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.
References
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 ksiLength = 20 ft
Calculations
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
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Design flexural strength, ϕbMn (in·kips) | 952.6 | 952.6 | none | |
| Capacity ratio | 0.945 | 0.945 | none |
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\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
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
FINISHOutput
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=0.1636E+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 |
|* *|
|**************************************************************************|
| |
|--------------------------------------------------------------------------|