V. AISI 2016 CS Compressive Strength
Verify the compressive strength of a cold-formed channel section with lips per the AISI S100 2016 specification.
Details
A 10' long, simply supported beam is subjected to a 10 kip axial load (compression). The section used is a 362CS162-54, Grade 50 steel.
Section Properties
Taken from AISI Manual, Cold-Formed Steel Design - Vol. 1, 2017 Table I-2.
- Area, Ag = 0.422 in2
- Radius of gyration z axis, rz = 1.44in
- Radius of gyration y axis, ry = 0.605 in
- Distance from centroid to shear center, xo = -1.28 in
- Elastic section modulus y axis, Sfz = 0.482 in3
- Elastic section modulus z axis, Sfy = 0.142 in3
- Torsional constant, J = 0.000451 in4
- Warping constant, Cw = 0.457 in6
- j = 2.02 in
Material Properties
- E = 29,000 ksi
- G = 11,300 ksi
- Fy = 50 ksi
(Eq. E2.1-1) |
Polar radius of gyration of cross-section about shear center:
(Eq. E2.2-4) |
(Eq. E2.2-3) |
(Eq. E2.2-5) |
(Eq. E2.2-6) |
(Eq. E2.2-1) |
The elastic global buckling stress about the z axis is the minimum of Fcre and Fcrez1; so Fcrez = 7.560 ksi.
The compressive stress capacity is:
(Eq. E2-4) |
(Eq. E2-2) |
The elastic flexural buckling stress about the y axis:
(Eq. E2.1-1) |
The elastic global buckling stress about the z axis is the minimum of Fcre and Fcrey1; so Fcrey = 7.275 ksi.
(Eq. E2-4) |
(Eq. E2-2) |
Global buckling about the Y axis governs.
Nominal capacity against global buckling:
Pn = AgFn = 0.422 × 6.380 = 2.692 kips
The available axial strength:
- LRFD: ϕcPn = 0.85 × 2.692 = 2.289 kips
- ASD: Pn/Ωc = 2.692 / 1.8 = 1.496 kips
The effective area, Ae, is equal to the gross area, Ag = 0.422 in2. By inspection, the local capacity, Pnℓ is equal to the global buckling capacity in this case.
- LRFD: ϕcPnℓ = 0.85 × 2.692 = 2.289 kips
- ASD: Pnℓ/Ωc = 2.692 / 1.8 = 1.496 kips
Determine the compression capacity for distortional buckling as per E4:
The elastic distortional buckling stress, Fcrd = 149.8 ksi.
The elastic distortional buckling load, Pcrd = Ag × Fcrd = 0.422 × 149.8 = 63.21 kips.
Py = Ag × Fy = 0.422 × 50 = 21.1 kips | (Eq. E4.1-4) |
(Eq. E4.1-3) |
(Eq. 4.1-2) |
The available axial strength:
- LRFD: ϕcPnd = 0.85 × 21.08 = 17.91 kips
- ASD: Pnd/Ωc = 21.08 / 1.8 = 11.71 kips
Results
Result Type | Reference | STAAD.Pro | Difference | Comments | |
---|---|---|---|---|---|
LRFD | Local compression capacity (kips) | 2.289 | 2.282 | negligible | |
Distorional buckling capacity (kips) | 17.91 | 17.914 | negligible | ||
Axial compression capacity (kips) | 2.289 | 2.282 | negligible | ||
ASD | Local compression capacity (kips) | 1.496 | 1.491 | negligible | |
Distorional buckling capacity (kips) | 11.71 | 11.709 | negligible | ||
Axial compression capacity (kips) | 1.496 | 1.491 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISI\AISI 2016 CS Compressive 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 10 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 362CS162-54
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FX 10
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISI 2016
METHOD LRFD
FYLD 50 ALL
FU 58 ALL
FLX 0 ALL
TSA 0 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
METHOD ASD
