Design of joints 11-12, 11-12′ (tube-in-tube joints) — 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, X₂ = 220 mm, Y₁ = 550 mm, Z₁ = 180 mm, h₁₁ = 60 mm; the forces and moments at the centres of the joints are:

F_Xs = F_Xd = F_X/2 = 750 N,

F_Zs = F_Zd = F_Z/2 = 350 N,

M_X11s = M_X11d = F_Y (L_c + Z₁)/2 + F_Z (Y₁ − h₁₁)/2 = 209000 Nmm,

M_Y11s = M_Y11d = F_X (L_c + Z₁)/2 + F_Z (X₁ + X₂)/2 = 292500 Nmm,

M_Z11s = M_Z11d = F_Y (X₁ + X₂)/2 + F_X (Y₁ − h₁₁)/2 = 472500 Nmm.

Note. Since the forces F_X, F_Y and F_Z can act in both directions during operation of the towing device, the combinations giving the maximum values were used when calculating the moments.

Dimensional constraints: the square tubes 12, 12′, of side h₁₂ = 50 mm and thickness t₁₂ = 5 mm, are assembled with the square tube 11, of side h₁₁ = 60 mm and thickness t₁₁ = 5 mm.

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

Design constraints: tubes 12, 12′ are inserted into tube 11, with clearance fits on the sides of the squares in contact.

Materials and heat treatments

Weldable S235 steel according to SR EN 10025-2 (STAS 500/2) was adopted for elements 11, 12, 12′.

Material properties

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

Sizing

Calculation data

– loads: F_X = 750 N, F_Y = 350 N, M_X = M_X11s = 209000 Nmm, M_Y = M_Z11s = 472500 Nmm, M_Z = M_Y11s = 292500 Nmm;

– shapes and dimensions: the size of the square bore H = h₁₂ = 50 mm; the wall thickness of the inner tube t₁₂ = 5 mm and of the outer tube t₁₁ = 5 mm; the length L is unknown;

– materials: σ_as = 70 MPa – the allowable crushing stress.

From the sizing relations obtained from the crushing strength conditions of the tube-in-tube joint, with F_X = 750 N, F_Y = 350 N, M_X = 209000 Nmm, M_Y = 472500 Nmm, M_Z = 292500 Nmm, H = 50 mm and σ_as = 70 MPa, the length of the tube-in-tube joint 11-12 (11-12′) is L = max (42.95; 29.45) = 42.95 mm; L_11-12 = 70 mm is adopted (a larger value was chosen to leave extra room for the pin joint).

Constructive-technological shape

Constructive-technological drawings

Adopted dimensions and constructive-technological parameters

– section dimensions: h₁₁ = 60 mm, t₁₁ = 5 mm, h₁₂ = 50 mm, t₁₂ = 5 mm; L₁₁ = 550 mm, L₁₂ = 345 mm; l = 35 mm; the bore diameter D_b is determined from the pin joint calculation;

– the number of adjustment pin holes, and hence the adjustment travel, is set when drawing the assembly;

– technological operations: milling (the bar ends) and drilling;

– sharp edges are chamfered 1×45°;

– roughness of the surfaces machined by milling (bar ends) and drilling: R_a1 = 12.5 µm, R_a2 = 6.3 µm.