V. AISI 2016 ZS Compressive Strength
Verify the compressive strength of a cold-formed zee section with lips per the AISI S100 2016 specification.
Details
A 15' long, simply supported beam is subjected to a 10 kip axial load (compression). The section used is a 12ZS3.25x105, Grade 36 steel.
Section Properties
Taken from AISI Manual, Cold-Formed Steel Design - Vol. 1, 2017 Table I-1.
- Area, Ag = 2.09 in2
- Radius of gyration z axis, rz = 4.57 in
- Radius of gyration y axis, ry = 1.49 in
- Elastic section modulus y axis, Sfy = 1.22 in3
- Elastic section modulus z axis, Sfz = 7.29 in3
- Torsional constant, J = 0.00769 in4
- Warping constant, Cw = 123 in6
Material Properties
- E = 29,000 ksi
- G = 11,300 ksi
- Fy = 36 ksi
(Eq. E2.1-1) |
Polar radius of gyration of cross-section about shear center:
(Eq. E2.2-4) |
(Eq. E2.2-5) |
(Eq. E2.2-6) |
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 Fcrey1 and σt; so Fcrey = 19.61 ksi.
(Eq. E2-4) |
(Eq. E2-2) |
Global buckling about the Y axis governs.
Nominal capacity against global buckling:
Pn = AgFn = 2.09 × 16.69 = 34.89 kips
The available axial strength:
- LRFD: ϕcPn = 0.85 × 34.89 = 29.66 kips
- ASD: Pn/Ωc = 34.89 / 1.8 = 19.38 kips
For local buckling about the Z axis, the effective area, Ae = 1.586 in2.
Pnℓz = Ae × Fnz = 1.586 × 19.28 = 30.56 kips
For local buckling about the Y axis, the effective area, Ae = 1.627 in2.
Pnℓy = Ae × Fnz = 1.627 × 16.69 = 27.15 kips
Pnℓ is taken as the minimum of Pnℓz, Pnℓy, and Pne; so Pnℓ = 27.15 kips.
- LRFD: ϕcPnℓ = 0.85 × 27.15 = 23.08 kips
- ASD: Pnℓ/Ωc = 27.15 / 1.8 = 15.06 kips
Determine the compression capacity for distortional buckling as per E4:
The elastic distortional buckling stress, Fcrd = 30.84 ksi.
The elastic distortional buckling load, Pcrd = Ag × Fcrd = 2.09 × 30.84 = 64.46 kips.
Py = Ag × Fy = 2.09 × 36 = 75.24 kips | (Eq. E4.1-4) |
(Eq. E4.1-3) |
(Eq. 4.1-2) |
The available axial strength:
- LRFD: ϕcPnd = 0.85 × 52.95 = 45.01 kips
- ASD: Pnd/Ωc = 52.95 / 1.8 = 29.42 kips
Results
Result Type | Reference | STAAD.Pro | Difference | Comments | |
---|---|---|---|---|---|
LRFD | Local compression capacity (kips) | 23.08 | 23.212 | negligible | |
Distorional buckling capacity (kips) | 45.01 | 45.006 | negligible | ||
Axial compression capacity (kips) | 29.66 | 29.809 | negligible | ||
ASD | Local compression capacity (kips) | 15.06 | 15.171 | negligible | |
Distorional buckling capacity (kips) | 29.42 | 29.416 | negligible | ||
Axial compression capacity (kips) | 19.38 | 19.483 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISI\AISI 2016 ZS 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 15 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 12ZS3.25X105
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
AXIS 1 ALL
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
AXIS 1 ALL
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 12ZS3.25X105 LEN: 180.000 LOC: 0.000 | | STATUS: PASS RATIO: 0.431 REF: Sec. E3 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 0.000 Criteria: Sec. E3 LC: 1 | | Fx:(C) 10.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -0.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 2.09000 Az: 0.59243 Ay: 1.19857 | | Cz: 0.00000 Cy: 0.00000 | | Iz: 43.70000 Iy: 4.67000 J: 0.00769 | | Sz: 7.28333 Sy: 1.20164 | | Rz: 4.57265 Ry: 1.49481 Cw: 123.00000 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 36.