Design of elements 7, 8 (lower tie rod, body) — 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, Z₁ = 180 mm and h₆ = 60 mm; the moments at the centre of the square section are:

M_X7 = F_Y (L_c + Z₁) = 75000 Nmm,

M_Y7 = F_X (L_c + Z₁) + F_Z (X₁ + h₆/2) = 452000 Nmm,

M_Z7 = F_Y (X₁ + h₆/2) = 33000 Nmm.

Dimensional constraints: square tube semi-finished products are used, welded to body 6 (square section of side h₆ = 60 mm and thickness t₆ = 5 mm); so that a continuous weld bead can be applied, the side of square tube 7 must satisfy h₇ ≤ h₆; tube 7 slides into tube 8, so h₇ = h₈ – 2t₈.

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

Design constraints: weldable material.

Material and heat treatments

Since elements 7 (lower tie rod) and 8 (lower tie rod body) are welded parts, S235 according to SR EN 10025-2 (STAS 500/2) is adopted.

Material properties

Sizing and checking

Calculation data

– loads: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N, M_Y7 = 452000 Nmm, M_Z7 = 33000 Nmm;

– dimensions: lengths a = X₂ – h₆/2 – h₁₁/2 – 2g = 140 mm (X₂ = 220 mm, h₆ = 60 mm, h₁₁ ≈ 60 mm, g = 10 mm) and b = (0.35…0.45)a = (49…63) mm, b = 55 mm adopted;

– for square tubes the thickness/side ratio k = t/h = 0.05…0.15; k = 0.1 is adopted;

– material: σ₀₂ = 235 MPa – the yield strength; c = 2…3 – the safety factor; σ_at = σ₀₂/c = 235/(2…3) = (78.3…117.5) MPa, σ_at = 100 MPa adopted; σ_aî = (1.05…1.15)σ_at = (105…115) MPa, σ_aî = 110 MPa adopted – the allowable bending stress.

Sizing

Sizing tube 7

From the bending strength condition (the cubic equation), with F_X = 1500 N, F_Y = 300 N, F_Z = 700 N, M_Y7 = 452000 Nmm, M_Z7 = 33000 Nmm, k = 0.1, b = 55 mm and σ_at = 100 MPa, = 38.4 mm; a standard square tube with h₇ = 50 mm and t₇ = 5 mm is adopted.

Sizing tube 8

From the oblique bending strength condition, with F_Y = 300 N, F_Z = 700 N, M_Y7 = 452000 Nmm, M_Z7 = 33000 Nmm, k = 0.1, a = 140 mm and σ_aî = 110 MPa, = 3.9 mm; a standard square tube with h₈ = 60 mm and t₈ = 5 mm is adopted.

Constructive-technological shapes

Constructive-technological drawings

Adopted dimensions and constructive-technological parameters

– dimensions: h₇ = 50 mm, t₇ = 5 mm, h₈ = 60 mm, t₈ = 5 mm, L₇ = 55 mm; the other dimensions are determined from the calculation of the tube-in-tube joint length L_7-8 and of the pin diameter D_b, after 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 holes) is set when drawing the assembly.