Checking elements 11, 12, 12′ and joints 11-12, 11-12′ by FEA (ANSYS) — example

1. Analysis model and input data

Analysis model

Loading diagram in the XYZ coordinate system of the ATD

Geometric model in the ANSYS coordinate system

Geometric parameters in ANSYS

Input data

Forces: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N.

Moments: M_X11 = 75000 Nmm, M_Y11 = 585000 Nmm, M_Z11 = 90000 Nmm.

Geometric parameters: L₁₁ = 550 mm; L_11-12 = 70 mm; h₁₂ = 50 mm, t₁₂ = 5 mm, h₁₁ = 60 mm, t₁₁ = 5 mm; L_f = 120 mm.

Material: S235, weldable general-purpose steel.

Operating constraints: temperature T = (−30…40) °C.

Parameters of the ANSYS model

Forces: F_x = F_X = 1500 N, F_y = −F_Z = −700 N, F_z = −F_Y = −300 N.

Moments: M_x = −M_X11 = −75000 Nmm, M_y = M_Z11 = 90000 Nmm; M_z = −M_Y11 = −585000 Nmm.

Geometric parameters: H_e = 60 mm, V_e = 60 mm, H = 50 mm, V = 50 mm, H_i = 40 mm, V_i = 40 mm; for Body1 (Body3): FD1 = 310 mm and FD4 = 35 mm; for Body2: FD1 = 35 mm and FD4 = 515 mm; for Plane1: FD1 = 240 mm; for the support footprint (relative to Plane2): D = 215 mm and L = 120 mm.

Material: S235, weldable general-purpose steel, with σ_at = σ₀₂/c = 235/1.3 = 180 MPa (since the FEA model is more accurate, a lower safety factor c = 1.3 was adopted than for the classical, less accurate design models); allowable contact stresses: σ_as = 90 MPa, the allowable steel-on-steel normal crushing stress, and τ_as = 45 MPa, the allowable steel-on-steel tangential contact stress.

Viewing the support (fixed) zones and the applied forces and moments

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2. Results

Viewing the forces in the reaction zones

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Viewing the displacements

🖱 → the model appears

Viewing the stresses

Equivalent stresses on the global model

🖱 → 🖱 (marks local stress values at points) → [move the cursor and 🖱 click the point on the model where the stress value should be shown]; to delete a local value: 🖱 (Label) → [🖱 select the value, then press the Delete key].

Equivalent stresses on the model of the central tube

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Equivalent stresses on the model of the right tube

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Equivalent stresses on the model of the left tube

Viewing the pressures and stresses in the contact zones

Pressures on the contact surfaces

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Tangential (friction) stresses on the contact surfaces

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3. Checks

Deformation check

δ ≤ δ_a; 0.507 ≤ 5 mm (satisfied).

Note. The allowable deflection is set by the operating conditions.

Equivalent (von Mises) stress check

σ_{ech_max} ≤ σ_at; 137.2 > 132 MPa (NOT satisfied),

where σ_{ech_max} is the maximum equivalent stress in the figure above.

If the inequality above is NOT satisfied, one of the following options can be chosen:

a. choose a better material;

b. change the cross-section geometry, taking larger values of the square side h₁₁ and wall thickness t₁₁, while keeping the inner dimension that contacts the inserted tube;

c. change both the material and the geometry.

Option a is adopted here: material S295 is chosen, so

σ_{ech_max} ≤ σ_at; 137.2 < 295/1.3 = 226.9 MPa (satisfied).

Normal contact pressure check

p_max ≤ σ_as; 10.33 ≤ 90 MPa (satisfied),

where p_max is the maximum (absolute value) of the pressure in the figure above.

Tangential contact stress check

τ_max ≤ τ_as; 9.23 ≤ 44 MPa (satisfied),

where τ_max is the maximum tangential contact stress (frictional stress) in the figure above and τ_as the allowable tangential contact stress.