Instructiona Objectives: At te end of tis esson, te students soud be abe to understand: Ways in wic eccentric oads appear in a weded joint. Genera procedure of designing a weded joint for eccentric oading. How to avoid eccentric oading in simpe cases.. Tere are many possibe ways in wic an eccentric oading can be imposed on a weded joint. A few cases are discussed beow.. Eccentricay oaded transverse fiet joint: Consider a cantiever beam fixed to a wa by two transverse fiet joints as sown in figure... Te beam is subjected to a transverse oad of magnitude. L igure..: Eccentricay oaded weded joint Like any weded joint, te design is based upon te strengt of te joint against faiure due to sear force aong te troat section. In tis case any sma section of te troat is subjected to (a) direct sear stress of magnitude were b = engt of te wed, bt, Version ME, IIT Karagpur
t = tickness at te troat and te factor appears in te denominator for doube wed. (b) Indirect sear stress due to bending of te beam, wose magnitude is cacuated in te foowing manner and wose direction is perpendicuar to tat of te direct sear stress. Consider a sma area da in troat section ying at a distance y from te centerine, wic is aso te centroida axis of te wed. An important assumption is made regarding te magnitude of te sear stress at a point witin te area da. It is assumed tat te sear stress is proportiona to te distance from te centroida axis, tat is y in tis case, and directed aong te orizonta. Te proportionaity constant is cacuated using te moment equiibrium equation about centroid of te troat section. Tis gives, Hence, τ ( y) y da = L were τ ( y ) = cy. c = L. Terefore te magnitude of te sear stress is y da τ = Ly I y 3 tb were te second moment of area of te troat section I p = y da =. So, for an eccentricay oaded joint sown in figure.. te maximum sear stress occurs at te extreme end and its magnitude is 3L τ max = +. bt tb In order to design a safe weded joint τ, max S S were S S is te aowabe sear stress of te wed materia. Version ME, IIT Karagpur
d y Sma area da Troat tickness igure..: orces on wed in bending. Eccentricay oaded parae fiet joint: Consider a cantiever beam connected to a wa by means of two parae joints as sown in figure..3. Te beam is required to carry a oad in transverse direction. igure..3: Eccentricay oaded parae fiet joint L Version ME, IIT Karagpur
In order to seect te size of te wed it is once again considered tat te joint fais in sear aong te troat section. or te given oading, te troat area is subjected to two sear stresses. (a) Direct sear of magnitude t were = engt of te wed t = tickness of te troat. (b) Indirect sear stress owing to eccentricity of te oading. Te magnitude and direction of te sear stresses are cacuated using te simiar assumption as in te ast section. Te magnitude of sear stress at any point is assumed to be proportiona to its distance from te centroid of te troat area and te direction is perpendicuar to te ine joining te point and te centroid. Te sense is te same as tat of te rotation of te weded jont as a woe (if permitted). Wit tis assumption te sear stress at a point at a distance r from te centroid is given by τ ( r ) = cr were te proportionaity constant c is to cacuated using te moment equiibrium equation. Taking moment about te centroid one finds τ (r)r da = L, were L = distance of te ine of action of from centroid. Tus, were L c =, J J = r da is te poar moment of te troat section about its centroid. Te net sear stress at a point is cacuated by vector addition of te two kinds of sear stresses discussed above. (Note tat te vector addition of stresses is in genera not defined. In tis case te resutant force at a point witin an infinitesima area is obtained using vector addition of forces cacuated from te individua stress vaues. Te resutant stress is te force divided by area. Since everywere te same vaue of area is invoved in cacuation, te net stress is terefore te vector sum of te component stresses.) Te wed size is Version ME, IIT Karagpur
designed suc tat te maximum sear stress does not exceed its aowabe imiting vaue. Centroid d igure...4: orces on troat section due to torsion 3. Asymmetric Weded Section: It is observed from section and tat an eccentricity in oading causes extra sear stress in a weded joint. Tus it may be usefu to reduce te eccentricity in oading. In some appications tis is acieved by making te wed section asymmetric. Consider a pate subjected to an axia oad as sown in figure..5. Te pate is connected to te wa by means of parae fiet joint. Assume tat te axia oad is aong te centroida axis if te beam wic is sown by dotted ines. If te weds are made of equa engts in bot sides, ten te centroid of te weded section, being aong te centerine of te beam wi not ie on te cetroida axis of te beam. Tus an eccentricity in oading is introduced. Tis situation may be avoided by making te two wed engts unequa in suc proportion tat te eccentricity is removed. Te reationsip between and wi be as foowing: Version ME, IIT Karagpur
=, were = engt of te upper wed = engt of te ower wed, = distance of te upper wed from centroida axis, = distance of te ower wed from centroida axis. centroid igure..5: Parae wed for asymmetric section Te net engt of te wed = + can be cacuated from te strengt consideration tat is S, S t were t = tickness of te troat. Tus te individua engts of te wed are as foowing: and were b= widt of te pate. b = b =, Version ME, IIT Karagpur
Review questions and answers: Q.. A rectanguar stee pate is weded as a cantiever to a vertica coumn and supports a singe concentrated oad of 60 kn as sown in figure beow. Determine te wed size if te aowabe sear stress in te wed materia is 40 MPa. 00 50 00 Ans. Te wed is subjected to two sear stresses () Direct sear of magnitude 60,000/Area of te wed. Te area of te troat section is easiy found out to be 00 t were t=0.707. Tus direct sear stress is 44/ MPa. () Te indirect sear stress as a point r distance away from te centroid of te troat section as magnitude Lr τ =, J were J is te poar moment of area of te troat section and L is te eccentricity of te oad. rom te geometry of te troat section it may be cacuated tat te distance of centroid from eft end = x = =.5 mm (see figure beow) and te poar moment about G + b is J = ( b + ) 3 ( b + ) b + = 7530 mm 4. Version ME, IIT Karagpur
G b x 4.8 Tus te indirect sear stress as magnitude r MPa. Te maximum resutant sear stress depends on bot te magnitude and direction of te indirect sear stress. It soud be cear tat te maximum sear stress appears at te extreme corner of te wed section wic is at a distance b ( ) x + ( ) = 6.5 mm away from te centroid. Noticing tat te incuded ange between te two sear forces as x rmax 0 cos 53.3, te maximum vaue of te resutant sear stress is found out to be f max = 854.6 MPa. Since tis vaue soud not exceed 40 MPa te minimum wed size must be = 0.39 mm. Version ME, IIT Karagpur