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
Validation
Polar radius of gyration of cross-section about shear center:
The flexural-torsional buckling stress: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:
The elastic flexural buckling stress about the y axis:
The elastic global buckling stress about the z axis is the minimum of Fcre and Fcrey1 ; so Fcrey = 7.275 ksi.
Global buckling about the Y axis governs.
Nominal capacity against global buckling:
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.
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 2024\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 |
|-----------------------------------------------------------------------------|