Design Example 5 Welded joint - Steel-stainless.org

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Job No. Sheet 2 of 8 Rev B102, Route de LimoursF-78471 St Rémy Lès Chevreuse CedexFranceTel : +33 (0)1 30 85 25 00Fax : +33 (0)1 30 52 75 38CALCULATION SHEETJob TitleSubjectClientECSCECSC Stainless Steel Valorisation ProjectDesign Example 5 Welded jointMade by IR Date Aug 2002Checked by FH/NB Date Oct 2002Revised by MEB Date April 2006The vectors of the applied force, its eccentricity and the resulting moments acting on awelded joint of general form and centre of gravity C can be expressed as follows :Applied forceN =[ N , N N ]w, Edx,Ed y,Ed,Eccentricity of the applied force[ e , e e ]N xc yc,zcz,Ede = which are the co-ordinates of the point of application of theforce vectorN w, EdApplied momentsM xc, Ed = eycNM yc, Ed = ezcNM = e Nzc, Edxcz,Edx,Edy,Ed− e− e− ezcxcycNNNy,Edz,Edx,EdA linear elastic analysis of the joint for a general load case leads to the following inducedforce components per unit length of weld at a point with co-ordinates (x c , y c , , z c ) , wherethe throat size is denoted by a:F wx,Ed =⎡ Na ⎢⎢⎣Ax,EdwzcM+Iyc,EdycycM−Izc,Ed⎡ Ny,Edx⎤F wy,Ed =cMzc,EdzcMxc,Eda ⎢ + − ⎥⎣ AwIzcIxc⎦F wz,Ed =⎡ Na ⎢⎢⎣Az,EdwycM+Ixc,EdxcxcM−Izcyc,Edyc⎤⎥⎥⎦⎤⎥⎥⎦In the above expressions, the resisting sectional throat area and the inertias about theprincipal axes of the welded joint are:A w = a dl =∑a i lifor a weld of straight segments of length l∫ i and throat size a i ,∫∫∫2c +2cI xc = a ( y z ) dl2c +2cI yc = a ( x z ) dl2c +2cI zc = a ( x y ) dlAs the throat size, a, is constant throughout the plane joint, one can write :Aw= dl =∫ ∑li,aSince x c = 0,136
Job No. Sheet 3 of 8 Rev B102, Route de LimoursF-78471 St Rémy Lès Chevreuse CedexFranceTel : +33 (0)1 30 85 25 00Fax : +33 (0)1 30 52 75 38CALCULATION SHEETJob TitleSubjectClientECSCECSC Stainless Steel Valorisation ProjectDesign Example 5 Welded jointMade by IR Date Aug 2002Checked by FH/NB Date Oct 2002Revised by MEB Date April 2006IazcI( y2 yc= ∫ c) dl , = ( z2 c) dla∫,IaxcI2 2yc I= ∫ ( yc+ zc) dl = +a aDesign approaches Section 6.4.2Determine the required weld throat size at the critical point.Two different procedures are allowed for designing fillet welds:The first procedure is based on the simplified, and more conservative, design shearstrength for a fillet weld. The design shear force per unit length of weld at any point of thejoint is defined as the vector sum of the induced forces per unit length due to all forcesand moments transmitted by the welded joint. This design shear force per unit lengthshould not exceed the design resistance per unit length which is taken as the design shearstrength multiplied by the throat size. This approach ignores the throat plane orientation tothe direction of resultant weld force per unit length.The second procedure is based on comparing the basic design strength of the weaker partjoined to the applied design weld stress in the weld throat determined by a Von Mises typeof formula. This approach is the most precise as it allows for the throat plane orientationto the direction of resultant weld force per unit length.zc1. Simplified design shear strength of the weldThe design resistance check of the fillet weld is as follows:⎛ ⎞2 2 2fF w,Ed =⎜u / 3EN 1993-1-8,F + + ≤ = = ⎟wx,Ed Fwy,EdFwz,EdFw,Rdaf vw,d aclause 4.5.3.3⎝ β wγM2 ⎠Where:f vw,d is the design shear strength of the weldF w,Rd is the design (shear) resistance per unit length of weld of throat size a.For stainless steel β w may be take as 1.0 Section 6.4.2When the design procedure requires that a suitable throat size be obtained, the designexpression becomes :F w,Eda ≥fvw,d2. Basic design strength of the weldIn this approach one must check the Von Mises type stress in the weld throat against thebasic design strength of the fillet weld material. In general this requires that the stresses inthe weld throat, σ ⊥ , τ ⊥ and τ ⎥⎥ be obtained, thus taking account of the orientation of theplane of the throat area to the direction of the resultant induced weld force per unit length.The design formula is as follows:2 2 2 f uEq. 6.12aσ ⊥ + 3( τ ⊥ + τ ) ≤⎥⎥β γwM2It is also required to check the normal stress separately:0.9f uσ ⊥ ≤γM2137Eq 6.12b
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