# V. AISC 360-16 I Compression LRFD

Verify the flexural buckling capacity of an I section under compressive load using the LRFD method per the ASIC 360-16 code.

## References

1. Steel Construction Manual, 15th Edition, American Institute of Steel Construction, 2017

## Details

Verify the Flexural Buckling strength of an I Section (W14x90) using the LRFD method

Steel Gr. ASTM A992, about X and Y axis with a member length of 30 ft with dead load 140 kips and Live Load 420 kips.

## Validation

Strong axis unbraced length, Lx = 360 in

Torsional axis unbraced length Ly = 180 in

Ultimate load, Pu = 1.2(180 kips) + 1.6(420 kips) = 840 kips

Calculation for major axis (X axis)

From Table C-A-7.1 of ref. 1, K = 1.0 for a pinned-pinned condition.

$b f 2 t f = 10.211 < 0.56 E F y = 13.487$, thus the flange is non-slender.

Slenderness ratio about X axis $= K L x r x = 58.632 < 4.71 E F y = 113.432$

Calculate the elastic critical buckling stress: $F e X = π 2 E ( K L x / r x ) 2 = 83.259 ksi$

Calculate the flexural buckling stress: $F c r X = 0.658 F y / F e X F y = 38.887 ksi$

Compressive strength for flexural buckling along X: $ϕ c P n F B X = ϕ c F c r X A g = 947.462 kips$

Ratio for flexural buckling strength = 0.906

Calculation for minor axis (Y axis)

h = d - 2·tf = 12.58 in

$h t w = 28.591 < 35.884$, thus the flange is non-slender.

Slenderness ratio about Y axis $= K L y r y = 48.703 < 4.71 E F y = 113.432$

Calculate the elastic critical buckling stress: $F e Y = π 2 E ( K L y / r y ) 2 = 120.668 ksi$

Calculate the flexural buckling stress: $F c r Y = 0.658 F y / F e Y F y = 42.039 ksi$

Compressive strength for flexural buckling along Y: $ϕ c P n F B Y = ϕ c F c r Y A g = 1 , 002.625 kips$

Ratio for flexural buckling strength = 0.838

## Results

Table 1. Comparison of results
Flexural Buckling Capacity, X Axis (kips) 927.5 927.5 none
Ratio 0.906 0.906 none
Flexural Buckling Capacity, Y Axis (kips) 1,003 1,003 none
Ratio 0.838 0.838 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\360-2016\Compression\AISC 360-16 I Compression LRFD.STD is typically installed with the program.

