# V. AISI 2016 Channel section

Determine the flexural strength and shear strength of a cold-formed channel section without lips according to AISI S100 2016 Specification using both LRFD and ASD methods.

## Details

The member is a simply-supported, 6 ft span. The member is subject to a uniform load of 194.4 lbs/ft. The section used is a 550CU125-54.

Section Properties

• Depth of section, d = 5.698 in
• Width of section, b = 1.25 in
• Thickness, t = 0.0566 in
• Fillet radius, r = 0.0849 in
• Area, A = 0.452 in2
• Moment of inertia major axis, Izz = 1.9 in4
• Moment of inertia minor axis, Iyy = 0.053 in4
• Section modulus major axis, Zzz = 0.667 in3
• Section modulus minor axis, Zyy = 0.0512 in3
• Distance between centroid and shear center: x0 = -0.539 in
• Torsion constant, J = 0.00048 in4

Material Properties

• E = 29,500 ksi
• G = 11,300 ksi
• Fy = 33 ksi

Design Forces

• Mz = 10.5 ft·k
• Vy = 0.583 kips

## Validation

Lateral-Torsional Buckling Strength

Cb = 1.136

For singly symmetric sections bent about the axis of symmetry:

where
 Sf = the elastic section modulus for the unreduced section relative to the extreme compression fiber per AISI S100 2016. Hence, Sf = Sz .

For Fcre < 0.56Fy = 0.56 × 33 = 18.58, Fn = Fcre .

Mne = Fn × Sf = 14.15 × 0.667 = 9.433 in-k

Allowable nominal lateral-torsional buckling strength (ASD):

Design nominal lateral-torsional buckling strength (LRFD):

My = Fy × Sf = 33 × 0.667 = 22.01 in-k

Allowable nominal bending strength (ASD):

Design nominal bending strength (LRFD):

Local Buckling Interaction with Yield and Global Buckling

From Section F3:

Se = 0.665 in3

Mnl = Se × Fn = 0.665 × 14.15 = 9.412 in-k

Allowable nominal bending strength (ASD):

Design nominal bending strength (LRFD):

Governing strength ratio:

LRFD: 10.498 / 8.471 = 1.239

ASD: 10.498 / 5.636 = 1.862

Shear Strength along Minor Axis

h = D - 2× (t - r) = 5.698 - 2× (0.0566 - 0.0849) = 5.145 in

h /t = 5.415 / 0.0566 = 95.67

Aw = h × t = 5.415 × 0.0566 = 0.307 in2

Vy = 0.6 × Aw × Fy = 0.6 × 0.307 × 33 = 6.069 kip

Vcr = Aw × Fcr = 0.307 × 15.56 = 4.75 kip

$λ v = V y V cr = 6.069 4.75 = 1.128$

For 0.815 < λv ≤ 1.227,

Allowable nominal shear strength (ASD):

Design nominal shear strength (LRFD):

Governing strength ratio:

LRFD: 0.583 / 4.165 = 0.14

ASD: 0.583 / 2.74 = 0.213

Table 1. Comparison of results
LRFD Major bending (in-k) 19.81 19.807 negligible
LTB bending (in-k) 8.49 8.49 none
Major local bending (in-k) 8.471 8.477 negligible
Bending ratio 1.239 1.238 negligible
Shear strength (kips) 4.165 4.163 negligible
Shear ratio 0.14 0.14 none
ASD Major bending (in-k) 13.18 13.178 negligible
LTB bending (in-k) 5.649 5.649 none
Major local bending (in-k) 5.636 5.64 negligible
Bending ratio 1.862 1.861 negligible
Shear strength (kips) 2.739 2.739 none
Shear ratio 0.213 0.213 none

