V. AISI 2016 Channel section
Determine the flexural strength and shear strength of a cold-formed channel section without lips according to AISI S100 2016 Specification using both LRFD and ASD methods.
Details
The member is a simply-supported, 6 ft span. The member is subject to a uniform load of 194.4 lbs/ft. The section used is a 550CU125-54.
Section Properties
- Depth of section, d = 5.698 in
- Width of section, b = 1.25 in
- Thickness, t = 0.0566 in
- Fillet radius, r = 0.0849 in
- Area, A = 0.452 in2
- Moment of inertia major axis, Izz = 1.9 in4
- Moment of inertia minor axis, Iyy = 0.053 in4
- Section modulus major axis, Zzz = 0.667 in3
- Section modulus minor axis, Zyy = 0.0512 in3
- Distance between centroid and shear center: x0 = -0.539 in
- Radius of gyration about major axis:
- Radius of gyration about minor axis:
- Polar radius of gyration:
- Torsion constant, J = 0.00048 in4
Material Properties
- E = 29,500 ksi
- G = 11,300 ksi
- Fy = 33 ksi
Design Forces
- Mz = 10.5 ft·k
- Vy = 0.583 kips
Validation
Lateral-Torsional Buckling Strength
Cb = 1.136
For singly symmetric sections bent about the axis of symmetry:
where
= |
For Fcre < 0.56Fy = 0.56 × 33 = 18.58, Fn = Fcre .
Mne = Fn × Sf = 14.15 × 0.667 = 9.433 in-k
Allowable nominal lateral-torsional buckling strength (ASD):
Design nominal lateral-torsional buckling strength (LRFD):
Bending About Major Axis
My = Fy × Sf = 33 × 0.667 = 22.01 in-k
Allowable nominal bending strength (ASD):
Design nominal bending strength (LRFD):
Local Buckling Interaction with Yield and Global Buckling
From Section F3:
Se = 0.665 in3
Mnl = Se × Fn = 0.665 × 14.15 = 9.412 in-k
Allowable nominal bending strength (ASD):
Design nominal bending strength (LRFD):
Governing strength ratio:
LRFD: 10.498 / 8.471 = 1.239
ASD: 10.498 / 5.636 = 1.862
Shear Strength along Minor Axis
h = D - 2× (t - r) = 5.698 - 2× (0.0566 - 0.0849) = 5.145 in
h /t = 5.415 / 0.0566 = 95.67
Aw = h × t = 5.415 × 0.0566 = 0.307 in2
Vy = 0.6 × Aw × Fy = 0.6 × 0.307 × 33 = 6.069 kip
Vcr = Aw × Fcr = 0.307 × 15.56 = 4.75 kip
For 0.815 < λv ≤ 1.227,
Allowable nominal shear strength (ASD):
Design nominal shear strength (LRFD):
Governing strength ratio:
LRFD: 0.583 / 4.165 = 0.14
ASD: 0.583 / 2.74 = 0.213
Result Type | Reference | STAAD.Pro | Difference | Comments | |
---|---|---|---|---|---|
LRFD | Major bending (in-k) | 19.81 | 19.807 | negligible | |
LTB bending (in-k) | 8.49 | 8.49 | none | ||
Major local bending (in-k) | 8.471 | 8.477 | negligible | ||
Bending ratio | 1.239 | 1.238 | negligible | ||
Shear strength (kips) | 4.165 | 4.163 | negligible | ||
Shear ratio | 0.14 | 0.14 | none | ||
ASD | Major bending (in-k) | 13.18 | 13.178 | negligible | |
LTB bending (in-k) | 5.649 | 5.649 | none | ||
Major local bending (in-k) | 5.636 | 5.64 | negligible | ||
Bending ratio | 1.862 | 1.861 | negligible | ||
Shear strength (kips) | 2.739 | 2.739 | none | ||
Shear ratio | 0.213 | 0.213 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISI\AISI 2016 Channel section.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
JOB NAME AISI C-Section Without Lips Braced at Mid-Span
JOB CLIENT BENTLEY SYSTEMS Inc.
