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

Design data

External forces: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N act at distances L_c = 70 mm, X₁ = 80 mm, Z₁ = 180 mm, h₆ = 60 mm, h₇ = 50 mm, h₈ = 60 mm, a = 140 mm, b = 55 mm; the moments at the centre of the joint are:

M_X8 = F_Y (L_c + Z₁) = 75000 Nmm,

M_Z8 = F_Y (X₁ + h₆/2 + b + h₈/2) = 58500 Nmm,

M_Y8 = F_X (L_c + Z₁) + F_Z (X₁ + h₆/2 + b + h₈/2) = 511500 Nmm.

Dimensional constraints: the square tubes 7 and 8, with sides h₇ = 50 mm, h₈ = 60 mm and wall thicknesses t₇ = 5 mm, t₈ = 5 mm, 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 outer and inner squares.

Materials and heat treatments

Weldable S235 steel according to SR EN 10025-2 (STAS 500/2) was adopted for elements 7 and 8.

Material properties

Since all the materials in contact are steels, the allowable crushing stress is taken as σ_as = 70 MPa.

Sizing

From the sizing relations obtained from the crushing strength conditions of the tube-in-tube joint, with F_X = F_Z = 700 N, F_Y = 300 N, M_X = M_Z8 = 58500 Nmm, M_Y = 515500 Nmm, M_Z = M_X8 = 75000 Nmm and σ_as = 70 MPa, the following solutions result:

The length of the tube-in-tube joint 7-8 is therefore L = max (42.74; 14.86) = 42.74 mm; L_7-8 = 60 mm is adopted (a larger value was chosen to leave extra room for the pin joint).

Constructive-technological shape

Constructive-technological drawings

Adopted constructive-technological parameters

– dimensions: h₇ = 50 mm, t₇ = 5 mm, h₈ = 60 mm, t₈ = 5 mm, L₇ = 105 mm, L₈ = 95 mm, l = 30 mm; the pin bore diameter D_b is determined from the pin joint calculation;

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

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