Design of element 5 (upper column) — example

Design data

External forces: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N act at distances L_c = 70 mm, h₄ = 15 mm; X₁ = 80 mm; the moments at the centre of the square section (the welded joint) are:

M_X5 = F_Y (L_c + h₄) = 25500 Nmm,

M_Y5 = F_X (L_c + h₄) + F_Z X₁ = 183500 Nmm,

M_Z5 = F_Y X₁ = 24000 Nmm.

Dimensional constraints: a square hollow tube semi-finished product is used; since it is welded to tie rod 4 of width b₄ = 60 mm and thickness h₄ = 15 mm, and a fillet weld must be applied, the side of the square tube must be smaller than that width: h₅ < b₄ = 60 mm; the length of element 5 is determined taking dimension Z₁ = 180 mm into account.

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

Design constraints: weldable material.

Material and heat treatment

Since element 5 is a welded part, S235 steel according to SR EN 10025-2 (STAS 500/2) is adopted.

Material properties

Sizing

Maximum bending moments in the critical section (simplified model),

M_{î max_Y} = M_Y5 + F_X (Z₁ – h₄) = 183500 + 1500 · (180 − 15) = 431000 Nmm;

M_{î max_X} = M_X5 + F_Y (Z₁ – h₄) = 25500 + 300 · (180 − 15) = 75000 Nmm.

From the bending strength condition of the bar associated with element 5, with σ_aî = (1.05…1.1)σ₀₂/c = (82.5…129) MPa (σ_aî = 100 MPa is adopted) and k = 0.1, the side of the tube section is = 45 mm,

and = k = 0.1 · 45 = 4.5 mm; a square tube with standard dimensions h₅ = 50 mm, t₅ = 5 mm is adopted.

Constructive-technological shape

Constructive-technological drawing

Adopted dimensions and constructive-technological parameters

– dimensions: h₅ = 50 mm, t₅ = 5 mm; the other dimensions result from the design of joint 5-6 and of the pin joint;

– machining involves milling the end portions and drilling the pin holes; the other surfaces remain unmachined, as indicated by the attached symbol;

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

– the position of the pin hole (and, if needed, of the adjustment hole) is set when drawing the assembly.