V. AISC 360-05 Tapered I Section

Verify the axial compression capacity, flexure capacity, and interaction ratio of a tapered I section member per both the LRFD and ASD methods of the AISC 360-05 code.

Details

A 5' × 5' portal frame consists of W12x72 columns and a steel tapered member for the beam.

The following load cases are evaluated:

A uniformly distributed load of -3.5 k/ft along the beam in the global Y direction.
Lateral loads at the top of the left column of 50 kips in the global X direction and 25 kips in the global Z direction (out of plane).
Lateral loads at the top of the right column of -50 kips in the global X direction and 45 kips in the global Z direction (out of plane).
A concreted load of -100 kips in the global Y direction and a concentrated torque of 9 in·kips at mid-span of the beam.

Material Properties

E = 29,000 ksi
Fy = 50 ksi

Validation

Design Forces

By inspection, the left end of the beam (shallowest overall depth) governs under the symmetric loads present. The following design loads are used from the STAAD.Pro analysis are then used:

M_z = 32.26 in·kips, F_y = 8.755 kips
M_z = 677.6 in·kips, M_y = 2.942 in·kips, M_x = 5.106 in·kips, F_y = 22.98 kips, F_z = 0.098 kips, F_x = 24.70 kips
M_z = 275.9 in·kips, M_x = 4.497 in·kips, F_y = 50.23 kips, F_x = 5.473 kips
M_z = 654.5 in·kips, M_y = 5.298 in·kips, M_x = 9.192 in·kips, F_y = 22.50 kips, F_z = 0.177 kips, F_x = 24.35 kips

Section Properties

The section at the left end (D = 18 in.) has the following properties:

Web height, d_w = 18 - 2×0.84 = 16.32 in.
Area, A_g = (0.84)(9 + 7.5) + 16.32 (0.36) = 19.74 in²
Shear area in local y, A_vy = 18(0.36) = 6.48 in²
Shear area in local x, A_vx = 0.84(9 + 7.5) = 13.86 in²
Dist to centroid y, $c = \frac{7.5 (0.84) (\frac{0.84}{2}) + 0.36 (16.32) (0.84 + \frac{16.32}{2}) + 9 (0.84) (18 - \frac{0.84}{2})}{19.74} = 9.548 in.$
Moment of inertia about major axis,
$I_{zz} = \begin{matrix} \frac{7.5 {(0.84)}^{3}}{12} + 7.5 (0.84) {(9.548 - \frac{0.84}{2})}^{2} \\ + \frac{0.36 {(16.32)}^{3}}{12} + 0.36 (16.32) {(9.548 - \frac{16.32}{2} - 0.84)}^{2} \\ + \frac{9 {(0.84)}^{3}}{12} + 9 (0.84) {(18 - \frac{0.84}{2} - 9.548)}^{2} & = 1, 147 {in}^{4} \end{matrix}$
Moment of inertia about minor axis,
$I_{y y} = \frac{0.84 {(9)}^{3}}{12} + \frac{16.32 {(0.36)}^{3}}{12} + \frac{0.84 {(7.5)}^{3}}{12} = 80.62 {in}^{4}$
Elastic section modulus about major axis top flange fiber, $S_{x x, t o p} = \frac{I_{z z}}{D - c} = \frac{1, 146}{18 - 9.548} = 135.5 {in}^{3}$
Elastic section modulus about major axis bottom flange fiber, $S_{x x, b o t t o m} = \frac{I_{z z}}{c} = \frac{1, 146}{9.548} = 120.0 {in}^{3}$
Elastic section modulus about minor axis, $S_{y y} = \frac{I_{y y}}{b_{f 1} / 2} = \frac{80.62}{9 / 2} = 17.92 {in}^{3}$
Radius of gyration about major axis, $r_{x} = \sqrt{\frac{I_{z z}}{A_{g}}} = \sqrt{\frac{1, 147}{19.74}} = 7.619 in$
Radius of gyration about minor axis, $r_{y} = \sqrt{\frac{I_{y y}}{A_{g}}} = \sqrt{\frac{80.62}{19.74}} = 2.021 in$
Location of the plastic neutral axis, $y_{PNA} = 0.84 + \frac{19.74 - 2 (7.5) (0.84)}{2 \times 0.36} = 10.75 in.$
Plastic section modulus about major axis,
$Z_{z t} = \begin{matrix} \frac{7.5 {(10.75)}^{2}}{2} - \frac{(7.5 - 0.36) {(10.75 - 0.84)}^{2}}{2} \\ + \frac{9 {(18 - 10.75)}^{2}}{2} - \frac{(9 - 0.36) {(18 - 0.84 - 10.75)}^{2}}{2} & = 141.8 {in}^{3} \end{matrix}$
Plastic section modulus about minor axis, $Z_{y} = \frac{0.84 {(9)}^{2}}{4} + \frac{16.32 {(0.36)}^{2}}{4} + \frac{0.84 {(7.5)}^{2}}{4} = 29.35 {in}^{3}$
Torsional constant, $J = \frac{9 {(0.84)}^{3} + 16.32 {(0.36)}^{3} + 7.5 {(0.84)}^{3}}{3} = 3.514 {in.}^{4}$

