ISO 19902 Connections (2^nd 2020)

ISO 19902 Connections (2^nd, 2020) checks the strength of tubular joints (connections) according to chapter 14 of the standard.

To add the standard execute Standards - Main - ISO - ISO 19902 Connections (2^nd 2020) from the ribbon:

Press to Set Standard Custom Settings

Connection Checks are calculated on Connections. With the help of Connection Finder tool, it is possible to automatically recognize Chords and Braces with their dimensions.

By default, all supported Connections are included in the selection but it can be changed by pressing . If connections were not recognized press to run Connection Finder tool.

Standard uses material data (Yield/Tensile) in calculations. Wizard checks if the values are defined for all materials.

Constants

Constants are set to the Standard default values and normally do not need to be changed:

• Gamma_Rj - the partial resistance factor for tubular joints (chapter 14.3.2). Default value is 1 (reduced from 1.05 in the 1^st edition);
• C_x - critical elastic buckling coefficient used in the effective strength calculation per Chapter 13.2 (Formula 13.2-10). Default value is 0.3.

Note: The C₁, C₂, C₃ coefficients from Table 14.3-2 used in the Q_f formula are built into the standard and cannot be edited from the UI.

Options

Brace Type Method - use brace type of the selected method calculated by Brace Classification Tool (e.g. Left-to-Right, Total Force). The selected classification determines whether each brace is treated as K, TY or Cross in the joint strength calculation;

Is Load Transfer defines the braces for which chapter 14.3.5 (Y- and X-joints with chord cans) is applied. When set to Yes and the chord contains a can, the joint representative axial strength is calculated accounting for the chord can length;

According to the calculation procedure, Beam Length and Length Factor for Y and Z direction are required. Data from Beam Member Finder is used automatically to define characteristics KL Y and KL Z. If beam members are not recognized press .

KL Y - effective length factor (K) multiplied by the unbraced length (L) in the brace local Y direction (in-plane), used in 13.2-7, Section 13.2.3.2;

KL Z - effective length factor (K) multiplied by the unbraced length (L) in the brace local Z direction (out-of-plane), used in 13.2-7, Section 13.2.3.2;

Critical Joints - Critical joints are checked for axial loads with the 50% of braces capacity. Sections 14.2.3 and A.14.2.3.

Note: Compared to the 1^st edition, the characteristics Extra Partial Resistance Factor (γ_R,q, no longer used in Q_f) and Brace Utilization were removed. The characteristic Is Critical Brace was renamed to Critical Joints.

Calculations

Nomenclature and geometric parameters that are used in results:

The validity ranges of connection parameters:

0.2 ≤ β ≤ 1.0

10 ≤ γ ≤ 50

30° ≤ θ ≤ 90°

τ ≤ 1.0

f_y ≤ 800 N/mm²

g/D > -0.6 · γ (for K-joints)

f_y - chord representative yield strength = Min(yield stress, 0.8 · tensile strength).

For each brace connected to the chord, connection elements of the chord are taken into account. Minimum allowable stress is taken if elements are of different materials.

Note: If material yield stress > 800 MPa - allowable static stress is taken equal to material yield stress.

Note: According to chapter 14.2.1, the representative yield strength of a brace is calculated as Min(brace yield stress, 0.9 · brace tensile strength). This differs from the 1^st edition, where 0.8 was used for both chord and brace.

Basic Joint Strength.

Joint axial and bending capacities shall satisfy following equations:

where

P_d - is the design value of the joint axial strength, in force units;

M_d - is the design value of the joint bending moment strength, in moment units;

γ_Rj - is the partial resistance factor for tubular joints, γ_Rj = 1.00 (chapter 14.3.2, reduced from 1.05 in the 1^st edition);

Strengths for simple tubular joints are calculated by following formulas:

where

P_uj - representative joint axial strength, in force units;

M_uj - representative joint bending moment strength, in moment units;

f_y - representative yield strength of the chord member at the joint (SMYS or 0.8 of the tensile strength, if less), in stress units;

T - chord wall thickness at the intersection with the brace;

d - brace outside diameter;

θ - included angle between brace and chord;

Q_u - strength factor;

