V. AISI 2016 ZS Flexural Strength
Verify the flexural strength in yielding of a cold-formed zee section according to the AISI S100 2016 specification using both the LRFD and ASD methods.
Details
A 1.5' long, simply supported beam is subjected to a uniform load in the global Y direction. The section used is a 12ZS3.25x105, Gr. 50 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 = 50 ksi
The modification factor, Cb, for a simply-supported beam under a uniformly distributed load:
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(50) = 139 ksi, Fn = Fy (Eq. F2.1-3).
Nominal capacity against lateral-torsional buckling about the major axis:
Mnez = SfzFn = 7.29 × 50 = 364.5 in·kips
The available flexural strength about the major axis:
- LRFD: ϕbMnez = 0.9 × 364.5 = 328.1 in·kips
- ASD: Mnez/Ωb = 364.5 / 1.67 = 218.3 in·kips
Minor axis bending:
| (Eq. F2.1.1-1) |
Per F2.1, where Fcre > 2.78Fy = 2.78(50) = 139 ksi, Fny = Fy (Eq. F2.1-3).
Elastic section modulus of full unreduced cross-section relative to extreme fiber in first yielding: Sfyy = Sfy.
Nominal capacity against lateral-torsional buckling about the major axis:
Mney = SfyFn = 1.22 × 50 = 61.0 in·kips
The available flexural strength about the major axis:
- LRFD: ϕbMney = 0.9 × 61.0 = 54.9 in·kips
- ASD: Mney/Ωb = 61.0 / 1.67 = 36.5 in·kips
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments | |
|---|---|---|---|---|---|
| LRFD | Flexural capacity about major axis (in·kips) | 328.1 | 327.750 | negligible | |
| Flexural capacity about minor axis (in·kips) | 54.9 | 54.074 | negligible | ||
| ASD | Flexural capacity about major axis (in·kips) | 218.3 | 218.064 | negligible | |
| Flexural capacity about minor axis (in·kips) | 36.5 | 35.977 | 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 ZS Flexural Strength.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
JOB NAME Fully Braced Hat Section
JOB CLIENT BENTLEY SYSTEMS Inc.
ENGINEER DATE 04-Mar-20
JOB REV 1.0
JOB REF AISI Manual Cold-Formed Steel Design - Vol. 1
ENGINEER NAME Abrar Ahmed
CHECKER NAME Binith Anto
APPROVED NAME Ahmed A
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 18 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL_50_AISI
E 29500
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
G 11153.8
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
ISOTROPIC STEEL
E 29000
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 12ZS3.25X105
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED BUT MY MZ
UNIT FEET POUND
LOAD 2 LOADTYPE Live TITLE LL
MEMBER LOAD
1 UNI GY -700
UNIT INCHES KIP
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
METHOD ASD
AXIS 1 ALL
FLX 0 ALL
FU 58 ALL
FYLD 50 ALL
TSA 0 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
METHOD LRFD
CHECK CODE ALL
FINISH
STAAD.Pro Output
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: 18.000 LOC: 9.000 | | STATUS: PASS RATIO: 0.067 REF: Sec. F3 LC: 2 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 9.000 Criteria: Sec. F3 LC: 2 | | Fx:(C) 0.000 Fy: 0.000 Fz: 0.000 | | Mx: 0.000 My: 0.000 Mz: -2.363 | |-----------------------------------------------------------------------------| | 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: 50.000 Fu: 58.000 E: 29000.000 G: 11300.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 18.000 Lz: 18.000 Ly: 18.