# V.API X Joint

Verify the design of a simple X joint with axial load and in-plane bending.

## Details

Design of node 3 between members 2 and 6 in the following model.

Chord member (2 & 3): D = 500 mm, T = 20 mm (Ac = 30,159 mm2, Zc = 3,480,380 mm3)

Brace member (6): d = 475 mm, t = 15 mm (Ab = 21,677 mm2, Zb = 2,416,700 mm3)

Member Fx (kN) MIP (kN·m) MOP (kN·m)
Chord 49.99 (T) 17.34 4.97
Brace 66.082 (C) 0.921 6.255

## Validation

Design Parameters

β = d/D = 0.95

So, 0.2 < β < 1.0 (OK)

γ = D/2T = 12.5

So, 10 < γ < 50 (OK)

θ = tan-1(10/5) = 63.4°

So, 30° < θ < 90° (OK)

Fy = 500 MPa (OK)

Determination of Qu

Qβ = 0.3/[β(1 - 0.833×β)] = 1.513

Qu_ax = [2.8 + (12 + 0.1×γ)×β]×Qβ = [2.8 + (12 + 0.1×12.5)×0.95](1.513) = 23.289

Qu_ipb = (5 + 0.7×γ)×β1.2 = [5 + 0.7(12.5)](0.95)1.2 = 12.929

Qu_opb = 2.5 + (4.5 + 0.2×γ)×β2.6 = 2.5 + [4.5 + 0.2(12.5)](0.95)2.6 = 8.626

Determination of Qf

From Table 4.3.2:

C1ax = 0.2, C2axi = 0, C3ax = 0.35

For C1, C2, and C3, interpolate between values for β ≤ 0.9 and β = 1.0.

C1b = 0.2, C2b = 0, C3b = 0.4

Pyc = Ac×Fyc = 15,079.5 kN

Mpc = Zc×Fyc = 1,740.19 kN·m

Pc = 49.99 kN

Mc = √ (MIPC2+MOPC2) = 18.04 kN·m

$A = ( F S × P c P y c ) 2 + ( F S × M c M p c ) 2 = ( 1.6 × 49.99 17 , 079.5 ) 2 + ( 1.6 × 18.04 1 , 740.19 ) 2 = 0.0174$
$Qf_ax=1+C1ax(FS×PcPyc)−C2ax(FS×McMpc)−C3axA2$
$Q f _ a x = 1 + 0.2 ( 1.6 × 49.99 15 , 079.5 ) − 0 − 0.35 ( 0.0174 ) 2 = 1.0$
$Q f _ ipb = 1 + C 1 b ( F S × P c P y c ) − C 2 b ( F S × M c M p c ) − C 3 b A 2$
$Q f _ ipb = 1 + 0.2 ( 1.6 × 49.99 15 , 079.5 ) − 0 − 0.4 ( 0.0174 ) 2 = 1.001$
$Q f _ opb = 1 + C 1 b ( F S × P c P y c ) − C 2 b ( F S × M c M p c ) − C 3 b A 2$
$Q f _ opb = 1 + 0.2 ( 1.6 × 49.99 15 , 079.5 ) − 0 − 0.4 ( 0.0174 ) 2 = 1.001$

Axial Capacity

Moment Capacity

In-plane bending:

Out-of-plane bending:

Interaction Ratio

P/Pa + (M/Ma)ipb2+ (M/Ma)opb = (66.082 / 3,255.7) + (0.921 / 858.53)2 + (6.255 / 572.8) = 0.031

## Results

Table 2. Comparison of results
Qu_ax 23.829 23.921 negligible
Qu_ipb 12.929 12.934 negligible
Qu_opb 8.626 8.627 negligible
Qf_ax 1.0 1.0 none
Qf_ipb 1.001 1.001 none
Qf_opb 1.001 1.001 none
Axial capacity (kN) 3,255.7 3,250,61 negligible
In-plane Bending Capacity (kN·m) 858.53 858.33 negligible
Out-of-plane Bending Capacity (kN·m) 572.8 572.55 negligible
Interaction ratio 0.031 0.031 none

## STAAD.Pro Input File

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 12-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 10 0; 3 5 10 0; 4 10 10 0; 5 10 0 0; 6 5 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 3 5; 6 3 1; 7 3 6;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 4 TABLE ST W6X12
*5 6 7 TABLE ST HSSP16X0.625
*2 3 TABLE ST HSSP20x0.5
2 3 TABLE ST PIPE OD 0.5 ID 0.46
5 TO 7 TABLE ST PIPE OD 0.475 ID 0.445
*MEMBER PROPERTY EUROPEAN
*2 3 TABLE ST 610x20CHS
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 5 FIXED
6 PINNED
2 FX -50
2 3 UNI GY -5
2 3 CMOM Y 5
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE API
*FSJ 2.6 ALL
FYLD 500000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


Note: The generated .PUN file is required to generated this output for K or X joints. Otherwise, the program assumes all joints are Y joints. Refer to D1.J.8.2 Joint File Format for details.
======================================================================
NODE NO :      3   CHORD NO:     2   BRACE NO:     6
======================================================================
DESIGN DATA : (Units    : N , mm  )
Chord Memb :      D =  500.00  T = 19.99
Brace Memb :      d =  475.01  t = 15.01
Angle (THETA) =  63.4 deg  GAP   =    0.00   Fyc = 499.9
BETA          =  0.95      GAMMA =   12.51   TAU =  0.75
STAAD SPACE                                              -- PAGE NO.    7
JOINT CLASS :           X
FACTORS :
--------------------------------------------------------------------
Joint   Load   Strength     Chord Load    C1        C2        C3
Class   Cond   factor (Qu)  factor (Qf)
--------------------------------------------------------------------
X     AX      23.291        1.000      -0.000    0.000    0.350
X     IPB     12.934        1.001       0.200    0.000    0.400
X     OPB      8.627        1.001       0.200    0.000    0.400
----------------------------------------------------------------------
CAPACITY CHECKS        BRACE LOAD    LC   CAPACITY   RATIO   STATUS
(Cl. 4.3)             (KN, m )         (KN, m )
----------------------------------------------------------------------
AXIAL        :            -66.08      1     3250.61    0.020   PASS
IP BENDING   :              0.92      1      858.33    0.001   PASS
OP BENDING   :              6.26      1      572.55    0.011   PASS
INTERACTION  :                        1                0.031   PASS
----------------------------------------------------------------------
CRITICAL     :                        1                0.031   PASS
----------------------------------------------------------------------