Section Classification

Flange in compression

λ = \frac{b}{t} = \frac{1 / 2 \times 7.5}{0.84} = 4.464

k_{c} = \frac{4}{\sqrt{\frac{d_{w}}{t_{w}}}} = \frac{4}{\sqrt{\frac{16.32}{0.36}}} = 0.594

Per Table B4.1a, $λ < λ_{r} = 0.64 \sqrt{\frac{k_{c} E}{F_{y}}} = 0.64 \sqrt{\frac{0.594 (29,000)}{50}} = 11.88$ , therefore flanges are non-slender for compression.

Web in compression

λ = \frac{d_{w}}{t_{w}} = \frac{16.32}{0.36} = 45.33

Per Table B4.1a, Case 5, $λ > λ_{r} = 1.49 \sqrt{\frac{E}{F_{y}}} = 1.49 \sqrt{\frac{29,000}{50}} = 35.88$ , therefore the web is slender for compression.

Flange in bending (use half the longer flange width as the outstanding width):

λ = \frac{b_{f}}{t_{f}} = \frac{9}{2 (0.84)} = 5.36

Per Table B4.1b, Case 11, $λ < λ_{p} = 0.38 \sqrt{\frac{E}{F_{y}}} = 0.38 \sqrt{\frac{29,000}{50}} = 9.15$ , therefore flange is compact for bending.

Web in bending

λ = \frac{d_{w}}{t_{w}} = \frac{16.32}{0.36} = 45.33

Per Table B4.1b, Case 15, $λ < λ_{p} = 3.76 \sqrt{\frac{E}{F_{y}}} = 3.76 \sqrt{\frac{29,000}{50}} = 90.55$ , therefore web is compact for bending.

Compression Capacity

About X Axis:

\frac{k_{x} L_{x}}{r_{x}} = \frac{1.0 (60)}{7.619} = 7.875 < 4.71 \sqrt{\frac{E}{F_{y}}} = 4.71 \sqrt{\frac{29, 000}{50}} = 113.4

F_{ex} = \frac{π^{2} E}{{(\frac{k_{x} L_{x}}{r_{x}})}^{2}} = \frac{π^{2} \times 29, 000}{{(7.875)}^{2}} = 4,615 ksi

(Eq. E3-4)

\frac{F_{y}}{F_{ex}} = \frac{50}{4,615} = 0.011 < 2.25

F_{crx} = {0.658}^{\frac{F_{y}}{F_{ex}}} F_{y} = {0.658}^{(0.011)} 50 = 49.77 ksi

(Eq. E3-2)

Since the web is slender, use the effective area. The effective width imperfection adjustment factors (Table E7.1):

c₁ = 0.18

c₂ = 1.31

F_{el} = {(c_{2} \frac{λ_{r}}{λ})}^{2} F_{y} = {(1.31 \frac{35.88}{45.33})}^{2} = 53.76 ksi

(Eq. E7-5)

Therefore, the effective depth of the web in compression for the effective area:

d_{e} = d_{w} (1 - c_{1} \sqrt{\frac{F_{el}}{F_{crx}}}) \sqrt{\frac{F_{el}}{F_{crx}}} = 16.32 (1 - 0.18 \sqrt{\frac{53.76}{49.77}}) \sqrt{\frac{53.76}{49.77}} = 13.78 in.

