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V. AISC LRFD - Channel Shape Capacity

To check the adequacy of a fully braced C shape to carry a uniformly distributed load of 1.5 kips/ft.

Reference

AISC Load Factor Resistance Design, 3rd Edition, Table 5.9, page 5-120.

Problem

C12x25 shape. Beam is bent about its strong axis.

Fy = 50 ksi

Length = 20 ft

Hand Calculation

MNZ =952.6 in·kips = wl2/8

w = 8 M l 2 = 8 ( 952.6 ) ( 20 12 ) 2 = 0.132 kips/in

W = 0.132 kips/in(20ft)(12 in/ft) = 31.8 kips

ϕbWc = 31.8 kips (20 ft) = 635.1 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) 31.8 31.8 none
ϕbMc 635 635.1 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 - Channel Shape Capacity.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 5-9, PAGE 5-120, AISC LRFD 3RD ED.
*  OBJECTIVE : TO CHECK THE ADEQUACY OF A C SHAPE.
*
*  BEAM IS FULLY BRACED. ACCORDING TO ABOVE REFERENCE,
*  CAPACITY OF A 20 FT LONG C12X25 IS 31.8/20=1.59 KIP/FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 20 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST C12X25
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 -1.5
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 36 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=0.7340E+1 |
  |            *  | ST  C12X25                  |    |     --Z  AY=0.4644E+1 |
  |DESIGN CODE *  |                             |    |          AZ=0.2037E+1 |
  | LRFD 2001  *  ===============================    |===       PY=0.3820E+1 |
  |            *                                                PZ=0.2940E+2 |
  |            *  |<---LENGTH (FT)=   20.00 --->|               RY=0.7786E+0 |
  |*************                                                RZ=0.4429E+1 |
  |                                                                          |
  |                 75.0 (KIP-FEET)                                          |
  |PARAMETER        |               L1  L1  L1                  CAPACITIES   |
  |IN KIP  INCH     |                                           IN KIP  INCH |
  |---------------  +           L1              L1              -------------|
  | KL/R-Y= 308.23  |                                           PNC=0.1634E+2|
  | KL/R-Z=  54.18  +       L1                      L1          pnc=0.0000E+0|
  | UNL   =   1.00  |                                           PNT=0.2378E+3|
  | CB    =   1.00  +   L1                              L1      pnt=0.0000E+0|
  | PHIC  =   0.85  |                                           MNZ=0.9526E+3|
  | PHIB  =   0.90  +                                           mnz=0.9000E+3|
  | FYLD  =  36.00  |L0                                     L0  MNY=0.9102E+2|
  | NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.0000E+0|
  | DFF =     0.00  -4.2                                        VN =0.9028E+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       0.0        15.0        0.0         0.0        75.0      |
  |   LOCATION       0.0         0.0        0.0         0.0        10.0      |
  |    LOADING         0           1          0           0           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        LRFD-H1-1B-C     0.945              1               |
  |          0.00 C          0.00       -75.00            10.00              |
  |*                                                                        *|
  |**************************************************************************|
  |                                                                          |
  |--------------------------------------------------------------------------|