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V. AISC LRFD - Non Compact Wide Flange 1

To check the adequacy of a non-compact fully braced W shape to carry a uniformly distributed load of 5.5 kips/ft.

Reference

AISC Load Factor Resistance Design, 3rd Edition, Table 5.4, , page 5-65.

Problem

W14x90 shape. Beam is bent about its strong axis.

Fy = 50 ksi

Length = 30 ft

Hand Calculation

MNZ = 6,910 in·kips = wl2/8

w = 8 M l 2 = 8 ( 6 , 910 ) ( 30 12 ) 2 = 0.427 kips/in

W = 0.427 kips/in(30ft)(12 in/ft) = 153.6 kips

ϕbWc = 153.6 kips (30 ft) = 4,607 ft·kips

Comparison

The reported STAAD.Pro value is based on the term MNZ in the STAAD.Pro output.

Table 1. Comparison of results
Result Type Theory STAAD.Pro Difference
Maximum total Factored Load, W (kips) 154 153.6 none
ϕbWc 4,610 4,607 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 - Non Compact Wide Flange 1.STD is typically installed with the program.

STAAD SPACE BENDING CAPACITY PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  TABLE 5-4, PAGE 5-65, AISC LRFD 3RD ED.
*  OBJECTIVE : TO CHECK THE ADEQUACY OF A NON-COMPACT W SHAPE.
*
*  BEAM IS FULLY BRACED. ACCORDING TO ABOVE REFERENCE,
*  CAPACITY OF A 30 FT LONG W14X90 IS 154/30=5.133 KIP/FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 30 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X90
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 PINNED
2 FIXED BUT MZ
LOAD 1
MEMBER LOAD
1 UNI GY -5.5
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE LRFD
MAIN 1 ALL
* FULLY BRACED CONDITION IS ACHIEVED WITH A UNT OF 1.0 INCH
UNT 1 ALL
FYLD 50 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=0.2650E+2 |
  |            *  | ST  W14X90                  |      |   --Z  AY=0.6160E+1 |
  |DESIGN CODE *  |                             |      |        AZ=0.1373E+2 |
  | LRFD 2001  *  ===============================   ===|===     PY=0.7560E+2 |
  |            *                                                PZ=0.1570E+3 |
  |            *  |<---LENGTH (FT)=   30.00 --->|               RY=0.3696E+1 |
  |*************                                                RZ=0.6140E+1 |
  |                                                                          |
  |                618.7 (KIP-FEET)                                          |
  |PARAMETER        |               L1  L1  L1                  CAPACITIES   |
  |IN KIP  INCH     |                                           IN KIP  INCH |
  |---------------  +           L1              L1              -------------|
  | KL/R-Y=  97.40  |                                           PNC=0.5628E+3|
  | KL/R-Z=  58.63  +       L1                      L1          pnc=0.0000E+0|
  | UNL   =   1.00  |                                           PNT=0.1192E+4|
  | CB    =   1.00  +   L1                              L1      pnt=0.0000E+0|
  | PHIC  =   0.85  |                                           MNZ=0.6910E+4|
  | PHIB  =   0.90  +                                           mnz=0.7425E+4|
  | FYLD  =  50.00  |L0                                     L0  MNY=0.3280E+4|
  | NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.0000E+0|
  | DFF =     0.00 -34.4                                        VN =0.1663E+3|
  | 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       0.0        82.5        0.0         0.0       618.8      |
  |   LOCATION       0.0         0.0        0.0         0.0        15.0      |
  |    LOADING         0           1          0           0           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          FAIL        LRFD-H1-1B-C     1.074              1               |
  |          0.00 C          0.00      -618.75            15.00              |
  |*                                                                        *|
  |**************************************************************************|
  |                                                                          |
  |--------------------------------------------------------------------------|