(Eq. E7-3)

The reduced area of the section then becomes:

A_{e} = 19.75 - (16.32 - 13.78) 0.36 = 18.84 {in.}^{2}

P_nx = A_e× F_crx = 18.84 × 49.77 = 937.4 kips

(Eq. E7-1)

About Y Axis:

\frac{k_{y} L_{y}}{r_{y}} = \frac{1.0 (60)}{2.021} = 29.69 < 4.71 \sqrt{\frac{E}{F_{y}}} = 113.4

F_{ey} = \frac{π^{2} E}{{(\frac{k_{y} L_{y}}{r_{y}})}^{2}} = \frac{π^{2} \times 29, 000}{{(29.69)}^{2}} = 324.7 ksi

(Eq. E3-4)

\frac{F_{y}}{F_{ey}} = \frac{50}{324.7} = 0.154 < 2.25

F_{cry} = {0.658}^{(F_{y} / F_{ey})} F_{y} = {0.658}^{(0.154)} 50 = 46.88 ksi

(Eq. E3-2)

Therefore, the effective depth of the web in compression for the effective area:

d_{e} = d_{w} (1 - c_{1} \sqrt{\frac{F_{el}}{F_{cry}}}) \sqrt{\frac{F_{el}}{F_{cry}}} = 16.32 (1 - 0.18 \sqrt{\frac{53.76}{46.88}}) \sqrt{\frac{53.76}{46.88}} = 14.11 in.

(Eq. E7-3)

The reduced area of the section then becomes:

A_{e} = 19.75 - (16.32 - 14.11) 0.36 = 18.93 {in.}^{2}

P_ny = A_e× F_cry = 18.93 × 46.88 = 887.4 kips

(Eq. E7-1)

The Y axis governs; P_n = P_ny. The axial capacity:

The ultimate compression capacity (LRFD) = ϕ_cP_n = 0.9 × 887.4 = 798.3 kips
The allowable compression capacity (ASD) = P_n/Ω_c = 887.4 / 1.67 = 531.4 kips

Calculate Bending Capacity

Bending capacity in plastic yielding about Y axis:

M_y = F_y × Z_y = 50 × 29.35 = 1,468 in·kips > 1.6F_y × S_y = 1.6 (50) (17.92) = 1,434 in·kips

Use M_y =1,434 in·kips

The bending capacity for flexural yielding about the Y axis:

The ultimate bending capacity (LRFD) = ϕ_bM_y = 0.9 × 1,434 = 1,290 in·kips
The allowable bending capacity (ASD) = M_y/Ω_b = 1,434 / 1.67 = 858.4 in·kips

Bending capacity in plastic yielding about X axis:

The section is capacity is determined as per F4 in the specification. The design moments for this are from Load Case 4 and occur at mid-span (d = 18.9 in.). The section properties at this location are:

I_zz = 1,278 in⁴
I_yy = 80.63 in⁴
c = 10.01 in
h_c = 2×(10.01 - 0.84) = 18.35 in.
S_x = 143.8 in³
Z_x = 150.7 in³

M_yc = F_y × S_yc = 50 × 143.8 = 7,192 ksi

M_p = F_y × Z_x = 50 × 150.7 = 7,535 ksi ≤ 1.6 F_y × S_x = 11,504 ksi

The moment of inertia of the compression flange about the Y axis $I_{yc} = \frac{0.84 {(7.5)}^{3}}{12} = 29.53 {in.}^{4}$ , and thus $I_{y c} / I_{y} = \frac{29.53}{80.63} = 0.366 > 0.23$ . $\frac{h_{c}}{t_{w}} = \frac{18.35}{0.36} = 50.99 < λ_{p w} = 90.55$ (limiting slenderness for a compact web per Table B4.1b case 15), so the web plastification factor, R_pc is determined as:

R_{pc} = \frac{M_{p}}{M_{yc}} = \frac{7,535}{7,192} = 1.048

(F4-9a)

Bending capacity in plastic yielding about Y axis:

M_n = R_pc × M_yc = 1.048 × 7,192 = 7,535 in·kips

The bending capacity for flexural yielding about the Y axis:

The ultimate bending capacity (LRFD) = ϕ_bM_y = 0.9 × 7,535 = 6,782 in·kips
The allowable bending capacity (ASD) = M_y/Ω_b = 7,535 / 1.67 = 4,512 in·kips

Interaction Ratio for Bending and Compression

Check the interaction ratio for Load Case 3:

\frac{P_{r}}{P_{c}} = \frac{5.473}{798.3} = 0.007 < 0.2 (LRFD)

\frac{P_{r}}{P_{c}} = \frac{5.479}{531.4} = 0.010 < 0.2 (ASD)

So use Eq. H1-1b for both methods: $\frac{P_{r}}{2 P_{c}} + (\frac{M_{r x}}{M_{c x}} + \frac{M_{r y}}{M_{c y}}) \leq 1.0$ .

