D12.A.7 Tubular Joint Check, NPD 3.5

For pipe members, punching shear capacity is checked in accordance with the NPD sections 3.5.1 to 3.5.2, except 3.5.2.4. The chord is defined as the member with the greater diameter in the joint. If the diameters are the same the program selects the member with the greater thickness of the two. The chord members must be collinear by 5 degrees.

The punching shear run sequence is performed in two steps. The program will first identify all tubular joints and classify them as T type joints (TRACK99). The joints to be checked will be listed in a file specified in the CODE NPD parameter list, below called GEOM1. This file is used as input in the second run. The file is an editable ACSII file saved under the file name given in the CODE NPD parameter. The TRACK parameter is then set to 98 which directs the program to read from the file GEOM1 file and use it as input to the second run, i.e., the joint capacity checking. The program will check the capacity for both chord members entering the joint. The local y and z moments will be transformed into the plane defined by the joint itself and the far end joints of the brace and chord, defined as in- and out-of plane moments.

The ASCII file should be edited to reflect the correct classification of the joints, gap, can or stub dimensions, yield stress and other geometric options if required. The program will not change the brace or chord definition if this is changed or modified in the input file GEOM1. See Appendix A page xx for GEOM1 example file.

Joint classification parameters in the file GEOM1 are:

KO K joint overlapped
KG K joint with gap
TY T or Y joint
X X joint

Input example for the classification run.

*CLASSIFICATION OF JOINTS, TRACK 99
UNITS MM NEWTON
PARAMETER
CODE NPD GEOM1
FYLD 350 ALL
TRACK 99 ALL
BEAM 1.0 ALL
CHECK CODE ALL

Static strength of tubular joints

The basic consideration is the chord strength. The required chord wall thickness shall be

determined when the other dimensions are given.

The following symbols are used:

T = Cord wall thickness
t = Brace wall thickness
R = Outer radius of chord
r = Outer radius of brace
Θ = Angel between chord and considered brace
D = Outer diameter of chord
d = Outer diameter of brace
a = Gap (clear distance) between considered brace and nearest load-carrying brace measured along chord outer surface
ß = r/R
g = R/T
g = a/D
f_y = Yield stress
Q_f = Factor
Q_g = See table 6.1
Q_u = See table 6.1
Q_ßd = See table 6.1
N = Design axial force in brace
M_IP = Design in-plane bending moment in brace
M_OP = Design out-of plane bending moment in brace
N_k = Characteristic axial load capacity of brace (as governed by the chord strength)
M_OPk = Characteristic out-of-plane bending moment capacity of brace (as governed by the chord strength)
σ_ax = Design axial stress in chord
σ_IP = Design in-plane bending stress in chord
σ_OP = Design out-of-plane bending stress in chord

This section gives design formulae for simple tubular joints without overlap and without gussets, diaphragms or stiffeners. Tubular joints in a space frame structure shall satisfy:

N \leq N_{k} / γ_{m}

Where:

N_{k} = Q_{u} Q_{f} \frac{f_{y} T^{2}}{\sin Θ}

Q_u is given in Table 6.1 and Q_f is a factor to account for the nominal longitudinal stress in the chord.

Q_f = 1.0 - 0.03γA²

A^{2} = \frac{σ_{a x}^{2} + σ_{I P}^{2} + σ_{O P}^{2}}{0.64 f_{y}^{2}}

Table 1. Values for Q_u
Type of joint and geometry	Type of load in brace member
	Axial	In-plane bending	Out-of-plane bending
T and Y	2.5 + 19β	5.0√(γ)β	3.2/(1-0.81β)
X	(2.7 + 13β)Q_β
K	0.90(2+21β)Q_β

For β > 0.6, Q_β = 0.3/[β(1 - 0.833β)]

For β ≤ 0.6, Q_β = 1.0

For γ ≤ 20, Q_g = 1.8 - 0.la/T

For γ > 20, Q_g = 1.8 - 4g

but in no case shall Q_g be taken as less than 1.0.

When β ≥ 0.9, Q_f is set to 1.0. This is also applicable for moment loading. For cases with tension in the chord, Qf is set to 1.0. This is also applicable for moment loading.

The brace end moments shall be accounted for in the following cases:

Out-of-plane bending moment when β > 0.85
When the brace acts as a cantilever
When the rotational stiffness of the connection is considered in the determination of effective buckling length, and / or the structural coefficient γ_mk = 1.00 for the beam-column design of the brace or chord. See Section 3.1.3.

The characteristic capacity of the brace subjected to in-plane bending moment shall be determined by:

M_{I P k} = Q_{u} Q_{f} \frac{d f_{y} T^{2}}{\sin Θ}

Where Q_u is given in Table 6.1 and

Q_f = 1.0 - 0.045γA²

The characteristic capacity of the brace subjected to out-of-plane bending moment shall be determined by:

M_{O P k} = Q_{u} Q_{f} \frac{d f_{y} T^{2}}{\sin Θ}

Where Q_u is given in Table 6.1 and

Q_f = 1.0 - 0.021γA²

For combined axial and bending loads in the brace, the following interaction equation should be satisfied:

\frac{N}{N_{k}} + {(\frac{M_{I P}}{M_{I P k}})}^{2} + \frac{M_{O P}}{M_{O P k}} \leq \frac{1}{γ_{m}}

For overlapping tubular joints without gussets, diaphragms, or stiffeners, the total load component normal to the chord, NN, shall not exceed

N_{N} = \frac{N_{k}}{γ_{m}} \frac{l_{1}}{l} \sin Θ + \frac{2 f_{y} t_{w} l_{2}}{\sqrt{3} γ_{m}}

where (see NPD fig. 3.10)

l_l = circumference for that portion of the brace in contact with the chord (actual length)
l = circumference of brace contact with chord, neglecting presence of overlap
N_k = characteristic axial load capacity of brace
t_w = the lesser of the throat thickness of the overlapping weld or the thickness t of the thinner brace
l₂ = length as shown in NPD fig. 3.10

The above formula for the capacity of overlapping joints is valid only for K joints, where compression in a brace is essentially balanced by tension in brace(s) in the same side of the joint.