Q_f - chord force factor;

Strength factor Q_u

Q_u is the strength factor which varies with the joint and load type. Formulas from Table 14.3-1 of the 2^nd edition are used:

Q_β = 0.3 / (β · (1 − 0.833 · β)) for β > 0.6, otherwise Q_β = 1.0 (Formulas 14.3-5, 14.3-6);

Q_{u,axial,tension} = Min(16 + 1.2 · γ, 40) · β^1.2 · Q_g · K_portion + (30 · β) · TY_portion + (6.4 + β² · γ^0.6) · X_portion;

Q_{u,axial,compression} = Min(16 + 1.2 · γ, 40) · β^1.2 · Q_g · K_portion + Min(2.8 + (20 + 0.8 · γ) · β^1.6, 2.8 + 36 · β^1.6) · TY_portion + (2.8 + (12 + 0.1 · γ) · β) · Q_β · X_portion;

Q_u,IPB = (5.0 + 0.7 · γ) · β^1.2;

Q_u,OPB = 2.5 + (4.5 + 0.2 · γ) · β^2.6;

where

f_y,b - representative yield strength of the brace at the intersection of the chord, Min(brace yield, 0.9 · brace tensile), in stress units;

t - brace wall thickness at the intersection of the chord;

Gap factor Q_g is calculated based on g/D ratio (Formulas 14.3-7, 14.3-8):

Q_g,1 = Max(1.0 − 0.2 · (1.0 − 2.8 · g/D)³, 1.0) for g/D ≥ 0.05;

Q_g,2 = 0.13 + 0.65 · Φ · γ^0.5 for g/D ≤ −0.05, where Φ = f_y,b · t / (f_y · T);

For −0.05 < g/D < 0.05, Q_g is calculated as linear interpolation between Q_g,1 (at g/D = 0.05, computed with g/D = 0.05) and Q_g,2.

Note: in the 2^nd edition Q_g is expressed via g/D (gap-to-diameter) instead of g/T (gap-to-thickness) used in the 1^st edition.

Note: g - total gap of the brace. From the following picture g = 0.023076 * 0.1362 + 0.196152 * 0.8638 = 0.172579;

Chord force factor Q_f

In the 2^nd edition, Q_f is calculated directly from parameter A (no auxiliary q_A parameter is used anymore). Per Formula 14.3-9:

Q_f = 1 + C₁ · (P_c / P_y) − C₂ · (M_ipb / M_p) − C₃ · A²

where parameter A is calculated as (Formula 14.3-10):

A = [ (P_c / P_y)² + (M_c / M_p)² ]^0.5

where

P_c - axial force in the chord member from factored actions;

M_c - bending moment resultant in the chord member from factored actions, M_c = (M_ipb² + M_opb²)^0.5;

P_y - representative axial strength due to yielding of the chord member not taking account of buckling, in force units:

P_y = A_chord * f_y

f_y - representative yield strength of the chord member, in stress units;

A_chord - cross-sectional area of the chord or chord can at the brace intersection;

M_p - representative plastic moment strength of the chord member;

M_p = W_e * f_y,

- plastic modulus;

D - chord member diameter;

T - chord member thickness;

ipb - in-plane bending;

opb - out-of-plane bending;

C₁, C₂, C₃ coefficients are taken from Table 14.3-2 of the standard:

Note: for X-joints subject to brace axial forces, C₁ and C₃ are linearly interpolated for 0.9 < β < 1.0.

Q_f calculation workflow

In the 2^nd edition, Q_f is calculated using the following workflow (the auxiliary parameter q_A from the 1^st edition is no longer used):

1. Parameter A and the chord bending moment resultant M_c are computed for each chord member from the left and right side of the intersection with the respective brace.
2. For each brace, Q_f is calculated separately for each joint type (K, TY, X) and each side (left, right), using the corresponding row from Table 14.3-2 to select C₁, C₂, C₃.
3. For each joint type, the maximum of the left and right side chord members is taken:

Q_f,max(K joint) = max( Q_f,left(K joint), Q_f,right(K joint) )

Q_f,max(TY joint) = max( Q_f,left(TY joint), Q_f,right(TY joint) )

