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 (A_c = 30,159 mm², Z_c = 3,480,380 mm³)

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

Table 1. Loads
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)

F_y = 500 MPa (OK)

g = 0

Determination of Q_u

Q_{u_ax} = 30×β = 30(0.8) = 24

Q_{u_ipb} = (5 + 0.7×γ)×β^1.2 = [5 + 0.7(12.5)](0.8)^1.2 = 10.52

Determination of Q_f

From Table 4.3.2:

C1_ax = 0.3, C2_axi = 0, C3_ax = 0.8

C1_b = 0.2, C2_b = 0, C3_b = 0.4

P_yc = A_c×F_yc = 15,079.5 kN

M_pc = Z_c×F_yc = 1,740.19 kN·m

P_c = -30 kN

M_c = √ (MIPC²+MOPC²) = 0.49 kN·m

A = \sqrt{{(\frac{F S \times P_{c}}{P_{y c}})}^{2} + {(\frac{F S \times M_{c}}{M_{p c}})}^{2}} = \sqrt{{(\frac{1.6 \times 30}{17, 079.5})}^{2} + {(\frac{1.6 \times 0.49}{1, 740.19})}^{2}} = 0.003

Q_{f_ax} = 1 + {C 1}_{a x} (\frac{F S \times P_{c}}{P_{y c}}) - {C 2}_{a x} (\frac{F S \times M_{c}}{M_{p c}}) - {C 3}_{a x} A^{2}

Q_{f_ax} = 1 + 0.3 (\frac{1.6 \times 30}{15, 079.5}) - 0 - 0.8 {(0.003)}^{2} = 0.999

Q_{f_bend} = 1 + {C 1}_{b} (\frac{F S \times P_{c}}{P_{y c}}) - {C 2}_{b} (\frac{F S \times M_{c}}{M_{p c}}) - {C 3}_{b} A^{2}

Q_{f_bend} = 1 + 0.2 (\frac{1.6 \times 30}{15, 079.5}) - 0 - 0.4 {(0.003)}^{2} = 0.999

Axial Capacity

P_{a} = Q_{u} Q_{f} \frac{F_{y c} T^{2}}{F S \sin θ} = 24 (0.999) \frac{500 {(20)}^{2}}{1.6 \sin (63.4 °) 10^{3}} = 3, 351.8 kN

Moment Capacity

M_{a} = Q_{u} Q_{f} \frac{F_{y c} T^{2} d}{F S \sin θ} = 10.52 (0.999) \frac{500 {(20)}^{2} 400}{1.6 \sin (63.4 °) 10^{6}} = 587.9 kN⋅m

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

Interaction Ratio

P/P_a + (M/M_a)² = (33.34 / 3,351.8) + (0.49 / 587.9)² = 0.010

Results

Table 2. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
Q_{u_ax}	24	24	none
Q_{u_ipb}	10.52	10.52	none
Q_{f_ax}	0.999	0.999	none
Q_{f_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

STAAD.Pro Input File

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
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
JOINT LOAD
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

STAAD.Pro Output

======================================================================          
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 :                                                                     
  --------------------------------------------------------------------          
  Joint   Load   Strength     Chord Load    C1        C2        C3              
  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             
----------------------------------------------------------------------