Product Technical Guides : CA-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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