Design of joint 9-10 (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; Z₁ = 180 mm and h₆ = 60 mm, a = 140 mm; the bending moments at the centre of the flange (the welded joint) are:

M_X9 = F_Y (L_c + Z₁) = 75000 Nmm,

M_Y9 = F_X (L_c + Z₁) + F_Z (X₁ + h₆/2 + a) = 550000 Nmm,

M_Z9 = F_Y (X₁ + h₆/2 + a) = 75000 Nmm.

Dimensional constraints: flanges 9 and 10, of thickness g = 10 mm, are connected by 4 bolted joints; the flange dimensions are chosen so as to give access to the wrenches used to tighten the standard bolts and nuts.

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

Design constraints: the flange materials must be weldable; the bolt and nut materials are chosen according to the relevant regulations.

Materials and heat treatments

Since elements 9 and 10 are welded parts, weldable S235 steel according to SR EN 10025-2 (STAS 500/2) is adopted.

For the bolts, property class 6.8 is adopted, with σ₀₂ ≈ 6·8·10 = 480 MPa and σ_r ≈ 6·100 = 600 MPa.

Material properties

Sizing

Calculation data

– loading: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N; M_X9 = 75000 Nmm, M_Y9 = 550000 Nmm, M_Z9 = 75000 Nmm;

– shapes and dimensions: square flange of size L_f = 120 mm; side of the hole-pattern square L = 90 mm; a = (L_f – L)/2 = 15 mm; r₁ = r₂ = r₃ = r₄ = r = L/2 = 63.64 mm;

– material: 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 adopted);

– friction parameters: µ = 0.2 – the sliding friction coefficient between flanges 9 and 10; µ₁ = 0.2 – the sliding friction coefficient in the thread; µ₂ = 0.25 – the sliding friction coefficient between nut and washer.

Loads

Finding the most heavily loaded bolt

Axial forces in the bolts due to each load:

– bolt forces due to the force F_X, which loads the joint axially and centrically,

= = = = = 375 N;

– bolt forces due to the moment M_Z9, which loads the joint axially and eccentrically; with M_Z9 = 75000 Nmm, L = 90 mm and a = 15 mm, = = 350 N, = = 50 N;

– bolt forces due to the moment M_Y9, which loads the joint axially and eccentrically; with M_Y9 = 550000 Nmm, L = 90 mm and a = 15 mm, = = 2566.7 N, = = 366.7 N;

– bolt forces due to the resultant of F_Y and F_Z, which loads the joint transversely and centrically; with F_Y = 300 N, F_Z = 700 N, β_a = 1.3 and µ₁ = 0.2, = = = = 1237.5 N;

– bolt forces due to the moment M_X9, which loads the joint transversely and centrically; with M_X9 = 75000 Nmm, r = 63.64 mm, β_a = 1.3 and µ₁ = 0.2, = = = = 1915 N;

Total axial forces in the bolts

F_aș1 = + + + + = 375 + 350 + 2566.7 + 1237.5 + 1915 = 6444.2 N

F_aș2 = + + + + = 375 + 50 + 2566.7 + 1237.5 + 1915 = 6144.2 N

F_aș3 = + + + + = 375 + 50 + 366.7 + 1237.5 + 1915 = 3944.2 N

F_aș4 = + + + + = 375 + 350 + 366.7 + 1237.5 + 1915 = 4244.5 N

The maximum total axial force, F_aș = max(F_aș1, F_aș2, F_aș3, F_aș4) = 6444.2 N, shows that bolt 1 is the most heavily loaded; it is sized below.

Axial tightening (preload) force at assembly

F_st = max( + , + , + , + ) = max(1237.5 + 1915, 1237.5 + 1915, 1237.5 + 1915, 1237.5 + 1915) = 3152.5 N.

Sizing

– sizing the most heavily loaded bolt from the tensile strength condition, with F_aș = 6444.2 N, β = 1.2 and σ_at = 200 MPa, gives the required minor thread diameter = 7.02 mm;

– standard dimensions adopted: d₁ = 8.376 mm, pitch diameter d₂ = 9.026 mm; d = 10 mm (M10), p = 1.5 mm; clearance hole diameter D₁ = 11 mm.

Tightening moments of the joint

– screwing moment (thread friction): with F_st = 3152.5 N, d₂ = 9.026 mm, p = 1.5 mm, µ = 0.2 and α = 60°, M_î = 4088.2 Nmm;

– pivoting friction moment between nut and washer: with F_st = 3152.5 N, D₁ = 11 mm, S = 17 mm and µ₂ = 0.2, M_p = 4481 Nmm;

– nut tightening (wrench) torque,

M_c = M_î + M_p = 4088.2 + 4481 = 8569.2 Nmm.

Checks

– checking the threaded bolt shank under combined loading (tension and torsion) when tightened under load (the most unfavourable case): with F_aș = 6444.2 N, d₁ = 8.376 mm and M_î = 4088.2 Nmm, σ_e = 136.7 MPa,

and 136.7 < (160…240) MPa (satisfied).

– checking the self-locking condition: with p = 1.5 mm, d₂ = 9.026 mm, μ = 0.2 and α = 60°, β₂ = 3.03°, φ′ = 13°,

and 3.03° < 13° (satisfied).

Design of the technological shape

Constructive-technological drawing

Adopted dimensions and constructive-technological parameters

– dimensions: L_f = 120 mm, L = 90 mm, g = 10 mm, D₁ = 11 mm;

– roughness of the surfaces machined by milling and drilling: R_a1 = 12.5 µm; R_a2 = 6.3 µm;

– sharp edges are chamfered 1×45°.

Adopted fastener dimensions

– hexagon head bolt: M10, d = 10 mm, S = 17 mm, D = 18 mm, k = 7 mm, l_ș = 40 mm, l_f = 25 mm;

– hexagon nut: M10, S = 17 mm, m = 8 mm;

– flat washer: d = 10 mm, d₁ = 10.5 mm, d₂ = 20 mm, h = 2 mm;

– Grower spring washer: MN 10, d₁ = 10.2 mm, d₂ = 15.2 mm, g = 2.5 mm.