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Module 1: Design of Compression Members and Lacing Systems

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Video 1
In this lecture I am going to discuss about the design of lacing system. Now in earlier lecturewe have shown what are the force coming on the lacing and what are the failure modes arecoming in lacing system for the built up member and how to calculate the number of bolts,how to calculate the thickness of the lacing, width of the lacing and how to decide the spacingof the lacing bar, what should be the length of the lacing bar all these things have beendiscussed but for designing we have to make a systemic way so that step by step we candesign.So first I will discuss the steps which can be used for design of a lacing system which is avery lengthy process. So we should remember the steps chronologically so that we can designsystematically a lacing system entirely and after discussion of the steps we will discuss aboutthe one software which has been developed to design the lacing system.
So let us come to the design steps, so in first step we will choose a lacing system means eitherwe will choose a single lacing or double lacing that we have to first decide because the designprocedure will be entirely changed for single lacing and double lacing because depending onthe single lacing or double lacing the force acting on the member will be different andaccordingly the number of bolts and the dimension of the lacing system.Similarly the radius of gyration and the slenderness ratio for single lacing and for doublelacing will different. So if we decide first the lacing system whether it is single lacing ordouble lacing then it will be better to proceed further. Then we have to decide an angle ofinclination (θ) with the axis of the compression member,So as we told earlier that theta should vary from 40 to 70 degree and generally we try to keeptheta from 40 to 45 degree to get maximum efficiency of the lacing system. Then once wedecide the lacing system and its angle of inclination then we can find out the gauge distance(g). Now if the clear spacing between two sections is S as shown in the figure then Thusaccording to the figure,a = 2g + SNow the distance between the bolt centres is calculated as followsL= 2atanθ For single lacingL ¿ atanθ For double lacingAlso we have to decide what should be the spacing (S) so that Ixx and Iyy become same.So that has already been decided and the size of the section has also been decided whether itis channel section or I section and whether sections are arranged back to back or toe to toethat has also been decided earlier.
Now we have to find out the length between two lacing which is calculated as followsL= 2a/tanθ For single lacingL = a/tanθ For double lacingl= a/sin θ For both single and double lacing
So this is what we have to do so that the local buckling of the member can be arrested andthat can be taken care by providing this restriction.In step 4, so once we find out the length of each lacing then I can find out the effectivelength. Now effective length is calculated as followsFor single lacing system (bolted ends), le = lDouble lacing system (bolted ends), le = 0.7lFor welded lacing system, le = 0.7l
Now in step 5, we can find out the thickness of the lacing, so for lacing member we need toknow length, then thickness and width. These are the three things we need to know. Nowalready we knew the spacing between lacing member and angle of inclination. So thethickness can be found as followst>l40 for single lacingt>l60 for double lacingNow we have to check for slenderness ratio, so we can find out the maximum slendernessratio of the lacing system and generally in case of lacing system, lacing members are eitherflat plate or may be angles or may be channel. In case of flat plate we have calculated alreadyin earlier classes which is as follows
Now if it is not less than 145 we can increase the thickness of the lacing, if we increase thethickness of the lacing, then λlacing will be reduced and we can make the λlacing below145.In step 7 we will calculate the compressive strength of the member. Then in step 8 we willcalculate transverse shear, V, which is calculated as follows
V = 0.025PAnd then after finding out the transverse shear we can find out the force in lacing.
