# V. AISI 2016 CS Flexural Strength

Verify the flexural strength of a cold-formed channel section according to the AISI S100 2016 specification using both the LRFD and ASD methods.

## Details

A 5' long, simply supported beam is subjected to a concentrated load of 1 kip/in at midspan in both the global Y and Z directions. The section used is a 12CS4x105, Gr. 36 steel.

Section Properties

Taken from AISI Manual, Cold-Formed Steel Design - Vol. 1, 2017 Table I-1.

• Area, Ag = 2.20 in2
• Radius of gyration z axis, rz = 4.65in
• Radius of gyration y axis, ry = 1.39 in
• Distance from centroid to shear center, xo = -2.63 in
• Elastic section modulus y axis, Sfy = 1.45 in3
• Elastic section modulus z axis, Sfz = 7.91 in3
• Torsional constant, J = 0.00808 in4
• Warping constant, Cw = 122 in6
• j = 6.74 in

Material Properties

• E = 29,000 ksi
• G = 11,300 ksi
• Fy = 36 ksi

## Validation

The modification factor, Cb, for a simply-supported beam under a concentrated load at midspan:

 $C b = 12.5 × M max 2.5 × M max + 3 × M a + 4 × M b + 3 × M c = 1.32$ (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(36) = 100.1 ksi, Fn = Fy (Eq. F2.1-3).

Nominal capacity against lateral-torsional buckling about the major axis:

Mnez = SfzFn = 7.91 × 36 = 284.8 in·kips

The available flexural strength about the major axis:

• LRFD: ϕbMnez = 0.9 × 284.8 = 256.3 in·kips
• ASD: Mnezb = 284.8 / 1.67 = 170.5 in·kips

Minor axis bending:

 (Eq. F2.1.2-2)

Simply-supported beam, so CTF = 1; assume compression on shear center side of centroid, so CS = +1.

 (Eq. F2.1.2-1)

Per F2.1, where Fcre > 2.78Fy = 2.78(36) = 100.1 ksi, Fn = Fy (Eq. F2.1-3).

Nominal capacity against lateral-torsional buckling about the major axis:

Mney = SfyFn = 1.45 × 36 = 52.2 in·kips

The available flexural strength about the major axis:

• LRFD: ϕbMney = 0.9 × 52.2 = 47.0 in·kips
• ASD: Mneyb = 52.2 / 1.67 = 31.3 in·kips

## Results

LRFD Flexural capacity about major axis (in·kips) 256.3 256.5 negligible
Flexural capacity about minor axis (in·kips) 47.0 46.898 negligible
ASD Flexural capacity about major axis (in·kips) 170.5 170.659 negligible
Flexural capacity about minor axis (in·kips) 31.3 31.203 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISI\AISI 2016 CS Flexural Strength.STD is typically installed with the program.