\frac{0.007}{2} + (\frac{1,225}{6,783} + \frac{0}{1,290}) = 0.184 (LRFD)

\frac{0.010}{2} + (\frac{1,225}{4,513} + \frac{0}{858}) = 0.277 (ASD)

Results

Table 1.
Result Type		Reference	STAAD.Pro	Difference
LRFD	Compression capacity (kips)	798.3	799	negligible
	Major axis bending capacity (in·kips)	6,782	6,780	negligible
	Minor axis bending capacity (in·kips)	1,290	1,290	none
	Interaction ratio	0.184	0.184	none
ASD	Compression capacity (kips)	531.4	532	negligible
	Major axis bending capacity (in·kips)	4,512	4,510	negligible
	Minor axis bending capacity (in·kips)	858.4	858	negligible
	Interaction ratio	0.277	0.277	none

STAAD.Pro Input

The following design parameters are used:

The welded tapered member is specified using STP 2

The remaining parameters all use their default values.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 Tapered I Section.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 14-Jan-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 5 0; 3 5 0 0; 4 5 5 0;
MEMBER INCIDENCES
1 1 2; 2 2 4; 3 3 4;
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
2 TAPERED 1.5 0.03 1.65 0.75 0.07 0.625 0.07
MEMBER PROPERTY AMERICAN
1 3 TABLE ST W12X72
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 3 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
2 UNI GY -3.5
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
JOINT LOAD
2 FX 50 FZ 25
LOAD 4 LOADTYPE None  TITLE LOAD CASE 4
JOINT LOAD
4 FX -50 FZ 45
LOAD 3 LOADTYPE None  TITLE LOAD CASE 3
MEMBER LOAD
2 CON GY -100
2 CMOM GX 0.75
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
UNIT INCHES KIP
PARAMETER 1
CODE AISC UNIFIED 2005
FYLD 50 ALL
FU 60 ALL
METHOD LRFD
STP 2 MEMB 2
TRACK 2 MEMB 2
CHECK CODE MEMB 2
PARAMETER 2
CODE AISC UNIFIED 2005
FYLD 50 ALL
FU 60 ALL
METHOD ASD
STP 2 MEMB 2
TRACK 2 MEMB 2
CHECK CODE MEMB 2
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       2      TAPERED                  (AISC SECTIONS)
                           PASS   Sec. G1              0.286         3
                        5.47 C          0.00         275.86        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     29.685  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.286(PASS)                 |
|          Loc  :    0.00   Condition :   Sec. G1                       |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   5.473E+00(C ) Fy:   5.002E+01     Fz:   0.000E+00               |
| Mx:  -4.497E+00     My:   1.731E-05     Mz:   2.759E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.386E+01     Ayy:   6.480E+00     Cw:  5.508E+03              |
| Szz:   1.200E+02     Syy:   1.792E+01                                 |
| Izz:   1.146E+03     Iyy:   8.062E+01     Ix:  3.514E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          60.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        60.000                                   |
| 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     5.36     N/A     11.88    T.B4.1-4     |
|                Slender        45.33     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         5.36     9.15    21.15    T.B4.1-2     |
|                Compact        44.73    94.06   137.27    T.B4.1-11    |
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   8.88E+02   0.000      Eq. D2-1      1     0.00 |
| Rupture     0.00E+00   8.88E+02   0.000      Eq. D2-2      1     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    2.47E+01   8.41E+02   0.029      Sec. E1       2     0.00 |
| Min Buck    2.47E+01   7.99E+02   0.031      Eq. E7-1      2     0.00 |
| Flexural                                                              |
| Tor Buck    2.47E+01   7.93E+02   0.031      Eq. E7-1      2     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.88E+01     7.88   4.74E+01   4.62E+03   9.35E+02        |
| Min Buck    1.89E+01    29.69   4.50E+01   3.25E+02   8.88E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.89E+01   4.46E+01   8.81E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     1.77E-01   3.74E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     5.00E+01   1.75E+02   0.286      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.39E+01     1.00     1.20    10.71   4.16E+02            |
| Local-Y     6.48E+00     1.00     5.00    45.33   1.94E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.22E+03   6.78E+03   0.181      Sec. F4.2     3    30.00 |
| Minor       5.30E+00   1.29E+03   0.004      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.54E+03   0.00E+00                                       |
| Minor       1.43E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major      -6.55E+02   6.31E+03   0.104      Eq. F4-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       7.01E+03   0.00E+00    1.00    54.78   242.74    60.00    |
      STAAD SPACE                                              -- PAGE NO.    9
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-COMPRESSION FLANGE YIELDING                         |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             1.22E+03   6.78E+03   0.181      Eq. F4-1      3    30.00 |
| Intermediate   Mn        Rpc                                          |
