V. AISI 2016 Hat Section

Determine the flexural strength of a cold-formed hat section according to the AISI S100 2016 specification.

Reference

Cold-Formed Steel Design: AISI Manual. 2013 ed. Washington, D.C.: American Iron and Steel Institute, 2014. Example II-7.

Details

The member is 6' simply supported span. The section is a 3HU4.5X135. The top flange is in compression and is fully braced. Inelastic reserve is not considered.

• Live load: wLL = 700 plf
Section properties:
• t = 0.135 in (Note that STAAD.Pro uses a thickness of 0.14")
• R = 0.1875 in (Note that STAAD.Pro uses a bend radius of 0.19")
• Area: A = 1.74 in2
• Moment of inertia, weak axis: Iz = 2.47 in4
• Moment of inertia, strong axis: Iy = 8.29 in4
• Section modulus, strong axis: Sy = 1.52 in3
Material properties:
• E = 29,500 ksi
• G = 11,153 ksi
• Fy = 50 ksi
• Fu = 58 ksi

Validation

Design forces

My = (0.12)(6)2/8 + (0.7)(6)2/8 = 3.69 ft·kips = 44.3 in·kips

Muy = 1.2[(0.12)(6)2/8] + 1.6[(0.7)(6)2/8] = 5.69 ft·kips = 68.3 in·kips

Bending Capacity

Calculate nominal strength:

Mn = Se×Fy = 1.52 × 50 = 76.0 in·kips

Allowable strength:

Ultimate strength:

Results

Table 1.
Flexural strength, ASD $M n e Ω b$ (in·kips) 45.5 45.373 negligible
Flexural strength, LRFD $ϕ b M n e$ (in·kips) 68.4 68.196 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISI\AISI 2016 Hat Section.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 Poulami Raha
CHECKER NAME Aksha Saha
APPROVED NAME Carlos Aguera
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_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
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AMERICAN
1 TABLE ST 3HU4.5x135
CONSTANTS
MATERIAL STEEL_50_AISI ALL
SUPPORTS
1 2 FIXED BUT MY MZ
UNIT FEET POUND
1 UNI GY -120
1 UNI GY -700
UNIT INCHES KIP
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
METHOD LRFD
BEAM 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 ASD
BEAM 1 ALL
FLX 0 ALL
FU 58 ALL
FYLD 50 ALL
TSA 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
FINISH


            STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1     SECTION:3HU4.5X135          LEN:   72.000     LOC:  36.000 |
| STATUS: PASS       RATIO:  0.554             REF: Sec. F2       LC:      2  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   36.000  Criteria:   Sec. F2              LC:           2       |
|  Fx:(C)        0.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -37.800       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         1.73640       Az:     0.56954            Ay:     0.63585       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         2.46898       Iy:     8.28406             J:     0.01055       |
|  Sz:         1.51546       Sy:     2.18866                                  |
|  Rz:         1.19243       Ry:     2.18422            Cw:     5.19394       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    50.000        Fu:    58.000      E:  29500.000       G:  11153.000  |
|-----------------------------------------------------------------------------|
| 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 :   60.381   Allowable :  300.000   Ratio :   0.201    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.389   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     28.556   |    500.000   |      PASS     |
|  Web Depth To Thickness Ratio |     17.444   |    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            |   -   |   -    |     -    |   75.533 |  -  |Sec. D3    |
|   Yielding         |   -   |   -    |     -    |   78.138 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   75.533 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |   56.784 |  -  |Sec. E2    |
|   Local Comp       |   -   |   -    |     -    |   56.784 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |   56.784 |  -  |Sec. E2    |
| Bending            |     2 |  36.00 |   37.800 |   68.196 |0.554|Sec. F2    |
|   Local Bend       |     2 |  36.00 |   37.800 |   98.568 |0.383|Sec. F3    |
|   Major Sectional  |     2 |  36.00 |   37.800 |   68.196 |0.554|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |   98.490 |  -  |Sec. F2    |
| Shear              |     2 |   0.00 |    2.100 |   18.122 |0.116|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |   14.832 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     2 |   0.00 |    2.100 |   18.122 |0.116|Sec. G2    |
| Interaction        |     2 |  36.00 |     -    |     -    |0.554|Eq. H1.1-1 |
|   (Bend+Ten) Int1  |     2 |  36.00 |     -    |     -    |0.554|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     2 |  36.00 |     -    |     -    |0.554|Eq. H1.1-2 |
|   (Bend+Comp)      |     2 |  36.00 |     -    |     -    |0.554|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     2 |  36.00 |     -    |     -    |0.554|Sec. H2    |
|-----------------------------------------------------------------------------|
54. PARAMETER 2
55. CODE AISI 2016
56. METHOD ASD
57. BEAM 1 ALL
58. FLX 0 ALL
59. FU 58 ALL
60. FYLD 50 ALL
61. TSA 0 ALL
62. TRACK 2 ALL
63. 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:3HU4.5X135          LEN:   72.000     LOC:  36.000 |
| STATUS: PASS       RATIO:  0.833             REF: Sec. F2       LC:      2  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   36.000  Criteria:   Sec. F2              LC:           2       |
|  Fx:(C)        0.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -37.800       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         1.73640       Az:     0.56954            Ay:     0.63585       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         2.46898       Iy:     8.28406             J:     0.01055       |
|  Sz:         1.51546       Sy:     2.18866                                  |
|  Rz:         1.19243       Ry:     2.18422            Cw:     5.19394       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    50.000        Fu:    58.000      E:  29500.000       G:  11153.000  |
|-----------------------------------------------------------------------------|
| 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 :   60.381   Allowable :  300.000   Ratio :   0.201    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.389   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     28.556   |    500.000   |      PASS     |
|  Web Depth To Thickness Ratio |     17.444   |    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            |   -   |   -    |     -    |   50.356 |  -  |Sec. D3    |
|   Yielding         |   -   |   -    |     -    |   51.988 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   50.356 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |   37.114 |  -  |Sec. E2    |
|   Local Comp       |   -   |   -    |     -    |   37.114 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |   37.114 |  -  |Sec. E2    |
| Bending            |     2 |  36.00 |   37.800 |   45.373 |0.833|Sec. F2    |
|   Local Bend       |     2 |  36.00 |   37.800 |   65.581 |0.576|Sec. F3    |
|   Major Sectional  |     2 |  36.00 |   37.800 |   45.373 |0.833|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |   65.529 |  -  |Sec. F2    |
| Shear              |     2 |   0.00 |    2.100 |   11.922 |0.176|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    9.758 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     2 |   0.00 |    2.100 |   11.922 |0.176|Sec. G2    |
| Interaction        |     2 |  36.00 |     -    |     -    |0.833|Eq. H1.1-1 |
|   (Bend+Ten) Int1  |     2 |  36.00 |     -    |     -    |0.833|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     2 |  36.00 |     -    |     -    |0.833|Eq. H1.1-2 |
|   (Bend+Comp)      |     2 |  36.00 |     -    |     -    |0.833|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     2 |  36.00 |     -    |     -    |0.833|Sec. H2    |
|-----------------------------------------------------------------------------|