# V. AISC 360-10 C LTB Test F.2-2

Verify the lateral flexural strength of a compact channel section braced at the fifth points per the LRFD and ASD methods of the AISC 360-10 code.

## Reference

1. American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
2. American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example F.2-2A and F.2-2B, pp F-19 - F21

## Problem

Check a C15x33.9 channel of ASTM A36 steel which serves as a roof edge beam. The simple span is 25 ft. The nominal loads on the member are a dead load 0.23 kip/ft and a uniform live load of 0.69 kip/ft. The beam is braced at fifth points and at ends.

## Validation

Ultimate moment:

Service moment:

The unbraced length, >Lb = 5 ft.

Try a C15×33.9, which has a plastic section modulus, Zx = 50.8 in3.

The lateral-torsional buckling modification factor, Cb = 1.0 for the center span of this bracing & loading condition.

 $L p = 1.76 r y E F y = 1.76 ( 0.901 ) 29 , 000 36 ( 1 12 ) = 3.75 ft$ (F2-5)
 (F2-6)
Note: This is the simplified, conservative calculation for Lr per the User Note used to verify that the section is in the plastic-elastic range. The reference uses the more exact calculation but the resulting flexural strength values are essentially equal.

Lp < Lb ≤ Lr

All ASTM A36 grade C-shapes are compact.

The nominal flexural strength for the flexural yielding limit state is:

The nominal flexural strength for the lateral-torsional buckling limit state is:

$M n = C b [ M p − ( M p − 0.7 F y S x ) ( L b − L p L r − L p ) ]$

The available flexural strength:

LRFD:

ASD:

## Comparison

Table 1. Comparison of results
ϕbMn (kips) [LRFD] 131 130 negligible
Mnb (kips) [ASD] 86.8 86.7 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 C LTB Test F.STD is typically installed with the program.

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 30-Mar-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 25 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
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST C15X33
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
1 UNI GY -0.23
1 UNI GY -0.69
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2010
FYLD 5184 ALL
FU 8352 ALL
CB 1 ALL
FLX 1 ALL
METHOD LRFD
TRACK 2 ALL
UNB 5 ALL
UNT 5 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FYLD 5184 ALL
FU 8352 ALL
CB 1 ALL
FLX 1 ALL
METHOD ASD
TRACK 2 ALL
UNB 5 ALL
UNT 5 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*     1 ST   C15X33                   (AISC SECTIONS)
FAIL   SLENDERNESS          1.113         3
0.00            0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    333.952  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     1.113(FAIL)                 |
|          Loc  :    0.00   Condition :   SLENDERNESS                   |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   1.725E+01     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   4.420E+00     Ayy:   6.000E+00     Cw:  3.555E+02              |
| Szz:   4.200E+01     Syy:   3.178E+00                                 |
| Izz:   3.150E+02     Iyy:   8.070E+00     Ix:  9.595E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        5183.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        25.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     5.23     N/A     15.89    T.B4.1(a)-1  |
|                Non-Slender    34.25     N/A     42.29    T.B4.1(a)-5  |
| Flexure     :  Compact         5.23    10.79    28.38    T.B4.1(b)-10 |
|                Compact        34.25   106.72   161.78    T.B4.1(b)-15 |
STAAD SPACE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   3.24E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   4.35E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   2.79E+02   0.000      Eq. E3-1      3     0.00 |
| Min Buck    0.00E+00   2.03E+01   0.000      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   2.03E+02   0.000      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    6.94E-02    53.45   4.46E+03   1.44E+04   3.10E+02        |
| Min Buck    6.94E-02   333.95   3.24E+02   3.70E+02   2.25E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    6.94E-02   3.24E+03   2.25E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   8.59E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     1.72E+01   1.17E+02   0.148      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     3.07E-02     1.00     1.20     5.23   9.55E+01            |
| Local-Y     4.17E-02     1.00     5.00    34.25   1.30E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.08E+02   1.37E+02   0.786      Eq. F2-1      3    12.50 |
| Minor       0.00E+00   1.37E+01   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.52E+02   0.00E+00                                       |
| Minor       1.53E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.08E+02   1.30E+02   0.828      Eq. F2-2      3    12.50 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       1.45E+02   0.00E+00    1.00     3.74    14.26     5.00    |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.828      Eq. H1-1b     3    12.50             |
| Flexure Tens          0.828      Eq. H1-1b     3    12.50             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         1.30E+02   1.08E+02   2.03E+01                   |
|                      1.37E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         1.30E+02   1.08E+02   3.24E+02                   |
|                      1.37E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
52. PARAMETER 2
53. CODE AISC UNIFIED 2010
54. FYLD 5184 ALL
55. FU 8352 ALL
56. CB 1 ALL
57. FLX 1 ALL
58. METHOD ASD
59. TRACK 2 ALL
60. UNB 5 ALL
61. UNT 5 ALL
62. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*     1 ST   C15X33                   (AISC SECTIONS)
FAIL   SLENDERNESS          1.113         4
0.00            0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    333.952  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     1.113(FAIL)                 |
|          Loc  :    0.00   Condition :   SLENDERNESS                   |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   1.150E+01     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   4.420E+00     Ayy:   6.000E+00     Cw:  3.555E+02              |
| Szz:   4.200E+01     Syy:   3.178E+00                                 |
| Izz:   3.150E+02     Iyy:   8.070E+00     Ix:  9.595E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        5183.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        25.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     5.23     N/A     15.89    T.B4.1(a)-1  |
|                Non-Slender    34.25     N/A     42.29    T.B4.1(a)-5  |
| Flexure     :  Compact         5.23    10.79    28.38    T.B4.1(b)-10 |
|                Compact        34.25   106.72   161.78    T.B4.1(b)-15 |
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   2.16E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   2.90E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.85E+02   0.000      Eq. E3-1      4     0.00 |
| Min Buck    0.00E+00   1.35E+01   0.000      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.35E+02   0.000      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    6.94E-02    53.45   4.46E+03   1.44E+04   3.10E+02        |
| Min Buck    6.94E-02   333.95   3.24E+02   3.70E+02   2.25E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    6.94E-02   3.24E+03   2.25E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   5.72E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     1.15E+01   7.76E+01   0.148      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     3.07E-02     1.00     1.20     5.23   9.55E+01            |
| Local-Y     4.17E-02     1.00     5.00    34.25   1.30E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       7.19E+01   9.13E+01   0.788      Eq. F2-1      4    12.50 |
| Minor       0.00E+00   9.14E+00   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.52E+02   0.00E+00                                       |
| Minor       1.53E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       7.19E+01   8.67E+01   0.829      Eq. F2-2      4    12.50 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       1.45E+02   0.00E+00    1.00     3.74    14.26     5.00    |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.829      Eq. H1-1b     4    12.50             |
| Flexure Tens          0.829      Eq. H1-1b     4    12.50             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         8.67E+01   7.19E+01   1.35E+01                   |
|                      9.14E+00   0.00E+00   0.00E+00                   |
| Flexure Tens         8.67E+01   7.19E+01   2.16E+02                   |
|                      9.14E+00   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
63. FINISH