V. AISC N690 1994 Channel

Verify the design of channel section used for a beam member using the AISC N690 1994 code.

Details

The beam is a propped cantilever 80 inches long. The beam is loaded with a 2 kip concentrated load at midspan and a uniformly distributed load of 1 kip/in over the entire length.

The member is C15x50 channel section with Grade A36 steel.

Validation

Maximum shear force (at fixed end): V = 51.375 kips (taken from STAAD.Pro analysis)

Maximum moment (at fixed end): M = 830.0 in-kip (taken from STAAD.Pro analysis)

Slenderness Ratio

About z-axis: (KL/r)_z = 0.85(80 in)/(5.25 in) = 12.95

About y-axis: (KL/r)_y = 0.85(80 in)/(0.865 in) = 78.61

Max. slenderness ratio < 300, OK.

Bending About Major Axis (Z Axis)

\frac{b_{f}}{t_{f}} = 4.62 < \frac{65}{\sqrt{F_{y}}} = 10.83

The laterally unsupported length of the compression flange, $L_{b} = 80 < \frac{76 b_{f}}{\sqrt{F_{y}}} = 120$

and $< \frac{20, 000}{(d / A_{f}) F_{y}} = 89.56$

As b_f/t_f is not in the range of 65/√(Fy) and 95/√(Fy) , the value of allowable bending compressive and tensile stress = F_bty = F_bcy = 0.6×F_y = 21.6 ksi

Actual bending stress:

Bending Tensile Stress = bending compressive stress = f_btz = f_bcz= MzD / (2I_z) = 15.4 ksi

830.0 (15.0) / (2 × 404) = 15.41 ksi

Critical ratio = 15.41 ksi / 21.6 ksi = 0.713

Shear

Actual shear:

F_y = 51.375 kips

STAAD.Pro calculates the shear are based on the general shear stress equation, τ = V×Q/(I×t) from Timoshenko. Thus the shear area, A_y = I×t/Q = 8.47 in²

f_v = 51.375 / 8.47 = 6.07 ksi

Allowable shear:

a = clear distance between transverse stiffeners (here taken as length) = 80 in

h = clear distance flanges of the girder = D-2t_f = 14.35 in

Thus, a/h = 5.57, Therefore, k = 5.34 + [4.00/ (a/h)²] = 5.46

t = t_w = 0.72 in

Cv =17.2

F_{v} = {}_{m i n}{|\begin{matrix} F_{y} / 2.89 \times C_{v} = 25.6 k s i \\ 0.4 \times F_{y} = 14.4 k s i \end{matrix}}

Hence allowable=14.4 ksi

Therefore, Ratio = f_v/F_v = 6.07 / 14.4 = 0.422

Results

Table 1. Comparison of results
Parameter	Hand Calculation	STAAD.Pro	Difference
Slenderness ratio	78.61	78.61	none
Allowable bending stress (ksi)	21.6	21.6	none
Actual bending stress (ksi)	15.41	15.41	none
Critical ratio	0.713	0.713	none
Allowable shear stress (ksi)	14.4	14.4	none
Actual shear stress (ksi)	6.07	6.06	negligible

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC N690 1994 Channel.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 80 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.9e+07
POISSON 0.3
DENSITY 0.283
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 36000 FU 58000 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST C15X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 PINNED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -2000 40
1 UNI GY -1000 0 80
PERFORM ANALYSIS
PARAMETER 1
CODE AISC N690 1994
CMY 1 ALL
CMZ 1 ALL
FU 58000 ALL
FYLD 36000 ALL
KY 0.85 ALL
KZ 0.85 ALL
UNT 80 ALL
UNB 80 ALL
MAIN 200 ALL
NSF 0.9 ALL
RATIO 1 ALL
TMAIN 300 ALL
STYPE 1 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (  ANSI N690-1994)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|    |===       ------------ |
  |MEMBER   1  *  |  AISC SECTIONS              |    |          AX =  14.70  |
  |            *  | ST  C15X50                  |    |     --Z  AY =   8.47  |
  |DESIGN CODE *  |                             |    |          AZ =   2.67  |
  |ANSI N690-94*  ===============================    |===       SY =   3.83  |
  |            *                                                SZ =  53.87  |
  |            *  |&lt;---LENGTH (FT)=    6.67 --->|               RY =   0.87  |
  |*************                                                RZ =   5.24  |
  |                                                                          |
  |                 69.2 (KIP-FEET)                                          |
  |PARAMETER        |L1                                         STRESSES     |
  |IN KIP  INCH     |                                           IN KIP  INCH |
  |---------------  +                                           -------------|
  | KL/R-Y=  78.61  |   L1                                      FA  =   9.71 |
  | KL/R-Z=  12.97  +                   L1  L1                  fa  =   0.00 |
  | UNL   =  80.00  |               L1          L1              FCZ =  21.60 |
  | CB    =   1.00  +       L1                      L1          FTZ =  21.60 |
  | CMY   =   1.00  |                                   L1      FCY =  21.60 |
  | CMZ   =   1.00  +                                           FTY =  21.60 |
  | FYLD  =  36.00  |           L1                          L0  fbz =  15.41 |
  | NSF   =   0.90  +---+---+---+---+---+---+---+---+---+---|   fby =   0.00 |
  | DFF   =   0.00  -3.8                                        Fey =  21.54 |
  | dff=      0.00               ABSOLUTE MZ ENVELOPE           Fez = 791.24 |
  | (KL/R)max =  78.61              (WITH LOAD NO.)             FV  =  14.40 |
  |                                                             fv  =   6.06 |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE       0.0        51.4        0.0         0.0        69.2      |
  |   LOCATION       0.0         0.0        0.0         0.0         0.0      |
  |    LOADING         0           1          0           0           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        ANSI Q1.6-2      0.713              1               |
  |          0.00 T          0.00        69.17             0.00              |
  |*                                                                        *|
  |                                                                          |