START JOB INFORMATION
ENGINEER DATE 12-Jan-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 30 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 FY 7200 FU 9360 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X90
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
2 FY -140
2 FY -420
1 1.2 2 1.6
PERFORM ANALYSIS
*CODE AISC UNIFIED 2016
PARAMETER 1
CODE AISC UNIFIED 2016
FU 9360 ALL
FYLD 7200 ALL
KX 1 ALL
KY 1 ALL
KZ 1 ALL
LX 30 ALL
LY 15 ALL
LZ 30 ALL
METHOD LRFD
PROFILE W14 ALL
STP 1 ALL
*SGR 28 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
*****************************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted).
***NOTE : AISC 360-16 Design Statement for STAAD.Pro.
*** AXIS CONVENTION ***:
========================
The capacity results and intermediate results in the report follow the notations
and axes labels as defined in the AISC 360-16 code.
The analysis results are reported in STAAD.Pro axis convention and the AISC 360:16
design results are reported in AISC 360-16 code axis convention.
------------    -----------     -------------
X               Z          Axis typically parallel to the sections principal major axis.
Y               Y          Axis typically parallel to the sections principal minor axis.
Z               X          Longitudinal axis perpendicular to the cross section.
SECTION FORCES AXIS MAPPING: -
------------    -----------     -------------
Pz              FX         Axial force.
Vy              FY         Shear force along minor axis.
Vx              FZ         Shear force along major axis.
Tz              MX         Torsional moment.
My              MY         Bending moment about minor axis.
Mx              MZ         Bending moment about major axis.
*** DESIGN MESSAGES ***:
=======================
1. Section classification reported is for the cross section and loadcase that
produced the worst case design ratio for flexure/compression Capacity results.
2. Results for any Capacity/Check that is not relevant for a section/loadcase
based on the code clause in AISC 360-16 will not be shown in the report.
3. Bending results are reported as being �about� the relevant axis (X/Y), while
the results for shear are reported as being for shear forces �along� the axis.
E.g : Mx indicates bending about the X axis, while Vx indicates shear along
the X axis.
*** ABBREVIATIONS ***:
======================
F-T-B = Flexural-Torsional Buckling
L-T-B = Lateral-Torsional Buckling
F-L-B = Flange Local Buckling
W-L-B = Web Local Buckling
L-L-B = Leg Local Buckling
C-F-Y = Compression Flange Yielding
T-F-Y = Tension Flange Yielding
STAAD SPACE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
*****************************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted).
- Member :     1
|-----------------------------------------------------------------------------|
|  Member No:        1       Profile:  ST  W14X90              (AISC SECTIONS)|
|  Status:        FAIL       Ratio:         1.004       Loadcase:        3    |
|  Location:      0.00       Ref:      Cl.E4                                  |
|  Pz:       840.0     C     Vy:        0.000           Vx:      0.000        |
|  Tz:       0.000           My:        0.000           Mx:      0.000        |
|-----------------------------------------------------------------------------|
| SLENDERNESS                                                                 |
| Actual Slenderness Ratio    :     58.633                                    |
| Allowable Slenderness Ratio :    200.000            LOC  :     0.00         |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS                                                             |
| Critical L/C  :      3             Ratio     :        1.004(FAIL)           |
|          Loc  :    0.00            Condition :    Cl.E4                     |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES  (LOC:     0.00, PROPERTIES UNIT: IN  )                  |
| Ag  :   2.650E+01     Axx :   2.059E+01     Ayy :   6.160E+00               |
| Ixx :   9.990E+02     Iyy :   3.620E+02     J   :   4.060E+00               |
| Sxx+:   1.427E+02     Sxx-:   1.427E+02     Zxx :   1.570E+02               |
| Syy+:   4.993E+01     Syy-:   4.993E+01     Zyy :   7.560E+01               |
| Cw  :   1.593E+04     x0  :   0.000E+00     y0  :   0.000E+00               |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                         |
| Fyld:        7200.000              Fu:        9359.999                      |
|-----------------------------------------------------------------------------|
| Actual Member Length:        30.000                                         |
| Design Parameters                                            (Rolled)       |
| Kx:    1.00  Ky:    1.00  NSF:    1.00  SLF:    1.00  CSP:    1.00          |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C:      3 LOC:   360.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonSlender      10.21       N/A      13.49     Table.4.1a.Case1     |
| Web   : NonSlender      28.59       N/A      35.88     Table.4.1a.Case5     |
|                                                                             |
| FLEXURE CLASSIFICATION     (L/C:      3 LOC:   360.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonCompact      10.21       9.15     24.08     Table.4.1b.Case10    |
| Web   : Compact         28.59      90.55    137.27     Table.4.1b.Case15    |
|-----------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
*****************************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted).
- Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL TENSION                            |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING                                                            |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       1192.       0.000     Cl.D2          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Ten. Yld Cap         : Pn     =  1325.0     kip        Eq.D2-1        |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE                                                             |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       1292.       0.000     Cl.D2          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective area            : Ae     = 0.18403     ft2        Eq.D3-1        |
|  Nom. Ten. Rpt Cap         : Pn     =  1722.5     kip        Eq.D2-2        |
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL COMPRESSION                        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              840.0       927.5       0.906     Cl.E3          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcx/rx =  58.633                Cl.E2          |
|  Elastic Buckling Stress   : Fex    =  11989.     kip/ft2    Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrx   =  5599.7     kip/ft2    Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnx    =  1030.5     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              840.0       1003.       0.838     Cl.E3          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcy/ry =  48.701                Cl.E2          |
|  Elastic Buckling Stress   : Fey    =  17377.     kip/ft2    Eq.E3-4        |
|  Crit. Buckling Stress     : Fcry   =  6053.6     kip/ft2    Eq.E3-2        |
|  Nom. Flexural Buckling    : Pny    =  1114.0     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEX-TOR-BUCKLING                                                           |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              840.0       837.0       1.004     Cl.E4          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Elastic F-T-B Stress      : Fe     =  8513.5     kip/ft2    Eq.E4-2        |
|  Crit. F-T-B Stress        : Fcr    =  5053.6     kip/ft2    Eq.E3-2        |
|  Nom. Flex-tor Buckling    : Pn     =  930.01     kip        Eq.E4-1        |
|-----------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
*****************************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted).
- Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR SHEAR                                    |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       555.9       0.000     Cl.G1          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Coefficient Cv Along X    : Cv     =  1.0000                Eq.G2-9        |
|  Coefficient Kv Along X    : Kv     =  1.2000                Cl.G6          |
|  Nom. Shear Along X        : Vnx    =  617.70     kip        Eq.G6-1        |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       184.8       0.000     Cl.G1          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Coefficient Cv Along Y    : Cv     =  1.0000                -              |
|  Coefficient Kv Along Y    : Kv     =  5.3400                Eq.G2-5        |
|  Nom. Shear Along Y        : Vny    =  184.80     kip        Eq.G2-1        |
|-----------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
*****************************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted).
- Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR BENDING                                  |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (Y)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       283.5       0.000     Cl.F6.1        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along Y : Mny    =  315.00     kip-ft     Eq.F6-1        |
|-----------------------------------------------------------------------------|
| LAT TOR BUCK ABOUT X                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       465.8       0.000     Cl.F2.2        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom L-T-B Cap             : Mnx    =  517.55     kip-ft     Eq.F2-2        |
|  Mom. Distr. factor        : CbX    =  1.0000                Custom         |
|  Limiting Unbraced Length  : LpX    =  13.055     ft         Eq.F2-5        |
|  coefficient C             : Cx     =  1.0000                Eq.F2-8a       |
|  Effective Rad. of Gyr.    : Rts    = 0.34183     ft         Eq.F2-7        |
|  Limiting Unbraced Length  : LrX    =  42.564     ft         Eq.F2-6        |
|-----------------------------------------------------------------------------|
| FLANGE LOCAL BUCK(X)                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       573.6       0.000     Cl.F3.1        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom F-L-B Cap             : Mnx    =  637.28     kip-ft     Eq.F3-1        |
|-----------------------------------------------------------------------------|
| FLANGE LOCAL BUCK(Y)                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       272.7       0.000     Cl.F6.2        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom F-L-B Cap             : Mny    =  302.98     kip-ft     Eq.F6-2        |
|-----------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
*****************************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted).
- Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL BEND INTERACTION                   |
|-----------------------------------------------------------------------------|
| CLAUSE H1                                                                   |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            1.004      Eq.H1-1a            3        0.00     |
|                                                                             |
| Intermediate Results :                                                      |
|  Axial Capacity            : Pc     =  837.01     kip        Cl.H1.1        |
|  Moment Capacity           : Mcx    =  465.79     kip-ft     Cl.H1.1        |
|  Moment Capacity           : Mcy    =  272.68     kip-ft     Cl.H1.1        |