# 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

## Validation

The modification factor, Cb, for a simply-supported beam under a uniformly distributed load:

 $C b = 12.5 × M max 2.5 × M max + 3 × M a + 4 × M b + 3 × M c = 1.14$ (Eq. F2.1.1-2)

 (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: Mnezb = 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: Mneyb = 61.0 / 1.67 = 36.5 in·kips

## Results

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

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
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 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    |
|-----------------------------------------------------------------------------|