Design of joints 13-2 and 13′-2′ (bolted joints) — 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 (13′-2′) 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_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: width of element 2, b₂ = b₁₃ = 120 mm; thickness of element 13, g₁₃ = 15 mm; thickness of element 2, g₂ = 10 mm.

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

Design constraints: steels for threaded fasteners (bolts, nuts) are used.

Materials and heat treatments

Property class 6.8 is adopted for the bolts.

Material properties

Sizing

Calculation data

– loading: F_Xs = 750 N, F_Ys = 150 N, F_Zs = 350 N; M_X2s = 230000 Nmm, M_Y2s = 345000 Nmm, M_Z2s = 480000 Nmm;

– dimensions: L = 90 mm; a = 15 mm; r₁ = r₂ = r₃ = r₄ = r = L/2 = 63.64 mm;

– materials: property class 6.8, σ₀₂ = 480 MPa – the yield strength; c = 2…3 – the safety factor; σ_at = σ₀₂/c = 480/(2…3) = (160…240) MPa – the allowable tensile stress (σ_at = 200 MPa is adopted);

– friction parameters: µ = 0.2 – the sliding friction coefficient in the thread; µ₁ = 0.2 – the sliding friction coefficient between elements 13 and 2; µ₂ = 0.2 – the sliding friction coefficient between nut and washer.

Identifying the most heavily loaded bolt

Axial forces in the bolts for each load

– bolt forces due to the force F_Ys, which loads the joint axially and centrally:

= = = = = 37.5 N;

– bolt forces due to the moment M_Z2s, which loads the joint axially and eccentrically; with M_Z2s = 480000 Nmm, L = 90 mm and a = 15 mm: = = 2240 N, = = 320 N;

– bolt forces due to the moment M_X2s, which loads the joint axially and eccentrically; with M_X2s = 230000 Nmm, L = 90 mm and a = 15 mm: = = 1073.5 N, = = 153.5 N;

– bolt forces due to the resultant of the forces F_Xs and F_Zs, which load the joint transversely; with F_Xs = 750 N, F_Zs = 350 N, β_a = 1.2 and µ₁ = 0.2: = 1241.5 N;

– bolt forces due to the moment M_Y2s, which loads the joint transversely; with M_Y2s = 345000 Nmm, r = 63.64 mm, β_a = 1.2 and µ₁ = 0.2: = = = = 8131.7 N;

Total axial forces in the bolts

F_aș1 = + + + + = 37.5 + 2240 + 1073.5 + 1241.5 + 8131.7 = 12724.2 N,

F_aș2 = + + + + = 37.5 + 320 + 1073.5 + 1241.5 + 8131.7 = 9562.7 N,

F_aș3 = + + + + = 37.5 + 320 + 153.5 + 1241.5 + 8131.7 = 9884.2 N,

F_aș4 = + + + + = 37.5 + 2240 + 153.5 + 1241.5 + 8131.7 = 11804.2 N.

The total axial force F_aș = max(F_aș1, F_aș2, F_aș3, F_aș4) = 12724.2 N shows that bolt 1 is the most heavily loaded; it is sized by the strength calculation.

Axial tightening force in the bolts at assembly

F_st = max( + ; + ; + ; + ) = max(1241.5 + 8131.7; 1241.5 + 8131.7; 1241.5 + 8131.7; 1241.5 + 8131.7) = 9373.2 N.

Sizing

– sizing the most heavily loaded bolt: from the tensile strength condition, with F_aș = 12724.2 N, β = 1.2 and σ_at = 200 MPa, the required minor thread diameter is = 9.9 mm;

– adopted dimensions: metric thread M12, pitch p = 1.75 mm, nominal diameter d = 12 mm, minor diameter d₁ = 10.106 mm, pitch diameter d₂ = 10.863 mm; clearance hole diameter D₁ = 14 mm.

Tightening torques of the joint

– thread torque (friction in the thread): with F_st = 9373.2 N, d₂ = 10.863 mm, p = 1.75 mm, µ = 0.2 and α = 60°, M_î = 14540.1 Nmm;

– friction torque between nut and washer: with F_st = 9373.2 N, D₁ = 14 mm, S = 19 mm and µ₂ = 0.2, M_p = 15584.1 Nmm;

– nut tightening torque (applied with the wrench):

M_c = M_î + M_p = 14540.1 + 15584.1 = 30124.2 Nmm.

Checks

– check of the threaded shank under combined loading (tension and torsion) during tightening: with F_aș = 12724.2 N, d₁ = 10.106 mm and M_î = 14540.1 Nmm, σ_e = 213.9 MPa,

and 213.9 MPa < (160…240) MPa (satisfied);

– self-locking check: with p = 1.75 mm, d₂ = 10.863 mm, μ = 0.2 and α = 60°, β₂ = 2.93°, φ′ = 13°,

and 2.93° < 13° (satisfied).

Constructive-technological shape

Constructive-technological drawings

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, L_Z = 255 mm, L_Y = 120 mm, D₁ = 14 mm; the dimensions a₁, L₁, L₂, D₂ result from the design of the bolted joints of joint E;

– 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.

Adopted fastener dimensions

Joint with Bolt 1

– hexagon head bolt: M12, d = 12 mm, S = 19 mm, D = 21.1 mm, k = 8 mm, l_ș = 40 mm, l_f = 25 mm;

– hexagon nut: M12, S = 19 mm, m = 10 mm;

– plain washer: d = 12 mm, d₁ = 13 mm, d₂ = 24 mm, h = 2.5 mm;

– Grower spring washer: MN 12, d = 12 mm, d₁ = 12.2 mm, d₂ = 18.2 mm, g = 3 mm.

Joint with Bolt 2

– hexagon head bolt: Md, d, S, D, k, l_ș, l_f;

– hexagon nut: Md, S, m;

– plain washer: d, d₁, d₂, h;

– Grower spring washer: MN d, d, d₁, d₂, g.