FYLD 50 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 362CS162-54 LEN: 120.000 LOC: 0.000 | | STATUS: PASS RATIO: 0.545 REF: Sec. D3 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 0.000 Criteria: Sec. D3 LC: 1 | | Fx:(T) -10.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -0.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 0.42200 Az: 0.15191 Ay: 0.18916 | | Cz: 0.53600 Cy: 1.81250 | | Iz: 0.87300 Iy: 0.15400 J: 0.00045 | | Sz: 0.48166 Sy: 0.14141 | | Rz: 1.43830 Ry: 0.60409 Cw: 0.45700 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 50.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 120.000 Lz: 120.000 Ly: 120.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 198.645 Allowable : 300.000 Ratio : 0.662 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.500 | 10.000 | PASS | | Width To Thickness Ratio | 23.710 | 60.000 | PASS | | Web Depth To Thickness Ratio | 59.046 | 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 | 1 | 0.00 | -10.000 | 18.357 |0.545|Sec. D3 | | Yielding | 1 | 0.00 | -10.000 | 18.990 |0.527|Sec. D2 | | Rupture | 1 | 0.00 | -10.000 | 18.357 |0.545|Sec. D3 | | Compression | - | - | - | 2.282 | - |Sec. E2 | | Local Comp | - | - | - | 2.282 | - |Sec. E3 | | Distortional | - | - | - | 17.914 | - |Sec. E4 | | Axial Comp | - | - | - | 2.282 | - |Sec. E2 | | Bending | - | - | - | 5.920 | - |Sec. F2 | | Major Local Bend | - | - | - | 5.924 | - |Sec. F3 | | Minor Local Bend | - | - | - | 6.239 | - |Sec. F3 | | Distortional | - | - | - | 21.674 | - |Sec. F4 | | Major Sectional | - | - | - | 21.674 | - |Sec. F2 | | Minor Sectional | - | - | - | 6.364 | - |Sec. F2 | | LTB Major | - | - | - | 5.920 | - |Sec. F2 | | Shear | - | - | - | 4.330 | - |Sec. G2 | | Major Shear (Z) | - | - | - | 4.330 | - |Sec. G2 | | Minor Shear (Y) | - | - | - | 5.081 | - |Sec. G2 | | Interaction | 1 | 0.00 | - | - |0.545|Eq. H1.1-1 | | (Bend+Ten) Int1 | 1 | 0.00 | - | - |0.545|Eq. H1.1-1 | |-----------------------------------------------------------------------------| 42. PARAMETER 2 43. CODE AISI 2016 44. METHOD ASD 45. FYLD 50 ALL 46. FU 58 ALL 47. FLX 0 ALL 48. TSA 0 ALL 49. TRACK 2 ALL 50. 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 362CS162-54 LEN: 120.000 LOC: 0.000 | | STATUS: PASS RATIO: 0.817 REF: Sec. D3 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 0.000 Criteria: Sec. D3 LC: 1 | | Fx:(T) -10.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -0.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 0.42200 Az: 0.15191 Ay: 0.18916 | | Cz: 0.53600 Cy: 1.81250 | | Iz: 0.87300 Iy: 0.15400 J: 0.00045 | | Sz: 0.48166 Sy: 0.14141 | | Rz: 1.43830 Ry: 0.60409 Cw: 0.45700 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 50.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 120.000 Lz: 120.000 Ly: 120.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 198.645 Allowable : 300.000 Ratio : 0.662 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.500 | 10.000 | PASS | | Width To Thickness Ratio | 23.710 | 60.000 | PASS | | Web Depth To Thickness Ratio | 59.046 | 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 | 1 | 0.00 | -10.000 | 12.238 |0.817|Sec. D3 | | Yielding | 1 | 0.00 | -10.000 | 12.635 |0.791|Sec. D2 | | Rupture | 1 | 0.00 | -10.000 | 12.238 |0.817|Sec. D3 | | Compression | - | - | - | 1.491 | - |Sec. E2 | | Local Comp | - | - | - | 1.491 | - |Sec. E3 | | Distortional | - | - | - | 11.709 | - |Sec. E4 | | Axial Comp | - | - | - | 1.491 | - |Sec. E2 | | Bending | - | - | - | 3.939 | - |Sec. F2 | | Major Local Bend | - | - | - | 3.941 | - |Sec. F3 | | Minor Local Bend | - | - | - | 4.151 | - |Sec. F3 | | Distortional | - | - | - | 14.421 | - |Sec. F4 | | Major Sectional | - | - | - | 14.421 | - |Sec. F2 | | Minor Sectional | - | - | - | 4.234 | - |Sec. F2 | | LTB Major | - | - | - | 3.939 | - |Sec. F2 | | Shear | - | - | - | 2.848 | - |Sec. G2 | | Major Shear (Z) | - | - | - | 2.848 | - |Sec. G2 | | Minor Shear (Y) | - | - | - | 3.343 | - |Sec. G2 | | Interaction | 1 | 0.00 | - | - |0.817|Eq. H1.1-1 | | (Bend+Ten) Int1 | 1 | 0.00 | - | - |0.817|Eq. H1.1-1 | |-----------------------------------------------------------------------------|