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Module 1: Design of Compression Members and Lacing Systems

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Concepts of Lacing Systems

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Video 1
In this lecture we are going to discuss about the lacing systems. Lacing systems are usedbasically to keep the built up sections throughout its length and we need to tie them to makethem parallel and to make them equidistant and to make them act as a monolithically, so thatas a whole the built up section works.So for that we may use lacing which are basically some inclined member between the twovertical members. We can also use batten system instead of lacing system. Batten system isbasically it is a horizontal plate which are connected with the two main members. But in thislecture we will be discussing about the lacing member which are basically the inclinedmembers and these lacing members are used when compressive loads are acts eccentrically.Therefore especially for eccentric loading we generally prefer lacing system.Now for lacing system the lacing members are generally flat plate, it may be angle section, itmay be light channel section, or may be circular section means tubular section, so in differentway we can provide.
Now in case of lacing member again we can consider two type of lacing member as shown inthe figure.So we can provide as a single lacing or we can provide double lacing also. So in differentway we can connect the lacing members. So when we will be designing we have to firstdecide whether we are going for single lacing or double lacing because accordingly the forceon lacing member will come into picture that has to be taken care.
Now when we will be going for designing of a lacing we need to know what the failuremodes of the lattice member are. So what type of failure may happen that we will first seeand accordingly we will try to develop a design methodology so that the failure can bepretend. Built-up members may fail due to buckling of built up member as a whole. So incase of buckling of built up member as a whole, if column is very slender and axial load ismuch high then it may buckle as shown in the figure.Another way it may fail that buckling of main component as shown in the figure. So what wecould see if the loading whatever it is coming for that if the member is not able to carry thatmuch load due to excessive buckling then the main component may fail. if we use channelsection as a main component then the minimum radius of gyration will be about y-y, so thefailure will happen about that section. So as a local failure this can arise buckling of maincomponent.
Then another way of failure is the distortion of the section. Say for example there is a built upsection as shown in the figure where lacing has been provided. Now if distortion happens itwill be something like this, so due to distortion the failure may happen which has to be takencare.Another failure is the failure of lacing member or batten member whatever we are providingthat has to be also taken care. Say for example if we provide two built up sections with thelacing and its width is less compared to its length then it may buckle.Now what we need to do is that we will design the lacing system in such a way that it willarrest the failure of local buckling, it will arrest the failure of lacing system and it will takecare the failure of member as a whole means globally and also distortion.
Now L/rcmin, the slenderness ratio of the highlighted member as shown in the figure should belimited otherwise it may fail. Therefore we should provide some restriction and to restrict theslenderness ratio we have to restrict the length that means spacing between two lacing has tobe decided. So from failure of local buckling we can find out what should be the maximumdistance between two lacing L.
Again if the lacing cross section is not sufficient to take the load, lacing member may fail.Therefore what should be the width of the lacing member, what should be the thickness of thelacing member that has to be decided from which the slenderness ratio is calculated.
Now if we are providing two sections which will be connected by lacing or batten then toprevent the global failure we need to take the section spacing in such a way that theslenderness ratio of the built up section should not exceed the limiting value.
So now coming to the general requirements which has been given in the code. Clause 7.6 ofIS: 800-2007 says that the compression member comprising of two main components lacedand tied should where practicable, have a radius of gyration about the axis perpendicular tothe plane of lacing not less than the radius of gyration about the axis in the plane of lacing. Sothis has to be taken care. Therefore as far as practicable lacing system shall not be variedthroughout the length of the strut that means the lacing spacing and lacing dimension shouldnot be varied along its length.
Now coming to the single lacing system say for example we have a channel section toe to toeand we have face A and face B then we can provide the lacings as in the prefer orientation asshown in the figure. Whereas we cannot provide the lacing as not preferred orientation.
So this is also mentioned in the code, we can see here that the preferred lacing arrangementwhere lacing on face A and lacing on face B has been made. So one is shadow of the othersand this is given in the IS: 800-2007 figure 10A and in figure 10B. In the figure 10A,preferred arrangement for single lacing system is given. Whereas in figure 10B, preferredarrangement for double lacing system is given.
Again in the figure 10C of that code, it is given that double lacing system and single lacingsystem on opposite sides of the main components shall not be combined with cross membersperpendicular to the longitudinal axis of the strut unless all forces resulting from deformationof the strut members are calculated and provided for in the lacing and fastenings.