ENGINEER DATE 04-Mar-20
JOB REV 1.0
JOB REF AISI Manual Cold-Formed Steel Design - Vol. 1
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 72 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29500
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AMERICAN
1 TABLE ST 550CU125-54
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 2 LOADTYPE Live TITLE LL
MEMBER LOAD
1 UNI GY -0.0162
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
METHOD LRFD
BEAM 1 ALL
FYLD 33 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 1
CODE AISI 2016
METHOD ASD
BEAM 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0) ******************************************************** ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.) |-----------------------------------------------------------------------------| | MEMBER: 1(*) SECTION:ST 550CU125-54 LEN: 72.000 LOC: 36.000 | | STATUS: FAIL RATIO: 1.238 REF: Sec. F3 LC: 2 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 36.000 Criteria: Sec. F3 LC: 2 | | Fx:(C) -0.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -10.498 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 0.45200 Az: 0.12548 Ay: 0.30649 | | Cz: 0.21500 Cy: 2.84900 | | Iz: 1.90000 Iy: 0.05300 J: 0.00048 | | Sz: 0.66690 Sy: 0.05121 | | Rz: 2.05025 Ry: 0.34243 Cw: 0.31500 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 33.000 Fu: 58.000 E: 29500.000 G: 11300.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 72.000 Lz: 72.000 Ly: 72.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 2 Actual : 210.263 Allowable : 300.000 Ratio : 0.701 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.500 | 10.000 | PASS | | Width To Thickness Ratio | 19.585 | 60.000 | PASS | | Web Depth To Thickness Ratio | 95.671 | 200.000 | PASS | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 4 STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0) ******************************************************** ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.) | - MEMBER: 1 (Contd.....) | | | |-----------------------------------------------------------------------------| | Limit States | Load# |Location| Demand | Capacity |Ratio| Reference | |--------------------|-------|--------|----------|----------|-----|-----------| | Tension | - | - | - | 13.424 | - |Sec. D2 | | Yielding | - | - | - | 13.424 | - |Sec. D2 | | Rupture | - | - | - | 19.662 | - |Sec. D3 | | Compression | - | - | - | 2.185 | - |Sec. E3 | | Local Comp | - | - | - | 2.185 | - |Sec. E3 | | Axial Comp | - | - | - | 2.219 | - |Sec. E2 | | Bending | 2 | 36.00 | -10.498 | 8.477 |1.238|Sec. F3 | | Major Local Bend | 2 | 36.00 | -10.498 | 8.477 |1.238|Sec. F3 | | Minor Local Bend | - | - | - | 1.518 | - |Sec. F3 | | Major Sectional | 2 | 36.00 | -10.498 | 19.807 |0.530|Sec. F2 | | Minor Sectional | - | - | - | 1.521 | - |Sec. F2 | | LTB Major | 2 | 36.00 | -10.498 | 8.490 |1.236|Sec. F2 | | Shear | 2 | 0.00 | 0.583 | 4.163 |0.140|Sec. G2 | | Major Shear (Z) | - | - | - | 2.360 | - |Sec. G2 | | Minor Shear (Y) | 2 | 0.00 | 0.583 | 4.163 |0.140|Sec. G2 | | Interaction | 2 | 36.00 | - | - |1.238|Eq. H1.1-2 | | (Bend+Ten) Int1 | 2 | 36.00 | - | - |0.530|Eq. H1.1-1 | | (Bend+Ten) Int2 | 2 | 36.00 | - | - |1.238|Eq. H1.1-2 | | (Bend+Comp) | 2 | 36.00 | - | - |1.238|Eq. H1.2-1 | | (Bend+Shear) Z | 2 | 36.00 | - | - |0.591|Sec. H2 | |-----------------------------------------------------------------------------| 43. PARAMETER 1 44. CODE AISI 2016 45. METHOD ASD 46. BEAM 1 ALL 47. TRACK 2 ALL 48. CHECK CODE ALL STEEL DESIGN WARNING # 8 ~ The specified value of FU for member # 1 seems out of range. Reset back to default value. STAAD SPACE -- PAGE NO. 5 STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0) ******************************************************** ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.) |-----------------------------------------------------------------------------| | MEMBER: 1(*) SECTION:ST 550CU125-54 LEN: 72.000 LOC: 36.000 | | STATUS: FAIL RATIO: 1.861 REF: Sec. F3 LC: 2 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 36.000 Criteria: Sec. F3 LC: 2 | | Fx:(C) -0.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -10.498 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 0.45200 Az: 0.12548 Ay: 0.30649 | | Cz: 0.21500 Cy: 2.84900 | | Iz: 1.90000 Iy: 0.05300 J: 0.00048 | | Sz: 0.66690 Sy: 0.05121 | | Rz: 2.05025 Ry: 0.34243 Cw: 0.31500 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 33.000 Fu: 58.000 E: 29500.000 G: 11300.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 72.000 Lz: 72.000 Ly: 72.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 2 Actual : 210.263 Allowable : 300.000 Ratio : 0.701 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.500 | 10.000 | PASS | | Width To Thickness Ratio | 19.585 | 60.000 | PASS | | Web Depth To Thickness Ratio | 95.671 | 200.000 | PASS | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 6 STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0) ******************************************************** ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.) | - MEMBER: 1 (Contd.....) | | | |-----------------------------------------------------------------------------| | Limit States | Load# |Location| Demand | Capacity |Ratio| Reference | |--------------------|-------|--------|----------|----------|-----|-----------| | Tension | - | - | - | 8.932 | - |Sec. D2 | | Yielding | - | - | - | 8.932 | - |Sec. D2 | | Rupture | - | - | - | 13.108 | - |Sec. D3 | | Compression | - | - | - | 1.428 | - |Sec. E3 | | Local Comp | - | - | - | 1.428 | - |Sec. E3 | | Axial Comp | - | - | - | 1.450 | - |Sec. E2 | | Bending | 2 | 36.00 | -10.498 | 5.640 |1.861|Sec. F3 | | Major Local Bend | 2 | 36.00 | -10.498 | 5.640 |1.861|Sec. F3 | | Minor Local Bend | - | - | - | 1.010 | - |Sec. F3 | | Major Sectional | 2 | 36.00 | -10.498 | 13.178 |0.797|Sec. F2 | | Minor Sectional | - | - | - | 1.012 | - |Sec. F2 | | LTB Major | 2 | 36.00 | -10.498 | 5.649 |1.858|Sec. F2 | | Shear | 2 | 0.00 | 0.583 | 2.739 |0.213|Sec. G2 | | Major Shear (Z) | - | - | - | 1.553 | - |Sec. G2 | | Minor Shear (Y) | 2 | 0.00 | 0.583 | 2.739 |0.213|Sec. G2 | | Interaction | 2 | 36.00 | - | - |1.861|Eq. H1.1-2 | | (Bend+Ten) Int1 | 2 | 36.00 | - | - |0.797|Eq. H1.1-1 | | (Bend+Ten) Int2 | 2 | 36.00 | - | - |1.861|Eq. H1.1-2 | | (Bend+Comp) | 2 | 36.00 | - | - |1.861|Eq. H1.2-1 | | (Bend+Shear) Z | 2 | 36.00 | - | - |0.888|Sec. H2 | |-----------------------------------------------------------------------------| 49. FINISH *********** END OF THE STAAD.Pro RUN ***********