# V. AISC LRFD - Channel Shape Capacity

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

## Reference

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

## Details

C12x25 shape. Beam is bent about its strong axis.

 Fy = 36 ksi

 Length = 20 ft

## Validation

The beam is continuously braced, so by observation Lb < Lp.

The yielding limit state capacity in bending:

ϕbMn = ϕb[FyZx] = 0.9×[36 ksi × 29.4 in3] = 952.6 k·in

The ultimate moment is:

The capacity ratio is: 900 / 952.6 = 0.945

## Results

Table 1. Comparison of results
Design flexural strength, ϕbMn (in·kips) 952.6 952.6 none
Capacity ratio 0.945 0.945 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Channel Shape Capacity.STD is typically installed with the program.

Note: The UNT parameter is set to 1.0 in. in order to approximate a fully-braced condition.
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
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.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 |
|            *  |&lt;---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|
|                                                                          |
|                      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      |
|                                                                          |
|**************************************************************************|
|*                                                                        *|
|*                         DESIGN SUMMARY  (KIP-FEET)                     *|
|*                         --------------                                 *|
|*                                                                        *|