V.API K Joint
Verify the design of a simple K joint with axial load and in-plane bending.
Details
Design of node 3 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 (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 = 20 mm
g/D = 20 / 500 = 0.04
Determination of Qu
First, evaluate Qg. Since -0.05 ≤ g/D ≤ 0.05, use linear interpolation.
For g/D = 0.05: Qg = 1 + 0.2×(1 - 2.8×g/D)3 = 1 + 0.2×[1 - 2.8×(0.05)]3 = 1.127
For g/D = -0.05: Qg = 0.13 + 0.65×ϕ×γ0.5 = 0.13 + 0.65×(1)×(12.5)0.5 = 2.428
For g/D = 0.04: 1.127 + (2.428 - 1.127)×(0.05 - 0.04) / (0.05 - -0.05) = 1.257
Qu_ax = (16 + 1.2×γ)×β1.2×Qg = [16 + 1.2(12.5)](0.8)1.2(1.257) = 29.815
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 = 0.2, C2axi = 0.2, C3ax = 0.3
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) = 17.58 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 = (72.511 / 4,158.5) + (0.727 / 588.85)2 = 0.017
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Qu_ax | 29.815 | 29.824 | negligible | |
Qu_ipb | 10.52 | 10.523 | negligible | |
Qf_ax | 0.9977 | 0.999 | negligible | |
Qf_ipb | 1.001 | 1.001 | none | |
Axial capacity (kN) | 4,158.5 | 4,158.06 | negligible | |
In-plane Bending Capacity (kN·m) | 588.86 | 588.1 | negligible | |
Interaction ratio | 0.017 | 0.017 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\API\API KJoint.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
5 6 TABLE ST PIPE OD 0.4 ID 0.36
2 3 TABLE ST PIPE OD 0.5 ID 0.46
MEMBER PROPERTY AMERICAN
1 4 7 TABLE ST HSSP12.750X0.25
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
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 = 400.00 t = 19.99 Angle (THETA) = 63.4 deg GAP = 20.00 Fyc = 499.9 BETA = 0.80 GAMMA = 12.51 TAU = 1.00 ***WARNING - JNT 3: GAP GAP PROVIDED = 20.00 IS LESS THAN THE NOMINAL VALUE OF 2 inches (50 mm). STAAD SPACE -- PAGE NO. 7 JOINT CLASS : KG FACTORS : -------------------------------------------------------------------- Joint Load Strength Chord Load C1 C2 C3 Class Cond factor (Qu) factor (Qf) -------------------------------------------------------------------- K AX 29.824 0.999 0.200 0.200 0.300 K IPB 10.523 1.001 0.200 0.000 0.400 ---------------------------------------------------------------------- CAPACITY CHECKS BRACE LOAD LC CAPACITY RATIO STATUS (Cl. 4.3) (KN, m ) (KN, m ) ---------------------------------------------------------------------- AXIAL : -70.33 1 4158.06 0.017 PASS IP BENDING : 0.76 1 588.10 0.001 PASS INTERACTION : 1 0.017 PASS ---------------------------------------------------------------------- CRITICAL : 1 0.017 PASS ----------------------------------------------------------------------