Design of joint 4-5 (welded joint)

A. Loading diagram and design data

External loading diagram	Loading diagram of the welded joint 4-5
Design data External forces: FX, FY, FZ act at distances Lc (Ex.3.1, Ex.3.2) and X1 (Ex.1.2.2); the moments at the centre of the square section (the welded joint) are calculated (Calc.0): MX5 = FY (Lc + h4), MY5 = FX (Lc + h4) + FZ X1, MZ5 = FY X1. Dimensional constraints: the upper tie rod 4, of width b4 and thickness h4 (Ex.3.1), is welded to the square tube 5 of side h5 and wall thickness t5. Operating constraints: temperature T = (−30…40) °C; outdoor working environment with high humidity. Design constraints: weldable materials for elements 4 and 5.

B. Choice of material and heat treatments

Elements 4 and 5 were designed using weldable steels (Annex.M.01). These steels are not heat-treated before welding; after welding, the subassembly may undergo stress-relief annealing. For the adopted steels, the yield strength σ₀₂ and the ultimate tensile strength σ_r are retained for the calculations.

For the weld bead, the allowable shear stress corresponding to weldable steels is adopted: τ_afs = (0.6…0.7)σ_at.

C. Design of the constructive shape

Constructive model

Constructive features and constraints

– the weld throat thickness a should be smaller than the wall thickness t₅ of the square tube (a < t₅);

– the two elements must be perpendicular;

– a fillet weld is made along the closed contour (square section).

D. Calculation model, sizing and checking

Calculation model

a

b

c   d

e   f

Calculation assumptions and loads

– the external loading consists of the forces F_X, F_Y, F_Z and the moments M_X, M_Y, M_Z;

– the shear stresses are uniformly distributed along the weld bead in the longitudinal and transverse planes: fig. a for the force F_Xs, fig. b for F_Ys, fig. c for F_Zs, fig. d for the moment M_Ys, fig. e for M_Xs and fig. f for M_Zs;

– the tensile and bending stresses in the weld bead are neglected.

Calculation data

– loading: F_Xs = F_X, F_Ys = F_Y, F_Zs = F_Z; M_Xs = M_X5; M_Ys = M_Y5; M_Zs = M_Z5;

– shape and dimensions: the inner contour of the weld bead is a square of side h = h₅;

– materials: σ₀₂ – the yield strength; c = 2…3 – the safety factor; σ_at = σ₀₂/c – the allowable tensile stress; τ_afs = (0.6…0.7)σ_at – the allowable shear stress of the weld.

E. Calculation relations

– Shear strength condition of the weld

The shear stresses generated by F_Xs, F_Ys, F_Zs, M_Xs, M_Ys, M_Zs (figs. a, b, c, d, e and f, respectively) are:

τ_fsFX = , τ_fsFY = , τ_fsFZ = , τ_fsMX = , τ_fsMY = and τ_fsMZ =

They are added vectorially (for the most unfavourable case, considering that the forces and moments can act in both directions), giving the maximum shear stress at a corner of the square,

– Sizing the weld

From the relation above (last part), the weld throat thickness is obtained,

where τ_afs is the allowable shear stress of the weld; a whole value a > a^nec is adopted.

F. Design of the constructive-technological shape