|             7.54E+03   1.05E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-TENSION FLANGE YIELDING                             |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             1.22E+03   6.78E+03   0.181      Eq. F4-14     3    30.00 |
| Intermediate   Mn        Rpt                                          |
|             7.54E+03   1.18E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.184      Eq. H1-1b     3    30.00             |
| Flexure Tens          0.181      Eq. H1-1b     3    30.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         6.78E+03   1.22E+03   7.95E+02                   |
|                      1.29E+03   0.00E+00   5.47E+00                   |
| Flexure Tens         6.78E+03   1.22E+03   0.00E+00                   |
|                      1.29E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    53. PARAMETER 2
    54. CODE AISC UNIFIED 2005
    55. FYLD 50 ALL
    56. FU 60 ALL
    57. METHOD ASD
    58. STP 2 MEMB 2
    59. TRACK 2 MEMB 2
    60. CHECK CODE MEMB 2
 STEEL DESIGN    
      STAAD SPACE                                              -- PAGE NO.   10
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       2      TAPERED                  (AISC SECTIONS)
                           PASS   Sec. G1              0.430         3
                        5.47 C          0.00         275.86        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     29.685  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.430(PASS)                 |
|          Loc  :    0.00   Condition :   Sec. G1                       |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   5.473E+00(C ) Fy:   5.002E+01     Fz:   0.000E+00               |
| Mx:  -4.497E+00     My:   1.731E-05     Mz:   2.759E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.386E+01     Ayy:   6.480E+00     Cw:  5.508E+03              |
| Szz:   1.200E+02     Syy:   1.792E+01                                 |
| Izz:   1.146E+03     Iyy:   8.062E+01     Ix:  3.514E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          60.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        60.000                                   |
| 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     5.36     N/A     11.88    T.B4.1-4     |
|                Slender        45.33     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         5.36     9.15    21.15    T.B4.1-2     |
|                Compact        44.73    94.06   137.27    T.B4.1-11    |
      STAAD SPACE                                              -- PAGE NO.   11
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   5.91E+02   0.000      Eq. D2-1      1     0.00 |
| Rupture     0.00E+00   5.92E+02   0.000      Eq. D2-2      1     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    2.47E+01   5.60E+02   0.044      Sec. E1       2     0.00 |
| Min Buck    2.47E+01   5.32E+02   0.046      Eq. E7-1      2     0.00 |
| Flexural                                                              |
| Tor Buck    2.47E+01   5.27E+02   0.047      Eq. E7-1      2     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.88E+01     7.88   4.74E+01   4.62E+03   9.35E+02        |
| Min Buck    1.89E+01    29.69   4.50E+01   3.25E+02   8.88E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.89E+01   4.46E+01   8.81E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     1.77E-01   2.49E+02   0.001      Eq. G2-1      4     0.00 |
| Local-Y     5.00E+01   1.16E+02   0.430      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.39E+01     1.00     1.20    10.71   4.16E+02            |
| Local-Y     6.48E+00     1.00     5.00    45.33   1.94E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.22E+03   4.51E+03   0.271      Sec. F4.2     3    30.00 |
| Minor       5.30E+00   8.58E+02   0.006      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.54E+03   0.00E+00                                       |
| Minor       1.43E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major      -6.55E+02   4.20E+03   0.156      Eq. F4-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       7.01E+03   0.00E+00    1.00    54.78   242.74    60.00    |
      STAAD SPACE                                              -- PAGE NO.   12
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-COMPRESSION FLANGE YIELDING                         |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             1.22E+03   4.51E+03   0.271      Eq. F4-1      3    30.00 |
| Intermediate   Mn        Rpc                                          |
|             7.54E+03   1.05E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-TENSION FLANGE YIELDING                             |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             1.22E+03   4.51E+03   0.271      Eq. F4-14     3    30.00 |
| Intermediate   Mn        Rpt                                          |
|             7.54E+03   1.18E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.277      Eq. H1-1b     3    30.00             |
| Flexure Tens          0.271      Eq. H1-1b     3    30.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.51E+03   1.22E+03   5.29E+02                   |
|                      8.58E+02   0.00E+00   5.47E+00                   |
| Flexure Tens         4.51E+03   1.22E+03   0.00E+00                   |
|                      8.58E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|