 PM 2008
w
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 3
ASD (Pinned - Pinned) Case.xmcd
L :=
Beam Total Length of Beam in Feet
25
L :=
Torque1
7.5 Location of First Torque in Feet From Support A
NumberOfTorques
L :=
Torque2
17.5 Location of Second Torque in Feet From Support A
NumberOfTorques
L :=
Torque3
0 Location of Third Torque in Feet From Support A
NumberOfTorques
L :=
Torque4
0 Location of Fourth Torque in Feet From Support A
NumberOfTorques
Thu Dec 18 7:33:26 PM 2008
Unbraced Length := Unbraced Or Unsupported Length of Beam in
25 Feet (for Lateral Torsional Buckling)
Lateral Torsional Buckling Modification Factor
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 4
ASD (Pinned - Pinned) Case.xmcd
1.1 SECTIONAL PROPERTIES
Rolled Section
Built-Up Member
Thu Dec 18 7:33:48 PM 2008
W44X335
W44X290
W44X262
W44X230
W40X593
W40X503
W40X431
W44X335 Selected Beam
Thu Dec 18 7:34:10 PM 2008
b := t :=
fl fl
15.9 1.77
FlangeWidth FlangeThickness
t := d :=
web b
1.03 44
WebThickness BeamDepth
Thu Dec 18 7:34:24 PM 2008
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 5
ASD (Pinned - Pinned) Case.xmcd
1.2 SIGN CONVENTION FOR ROTATION DUE TO FORCES
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 6
ASD (Pinned - Pinned) Case.xmcd
2.0 UNFACTORED LOADS (DEAD AND LIVE)
0 Uniform Live Load Value in pounds force per linear foot
Uniform Dead Load Value (different from Steel Dead
0
Weight) in pounds force per linear foot
Thu Aug 28 3:08:48 PM 2008
F := F :=
X1 Y1 1st Load (Starting From
0 310000
Support A) in Pound Force
NumberOfTorques NumberOfTorques
F := F :=
X2 Y2 2nd Load (Starting From
0 420000
Support A) in Pound Force
NumberOfTorques NumberOfTorques
F := F :=
X3 Y3 3rd Load (Starting From
0 0
Support A) in Pound Force
NumberOfTorques NumberOfTorques
F := F :=
X4 Y4 4th Load (Starting From
0 0
Support A) in Pound Force
NumberOfTorques NumberOfTorques
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 7
ASD (Pinned - Pinned) Case.xmcd
4.0 SUMMARY OF STRESSES
Thu Dec 18 7:35:44 PM 2008
1
2
3
N/A 4 N/A
(A) CRITICAL STRESS POINTS ACROSS BEAM'S CROSS-SECTION
Thu Dec 18 9:54:11 PM 2008
Expand for Maximum Stresses at each Point Above - Thu Dec 18 7:36:27 PM 2008
7 Factored Strong Axis Moment
ϕM = 6.588× 10 ⋅lbf ⋅in
nx
Capacity if designed per AISC Specs F
7 Factored Weak Axis Moment Capacity if
ϕM = 1.18× 10 ⋅lbf ⋅in
ny
designed per AISC Specs F
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 8
ASD (Pinned - Pinned) Case.xmcd
4.1 GRAPHS OF GOVERNING DIFFRENTIAL EQUATIONS
Thu Dec 18 7:36:43 PM 2008
4.1.0 ROTATION
V = 2.203 α= 0.3
a
0.06
0 α
0.054
0.048
n
o
i
at 0.042
t
o
R

r 0.036
o
f

n
o
i 0.03
t
c
n
u
F
0.024
l
a
n
o
si 0.018
r
o
T
0.012
−3
6×10
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ratio of Point of Interest to Total Span (z/L)
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 9
ASD (Pinned - Pinned) Case.xmcd
4.1.1 FIRST DERIVATIVE
V = 2.203 α= 0.3
a
0.25
0 α
n
o
i
rs 0.21
o
T

t
n 0.17
a
n
e
V
0.13
t
n
i
a
S
m 0.09
o
r
f
r 0.05
a
e
h
S −3
r 10×10
o
f

n
o
i −0.03
t
c
n
u
F
−0.07

l
a
n
o
si −0.11
r
o
T
−0.15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ratio of Point of Interest to Total Span (z/L)
AISC Torsional Design LRFD AND 12/18/2008 11:25 PM 10
ASD (Pinned - Pinned) Case.xmcd
4.1.2 SECOND DERIVATIVE
V = 2.203 α= 0.3
a
0
0 α
g
n
pi −0.04
r
a
W
−0.08
m
o
r
f
g −0.12
n
i
d
n
e −0.16
B

l
a
m
−0.2
r
o
N

or −0.24
f

n
o
ti −0.28
c
n
u
F
l −0.32
a
n
o
i
rs −0.36
o
T
−0.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ratio of Point of Interest to Total Span (z/L)