Q_f,max(X joint) = max( Q_f,left(X joint), Q_f,right(X joint) )

Then the final Q_{f Axial} for a brace is interpolated by brace classification percentages coming from the Brace Classification Tool:

Q_{f Axial} = Q_f,max(K joint) · brace percentage(K joint) + Q_f,max(TY joint) · brace percentage(TY joint) + Q_f,max(X joint) · brace percentage(X joint)

Q_{f Bending} is calculated for all joints using the "All joints subject to brace bending moments" row from Table 14.3-2 (C₁ = 0.2, C₂ = 0, C₃ = 0.4), and the maximum of left and right side is taken.

Note: Compared to the 1^st edition, the auxiliary parameter q_A and the multipliers λ (0.03 / 0.045 / 0.021) are no longer used. The partial resistance factor γ_R,q is also no longer part of the Q_f formula.

Extra joint axial capacity calculations are performed to connections that contain increased thickness of the chord. Axial strength is calculated by following formula:

where

P_uj - joint axial strength, in force units;

P_uj,c - is the value P_uj,c from Equation (14.3-1), based on the chord geometrical and material properties, including Q_f calculated from chord can properties and dimensions;

Note: r cannot be taken greater than 1;

L_c - effective total length;

Y_n - the lesser chord member thickness on either side of the joint;

T_c - chord can thickness;

Effective length L is calculated for each brace separately. It is a minimum distance from the end of can till the point of intersection of chord and brace multiplied on 2.

T_c ≥ T nominal;

L₁, L₂ ≤ 1.25 * D. If L₁ and L₂ exceed 1.25 * D distance, can will not be recognized;

D - can diameter;

L = 2 * L₁ - effective length for the left brace;

L = 2 * L₃ = 2 * L₄ - effective length for the middle brace;

L = 2 * L₂ - effective length for the right brace.

Note: This section is applied to connections with cans. If brace L_c = 0 section is not applied. If the brace is overlapping section is not applied.

Strength check

Each brace in a joint that is subjected to an axial force or a bending moment alone, or to an axial force combined with bending moments, shall be designed to satisfy the following condition (Formula 14.3-12):

U_j = |P_B / P_D| + (M_B / M_D)²_ipb + |M_B / M_D|_opb ≤ 1.0

for all joints

where

U_j - joint utilization;

P_B - axial force in the brace member from factored actions;

M_B - bending moment in the brace member from factored actions;

P_D - design value of the joint axial strength (see 14.3.2);

M_D - design value of the joint bending moment strength (see 14.3.2);

ipb - in-plane bending;

opb - out-of-plane bending;

Note: compared to the 1^st edition there is a single equation for all joints. The separate equation 14.3-13 for non-critical joints (with U_b/γ_zj as the limit) is no longer used, and the concept of Brace Utilization U_b and extra resistance factor γ_zj is removed.

Basic Joint Strength check (Chapter 14.2.3)

According to chapters 14.2.3 and A.14.2.3, chord cans shall have a minimum axial capacity of at least 50 % of the effective axial strength of each incoming brace. Only braces of joints marked as Critical Joints = Yes are verified.

The effective axial strength of the brace is calculated per Chapter 13.2:

f_t - representative axial tensile strength (Formula 13.2-2): f_t = brace yield strength;

f_c - representative axial compressive strength (Formulas 13.2-5, 13.2-6):

f_c = (1 − 0.278 · λ²) · f_yc for λ ≤ 1.34;

f_c = (0.9 / λ²) · f_yc for λ > 1.34;

f_yc - local buckling strength (Formulas 13.2-8, 13.2-9):

f_yc = f_y for f_y / f_xe ≤ 0.17;

f_yc = (1.047 − 0.274 · f_y / f_xe) · f_y otherwise;

f_xe - nominal elastic local buckling strength (Formula 13.2-10):

f_xe = 2 · C_x · E · (t / D)

λ - column slenderness (Formula 13.2-7), taken as the maximum of Y and Z directions:

λ_Y = (KL_Y / (π · √(I_zz / A))) · √(f_yc / E);

λ_Z = (KL_Z / (π · √(I_yy / A))) · √(f_yc / E);

λ = max(λ_Y, λ_Z)

where

E - Young's modulus of the brace material;

C_x - critical elastic buckling coefficient (default 0.3, set in Constants);

t - brace wall thickness;

D - brace outside diameter;

KL Y, KL Z - product of K and L parameters in Y and Z directions (assigned per beam member);

I_zz, I_yy - second moments of area of the brace about Z and Y axes;

A - cross-sectional area of the brace.

