V. AISC LRFD - Select Wide Flange 2

To find the optimum W shape with a flexural design strength of 150 ft·kips. Beam is braced at ends and at mid-span point.

Reference

AISC. Load and Resistance Factor Design Specification, 3rd Edition. 1999. Example 5.4, page 5-21.

AISC. Manual of Steel Construction, 3rd Edition. 1999.

Details

The beam should also satisfy a deflection limit of 1.0 inches under service load.

F_y = 50 ksi

Length = 20 ft

L_b = 10 ft

Service load of 2.0 kip/ft. Deflection limit under service load = 1.0 in.

Validation

From the chart on p.4-160 of the Manual of Steel Construction, the most efficient wide-flange section to resist 150 kip-ft of moment with an unbraced length of 10 ft is a W16x31. From this same chart, the design bending strength can be taken as 150 kip-ft (the curve crosses at approximately the same point as the demand load).

Design flexural strength of beams with unbraced length greater than L_p

The deflection limit under service conditions can be met by determining the minimum required moment of inertia needed.

1 in. = \frac{5 (2.0 k/ft) {(20 ft)}^{4} {(12 in/ft)}^{3}}{384 (29, 000 ksi) I}

Solving for the minimum I = 248 in⁴. A W16x31 has an I_x = 375 in⁴, so it will have less deflection than the limit under service conditions.

Results

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference	Comments
Optimum Section	W16x31	W16x31	none
Design bending strength, ϕ_bM_n (in·kips)	1,800 (150 ft·kips)	1,801.66	negligible
Maximum permissible deflection (in)	1.0	0.6584	N/A	The STAAD.Pro reported maximum deflection is less than 1.0 in; therefore this section satisfies the requirement. However, this value is not to be directly compared with the limit itself.

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Select Wide Flange 2.STD is typically installed with the program.

STAAD SPACE BENDING PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  EXAMPLE 5.4, PAGE 5-21, AISC LRFD 3RD ED.
*  OBJECTIVE : TO FIND THE OPTIMUM W SHAPE WITH A FLEXURAL
*  DESIGN STRENGTH OF 150 KIP-FT.
*
*  ACCORDING TO ABOVE REFERENCE, THE SECTION SHOULD BE W16X31
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 20 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W12X26
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 -2
LOAD COMBINATION 2
1 1.5 
PERFORM ANALYSIS
LOAD LIST 2
UNIT INCHES KIP
PARAMETER 1
CODE LRFD
MAIN 1 ALL
UNT 120 ALL
FYLD 50 ALL
TRACK 1 ALL
SELECT ALL
LOAD LIST ALL
PERFORM ANALYSIS
LOAD LIST 1
SECTION 0.5 ALL
PRINT SECTION DISPL
LOAD LIST 2
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.Pro MEMBER SELECTION - (LRFD 3RD EDITION)   v1.0
                       **************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
      1  ST   W16X31                   (AISC SECTIONS)
                           PASS     LRFD-H1-1B-C       0.999         2
                        0.00 C          0.00       -1800.00      120.00
 +---------------------------------------------------------------------+
 | DESIGN STRENGTHS FOR MEMBER     1       UNITS - KIP IN              |
 | PNC=   45.93  PNT=  410.85  MNZ= 1801.66  MNY=  302.71  VN=  118.06 |
 +---------------------------------------------------------------------+
   ************** END OF TABULATED RESULT OF DESIGN **************
    46. LOAD LIST ALL
    47. PERFORM ANALYSIS
    48. LOAD LIST 1
    49. SECTION 0.5 ALL
    50. PRINT SECTION DISPL
  SECTION  DISPL                      
      BENDING PER AISC LRFD 3RD ED                             -- PAGE NO.    4
     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   -0.1731    0.0000
                     0.0000   -0.3331    0.0000    0.0000   -0.4690    0.0000
                     0.0000   -0.5722    0.0000    0.0000   -0.6365    0.0000
                     0.0000   -0.6584    0.0000    0.0000   -0.6365    0.0000
                     0.0000   -0.5722    0.0000    0.0000   -0.4690    0.0000
                     0.0000   -0.3331    0.0000    0.0000   -0.1731    0.0000
                     0.0000    0.0000    0.0000
     MAX LOCAL  DISP =    0.65839   AT     120.00  LOAD    1   L/DISP=    364
         ************ END OF SECT DISPL RESULTS ***********