V. AISC LRFD - Wide Flange Flexural Strength 1

To determine the design flexural strength of an ASTM A992 W18X40 bent about its strong axis on a 35-ft span with a uniformly distributed load.

Reference

Hand calculation using the following reference:

AISC Load Factor Resistance Design, 3rd Edition, Example 5.1, Case (a), page 5-12.

Details

The beam is braced such that L_b = 2 ft. The deflection at mid-span due to a uniformly distributed service load of 1 kip/ft is also to be calculated.

F_y = 50 ksi

Length = 35 ft

Validation

The beam is continuously braced, so by observation L_b < L_p.

The design flexural strength is:

ϕ_bM_n = ϕ_b[F_yZ_x] = 0.9×[50 ksi × 78.4 in³] = 3,528 k·in

The maximum deflection (at midpsan) due to a uniform load of 1 kip/ft is:

Δ = \frac{5 w \times l^{4}}{384 E I} = \frac{5 (1) {(35)}^{4} {(12)}^{3}}{384 (29,000) (612)} = 1.90 in.

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference	Comments
Design flexural strength, ϕ_bM_n (in·kips)	3,528	3,528	none
Deflection (in)	1.90	1.8918	negligible

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Wide Flange Flexural Strength 1.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
*
*  EXAMPLE PROBLEM 5.1, CASE (A), PAGE 5-12, AISC LRFD 3RD ED.
*  CAPACITY (MNZ) SHOULD BE ABOUT 294 KIP-FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 35 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W18X40
UNIT FEET KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
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
LOAD COMBINATION 2
1 1.8 
PERFORM ANALYSIS
LOAD LIST 1
SECTION 0.5 ALL
PRINT SECTION DISPL
LOAD LIST 2
UNIT FEET KIP
PARAMETER 1
CODE LRFD
MAIN 1 ALL
FYLD 7200 ALL
UNT 2 ALL
TRACK 1 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

  SECTION  DISPL                      
      BENDING CAPACITY PER AISC LRFD 3RD ED                    -- PAGE NO.    3
     MEMBER SECTION DISPLACEMENTS
     ----------------------------
     UNITS ARE - INCH
     MEMB  LOAD     GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS
       1     1       0.0000    0.0000    0.0000    0.0000   -0.4973    0.0000
                     0.0000   -0.9571    0.0000    0.0000   -1.3475    0.0000
                     0.0000   -1.6441    0.0000    0.0000   -1.8290    0.0000
                     0.0000   -1.8918    0.0000    0.0000   -1.8290    0.0000
                     0.0000   -1.6441    0.0000    0.0000   -1.3475    0.0000
                     0.0000   -0.9571    0.0000    0.0000   -0.4973    0.0000
                     0.0000    0.0000    0.0000
     MAX LOCAL  DISP =    1.89185   AT     210.00  LOAD    1   L/DISP=    222
         ************ END OF SECT DISPL RESULTS ***********
    37. LOAD LIST 2
    38. UNIT FEET KIP
    39. PARAMETER 1
    40. CODE LRFD
    41. MAIN 1 ALL
    42. FYLD 7200 ALL
    43. UNT 2 ALL
    44. TRACK 1 ALL
    45. CHECK CODE ALL
 STEEL DESIGN    
      BENDING CAPACITY PER AISC LRFD 3RD ED                    -- PAGE NO.    4
                         STAAD.Pro CODE CHECKING - (LRFD 3RD EDITION)   v1.0
                         ***********************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
      1  ST   W18X40                   (AISC SECTIONS)
                           PASS     LRFD-H1-1B-C       0.938         2
                        0.00 C          0.00        -275.62       17.50
 +---------------------------------------------------------------------+
 | DESIGN STRENGTHS FOR MEMBER     1       UNITS - KIP IN              |
 | PNC=   23.10  PNT=  531.00  MNZ= 3528.00  MNY=  428.32  VN=  152.24 |
 +---------------------------------------------------------------------+