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)
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
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
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 2023\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
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
*FSJ 2.6 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 = 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 ----------------------------------------------------------------------