|
3.0 Modular Support System
3.1.1 Cross-Section Properties of MT Profiles
| |||||
Table 11- Cross-Section Properties of MT Channel Profiles 1, 2, 3, 4, 5 |
Description Symbol Units |
MT-30D S MT-30D MT-30D S OC MT-30D OC |
MT-40D S MT-40D MT-40D S OC MT-40D OC |
MT-50D MT-50D S |
MT-50D U |
MT-60D MT-60D OC MT-60D S |
Profile of cross-section-- |
Design thickness |
t |
in
( mm)
|
0.079
( 2.00)
|
0.079
( 2.00)
|
0.108
( 2.75)
|
0.108
( 2.75)
|
0.108
( 2.75)
|
Width |
- |
in
( mm)
|
1.67
( 42.5)
|
1.67
( 42.5)
|
1.67
( 42.5)
|
1.67
( 42.5)
|
1.67
( 42.5)
|
Depth |
- |
in
( mm)
|
1.81
( 46)
|
3.35
( 85)
|
3.35
( 85)
|
3.35
( 85)
|
5.66
( 144)
|
Weight |
w |
lbs / ft
( kg / m)
|
1.98
( 2.94)
|
3.01
( 4.48)
|
3.91
( 5.82)
|
3.91
( 5.82)
|
5.66
( 8.42)
|
Minimum specified yield strength |
Fy |
ksi
( MPa)
|
40.6
( 280)
|
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)
|
29,500
( 203,400)
|
Gross Section Properties 2 Gross cross-sectional area |
Ag |
in 2
( mm 2)
|
0.644
( 415.90)
|
0.886
( 571.90)
|
1.159
( 747.57)
|
1.159
( 747.57)
|
1.665
( 1074.2)
|
Moment of inertia of the gross section about x-axis |
Ix |
in 4
( mm 4)
|
0.164
( 68,266)
|
0.823
( 342,808)
|
1.035
( 430,879)
|
1.035
( 430,879)
|
4.3946
( 1,829,170)
|
Moment of inertia of the gross section about y-axis |
Iy |
in 4
( mm 4)
|
0.255
( 106,037)
|
0.409
( 170,059)
|
0.517
( 215,335)
|
0.517
( 215,335)
|
0.8283
( 343,515)
|
Gross section-modulus about x-axis |
Sx |
in 3
( mm 3)
|
0.181
( 2,968)
|
0.492
( 8,066)
|
0.619
( 10,138)
|
0.619
( 10,138)
|
1.5503
( 25,400)
|
Gross section-modulus about y-axis |
Sy |
in 3
( mm 3)
|
0.304
( 4,990)
|
0.488
( 8,003)
|
0.618
( 10,133)
|
0.618
( 10,133)
|
0.9901
( 16,223)
|
Radius of gyration of the gross section about x-axis |
rx |
in
( mm)
|
0.504
( 12.81)
|
0.964
( 24.48)
|
0.945
( 24.01)
|
0.945
( 24.01)
|
1.624
( 41.25)
|
Radius of gyration of the gross section about y-axis |
ry |
in
( mm)
|
0.629
( 15.97)
|
0.679
( 17.24)
|
0.668
( 16.97)
|
0.668
( 16.97)
|
0.705
( 17.91)
|
Effective Section Properties Effective moment of inertia about x-axis |
Ix-eff |
in 4
( mm 4)
|
0.164
( 68,194)
|
0.823
( 342,736)
|
1.035
( 430,692)
|
1.035
( 430,879)
|
4.3941
( 1,828,963)
|
Effective moment of inertia about y-axis |
Iy-eff |
in 4
( mm 4)
|
0.253
( 105,217)
|
0.407
( 169,239)
|
0.515
( 214,207)
|
0.517
( 215,335)
|
0.8253
( 343,516)
|
Effective section modulus about x-axis at stress = Fy |
Sx-eff |
in 3
( mm 3)
|
0.181
( 2,964)
|
0.492
( 8,064)
|
0.618
( 10,134)
|
0.619
( 10,138)
|
1.5501
( 25,402)
|