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

STAAD SPACE
START JOB INFORMATION
JOB NAME AISI C-Section Without Lips Braced at Mid-Span
JOB CLIENT BENTLEY SYSTEMS Inc.
ENGINEER DATE 04-Mar-20
JOB REV 1.0
JOB REF AISI Manual Cold-Formed Steel Design - Vol. 1
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 72 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29500
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 550CU125-54
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
1 UNI GY -0.0162
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
METHOD LRFD
BEAM 1 ALL
FYLD 33 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 1
CODE AISI 2016
METHOD ASD
BEAM 1 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  550CU125-54     LEN:   72.000     LOC:  36.000 |
| STATUS: FAIL       RATIO:  1.238             REF: Sec. F3       LC:      2  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   36.000  Criteria:   Sec. F3              LC:           2       |
|  Fx:(C)        0.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -10.498       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.45200       Az:     0.12548            Ay:     0.30649       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         1.90000       Iy:     0.05300             J:     0.00048       |
|  Sz:         0.66690       Sy:     0.05121                                  |
|  Rz:         2.05025       Ry:     0.34243            Cw:     0.31500       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    33.000        Fu:    58.000      E:  29500.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:    72.000   Lz:    72.000   Ly:    72.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     2   Actual :  210.263   Allowable :  300.000   Ratio :   0.701    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.500   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     19.585   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |     95.671   |    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            |   -   |   -    |     -    |   13.424 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   13.424 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   19.662 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |    2.185 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |    2.185 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |    2.219 |  -  |Sec. E2    |
| Bending            |     2 |  36.00 |  -10.498 |    8.477 |1.238|Sec. F3    |
|   Major Local Bend |     2 |  36.00 |  -10.498 |    8.477 |1.238|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    1.518 |  -  |Sec. F3    |
|   Major Sectional  |     2 |  36.00 |  -10.498 |   19.807 |0.530|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    1.521 |  -  |Sec. F2    |
|   LTB Major        |     2 |  36.00 |  -10.498 |    8.490 |1.236|Sec. F2    |
| Shear              |     2 |   0.00 |    0.583 |    4.163 |0.140|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    2.360 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     2 |   0.00 |    0.583 |    4.163 |0.140|Sec. G2    |
| Interaction        |     2 |  36.00 |     -    |     -    |1.238|Eq. H1.1-2 |
|   (Bend+Ten) Int1  |     2 |  36.00 |     -    |     -    |0.530|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     2 |  36.00 |     -    |     -    |1.238|Eq. H1.1-2 |
|   (Bend+Comp)      |     2 |  36.00 |     -    |     -    |1.238|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     2 |  36.00 |     -    |     -    |0.591|Sec. H2    |
|-----------------------------------------------------------------------------|
43. PARAMETER 1
44. CODE AISI 2016
45. METHOD ASD
46. BEAM 1 ALL
47. TRACK 2 ALL
48. 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  550CU125-54     LEN:   72.000     LOC:  36.000 |
| STATUS: FAIL       RATIO:  1.861             REF: Sec. F3       LC:      2  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   36.000  Criteria:   Sec. F3              LC:           2       |
|  Fx:(C)        0.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -10.498       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.45200       Az:     0.12548            Ay:     0.30649       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         1.90000       Iy:     0.05300             J:     0.00048       |
|  Sz:         0.66690       Sy:     0.05121                                  |
|  Rz:         2.05025       Ry:     0.34243            Cw:     0.31500       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    33.000        Fu:    58.000      E:  29500.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:    72.000   Lz:    72.000   Ly:    72.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     2   Actual :  210.263   Allowable :  300.000   Ratio :   0.701    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.500   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     19.585   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |     95.671   |    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            |   -   |   -    |     -    |    8.932 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |    8.932 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   13.108 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |    1.428 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |    1.428 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |    1.450 |  -  |Sec. E2    |
| Bending            |     2 |  36.00 |  -10.498 |    5.640 |1.861|Sec. F3    |
|   Major Local Bend |     2 |  36.00 |  -10.498 |    5.640 |1.861|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    1.010 |  -  |Sec. F3    |
|   Major Sectional  |     2 |  36.00 |  -10.498 |   13.178 |0.797|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    1.012 |  -  |Sec. F2    |
|   LTB Major        |     2 |  36.00 |  -10.498 |    5.649 |1.858|Sec. F2    |
| Shear              |     2 |   0.00 |    0.583 |    2.739 |0.213|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    1.553 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     2 |   0.00 |    0.583 |    2.739 |0.213|Sec. G2    |
| Interaction        |     2 |  36.00 |     -    |     -    |1.861|Eq. H1.1-2 |
|   (Bend+Ten) Int1  |     2 |  36.00 |     -    |     -    |0.797|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     2 |  36.00 |     -    |     -    |1.861|Eq. H1.1-2 |
|   (Bend+Comp)      |     2 |  36.00 |     -    |     -    |1.861|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     2 |  36.00 |     -    |     -    |0.888|Sec. H2    |
|-----------------------------------------------------------------------------|