Video 2
Now in design specification first it is told that the total transverse shear force V will be the2.5 percent of the compressive force P, because in lacing when we are going to design alacing, lacing will be undergoing some compression or tension. Now the transverse shearforce is calculated from the axial compressive force.
Now if we can consider θ as the angle of inclination for a single lacing system of two parallelfaces then the force on each bar will beF= V/nsinθ =V/2sinθ
Where n is the number of transverse system in parallel plane which is generally 2. Now fordouble lacing the force will beF= V/4 sinθThis force will be tensile in one lacing bar and compressive in other bar.
Now as I told the lacing member may buckle locally, so the code has provided certainrestriction which is given in tabular form here that what should be the effective length andwhat should be the slenderness ratio. The slenderness ratio (le/r) of the lacing bar should notexceed by 145 that means as per the codal provision we have to make the dimension of alacing system in such a way that the slenderness ratio should not become more than 145.And to calculate the effective length it has been also discussed in the code that in case ofsingle lacing with bolted end, effective length, le will be the overall length,,l where l is thelength between inner end bolts of lacing bar. And for double lacing bolted at ends andintersections, le will be 0.7l and for welding lacing also it will be 0.7l
Now if we use flat bars as lacings then the slenderness ratio is calculated as follows:
Now in riveted/bolted connection, the minimum width of lacing bars should be more thanthree times the nominal diameter of the end connector. So if the width of lacing bar is b andthe nominal diameter of the end connector is d then b should be greater than or equal to 3d.
Then coming to thickness, thickness either we can find out from that the slenderness ratiovalue or at the beginning we can find out the thickness from the following criteria
t>l/40 for single lacingt>l/60 for double lacingWhere, l is the length between the inner end bolts or weldsSo the minimum thickness of the lacing bar can be found from these criteria for single lacingand as well as for double lacing
Then another important thing we have to decide that is the angle of inclination (θ) of thelacing bar. Lacing bars, whether in double or single systems, shall be inclined at an angle notless than 400 nor more than 700 to the axis of the member. However from the experience ithas been seen that the lacing system will be effective if we consider θ in between 35 and 45.
Now we need to find out certain number of bolts or welding dimensions for attachment oflacing to the main component and that is dependent on the force acting on lacing member orif we use weld connection the length of weld connection, size of weld connection should bedecided.So the codal provision says that the riveting, bolting or welding of the lacing bars to the mainmember should be sufficient to transmit the load in the bar. Then in case of weld connectionit is told that where welded lacing bars overlap the main members, the amount of lapmeasured along either edge of the lacing bar shall be not less than the four times the thicknessof the bar or the members whichever is less.And the welding should be sufficient to transmit the load in the bar and shall in any case weprovided along each side of the bar for the full length of lap, so this is what we have toremember in case of weld connection. And for bolt connection we have to find out thestrength and number of bolts.
So in case of such member means such type of connection where connections are madeseparately then the number of bolts can be decided asFor first case, the numbers of bolt, n=FRBut for second case where both the members are acting on this bolt, we have to find out theresultant force which will be 2Fcosθ and for this particular caseThe numbers of bolt, n=Resultant ForceBolt Value =2 FcosθRWhere, F = Force in lacing barθ = InclinationSo if we find out the force in lacing bar then we can find out the number of bolt required toconnect the lacing bar with the main plate and this depends on what type of connections weare going to consider whether it is separately connecting or two lacings are overlapped andacting as a double shear. So here also you can see that the bolt value of this case and boltvalue of this case will be different, because here the bolt value will be under single shear andhere the bolt value will be under double shear, so accordingly the bolt value has to becalculated.So these are the things we have to remember when we will be going to design a lacingmember so in short if we say that lacing members are designed or the entire built up sections
are designed on the basis of failure criteria, failure of the member as a whole. So we have torestrict the radius of gyration so that failure does not occur and to restrict the failure due tolocal buckling of the main member we have to provide the spacing for lacing in such a waythat the slenderness ratio should not exceed certain value.Also we have to find out a suitable arrangement of bolt or weld connection for attaching thelacing system into the main members if we use bolt connection then again we have to seewhether we are connecting the lacing member separately or we are overlapping accordinglythe forces will be calculated and then the number of bolts will be calculated and in fact if wesee the force on the lacing member is quite less and generally number of bolts become 1 to 2in maximum case and sometimes we will see 2 that is sufficient. So through work outexample we will also confirm this.