V. AISC N690 1994 Pipe

Verify the design of a pipe section used for a beam member per the AISC N690 1994 code.

Details

The simply supported beam is 50 inches long. The beam is loaded with a 1.5 kip concentrated load at midspan and a uniformly distributed load of 1 kip/in over the entire length.

The member is PIPS 120 pipe section with Grade A36 steel.

Validation

Maximum shear force, $V = \frac{P}{2} + \frac{w L}{2} = \frac{1.5}{2} + \frac{1.0 (50)}{2} = 25.75 kips$

Maximum moment, $M = \frac{P L}{4} + \frac{w L^{2}}{8} = \frac{1.5 (50)}{4} + \frac{1.0 {(50)}^{2}}{8} = 331.25 in⋅kip$

Slenderness ratio = (KL/r) = 9.72 < 300

Bending About Major Axis (Z-Axis)

Section is compact: $\frac{O D}{t} = 36.43 < \frac{3, 300}{F_{y}} = 91.67$

Allowable bending stress: F_b = 0.66×F_y = 23.76 ksi

Actual bending stress: $f_{b t z} = f_{b c z} = \frac{M_{z}}{I_{z}} (\frac{O D}{2}) = \frac{331.25}{262} (\frac{12.75}{2}) = 8.06 ksi$

Stress ratio: 0.339

Shear

From the reference, the shear area:

A_{y} = \frac{0.25 π ({r_{2}}^{4} - {r_{1}}^{4}) 2 (r_{2} - r_{1})}{\frac{2}{3} ({r_{2}}^{3} - {r_{1}}^{3})}

where

r₁	=	inner radius
r₂	=	outer radius

Shear area: A_y = 6.8 in²

Actual shear stress (at supports): f_v = 25.75 / 6.8 = 3.78 ksi

Actual shear stress (at midspan): f_v = 0.75 / 6.8 = 0.110 ksi

Allowable shear stress, F_v = 0.4×F_y = 14.4 ksi

Stress ratio: 3.78/14.4 = 0.263

Results

Table 1. Comparison of results
Parameter	Hand Calculation	STAAD.Pro	Difference
Slenderness ratio	9.72	9.72	none
Allowable bending stress (ksi)	23.76	23.76	none
Actual bending stress (ksi)	8.06	8.06	none
Critical stress ratio	0.339	0.339	none
Allowable shear stress (ksi)	14.4	14.4	none

STAAD Input

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 17-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 50 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 PIPS120
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -1500 25 0
1 UNI GY -1000 0 50
PERFORM ANALYSIS
PARAMETER 1
CODE AISC N690
CMY 1 ALL
CMZ 1 ALL
CT 0.85 ALL
FU 58000 ALL
FYLD 36000 ALL
KY 0.85 ALL
KZ 0.85 ALL
UNT 50 ALL
UNB 50 ALL
MAIN 200 ALL
NSF 0.9 ALL
RATIO 1 ALL
TMAIN 300 ALL
UNB 25 ALL
UNT 25 ALL
STYPE 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (  ANSI N690-1994)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ==| |==     ------------ |
  |MEMBER   1  *  |  AISC SECTIONS              |     | |       AX =  13.70  |
  |            *  | ST  PIPS120                 |     | |  --Z  AY =   6.80  |
  |DESIGN CODE *  |                             |     | |       AZ =   6.80  |
  |ANSI N690-94*  ===============================   ==| |==     SY =  41.10  |
  |            *                                                SZ =  41.10  |
  |            *  |&lt;---LENGTH (FT)=    4.17 --->|               RY =   4.37  |
  |*************                                                RZ =   4.37  |
  |                                                                          |
  |                 27.6 (KIP-FEET)                                          |
  |PARAMETER        |               L1  L1  L1                  STRESSES     |
  |IN KIP  INCH     |                                           IN KIP  INCH |
  |---------------  +           L1              L1              -------------|
  | KL/R-Y=   9.72  |                                           FA  =  15.87 |
  | KL/R-Z=   9.72  +       L1                      L1          fa  =   0.00 |
  | UNL   =  25.00  |                                           FCZ =  23.76 |
  | CB    =   1.00  +   L1                              L1      FTZ =  23.76 |
  | CMY   =   1.00  |                                           FCY =  23.76 |
  | CMZ   =   1.00  +                                           FTY =  23.76 |
  | FYLD  =  36.00  |L0                                     L0  fbz =   8.06 |
  | NSF   =   0.90  +---+---+---+---+---+---+---+---+---+---|   fby =   0.00 |
  | DFF   =   0.00  -1.5                                        Fey =1409.49 |
  | dff=      0.00               ABSOLUTE MZ ENVELOPE           Fez =1409.49 |
  | (KL/R)max =   9.72              (WITH LOAD NO.)             FV  =  14.40 |
  |                                                             fv  =   0.11 |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE       0.0        25.8        0.0         0.0        27.6      |
  |   LOCATION       0.0         0.0        0.0         0.0         2.1      |
  |    LOADING         0           1          0           0           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        ANSI Q1.6-2      0.339              1               |
  |          0.00 T          0.00       -27.60             2.08              |
  |*                                                                        *|
  |                                                                          |