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Module 1: Design of Compression Members and Lacing Systems

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Video 1
In this lecture we are going to discuss about the design procedure of built up members. Builtup members comprises of two or more rolled steel section. When a compressive load is soheavy that a single rolled section cannot withstand that much load because there is alimitation of maximum size of the rolled section. Therefore when load becomes very high wemay have to go for built up section.This is not only because of the high load but also sometimes we need equal radius of gyrationin both the direction because in rolled steel section we generally see that radius of gyration inone direction is much higher than the other direction. Therefore the buckling will happenabout the weaker section first and as a result the load carrying capacity of the steel rolledsection member will be less about a particular direction, to arrest that generally we provide abuilt up section where higher radius of gyration can be achieved in both the direction andthereby we can increase the load carrying capacity by providing such type of built upmembers.
Now coming to reason as I told that one is that the built up section provide large crosssectional area which cannot be furnished by single rolled steel section. Then built up sectionprovide special shape and depth. The special shape and depth facilitated connections betweendifferent members. And another important thing is that the built up section provide sufficientlarge radius of gyration in two directions. Therefore we generally prefer built up members incase of long length of column and with higher load.
Say for example if we consider a channel section as a compression member as shown in thefigure, as we can see the Izz is much higher than Iyy, right or rzz is much higher than ryy.Therefore the chances of buckling about y-y axis will be much earlier than about z-z axis. Soif we provide built up member then we can increase the radius of gyration by providinganother member and with a certain spacing.So if we do that then we can see that the new Iyy of the section will become much higher andthe built up member generally we provide in such a way that Izz become Iyy means we willvary this spacing between two members to such an extent that when Izz become Iyy upto thatwe will vary, or rzz become ryy. So in this way we provide the configuration of the built upmember.
Now examples of built-up member if we see, here we can see that we can use 4 angle sectionto make a box type of cross section by the use of certain tie plate which is called generallylacing or battening. So this is one example where we can use built up section to increase theIxx and Iyy of the section.
Another type of built-up members generally we used is that when two channel sections areplaced back to back, where built-up members are connected with the lacing or batteningmember.
Next is channel section when facing face to face this way also we can provide a built-upmember.
Then I section with channel section at the top as per the requirement, sometimes we see therequirement and according to that requirement we may have to provide that I section with achannel section at the top.
Sometimes two I sections are provided to withstand the load as shown in the figure.
Sometimes in place of plate girder we generally see that I sections are provided withadditional plates. So number of plates are added as per the requirement and in this way weincrease the load carrying capacity of the member. Generally we provide I section with plateswhen the bending moment of the member is becomes high. That means when a member isunder flexural action then because of bending stress may be the single I section is not capableof taking that much load.
So in that case we may have to provide the additional plates as per requirement. So this isanother example of built-up member.
This is an another type of built-up member which is consisting of 4 angles which is calledstar angle.
Now coming to design of built-up compression member, the following steps we have tofollow. In the first step for the design of built-up compression member we find out theeffective length. Therefore in step 1 we find out the effective length from the actual lengthand end condition.
Then in 2nd step we generally assume certain value of slenderness ratio λ as 30 to 60 for builtup section. We generally consider less value of λ because of the built up section the radius ofgyration is quite high and therefore the slenderness ratio we can consider quite less means itmay be from 30 to 60 which will be sufficient.Then in step 3 we find the compressive stress fcd from table 9c because the buckling class forbuilt-up member is c, therefore we can use table c and corresponding to table c for aparticular value of λ whatever we consider we can find out the fcd value for a given grade ofsteel. So once we get the fcd value, in step-4 we can find out the required cross-sectional area(A) which is P by fcd, where P is the axial compressive force which is acting on the member.
So once we get the area of the compressive member then in step-5 we can choose a built-upsection as per the requirement it may be channel section back to back, it may be channelsection face to face, it may be I section. As per the requirement we have to decide what typeof sections we are going to provide and what will be the arrangement. So accordingly we willfind out the area from that considered section and then we will arrange the section in such away may be if we use two channel section back to back, then we will arrange the section insuch a way that the Ixx or Izz become Iyy, so that we can find out the value of S, where S is thespacing between two section.So here our job is to find out the value of S in such a way that Izz will become Iyy. Once this Sis found we can find out the rmin value which will be practically more or less equal rzz and ryy.
So in step-6, from the minimum value of the radius of gyration we can calculate the λ, theslenderness ratio which is le/r.So from the slenderness ratio again we can go back to table 9c and in step-7 we can find outthe value of fcd corresponding to particular λ and grade of steel, right. So once we get fcd valuewe can find out the design compressive strength Pd which is Ae×fcd. So design compressivestrength we can find out and if we see the design compressive strength is more than the axialcompressive strength acting externally then it is okay, otherwise we can go for a highersection and we can repeat from step 5 to step 7.That means if we see the design strength is less than the actual load then we have to go fornext higher section and we have to repeat the steps so that we get Pd as greater than P andthen we can stop. So this is how we can find out the section size of the member and then wecan find out the arrangement of the section that what will be the spacing between twomembers. Then we have to design the lacing system or batten system as we provide becauselacing system or batten system along the length we provide to tie the compression membersin a proper way so that the built-up members become parallel to each other, also it has to beequidistance throughout its length.
Video 2
Now we will go through one example through which we will be able to understand how todesign a built up section.
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. Use 2 channel sectionplaced as back to back as shown in the figure below.
So what we need to do here is we have to find out what the section size of the channel is andwhat will be the distance between these 2 channel section that is S and the design of lacingwe will do later.
Now next question is that what will be the spacing of these two channel. As we have seen thatthe spacing will be decided on the basis of the equal strength from each direction.
So the spacing between these two members will become 184 and ISMC 300 section will beused. So in this lecture what we could see is that the design steps design procedure of built upsection and a work out example has been done to demonstrate the procedure for designing abuilt up section. In this example we have restricted upto the calculation of the section sizethat means what will be the section size and its spacing between two section.