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V. AISC LRFD - Tension and Strong Axis Bending

To check the adequacy of an ASTM A992 W10X22 subject to axial tension and flexure about the strong axis.

Reference

AISC Load Factor Resistance Design, 3rd Edition, Example 6.1 case(b), page 6-5.

Problem

W10x22 section.

Fy = 50 ksi

Fu = 65 ksi

Pu = 55 kips

Muy = 0, Muz = 55 ft·kips

Lb = 4 ft

Comparison

The reported STAAD.Pro value is based on the terms PNT and MNZ in the STAAD.Pro output.

Table 1. Comparison of results
Result Type Theory STAAD.Pro Difference
Design tensile strength, ϕtPn (kips) 292.0 292 none
Design bending strength, ϕbMny (ft·kips) 97.5

97.5

(1,170 in·kips)

none
Utilization ratio 0.98 0.98 none
Note: Fully braced condition can be achieved by setting the UNT parameter equal to 1.0 inch.

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\LRFD 3rd Edition\AISC LRFD - Tension and Strong Axis Bending.STD is typically installed with the program.

STAAD SPACE COMBINED AXIAL TENSION + FLEXURE PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  EXAMPLE PROBLEM 6.1, CASE (B), PAGE 6-5, AISC LRFD 3RD ED.
*  INTERACTION RATIO SHOULD BE ABOUT 0.98
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 10 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W10X22
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 29000
POISSON 0.3
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
LOAD 1
JOINT LOAD
2 FY 140
2 MZ 55
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE LRFD
FYLD 50 ALL
FU 65 ALL
UNT 48 ALL
UNB 48 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (LRFD 3RD EDITION)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ===|===     ------------ |
  |MEMBER   1  *  |  AISC SECTIONS              |      |        AX=0.6490E+1 |
  |            *  | ST  W10X22                  |      |   --Z  AY=0.2448E+1 |
  |DESIGN CODE *  |                             |      |        AZ=0.2760E+1 |
  | LRFD 2001  *  ===============================   ===|===     PY=0.6100E+1 |
  |            *                                                PZ=0.2600E+2 |
  |            *  |<---LENGTH (FT)=   10.00 --->|               RY=0.1325E+1 |
  |*************                                                RZ=0.4264E+1 |
  |                                                                          |
  |                 55.0 (KIP-FEET)                                          |
  |PARAMETER        |                               L1  L1  L1  CAPACITIES   |
  |IN KIP  INCH     |                               L1  L1  L1  IN KIP  INCH |
  |---------------  +                               L1  L1  L1  -------------|
  | KL/R-Y=  90.54  |                               L1  L1  L1  PNC=0.1515E+3|
  | KL/R-Z=  28.14  +                               L1  L1  L1  pnc=0.0000E+0|
  | UNL   =  48.00  |L1 L1  L1  L1  L1  L1  L1  L1              PNT=0.2920E+3|
  | CB    =   1.00  +L1 L1  L1  L1  L1  L1  L1  L1              pnt=0.1400E+3|
  | PHIC  =   0.85  |L1 L1  L1  L1  L1  L1  L1  L1              MNZ=0.1170E+4|
  | PHIB  =   0.90  +L1 L1  L1  L1  L1  L1  L1  L1              mnz=0.6600E+3|
  | FYLD  =  50.00  |L1 L1  L1  L1  L1  L1  L1  L1              MNY=0.2677E+3|
  | NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.0000E+0|
  | DFF =     0.00  55.0                                        VN =0.6610E+2|
  | dff =     0.00               ABSOLUTE MZ ENVELOPE           vn =0.0000E+0|
  |                                 (WITH LOAD NO.)                          |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE    -140.0         0.0        0.0         0.0        55.0      |
  |   LOCATION       0.0         0.0        0.0         0.0         0.0      |
  |    LOADING         1           0          0           0           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        LRFD-H1-1A-T     0.980              1               |
  |        140.00 T          0.00       -55.00             0.00              |
  |*                                                                        *|
  |**************************************************************************|
  |                                                                          |
  |--------------------------------------------------------------------------|