Effective section modulus about y-axis at stress = Fy |
Sy-eff |
in 3
( mm 3)
|
0.302
( 4951)
|
0.486
( 7,964)
|
0.615
( 10,080)
|
0.618
( 10,133)
|
0.9865
( 16,166)
|
Factored bending moment resistance based on local buckling about x-axis( φb = 0.9) |
φbMnl |
k-in
( kN m)
|
8.50
( 0.960)
|
23.12
( 2.612)
|
29.05
( 3.283)
|
29.07
( 3.284)
|
72.84
( 8.23)
|
Factored bending moment resistance based on local buckling about y-axis( φb = 0.9) |
φbMnl |
k-in
( kN m)
|
13.59
( 1.535)
|
20.05
( 2.265)
|
26.26
( 2.967)
|
26.40
( 2.983)
|
39.65
( 4.48)
|
Factored bending moment resistance for distortional buckling about x-axis based on Kϕ = 0( φb = 0.9) |
φbMnd |
k-in
( kN m)
|
8.50
( 0.960)
|
23.12
( 2.612)
|
29.05
( 3.283)
|
29.07
( 3.284)
|
61.19
( 6.91)
|
Factored bending moment resistance for distortional buckling about y-axis based on Kϕ = 0( φb = 0.9) |
φbMnd |
k-in
( kN m)
|
13.59
( 1.535)
|
20.05
( 2.265)
|
26.26
( 2.967)
|
26.40
( 2.983)
|
35.40
( 4.00)
|
Factored shear resistance about x-axis( φv = 0.8) |
φvVn |
lbs
( N)
|
4,170
( 18.547)
|
4,168
( 18.54)
|
5,067
( 22.54)
|
5,067
( 22.54)
|
5,234
( 23,284)
|
Factored shear resistance about y-axis( φv = 0.8) |
φvVn |
lbs
( N)
|
3,626
( 16.128)
|
8,337
( 37.08)
|
10,450
( 46.48)
|
10,450
( 46.48)
|
20,420
( 90,846)
|
Torsional Section Properties 2 St. Venant Torsional Constant |
J |
in 4
( mm 4)
|
0.0133
( 554.53)
|
0.0018
( 762.53)
|
0.0045
( 1,884.5)
|
0.0045
( 1,884.5)
|
0.0065
( 2,705.6)
|
Torsional Warping Constant |
Cw |
in 6
( mm 6)
|
0.0647
( 17,370,800)
|
0.294
( 78,960,780)
|
0.3108
( 83,471,060)
|
0.3131
( 84,065,340)
|
1.192
( 320,071,600)
|
Distance from the centroid to the shear center along the principal X-axis |
X0 |
in
( mm)
|
0 |
0 |
0 |
0 |
0 |
Distance from the centroid to the shear center along the principal Y-axis |
Y0 |
in
( mm)
|
0 |
0 |
0 |
0 |
0 |
Distance from shear center to centroid to mid-plane of web |
m |
in
( mm)
|
N. A. |
N. A. |
N. A. |
N. A. |
N. A. |
Net polar radius of gyration about the shear center |
r0 |
in
( mm)
|
0.806
( 20.5)
|
1.179
( 29.9)
|
1.158
( 29.4)
|
1.158
( 29.4)
|
1.771
( 45.0)
|
Coefficient for determining critical elastic lateraltorsional buckling stress |
β |
- |
1.0 |
1.0 |
1.0 |
1.0 |
1.0 |
1. Tabulated values are in accordance with and CSA S136-16, the North American Specification for the Design of Cold-Formed Steel Structural Members. | |||||||
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 φbMnl and φbMnd. | |||||||
5. C. G. is the center of gravity of the profile cross-section. | |||||||