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Module 1: Tension Members

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Video 1
Hello I am going to discuss about the codal provisions for calculation of designstrength of members under axial tension. Therefore, as I told in last class that design strengthwill be calculated based on three criteria; one is the due to gross yielding of the section, dueto rapture and due to block shear. And the minimum of these three will be the design strengthof the tension member.
So coming to the codal provisions, we will get the design strength calculation of tensionmember in clause 6 of IS: 800-2007. So details you can find out from clause 6 that the designtension T should satisfy the requirement of this Td . Where Td is the design strength of themember under axial tension and Td will be the least of these three, one is the yielding of grosssection (Tdg), then rapture of critical section (Tdn) and then block shear failure (Tdb).So on the basis of these three, the Td will be decided. So, Td will be the least of these threeand that Td has to be greater than the factor tensile force coming into the member. So comingto clause 6.2, we will see that design strength due to gross yielding Tdg can be calculated as,
Where,fy is the yield stress of material in MPa,Ag is the gross area of cross-sectionm0is the partial safety factor of failure in tension by yielding (Table 5, IS 800: 2007).
Similarly we can find out design strength due to rapture of critical section. So this can befound in clause 6.3 and in clause 6.3.1, you will get design strength in tension of a plate,
Where,fu is the ultimate stress of material in MPa,An is the net effective area of cross-sectionm1is the partial safety factor of failure in tension at ultimate stress (Table 5, IS 800: 2007)So, for plate in earlier lectures we have seen, how to calculate the net area of the plate meansabout the critical section. So this net area will be required to find out the rupture strength ofthe section.
The design strength of threaded rods in tension,( Tdn ) governed by rupture is given by
Where,An is the net root area at the threaded section.
Similarly for single angle section, now in case of single angle as I told that if it is connectedwith some gusset plate, or some other plates, or some other members then shear lag effectwill be going to be occur. So, we have to calculate the Tdn value taking care of the shear lageffect.
Here, w = outstanding leg width,bs = shear lag width, as shown in figure below.
LC = length of the end connection, that is the distance between the outermost bolts in the endjoint measured along the load direction or length of the weld along the load direction.Here,  is a factor which can be calculated from this formula that is= 1.4 – 0.076 (w/t) (fy /fu) (bs /Lc) and this should be less than or equal to fum0 /fym1 andshould be greater than or equal to 0.7
And at the beginning we may not know all the details, so for preliminary sizing we cancalculate Tdn from this formula
Here,  = 0.6 for one or two bolts, 0.7 for three bolts and 0.8 for four or more bolts along thelength in the end connection or equivalent weld length.An = net area of the total cross-section;Anc = net area of the connected leg;Ago = gross area of the outstanding leg; andt = thickness of the leg.
For other sections like double angles, channels, I-sections and other rolled steel sectionsconnected by one or more elements to end gusset is also governed by shear lag effect. Thedesign tensile strength of such sections as governed by tearing of net section may also becalculated using equation in clause 6.3.3, where  is the is calculated based on the shear lagdistance bs , and bs is taken from the furthest edge of the outstanding leg to the nearest bolt orweld line in the connected leg of the cross section. So, for rapture strength calculation otherthan the single angle section we can use this clause that is clause 6.3.3.
Then the design strength due to block shear can be calculated from clause 6.4 of the IS code,it is given in clause 6.4.Bolted ConnectionsThe block shear strength, Tdb of connection shall be taken as the smaller of,
whereAvg and Avn = minimum gross and net area in shear along bolt line parallel to external force,respectively (1-2 & 3-4 as shown in Figure above).Atg and Atn= minimum gross and net area in tension from the bolt hole to the toe of the angle,end bolt line, perpendicular to the line of force, respectively (2-3 as shown in Figure above),and fu and fy = ultimate and yield stress of the material, respectively.
Now for weld connections Tdb can be checked for welded connections by taking appropriatesection in the member around the end weld and this which can shear off as a block.
Video 2
Now another thing we have to check that is slenderness ratio, theoretically there should notbe any upper limit of the slenderness ratio because it is under tension if it is compression thenthere is a chance of buckling so for that we have to consider the limiting value of slendernessratio. But in this case, theoretically we should not, but we consider certain slenderness ratiofrom serviceability point of view, because limitation is necessary to prevent undesirablevibration and lateral movement.So permissible values of slenderness ratio is given in clause 3.8, table 3 in the IS code. So weare checking slenderness ratio in case of tension member because to make sure that vibrationis not going to be more from limit state of serviceability point of view also sometimes themember get reverse load due to wind and earthquake . So in that case slenderness ratio willbe a big factor.
So the slenderness value slenderness ratio value are given in table 3 of IS: 800-2007, if wesee when the tension member has reversal of direct stress due to loads other than wind andseismic it is 180.Whereas when a member subjected to compressive forces resulting only from a combinationof wind and earthquake actions, provided the deformation of such a member does notadversely affect the stresses in any part of the structure. In that case, the permissible value ofslenderness ratio is 250.And, if a member normally acting as a tie in a roof truss or a bracing member which is notconsidered effective when subjected to reversal of stress resulting from the action of wind orearthquake we can consider as 350.And, when members are always in tension other than pre-tensioned members we can consideras 400. So this is how the IS code has provided certain limit on maximum effectiveslenderness ratio, so that has to be kept in mind.So that means when we are going to design a tension member not only we have to find outthe strength but also we have to find out whether it is under the permissible limit ofslenderness ratio or not, so both the things we have to see.So this is how one can calculate the design capacity of a particular section, in tension andcheck whether that section is violating the slenderness ratio or not.