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
So, 0.2 < β < 1.0 (OK)
So, 10 < γ < 50 (OK)
So, 30° < θ < 90° (OK)
Fy = 500 MPa (OK)
Determination of Qu
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
Axial Capacity
Moment Capacity
In-plane bending:
Out-of-plane bending:
Interaction Ratio
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
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 2024\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
2 3 TABLE ST PIPE OD 0.5 ID 0.46
5 TO 7 TABLE ST PIPE OD 0.475 ID 0.445
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 5 FIXED
6 PINNED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FX -50
MEMBER LOAD
2 3 UNI GY -5
2 3 CMOM Y 5
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE API
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 = 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
----------------------------------------------------------------------