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Module 1: Eccentric Connections

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Video 1
In this lecture we are going to discuss about the load line perpendicular to the plane of boltedjoint, that means when loaded in out of plane then how reactions on the bolt will be comingin to picture that we will try to understand. And in each bolt we know that due to theeccentricity of the load the moment will come in the bold group as well as direct force willcome. Now as it is out of plane loading that is why here if we see the 2 type of stresses willdevelop. One is the shear stress due to direct load and another is the tensile stress due tomoment.
So if we draw the diagram say for example a bolt group is connected with certain bracket sayfor example this is connected here and we have bolt group at different positions. Now a loadof magnitude P is acting at a distant of e, so moment will be basically P×e, this moment willcome into picture and because of this P the shear stress will develop in this direction andbecause of this moment tensile force will come in this direction and we know this tensileforce will be in this top portion and in bottom portion there will be compressive force.If we draw the stress diagram this will develop as shown above. Now where will be the centerof rotation that means the neutral axis, so there are different opinions for finding out theneutral axis because it will not be at the cg of the bolt group. This is because bolt lying abovethe neutral axis will be in tension but in this portion the bracket if we draw this the bracket isgoing to take the compression, so the amount of compressive force will be huge in thisdirection compared to the bolt force in as a tension therefore the center of rotation cannot beat the center of gravity or at the mid-point.Another opinion has come that it may be at the bottom of the bolt but this is also not truebecause the bottom flanged of the bracket and the stanchion are not perfectly rigid so if it isnot perfectly rigid we cannot consider that all the bolts are going to be carry out by thetension, this is not also practicable, so that we actually need to make some trial and error.Trial and error means we have to find out where it can lie so through trial and error analysiswe can find out otherwise there is an opinion that we can consider at a distance of h/7, where
h is the height from the bottom of the bracket to the top most bolt position which are intension.
So if we consider the neutral axis at h/7 then we can find out the total tensile force on the boltand total compressive force on the bracket, so and we can make equal to find out theequilibrium equation.So the assumption is here that the tensile force develop on the bracket will be proportionate tothe distance from NA, that means it will be meeting with distance at NA, say if this isdistance y then t will be vary with y or I can writeT ky i i Where Ti is the tensile force developed at ith bolt and yi is the perpendicular distance fromcenter of rotation or from neutral axis to that center of the particular bolt.So this is what we can assumed and then we can find out the constant which is called elasticconstant or proportionality constant that I can write as
The moment of resistance due to this tensile force
So, total Moment of resistance provided by the bolts in tension,
So moment of resistance provided by the bolt intension we can write down in this way.
So we can find out the value of moment in terms of its tensile force.Now tensile force in bolt i,
Tensile force in the extreme critical bolt will be:
Total tensile force exerted by the bolt,
This is the total tensile force exerted by the bolt and these has to be equal to the totalcompressive force because we know about neutral axis the total tensile force and totalcompressive force has to be equal.Thus total compressive force,
Hence taking moment about NA we getExternal moment (M) = Moment resisted by bolts in tension (M’) + Moment resisted bycompressive force.
Now depending on the number of bolts position of the bolt we can find out what is thefraction of moment is carrying by the bolts, so this is how we can analyze.
Now we will find out the maximum tensile force at the bolt, what will be the maximumtensile force? Maximum tensile force will develop at the extreme bolt.Therefore, the tensile force in the extreme bolt,
Where ymax is the maximum distance of the bolt from neutral axis.
So maximum tension in the bolt I can find out from this formula and where M' already wehave found out.
Now I will go to the design steps means I did not know. I have been given a tension andwhich is connected to a bracket and then this bracket is carrying an eccentric load of say P ata distance of e. Now what should be the number of bolt, we have to find out. So if P and e isgiven then how to find out the number of bolts. So what we can do we can write as designsteps.Design Steps1. Select nominal diameter of bolt and provide pitch and edge distance suitably.2. Calculate the design shear strength (Vdsb)3. Select number of bolt lines, n' and external moment (M) due to eccentricity.4. Find the approximate number of bolts (n) per line from the following formula:
5. Compute the shear force (Vsb) in the bolt.6. Calculate the design tensile strength of the bolt (Tdb).7. Calculate tensile force (Tb) in the extreme critical bolt.8. Check for developed shear and tension individually:Vsb < Vdsb and Tb < Tdb.9. The connection should be checked against combined shear and tension using theinteraction formula:
So this is how we can go for design, design is basically a trial and error method, so we willstart with an approximate number of bolt per bolt line, then we will check whether it is okayor not. If it is not okay then we have to again increase the number of bolts, so it is an iterativeprocess.
Video 2