Product Technical Guides : US-EN Modular Systems Product Technical Guide | Page 29

Modular Support Systems Technical Guide , Edition 1
3.0 MODULAR SUPPORT SYSTEM 3.1.1 CROSS-SECTION PROPERTIES OF MT PROFILES
Table 9 - Cross-Section Properties of MT Channel Profiles 1 , 3 , 4 , 5
Description
Symbol Units
MT-20 MT-20 OC
MT-30 S MT-30 MT-30 S OC MT-30 OC
MT-50 S MT-50 MT-50 S OC MT-50 OC
MT-60 S MT-60 MT-60 S OC MT-60 OC
Profile of cross-section - -
Design thickness
t
in
( mm )
0.069
( 1.75 )
0.079
( 2 )
0.108
( 2.75 )
0.108
( 2.75 )
Width
-
in
( mm )
1.10
( 28 )
1.67
( 42.5 )
1.67
( 42.5 )
1.67
( 42.5 )
Depth
-
in
( mm )
1.67
( 42.5 )
0.91
( 23 )
1.67
( 42.5 )
2.83
( 72 )
Weight
w
lbs / ft
( kg / m )
0.84
( 1.25 )
1.1
( 1.64 )
1.97
( 2.93 )
2.83
( 4.21 )
Minimum specified yield strength
F y
ksi
( MPa )
40.6
( 280 )
40.6
( 280 )
40.6
( 280 )
40.6
( 280 )
Modulus of elasticity
E
ksi
( MPa )
29,500
( 203,400 )
29,500
( 203,400 )
29,500
( 203,400 )
29,500
( 203,400 )
Gross Section Properties 2
Gross cross-sectional area
A g
in 2
( mm 2 )
0.291
( 187.59 )
0.322
( 207.95 )
0.583
( 376.02 )
0.834
( 538.27 )
Moment of inertia of the gross section about x-axis
I x
in 4
( mm 4 )
0.0489
( 20,349 )
0.0351
( 14,621 )
0.2033
( 84,619 )
0.7904
( 329,006 )
Moment of inertia of the gross section about y-axis
I y
in 4
( mm 4 )
0.1272
( 52,943 )
0.1274
( 53,018 )
0.2611
( 108,670 )
0.4153
( 172,864 )
Gross section-modulus about x-axis
S x
in 3
( mm 3 )
0.0742
( 1,216 )
0.067
( 1,098 )
0.2165
( 3,548 )
0.5146
( 8,432 )
Gross section-modulus about y-axis
S y
in 3
( mm 3 )
0.152
( 2,491 )
0.1523
( 2,495 )
0.3121
( 5,114 )
0.4964
( 8,135 )
Radius of gyration of the gross section about x-axis
r x
in
( mm )
0.41
( 10.42 )
0.33
( 8.39 )
0.591
( 15 )
0.973
( 24.72 )
Radius of gyration of the gross section about y-axis
r y
in
( mm )
0.661
( 16.8 )
0.629
( 15.97 )
0.669
( 17 )
0.706
( 17.92 )
Effective Section Properties
Effective moment of inertia about x-axis
I x-eff
in 4
( mm 4 )
0.0443
( 18,439 )
0.0327
( 13,594 )
0.2005
( 83,452 )
0.7802
( 324,725 )
Effective moment of inertia about y-axis
I y-eff
in 4
( mm 4 )
0.0901
( 37,509 )
0.1264
( 52,608 )
0.2611
( 108,664 )
0.4153
( 172,858 )
Effective section modulus about x-axis at stress = F y
S x-eff
in 3
( mm 3 )
0.0673
( 1,102 )
0.0623
( 1,021 )
0.2135
( 3,499 )
0.5079
( 8,323 )
Effective section modulus about y-axis at stress = F y
S y-eff
in 3
( mm 3 )
0.1077
( 1765 )
0.1511
( 2476 )
0.3121
( 5114 )
0.4964
( 8135 )
Factored bending moment resistance based on local buckling about x-axis ( ϕ b = 0.9 )
ϕ b
M nl
k-in
( kN m )
2.77
( 0.313 )
2.88
( 0.325 )
10.22
( 1.15 )
23.34
( 2.64 )
Factored bending moment resistance based on local buckling about y-axis ( ϕ b = 0.9 )
ϕ b
M nl
k-in
( kN m )
4.33
( 0.489 )
6.33
( 0.716 )
12.71
( 1.436 )
19.24
( 2.173 )
Factored bending moment resistance for distortional buckling about x-axis based on Kφ = 0 ( ϕ b = 0.9 )
ϕ b
M nd
k-in
( kN m )
2.53
( 0.286 )
2.66
( 0.300 )
9.06
( 1.024 )
18.65
( 2.107 )
Factored bending moment resistance for distortional buckling about y-axis based on Kφ = 0 ( ϕ b = 0.9 )
ϕ b
M nd
k-in
( kN m )
3.76
( 0.425 )
5.70
( 0.644 )
12.71
( 1.436 )
17.86
( 2.017 )
Factored shear resistance about x-axis ( ϕ v = 0.8 )
ϕ v
V n
lbs
( N )
1,877
( 8,350 )
2,085
( 9,274 )
2,691
( 11,972 )
2,692
( 11,975 )
Factored shear resistance about y-axis ( ϕ v = 0.8 )
ϕ v
V n
lbs
( N )
2,220
( 9,871 )
1,813
( 8,064 )
5,383
( 23,944 )
10,286
( 45,756 )
Torsional Section Properties 2
St . Venant Torsional Constant
J
in 4
( mm 4 )
0.0005
( 191.50 )
0.0007
( 277.26 )
0.0023
( 947.89 )
0.0033
( 1,356.90 )
Torsional Warping Constant
C w
in 6
( mm 6 )
0.0368
( 9,881,442 )
0.0323
( 8,685,395 )
0.1593
0.5991
( 42,771,610 ) ( 160,884,400 )
Distance from the centroid to the shear center along the principal x-axis
X 0
in
( mm )
0
0
0
0
Distance from the centroid to the shear center along the principal y-axis
Y 0
in
( mm )
0.988
( 25.1 )
0.868
( 22.05 )
1.579
( 40.11 )
2.740
( 69.59 )
Distance from shear center to centroid to mid-plane of web
m
in
( mm )
0.60
( 15.1 )
0.45
( 11.4 )
0.90
( 22.9 )
1.50
( 38.0 )
Net polar radius of gyration about the shear center
r 0
in
( mm )
1.258
( 31.95 )
1.122
( 28.49 )
1.814
( 46.07 )
2.992
( 76.00 )
Coefficient for determining critical elastic lateral-torsional buckling stress β - 0.4 0.4 0.2 0.2
1 . Tabulated values are in accordance with ICC-ES ELC-5019 and CSA S136-16 , the North American Specification for the Design of Cold-Formed Steel Structural Members
( using the Appendix B provisions applicable to Canada ), CSA Group . 2 . Tabulated gross properties , including torsional properties , are based on the full unreduced cross section of the profiles , away from the punched holes and slots . 3 . For deflection calculations , use the effective moment of inertia . 4 . Design moment capacity is taken as the lesser of Φ b
M nl and Φ b
M nd
.
5 . C . G . is the center of gravity of the profile cross-section . 2023
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