Design of joints 11-12, 11-12′ (tube-in-tube joints)

A. Loading diagram and design data

External loading diagram	Loading diagram of joints 11-12, 11-12′

Design data

External forces: F_X, F_Y, F_Z act at distances L_c (Ex.3.1), X₁, X₂, Y₁, Z₁ (Ex.1.2.2), with the size of bar 11, h₁₁ (Ex.6.1); the forces and moments at the centres of the joints are calculated (Calc.0):

F_Xs = F_Xd = F_X/2,

F_Zs = F_Zd = F_Z/2 and, respectively,

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

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

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

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 and thickness t₁₂ (Ex.6.1), are assembled with the square tube 11, of side h₁₁ and thickness t₁₁ (Ex.6.1).

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.

B. Choice of material and heat treatments

Since elements 12, 12′ and 11 are welded to other elements, weldable steels were adopted (Annex.M.01). For the adopted steels, the yield strength σ₀₂, the ultimate tensile strength σ_r and the allowable crushing stress σ_as = 60…90 MPa 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 between tubes 12, 12′ and 11; they are obtained by a clearance fit; – the pin joints are placed in the middle of the contact zone of the tube-in-tube joint.

D. Calculation model and sizing

Specific features of joint 11-12 (11-12′)

– the calculation model of the joint between square tubes 11 and 12 is similar to that of the joint between tubes 5 and 6, with the following differences related to the coordinate systems:

– the coordinate system of joint 11-12 has Y as the axial axis instead of Z, and Z as the transverse axis instead of Y;

– the size of the square bore is H = h₁₂.

Calculation data

– loads: F_X = F_Xs, F_Y = F_Zs, F_Z = F_Xs, M_X = M_X11s, M_Y = M_Z11s, M_Z = M_Y11s;

– dimensions: the size of the contact square H = h₁₂; the wall thickness of the inner tube t₁₂ and of the outer tube t₁₁; the length L 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_11-12 is taken as the largest positive value of L (rounded up to a whole value).

E. Design of the technological shape

Constructive-technological drawings

Recommendations for choosing the dimensions and constructive-technological parameters

– section dimensions: h₁₁, t₁₁, h₁₂, t₁₂, L₁₁ = Y₁, L₁₂ = Y₁/2 + L_11-12, l = L_11-12/2; the bore diameter D_b is determined from the pin joint calculation (Sec.6.7, Ex.6.7);

– 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 = 6.3 µm or R_a1 = 12.5 µm; R_a2 = 6.3 µm or R_a2 = 12.5 µm.