Design of elements 2 and 2′ (left/right bracket) — 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, Z₂ = 150 mm; the forces and moments at the centre of joint 13-2 are:

F_Xs = F_X/2 = 750 N,

F_Ys = F_Y/2 = 150 N,

F_Zs = F_Z/2 = 350 N;

M_X2s = F_Y (L_c + Z₁)/2 + F_Z Y₁/2 = 230000 Nmm,

M_Y2s = F_X (L_c + Z₁)/2 + F_Z (X₁ + X₂ + X₃)/2 = 345000 Nmm,

M_Z2s = F_X Y₁/2 + F_Y (X₁ + X₂ + X₃)/2 = 480000 Nmm.

Dimensional constraints: dimensions of element 2: b₂ = b₁₃ = 120 mm, L = 90 mm, a = 15 mm.

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

Design constraints: steel for mechanical construction.

Materials and heat treatments

For elements 2 (2′), the steel for mechanical construction E335 according to SR EN 10025-2 (STAS 500/2) is adopted.

Material properties

Sizing

Calculation data

– loading: F_Ys = 150 N, M_X2s = 230000 Nmm;

– shape and dimensions: flat bar of width b₂ = b₁₃ = 120 mm; the thickness g₂ is unknown;

– materials: σ₀₂ = 335 MPa – the yield strength; σ_at = σ₀₂/c = 335/(2…3) = (111.66…167.5) MPa – the allowable tensile stress (σ_at = 140 MPa is adopted); σ_aî = (1.05…1.1)σ_at = (147…154) MPa – the allowable bending stress (σ_aî = 150 MPa is adopted);

– bending moment in the critical section: M_îmax = M_X2s + F_Ys Z₂ = 230000 + 150·150 = 252500 Nmm.

Sizing

From the bending strength condition, with M_îmax = 252500 Nmm, b₂ = 120 mm and σ_aî = 150 MPa, = 9.2 mm; a flat-bar blank of standard thickness g₂ = 10 mm and width b₂ = 120 mm is adopted.

Constructive-technological shape

Constructive-technological drawing

Adopted dimensions and constructive-technological parameters

– dimensions: Z₂ = 150 mm, Y_E = 60 mm, b₂ = 120 mm, g₂ = 10 mm, a = 15 mm, L = 90 mm, R = 20 mm, L_Z = 210 mm, L_Y = 120 mm, a₁ = 15 mm, L₁ = 70 mm, L₂ = 90 mm; the other dimensions (D₁, D₂) result from the calculation of the bolt-nut joints (Bolt 1, Bolt 2);

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

– technological operations: milling, bending, drilling; fillet radius in the bending zone R = 20 mm;

– 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.