V. AISI 2016 CS Flexural Strength
Verify the flexural strength of a cold-formed channel section according to the AISI S100 2016 specification using both the LRFD and ASD methods.
Details
A 5' long, simply supported beam is subjected to a concentrated load of 1 kip/in at midspan in both the global Y and Z directions. The section used is a 12CS4x105, Gr. 36 steel.
Section Properties
Taken from AISI Manual, Cold-Formed Steel Design - Vol. 1, 2017 Table I-1.
- Area, Ag = 2.20 in2
- Radius of gyration z axis, rz = 4.65in
- Radius of gyration y axis, ry = 1.39 in
- Distance from centroid to shear center, xo = -2.63 in
- Elastic section modulus y axis, Sfy = 1.45 in3
- Elastic section modulus z axis, Sfz = 7.91 in3
- Torsional constant, J = 0.00808 in4
- Warping constant, Cw = 122 in6
- j = 6.74 in
Material Properties
- E = 29,000 ksi
- G = 11,300 ksi
- Fy = 36 ksi
The modification factor, Cb, for a simply-supported beam under a concentrated load at midspan:
Polar radius of gyration of cross-section about shear center:
| (Eq. F2.1.1-3) |
Major axis bending:
| (Eq. F2.1.1-4) |
| (Eq. F2.1.1-5) |
| (Eq. F2.1.1-1) |
Per F2.1, where Fcre > 2.78Fy = 2.78(36) = 100.1 ksi, Fn = Fy (Eq. F2.1-3).
Nominal capacity against lateral-torsional buckling about the major axis:
Mnez = SfzFn = 7.91 × 36 = 284.8 in·kips
The available flexural strength about the major axis:
- LRFD: ϕbMnez = 0.9 × 284.8 = 256.3 in·kips
- ASD: Mnez/Ωb = 284.8 / 1.67 = 170.5 in·kips
Minor axis bending:
| (Eq. F2.1.2-2) |
Simply-supported beam, so CTF = 1; assume compression on shear center side of centroid, so CS = +1.
| (Eq. F2.1.2-1) |
Per F2.1, where Fcre > 2.78Fy = 2.78(36) = 100.1 ksi, Fn = Fy (Eq. F2.1-3).
Nominal capacity against lateral-torsional buckling about the major axis:
Mney = SfyFn = 1.45 × 36 = 52.2 in·kips
The available flexural strength about the major axis:
- LRFD: ϕbMney = 0.9 × 52.2 = 47.0 in·kips
- ASD: Mney/Ωb = 52.2 / 1.67 = 31.3 in·kips
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments | |
|---|---|---|---|---|---|
| LRFD | Flexural capacity about major axis (in·kips) | 256.3 | 256.5 | negligible | |
| Flexural capacity about minor axis (in·kips) | 47.0 | 46.898 | negligible | ||
| ASD | Flexural capacity about major axis (in·kips) | 170.5 | 170.659 | negligible | |
| Flexural capacity about minor axis (in·kips) | 31.3 | 31.203 | negligible | ||
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISI\AISI 2016 CS Flexural Strength.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 11-Jan-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
G 1.6128e+06
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AMERICAN
1 TABLE ST 12CS4X105
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
UNIT INCHES KIP
MEMBER LOAD
1 CON GY -1
1 CON GZ 1
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
METHOD LRFD
FYLD 36 ALL
FU 58 ALL
FLX 0 ALL
TSA 0 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
METHOD ASD
FYLD 36 ALL
FU 58 ALL
FLX 0 ALL
TSA 0 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 12CS4X105 LEN: 60.000 LOC: 30.000 | | STATUS: PASS RATIO: 0.400 REF: Eq. H1.1-2 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 30.000 Criteria: Eq. H1.1-2 LC: 1 | | Fx:(C) 0.000 Fy: 0.500 Fz: -0.500 | | Mx: 0.000 My: -15.000 Mz: -15.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 2.20000 Az: 0.71715 Ay: 1.19857 | | Cz: 0.00000 Cy: 0.00000 | | Iz: 47.50000 Iy: 4.27000 J: 0.00808 | | Sz: 7.91667 Sy: 1.44746 | | Rz: 4.64660 Ry: 1.39317 Cw: 122.00000 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 36.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 60.000 Lz: 60.000 Ly: 60.