# V.API Y Joint

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

## Details

Consider the Y joint at node 3 between members 2 and 6.

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

Brace member (5 & 7): d = 400 mm, t = 20 mm (Ab = 23,876 mm2, Zb = 2,160,790 mm3)

Member Fx (kN) MIP (kN·m) MOP (kN·m)
Chord 30 (C) 0.49 0
Brace 33.34 (T) 0.485 0

## Validation

Design Parameters

β = d/D = 0.8

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)

g = 0

Determination of Qu

Qu_ax = 30×β = 30(0.8) = 24

Qu_ipb = (5 + 0.7×γ)×β1.2 = [5 + 0.7(12.5)](0.8)1.2 = 10.52

Determination of Qf

From Table 4.3.2:

C1ax = 0.3, C2axi = 0, C3ax = 0.8

C1b = 0.2, C2b = 0, C3b = 0.4

Pyc = Ac×Fyc = 15,079.5 kN

Mpc = Zc×Fyc = 1,740.19 kN·m

Pc = -30 kN

Mc = √ (MIPC2+MOPC2) = 0.49 kN·m

$A = ( F S × P c P y c ) 2 + ( F S × M c M p c ) 2 = ( 1.6 × 30 17 , 079.5 ) 2 + ( 1.6 × 0.49 1 , 740.19 ) 2 = 0.003$
$Q f _ ax = 1 + C 1 a x ( F S × P c P y c ) − C 2 a x ( F S × M c M p c ) − C 3 a x A 2$
$Q f _ ax = 1 + 0.3 ( 1.6 × 30 15 , 079.5 ) − 0 − 0.8 ( 0.003 ) 2 = 0.999$
$Q f _ bend = 1 + C 1 b ( F S × P c P y c ) − C 2 b ( F S × M c M p c ) − C 3 b A 2$
$Q f _ bend = 1 + 0.2 ( 1.6 × 30 15 , 079.5 ) − 0 − 0.4 ( 0.003 ) 2 = 0.999$

Axial Capacity

Moment Capacity

Out-of-plane bending is zero so moment capacity is not calculated.

Interaction Ratio

P/Pa + (M/Ma)2 = (33.34 / 3,351.8) + (0.49 / 587.9)2 = 0.010

## Results

Table 2. Comparison of results
Qu_ax 24 24 none
Qu_ipb 10.52 10.52 none
Qf_ax 0.999 0.999 none
Qf_ipb 0.999 0.999 none
Axial capacity (kN) 3,351.8 3,350.87 negligible
In-plane Bending Capacity (kN·m) 587.86 587.7 negligible
Interaction ratio 0.010 0.010 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\API\API YJoint.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 7 TABLE ST W6X12
5 6 TABLE ST PIPE OD 0.4 ID 0.36
2 3 TABLE ST PIPE OD 0.5 ID 0.46
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 5 6 FIXED
2 FX 30
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE API
FSJ 1.6 ALL
FYLD 500000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


======================================================================
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 =  400.00  t = 19.99
Angle (THETA) =  63.4 deg  GAP   =    0.00   Fyc = 499.9
BETA          =  0.80      GAMMA =   12.51   TAU =  1.00
JOINT CLASS :           Y
STAAD SPACE                                              -- PAGE NO.    7
FACTORS :
--------------------------------------------------------------------
Class   Cond   factor (Qu)  factor (Qf)
--------------------------------------------------------------------
Y     AX      24.000        0.999       0.300    0.000    0.800
Y     IPB     10.523        0.999       0.200    0.000    0.400
----------------------------------------------------------------------
CAPACITY CHECKS        BRACE LOAD    LC   CAPACITY   RATIO   STATUS
(Cl. 4.3)             (KN, m )         (KN, m )
----------------------------------------------------------------------
AXIAL        :             33.34      1     3346.58    0.010   PASS
IP BENDING   :             -0.48      1      587.14    0.001   PASS
INTERACTION  :                        1                0.010   PASS
----------------------------------------------------------------------
CRITICAL     :                        1                0.010   PASS
----------------------------------------------------------------------