The utilization factor for critical joints is calculated as:

Uf_{Basic Joint Strength} = max( P_d,tension / (0.5 · f_t), P_{d,compression} / (0.5 · f_c) )

where P_d,tension and P_{d,compression} are the joint axial strengths in tension and compression respectively. This utilization factor is also included in the combined utilization factor along with U_j.

Overlapping joints

The strength of joints that have in-plane overlap involving two or more braces may be determined using the requirements for simple joints defined in 14.3, with the following exceptions and additions.

a) Shearing of the brace parallel to the chord face is a potential failure mode and shall be checked.

b) Section 14.3.5 (can calculations) does not apply to overlapping joints.

Shear capacity = f_y * effective area / (√3 * γ_Rj)

Effective area is the total area of two braces that overlap:

Area₁ = 2 * p₁ * t₁ - area of the through brace; Area₂ = 2 * (p₂ − q) * t₂ - area of the overlapping brace;

where

t₁ - thickness of the through brace;

t₂ - thickness of the overlapping brace;

p₁ = d₁ / sin(θ₁);

p₂ = d₂ / sin(θ₂);

d₁, d₂ - original diameter of the through and overlapping braces respectively;

θ₁, θ₂ - inclination of the through and overlapping braces respectively to the chord;

q - overlapping distance (negative gap);

Applied shear force is taken as summation of forces, perpendicular to the chord of the through and the overlapping braces;

Shear UC (Ultimate Capacity) is calculated as the relation of Applied shear force to shear capacity:

Shear UC = Applied shear force / Shear capacity

c) If axial forces in the overlapping and through braces have the same sign (both in compression or both in tension), the check of the intersection strength of the through brace on the chord shall use the combined axial force representing the force in the through brace plus the portion of the overlapping brace force(s). The portion of the overlapping brace force may be calculated from the ratio of the cross-sectional area of the brace that bears onto the through brace to the full area of the overlapping brace.

Modified axial force = P_d1 + P_d2 * ov;

where

P_d1 - the axial force of the through brace perpendicular to the chord.

P_d2 - the axial force of the overlapping brace perpendicular to the chord.

ov - overlapping percentage,

ov = q / p * 100%;

Modified axial UC = Modified axial force / P_uj;

P_uj - joint axial capacity from formula (14.3-1);

d) For both in-plane or out-of-plane moments, the combined moments on the overlapping and through braces shall be used to check the intersection strength of the through brace on the chord. This combined moment shall account for the sign of the moments.

M_d1, M_d2 - respective in-plane and out-of-plane bending moments of the through and overlapping brace;

Modified moment UC = (Modified ipb moment / M_uj(ipb))² + Modified opb moment / M_uj(opb)

Modified axial and moment UC = Modified axial UC + Modified moment UC

e) The overlap onto the through brace shall be checked by using the through brace as the chord in the equations in 14.3. The through brace strength shall also be checked for combined axial force and bending moment in the overlapping brace in accordance with 14.3.6 using the value of Q_f calculated for the through brace. For the through-brace allowable stress, the brace yield stress is limited to min(brace yield, 0.9 · brace tensile) and capped at 800 MPa.

Note:

• Through brace is taken as a chord and overlapping brace is calculated once again with TY = 100% classification to obtain axial, bending and combined UFs;
• Through brace is recalculated once again using the overlapping brace element;
• If a brace is overlapping/through at the same time for few braces – absolute maximum value is taken into account;

f) Where nominal thicknesses of the overlapping and through braces differ by more than 10 %, the thicker brace shall be the through brace

Note: through brace is a brace with a maximum diameter, or maximum thickness if equal or minimum angle if equal.