START JOB INFORMATION
ENGINEER DATE 11-Jan-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 5 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 12CS4X105
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT MY MZ
UNIT INCHES KIP
1 CON GY -1
1 CON GZ 1
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
METHOD LRFD
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
FYLD 36 ALL
FU 58 ALL
FLX 0 ALL
TSA 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1     SECTION:ST  12CS4X105       LEN:   60.000     LOC:  30.000 |
| STATUS: PASS       RATIO:  0.400             REF: Eq. H1.1-2    LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   30.000  Criteria:   Eq. H1.1-2           LC:           1       |
|  Fx:(C)        0.000       Fy:         0.500          Fz:      -0.500       |
|  Mx:           0.000       My:       -15.000          Mz:     -15.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         2.20000       Az:     0.71715            Ay:     1.19857       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:        47.50000       Iy:     4.27000             J:     0.00808       |
|  Sz:         7.91667       Sy:     1.44746                                  |
|  Rz:         4.64660       Ry:     1.39317            Cw:   122.00000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    36.000        Fu:    58.000      E:  29000.000       G:  11200.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:    60.000   Lz:    60.000   Ly:    60.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :   43.067   Allowable :  300.000   Ratio :   0.144    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.786   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     32.524   |     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            |   -   |   -    |     -    |   71.280 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   71.280 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   95.700 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |   39.758 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |   39.758 |  -  |Sec. E3    |
|   Distortional     |   -   |   -    |     -    |   50.926 |  -  |Sec. E4    |
|   Axial Comp       |   -   |   -    |     -    |   60.583 |  -  |Sec. E2    |
| Bending            |     1 |  30.00 |  -15.000 |   44.537 |0.337|Sec. F3    |
|   Major Local Bend |     1 |  30.00 |  -15.000 |  235.933 |0.064|Sec. F3    |
|   Minor Local Bend |     1 |  30.00 |  -15.000 |   44.537 |0.337|Sec. F3    |
|   Distortional     |     1 |  30.00 |  -15.000 |  242.008 |0.062|Sec. F4    |
|   Major Sectional  |     1 |  30.00 |  -15.000 |  256.500 |0.058|Sec. F2    |
|   Minor Sectional  |     1 |   0.00 |  -15.000 |   46.898 |0.320|Sec. F2    |
| Shear              |     1 |   0.00 |    0.500 |   13.487 |0.037|Sec. G2    |
|   Major Shear (Z)  |     1 |   0.00 |   -0.500 |   14.716 |0.034|Sec. G2    |
|   Minor Shear (Y)  |     1 |   0.00 |    0.500 |   13.487 |0.037|Sec. G2    |
| Interaction        |     1 |  30.00 |     -    |     -    |0.400|Eq. H1.1-2 |
|   (Bend+Ten) Int1  |     1 |  30.00 |     -    |     -    |0.378|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     1 |  30.00 |     -    |     -    |0.400|Eq. H1.1-2 |
|   (Bend+Comp)      |     1 |  30.00 |     -    |     -    |0.400|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     1 |  30.00 |     -    |     -    |0.074|Sec. H2    |
|   (Bend+Shear) Y   |     1 |  30.00 |     -    |     -    |0.339|Sec. H2    |
|-----------------------------------------------------------------------------|
44. PARAMETER 2
45. CODE AISI 2016
46. METHOD ASD
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  12CS4X105       LEN:   60.000     LOC:  30.000 |
| STATUS: PASS       RATIO:  0.602             REF: Eq. H1.1-2    LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   30.000  Criteria:   Eq. H1.1-2           LC:           1       |
|  Fx:(C)        0.000       Fy:         0.500          Fz:      -0.500       |
|  Mx:           0.000       My:       -15.000          Mz:     -15.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         2.20000       Az:     0.71715            Ay:     1.19857       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:        47.50000       Iy:     4.27000             J:     0.00808       |
|  Sz:         7.91667       Sy:     1.44746                                  |
|  Rz:         4.64660       Ry:     1.39317            Cw:   122.00000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    36.000        Fu:    58.000      E:  29000.000       G:  11200.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:    60.000   Lz:    60.000   Ly:    60.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :   43.067   Allowable :  300.000   Ratio :   0.144    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.786   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     32.524   |     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            |   -   |   -    |     -    |   47.425 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   47.425 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   63.800 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |   25.986 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |   25.986 |  -  |Sec. E3    |
|   Distortional     |   -   |   -    |     -    |   33.285 |  -  |Sec. E4    |
|   Axial Comp       |   -   |   -    |     -    |   39.597 |  -  |Sec. E2    |
| Bending            |     1 |  30.00 |  -15.000 |   29.632 |0.506|Sec. F3    |
|   Major Local Bend |     1 |  30.00 |  -15.000 |  156.974 |0.096|Sec. F3    |
|   Minor Local Bend |     1 |  30.00 |  -15.000 |   29.632 |0.506|Sec. F3    |
|   Distortional     |     1 |  30.00 |  -15.000 |  161.016 |0.093|Sec. F4    |
|   Major Sectional  |     1 |  30.00 |  -15.000 |  170.659 |0.088|Sec. F2    |
|   Minor Sectional  |     1 |   0.00 |  -15.000 |   31.203 |0.481|Sec. F2    |
| Shear              |     1 |   0.00 |    0.500 |    8.873 |0.056|Sec. G2    |
|   Major Shear (Z)  |     1 |   0.00 |   -0.500 |    9.682 |0.052|Sec. G2    |
|   Minor Shear (Y)  |     1 |   0.00 |    0.500 |    8.873 |0.056|Sec. G2    |
| Interaction        |     1 |  30.00 |     -    |     -    |0.602|Eq. H1.1-2 |
|   (Bend+Ten) Int1  |     1 |  30.00 |     -    |     -    |0.569|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     1 |  30.00 |     -    |     -    |0.602|Eq. H1.1-2 |
|   (Bend+Comp)      |     1 |  30.00 |     -    |     -    |0.602|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     1 |  30.00 |     -    |     -    |0.111|Sec. H2    |
|   (Bend+Shear) Y   |     1 |  30.00 |     -    |     -    |0.509|Sec. H2    |
|-----------------------------------------------------------------------------|