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 43.067 Allowable : 300.000 Ratio : 0.144 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.786 | 10.000 | PASS | | Width To Thickness Ratio | 32.524 | 60.000 | PASS | | Web Depth To Thickness Ratio | 108.714 | 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 | - | - | - | 71.280 | - |Sec. D2 | | Yielding | - | - | - | 71.280 | - |Sec. D2 | | Rupture | - | - | - | 95.700 | - |Sec. D3 | | Compression | - | - | - | 39.758 | - |Sec. E3 | | Local Comp | - | - | - | 39.758 | - |Sec. E3 | | Distortional | - | - | - | 50.926 | - |Sec. E4 | | Axial Comp | - | - | - | 60.583 | - |Sec. E2 | | Bending | 1 | 30.00 | -15.000 | 44.537 |0.337|Sec. F3 | | Major Local Bend | 1 | 30.00 | -15.000 | 235.933 |0.064|Sec. F3 | | Minor Local Bend | 1 | 30.00 | -15.000 | 44.537 |0.337|Sec. F3 | | Distortional | 1 | 30.00 | -15.000 | 242.008 |0.062|Sec. F4 | | Major Sectional | 1 | 30.00 | -15.000 | 256.500 |0.058|Sec. F2 | | Minor Sectional | 1 | 0.00 | -15.000 | 46.898 |0.320|Sec. F2 | | Shear | 1 | 0.00 | 0.500 | 13.487 |0.037|Sec. G2 | | Major Shear (Z) | 1 | 0.00 | -0.500 | 14.716 |0.034|Sec. G2 | | Minor Shear (Y) | 1 | 0.00 | 0.500 | 13.487 |0.037|Sec. G2 | | Interaction | 1 | 30.00 | - | - |0.400|Eq. H1.1-2 | | (Bend+Ten) Int1 | 1 | 30.00 | - | - |0.378|Eq. H1.1-1 | | (Bend+Ten) Int2 | 1 | 30.00 | - | - |0.400|Eq. H1.1-2 | | (Bend+Comp) | 1 | 30.00 | - | - |0.400|Eq. H1.2-1 | | (Bend+Shear) Z | 1 | 30.00 | - | - |0.074|Sec. H2 | | (Bend+Shear) Y | 1 | 30.00 | - | - |0.339|Sec. H2 | |-----------------------------------------------------------------------------| 44. PARAMETER 2 45. CODE AISI 2016 46. METHOD ASD 47. FYLD 36 ALL 48. FU 58 ALL 49. FLX 0 ALL 50. TSA 0 ALL 51. TRACK 2 ALL 52. CHECK CODE ALL STEEL DESIGN 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 12CS4X105 LEN: 60.000 LOC: 30.000 | | STATUS: PASS RATIO: 0.602 REF: Eq. H1.1-2 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 30.000 Criteria: Eq. H1.1-2 LC: 1 | | Fx:(C) 0.000 Fy: 0.500 Fz: -0.500 | | Mx: 0.000 My: -15.000 Mz: -15.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 2.20000 Az: 0.71715 Ay: 1.19857 | | Cz: 0.00000 Cy: 0.00000 | | Iz: 47.50000 Iy: 4.27000 J: 0.00808 | | Sz: 7.91667 Sy: 1.44746 | | Rz: 4.64660 Ry: 1.39317 Cw: 122.00000 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 36.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 60.000 Lz: 60.000 Ly: 60.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 43.067 Allowable : 300.000 Ratio : 0.144 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.786 | 10.000 | PASS | | Width To Thickness Ratio | 32.524 | 60.000 | PASS | | Web Depth To Thickness Ratio | 108.714 | 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 | - | - | - | 47.425 | - |Sec. D2 | | Yielding | - | - | - | 47.425 | - |Sec. D2 | | Rupture | - | - | - | 63.800 | - |Sec. D3 | | Compression | - | - | - | 25.986 | - |Sec. E3 | | Local Comp | - | - | - | 25.986 | - |Sec. E3 | | Distortional | - | - | - | 33.285 | - |Sec. E4 | | Axial Comp | - | - | - | 39.597 | - |Sec. E2 | | Bending | 1 | 30.00 | -15.000 | 29.632 |0.506|Sec. F3 | | Major Local Bend | 1 | 30.00 | -15.000 | 156.974 |0.096|Sec. F3 | | Minor Local Bend | 1 | 30.00 | -15.000 | 29.632 |0.506|Sec. F3 | | Distortional | 1 | 30.00 | -15.000 | 161.016 |0.093|Sec. F4 | | Major Sectional | 1 | 30.00 | -15.000 | 170.659 |0.088|Sec. F2 | | Minor Sectional | 1 | 0.00 | -15.000 | 31.203 |0.481|Sec. F2 | | Shear | 1 | 0.00 | 0.500 | 8.873 |0.056|Sec. G2 | | Major Shear (Z) | 1 | 0.00 | -0.500 | 9.682 |0.052|Sec. G2 | | Minor Shear (Y) | 1 | 0.00 | 0.500 | 8.873 |0.056|Sec. G2 | | Interaction | 1 | 30.00 | - | - |0.602|Eq. H1.1-2 | | (Bend+Ten) Int1 | 1 | 30.00 | - | - |0.569|Eq. H1.1-1 | | (Bend+Ten) Int2 | 1 | 30.00 | - | - |0.602|Eq. H1.1-2 | | (Bend+Comp) | 1 | 30.00 | - | - |0.602|Eq. H1.2-1 | | (Bend+Shear) Z | 1 | 30.00 | - | - |0.111|Sec. H2 | | (Bend+Shear) Y | 1 | 30.00 | - | - |0.509|Sec. H2 | |-----------------------------------------------------------------------------|