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)
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
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
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
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 |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\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 ----------------------------------------------------------------------