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 180.000 Lz: 180.000 Ly: 180.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 120.417 Allowable : 200.000 Ratio : 0.602 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.786 | 10.000 | PASS | | Width To Thickness Ratio | 26.868 | 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 | - | - | - | 67.716 | - |Sec. D2 | | Yielding | - | - | - | 67.716 | - |Sec. D2 | | Rupture | - | - | - | 90.915 | - |Sec. D3 | | Compression | 1 | 0.00 | -10.000 | 23.212 |0.431|Sec. E3 | | Local Comp | 1 | 0.00 | -10.000 | 23.212 |0.431|Sec. E3 | | Distortional | 1 | 0.00 | -10.000 | 45.006 |0.222|Sec. E4 | | Axial Comp | 1 | 0.00 | -10.000 | 29.809 |0.335|Sec. E2 | | Bending | - | - | - | 38.933 | - |Sec. F2 | | Major Local Bend | - | - | - | 99.087 | - |Sec. F3 | | Minor Local Bend | - | - | - | 39.498 | - |Sec. F3 | | Distortional | - | - | - | 222.225 | - |Sec. F4 | | Major Sectional | - | - | - | 235.980 | - |Sec. F2 | | Minor Sectional | - | - | - | 38.933 | - |Sec. F2 | | LTB Major | - | - | - | 98.978 | - |Sec. F2 | | Shear | - | - | - | 12.157 | - |Sec. G2 | | Major Shear (Z) | - | - | - | 12.157 | - |Sec. G2 | | Minor Shear (Y) | - | - | - | 13.487 | - |Sec. G2 | | Interaction | 1 | 0.00 | - | - |0.431|Eq. H1.2-1 | | (Bend+Comp) | 1 | 0.00 | - | - |0.431|Eq. H1.2-1 | |-----------------------------------------------------------------------------| 43. PARAMETER 2 44. CODE AISI 2016 45. METHOD ASD 46. AXIS 1 ALL 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 12ZS3.25X105 LEN: 180.000 LOC: 0.000 | | STATUS: PASS RATIO: 0.659 REF: Sec. E3 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 0.000 Criteria: Sec. E3 LC: 1 | | Fx:(C) 10.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -0.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 2.09000 Az: 0.59243 Ay: 1.19857 | | Cz: 0.00000 Cy: 0.00000 | | Iz: 43.70000 Iy: 4.67000 J: 0.00769 | | Sz: 7.28333 Sy: 1.20164 | | Rz: 4.57265 Ry: 1.49481 Cw: 123.00000 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 36.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 180.000 Lz: 180.000 Ly: 180.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 120.417 Allowable : 200.000 Ratio : 0.602 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.786 | 10.000 | PASS | | Width To Thickness Ratio | 26.868 | 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 | - | - | - | 45.054 | - |Sec. D2 | | Yielding | - | - | - | 45.054 | - |Sec. D2 | | Rupture | - | - | - | 60.610 | - |Sec. D3 | | Compression | 1 | 0.00 | -10.000 | 15.171 |0.659|Sec. E3 | | Local Comp | 1 | 0.00 | -10.000 | 15.171 |0.659|Sec. E3 | | Distortional | 1 | 0.00 | -10.000 | 29.416 |0.340|Sec. E4 | | Axial Comp | 1 | 0.00 | -10.000 | 19.483 |0.513|Sec. E2 | | Bending | - | - | - | 25.904 | - |Sec. F2 | | Major Local Bend | - | - | - | 65.926 | - |Sec. F3 | | Minor Local Bend | - | - | - | 26.280 | - |Sec. F3 | | Distortional | - | - | - | 147.854 | - |Sec. F4 | | Major Sectional | - | - | - | 157.006 | - |Sec. F2 | | Minor Sectional | - | - | - | 25.904 | - |Sec. F2 | | LTB Major | - | - | - | 65.854 | - |Sec. F2 | | Shear | - | - | - | 7.998 | - |Sec. G2 | | Major Shear (Z) | - | - | - | 7.998 | - |Sec. G2 | | Minor Shear (Y) | - | - | - | 8.873 | - |Sec. G2 | | Interaction | 1 | 0.00 | - | - |0.659|Eq. H1.2-1 | | (Bend+Comp) | 1 | 0.00 | - | - |0.659|Eq. H1.2-1 | |-----------------------------------------------------------------------------|