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 2 Actual : 12.042 Allowable : 300.000 Ratio : 0.040 | |-----------------------------------------------------------------------------| | 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) [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 | - | - | - | 60.610 | - |Sec. D3 | | Yielding | - | - | - | 62.575 | - |Sec. D2 | | Rupture | - | - | - | 60.610 | - |Sec. D3 | | Compression | - | - | - | 33.801 | - |Sec. E4 | | Local Comp | - | - | - | 33.826 | - |Sec. E3 | | Distortional | - | - | - | 33.801 | - |Sec. E4 | | Axial Comp | - | - | - | 57.443 | - |Sec. E2 | | Bending | 2 | 9.00 | -2.295 | 34.319 |0.067|Sec. F3 | | Major Local Bend | 2 | 9.00 | -0.562 | 202.771 |0.003|Sec. F3 | | Minor Local Bend | 2 | 9.00 | -2.295 | 34.319 |0.067|Sec. F3 | | Distortional | 2 | 9.00 | -0.562 | 182.264 |0.003|Sec. F4 | | Major Sectional | 2 | 9.00 | -0.562 | 218.064 |0.003|Sec. F2 | | Minor Sectional | 2 | 0.00 | -2.295 | 35.977 |0.064|Sec. F2 | | Shear | 2 | 0.00 | -0.510 | 11.108 |0.046|Sec. G2 | | Major Shear (Z) | 2 | 0.00 | -0.510 | 11.108 |0.046|Sec. G2 | | Minor Shear (Y) | 2 | 0.00 | 0.125 | 8.873 |0.014|Sec. G2 | | Interaction | 2 | 0.00 | - | - |0.059|Sec. H2 | | (Bend+Ten) Int1 | 2 | 9.00 | - | - |0.011|Eq. H1.1-1 | | (Bend+Ten) Int2 | 2 | 9.00 | - | - |0.013|Eq. H1.1-2 | | (Bend+Comp) | 2 | 9.00 | - | - |0.013|Eq. H1.2-1 | | (Bend+Shear) Z | 2 | 0.00 | - | - |0.059|Sec. H2 | |-----------------------------------------------------------------------------| 59. PARAMETER 2 60. CODE AISI 2016 61. METHOD LRFD 62. CHECK CODE ALL STEEL DESIGN STAAD SPACE -- PAGE NO. 5 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: 18.000 LOC: 9.000 | | STATUS: PASS RATIO: 0.044 REF: Sec. F3 LC: 2 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 9.000 Criteria: Sec. F3 LC: 2 | | Fx:(C) 0.000 Fy: 0.000 Fz: 0.000 | | Mx: 0.000 My: 0.000 Mz: -2.363 | |-----------------------------------------------------------------------------| | 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: 50.000 Fu: 58.000 E: 29000.000 G: 11300.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 18.000 Lz: 18.000 Ly: 18.000 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 2 Actual : 12.042 Allowable : 300.000 Ratio : 0.040 | |-----------------------------------------------------------------------------| | 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) [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 | - | - | - | 90.915 | - |Sec. D3 | | Yielding | - | - | - | 94.050 | - |Sec. D2 | | Rupture | - | - | - | 90.915 | - |Sec. D3 | | Compression | - | - | - | 51.715 | - |Sec. E4 | | Local Comp | - | - | - | 51.753 | - |Sec. E3 | | Distortional | - | - | - | 51.715 | - |Sec. E4 | | Axial Comp | - | - | - | 87.888 | - |Sec. E2 | | Bending | 2 | 9.00 | -2.295 | 51.581 |0.044|Sec. F3 | | Major Local Bend | 2 | 9.00 | -0.562 | 304.765 |0.002|Sec. F3 | | Minor Local Bend | 2 | 9.00 | -2.295 | 51.581 |0.044|Sec. F3 | | Distortional | 2 | 9.00 | -0.562 | 273.942 |0.002|Sec. F4 | | Major Sectional | 2 | 9.00 | -0.562 | 327.750 |0.002|Sec. F2 | | Minor Sectional | 2 | 0.00 | -2.295 | 54.074 |0.042|Sec. F2 | | Shear | 2 | 0.00 | -0.510 | 16.884 |0.030|Sec. G2 | | Major Shear (Z) | 2 | 0.00 | -0.510 | 16.884 |0.030|Sec. G2 | | Minor Shear (Y) | 2 | 0.00 | 0.125 | 13.487 |0.009|Sec. G2 | | Interaction | 2 | 0.00 | - | - |0.039|Sec. H2 | | (Bend+Ten) Int1 | 2 | 9.00 | - | - |0.007|Eq. H1.1-1 | | (Bend+Ten) Int2 | 2 | 9.00 | - | - |0.009|Eq. H1.1-2 | | (Bend+Comp) | 2 | 9.00 | - | - |0.009|Eq. H1.2-1 | | (Bend+Shear) Z | 2 | 0.00 | - | - |0.039|Sec. H2 | |-----------------------------------------------------------------------------|