Design of elements 13 and 13′ (left/right tie rod) — 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, X₃ = 150 mm, Y₁ = 550 mm, Z₁ = 180 mm; the forces and moments at the centre of the welded joint 12-13 (12′-13′) are:

F_Xs = F_Xd = F_X/2 = 750 N,

F_Ys = F_Yd = F_Y/2 = 150 N,

F_Zs = F_Zd = F_Z/2 = 350 N,

M_X13 = F_Y (L_c + Z₁)/2 = 37500 Nmm,

M_Y13 = F_X (L_c + Z₁)/2 + F_Z (X₁ + X₂)/2 = 292500 Nmm,

M_Z13 = F_X Y₁/2 + F_Y (X₁ + X₂)/2 = 457500 Nmm.

Dimensional constraints: the square tube 12, with h₁₂ = 50 mm, t₁₂ = 5 mm, will be welded to tie rod 13.

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

Design constraints: weldable materials.

Materials and heat treatments

Since elements 13 (13′) are welded parts, a weldable steel is adopted (e.g. S185, S235, S275) according to SR EN 10025-2 (STAS 500/2).

Material properties

Sizing

Calculation data

– loading: F_Ys = 150 N, M_Z13 = 457500 Nmm;

– shape and dimensions: flat bar with b₁₃ = h₁₂ + (60…80) mm = 120 mm; X₃ = 150 mm;

– materials: σ₀₂ = 235 MPa – the yield strength; c = 2…3 – the safety factor; σ_at = σ₀₂/c = 235/(2…3) = (80…120) MPa – the allowable tensile stress (σ_at = 100 MPa is adopted); σ_aî = (1.05…1.1)σ_at (σ_aî = 110 MPa is adopted);

– bending moment in the critical section (simplified model): M_îmax = M_Z13 + F_Ys X₃ = 457500 + 150·150 = 480000 Nmm.

Sizing

From the bending strength condition, with M_îmax = 480000 Nmm, b₁₃ = 120 mm and σ_aî = 110 MPa, = 14.8 mm; a standard flat-bar blank with thickness g₁₃ = 15 mm and width b₁₃ = 120 mm is adopted.

Constructive-technological shape

Constructive-technological drawing

Adopted dimensions and constructive-technological parameters

– dimensions: b₁₃ = 120 mm, g₁₃ = 15 mm, L₁₃ = 270 mm, a = 15 mm, L = 90 mm; the clearance hole diameter D₁ results from the calculation of the bolted joint;

– the number of sets of adjustment holes is set when drawing the assembly;

– technological operations: milling the ends and drilling; tolerances and fits;

– sharp edges are chamfered 1×45°;

– roughness of the surfaces machined by milling or drilling: R_a1 = 12.5 µm, R_a2 = 6.3 µm.