Design of joint 7-8 (tube-in-tube joint)

A. Loading diagram and design data

External loading diagram	Loading diagram of joint 7-8

Design data

External forces: F_X, F_Y, F_Z act at distances L_c (Ex.3.1), X₁, Z₁ (Ex.1.2.2), h₆ (Ex.4.1), h₇, h₈, a, b (Ex.4.3); the moments at the centre of the joint are calculated (Calc.0):

M_X8 = F_Y (L_c + Z₁),

M_Z8 = F_Y (X₁ + h₆/2 + b + h₈/2),

M_Y8 = F_X (L_c + Z₁) + F_Z (X₁ + h₆/2 + b + h₈/2).

Dimensional constraints: the square tubes 7 and 8, with sides h₇, h₈ and wall thicknesses t₇, t₈ (Ex.4.3), are assembled together.

Operating constraints: temperature T = (−30…40) °C; outdoor working environment with high humidity.

Design constraints: tube 7 is inserted into tube 8, with loose clearance fits on the sides of the squares in contact.

B. Choice of materials

Since elements 7 and 8 are welded to other elements, weldable steels are adopted (Annex.M.01). For the adopted steels, the yield strength σ₀₂, the ultimate tensile strength σ_r and σ_as = 60…90 MPa, the allowable crushing stress for conforming steel-on-steel contacts, are retained for the calculations.

C. Design of the constructive shape

Constructive features and constraints: – for correct operation, conforming contacts (over large surfaces) are required, ensured by the tube dimensions; – the dimensions of the pin joint are determined from the pin joint calculation (Sec.5.2, Ex.5.2).

D. Calculation model, sizing and checking

Specific features of the model of joint 7-8

The calculation model of the joint between square tubes 7 and 8 is similar to the (general) calculation model of the joint between tubes 5 and 6 (Sec.4.1), with the following differences related to the coordinate systems:

– the coordinate system of joint 7-8 has X as the axial axis instead of Z, and Z as the transverse axis instead of X;

– the size of the square bore is H = h₇.

Calculation data

– loads: F_X = F_Z, F_Y, M_X = M_Z8, M_Y = M_Y8, M_Z = M_X8;

– shapes and dimensions: the size of the square bore H = h₇; the wall thickness of the inner tube t₇ and of the outer tube t₈; the length L of the contact prism is unknown;

– materials: σ_as = 60…90 MPa – the allowable crushing stress.

Sizing

With calculation window Calc.4.1.1, after substituting the known parameters and solving, two positive solutions are usually obtained.

Finally, L_7-8 is taken as the largest positive value of L (rounded up to a whole value).

E. Design of the constructive-technological shape

Constructive-technological drawings

Recommendations for choosing the dimensions and constructive-technological parameters

– dimensions: h₇, t₇, h₈, t₈, L₇ = b + h₈/2 + L_7-8/2, L₈ = a – L₇ + L_7-8, l = L_7-8/2; the pin bore diameter D_b is determined from the pin joint calculation (Sec.5.2, Ex.5.2); Note. If L₇ > a or L₈ < 0, the tube-in-tube joint cannot be integrated because larger dimensions would be needed, so it is dropped (together with element 8 and the pin);

– technological operations: milling the tube ends, drilling/reaming the pin holes;

– roughness of the machined surfaces: R_a1 = 6.3 µm or R_a1 = 12.5 µm; R_a2 = 6.3 µm or R_a2 = 3.2 µm;

– sharp edges are chamfered 1×45°;

– the position of the pin hole (and, if needed, of the adjustment pin hole) is set when drawing the assembly.