Now coming to step 9, we can find out the compressive stress and tensile stress of the lacingsystem and we have to check that this compressive stress and tensile stress is less than thepermissible compressive and tensile stress. So we know permissible compressive stress of thelacing member, fcd value for a particular slenderness ratio and for a particular grade of steel.Now the compressive and tensile force developed in the lacing system should be less than thepermissible value.If it is not less than that then we have to increase the section size, section size means eitherwe have to increase the thickness or width of the flat plate or if we use angle section then wehave to increase the section, right once it is done we can go for connection. So if we use boltconnection then we have to choose a suitable bolt diameter and we have to find the minimumwidth, b of the flat plate. This b should be more or equal to 3d, where d is the nominaldiameter of bolt. After selecting bolt diameter, d and minimum width, b of the lacing flats thenumber of bolt required can be found from the following equation:n=F/RWhere F is the force on that lacing member and R is the bolt value. Therefore before findingout the number of bolt we have to find out the bolt value R and depending on the spacing and pitch distance and edge distance and whether it is single shear or double shear R will becalculated so once R is calculated we can find out the number of bolt.Now in step 11 we will design the end connections for the lacing system that means we willcheck for the number of bolts whether it is sufficient or not to withstand the load and if we gofor weld connection we will check whether the length of weld connection is sufficient or notto withstand that load and the weld length will be decided on the basis of weld strength andthe force acting on the lacing member. So this are the steps we have to follow to find out thelacing dimensions and its configuration.
Video 2
Now this is a sample software of root we have shown here, in fact one of my student hasdeveloped this software where the lacing member can be designed. Now the most importantpart of this is that how to make a GUI to take the input. I am showing an example to give anidea about how to develop a GUI means how it should look and how user friendly. If one canmake a GUI then the user can make the design means they can easily find out the dimensionsof the lacings and its design details.Now suppose first if we come to the type of column, where have been incorporated fewoptions in the program, one is column containing angle section and channel section. Channelcan be placed toe to toe or back to back. So these are the options we have.Now if we click on column containing angle then we can find out a particular section andtheir properties have been taken from SP: 6. The different section size has been taken and their properties which have stored in the library of the software and then when we areclicking a particular size of the section its properties will be taken.Now the spacing has to be decided because spacing will be decided on the basis of Ixx is equalto Iyy on that basis we have to decide spacing, so the spacing will be provided here and wehave to provide yield stress of steel and then whether we are going for angle lacing or flatplate that also we can decide. So these options also are incorporate in the software that wecan provide not only flat plate but also we can provide angle lacing.And then another option we have created that is whether it is single lacing or double lacingand accordingly, the calculation shall be done and if it is double lacing then its calculationwill be different. Then we have to go to the load what is the compressive load coming andwhat will be the height of column that has to be defined.And here you see we have given a help button, in help button if you click then will get the allthe design criteria means what are the design steps and how design has been done. And inflowchart how step by step it has been progressed that has been shown in this flowchart. Andif we click in analyze then it will go for analysis of the system.
So here you see if we select the column containing channel then there are two options wehave the channel facing each other and channel opposite to each other, right. So that will betaken care and others will be similarly we can consider say angle section or plate section forlacing system then single lacing or double lacing all these things will be similar, only thing iswhen column containing channel so all the properties of the channel sections as given in theIS SP: 6 will be taken.
Here channel opposite to each other has been consider, here another option has been considerthat is if we consider double lacing system then how the orientation will be done that has been shown here. So the program can take care the design of double lacing system as well,right.
Now we will go through one example so the design steps whatever we have discussed will befollowed in this design example and in this design example the previous example fromlecture 35 have considered against a certain load and length of the column and then we haveconsidered that ISMC 300 section and back to back with 184 millimetre spacing that has beendecided, so on that basis we will try to find out the details of lacing.Example: Design a laced column 10.5 m long to carry factored axial load of 1000 kN. Thecolumn is restrained in position but not in direction at both the ends. Provide single lacingsystem. Use 2 channel section placed as back to back. Assume steel of grade Fe 410 and boltsof grade 4.6.a) Design the lacing system with bolted connectionsb) Design the lacing system with site welded connections.
So if we recall the design example provided in lecture 35 we can see that we obtained ISMC300 channel section and having a spacing between these two as 184 and channels were placedback to back. So this is what already we have calculated. Now we will calculate the forcescoming on lacing and the dimensions of lacing.
Lacing flats:Now the size of lacing flat we can find out where we can choose lacing member as a flatplate. If we choose that then we have to decide the thickness and width of the lacing memberas well as the length of the lacing member. So to find out the thickness of the lacing memberwe have to find out the length and also to find out the width of the lacing member we knowthat it should be dependent on the diameter of bolt.
 
Video 3