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Module 1: Design of Compression Members and Lacing Systems

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Video 1
So far we have discussed about the design strength of compression member that means howto calculate the strength of a compression member that we have understood. If the crosssectional dimension of a member is given and the type of member is given then we can findout the strength of that member. In this lecture I will discuss how to design a compressionmember when the load is given and accordingly how to find out an appropriate section.Now to find out appropriate section first we have to decide what type of sections we aregoing to choose it may be I section, it may be channel section, it may be angle section or itmay be built-up section. So according to the requirement we have to choose a particular typeof section.
Now to design the section we have to follow an iterative process. If we see the designstrength (Pd) calculation, the design compressive force Pd can be calculated as follows
Now we do not know Ae because we do not know the dimension of the section, so effectivearea we do not know. Also we do not know the allowable compressive stress (fcd) of themember because it depends on the slenderness ratio which is depends on the radius ofgyration. Now the radius of gyration will be depending on the dimension of the section. Soboth the parameters are unknown and dependent on each other. Therefore there is no linearprocess to find out simply the dimension of the section.So what we need to do either we have to assume certain compressive stress fcd, then we canfind out the area required and then again we can go for the design. Now we can find out thefcd directly where we generally consider fcd as 0.4fy to 0.6fy. However this is a trial processmeans at the beginning we can start with this fcd and then we will be able to understand at theend whether the member is fine or not, if it is not fine then either we have to increase ordecrease according to the results.Also we can consider the lambda value or the radius of gyration. Now the radius of gyrationif we know then from table 9 we can find out the value of fcd. So either we can choose radiusof gyration or we can choose fcd directly then we have to go.
Now let us see what the steps we should follow are1) Assume a suitable design compression stress ( f cd ) as 0.4fy to 0.6 fy.Now if the slenderness ratio is less then we can consider little higher side, if the slendernessratio is high we can consider lower side but we do not know slenderness ratio but we knowthe effective length, length of the member is known.So if length of member is high then we have to choose a lower value and if effective length isless then we can choose a higher value also.2) Effective sectional area required is, Ae=Pdf cd3) A section is to be selected which gives effective area required and then calculate rmin.4) Determine effective length, knowing the end conditions and by deciding the type ofconnection.5) Determine the slenderness ratio and hence design stress fcd and load carrying capacity Pd.6) Modify the section if calculated Pd differs significantly from the design load.
Now another way to find out the lambda value means in place of fcd one can choose a lambdawhich are given in this table. Approximately we can choose this set of slenderness ratio, likein case of single angle section we can choose slenderness ratio as 100 to 150, in case ofchannel section single channel section 90 to 150, in case of double angle 80 to 120, fordouble channel the slenderness ratio value can be considered much less 40 to 80, similarlysingle I-sections 80 to 150, double I-sections 30 to 60. So from this l/r value we can find outand accordingly the fcd value from table 9 and then we can find out the particular section thenwe can iterate.
Video 2
Example: Design a compression member carrying an axial load of 250kN. The effectivelength of the member is 3 m. Design the member with 2 equal angles in star orientation asshown in the figure below.
Hence strength of the member ¿147.42× 2094×10−3¿308.7k N >250kNHence the member is safe.So though member is safe theoretically what we should do we should decrease the membersize and we should see in which member it is going to be safe marginally, right. So once it isdone now suppose we are making safe this one and we are using this section.Tack welding:Tack welding should be provided along the length to avoid local buckling of each of theelementsλe≤ 0.6 λ=0.6×72.86=43.716 or 40, whichever is less (clause 7.8.1)
So, λ e=S/r v=40Hence, spacing between welds, S=40×rv (Min r of the individual member)¿40×17.5=700 mmWelding is designed to resist a transverse load (P) of 2.5% of axial load¿2.5×250/100=6.25 kNUsing 5 mm weld size (shop weld)
Hence provide a 5mm tack welding of 10 mm length at 700 mm spacing.So we have seen here how to make tack welding and how to find out the weld distribution,weld size and weld length for tack welding. Now in earlier case we have seen that the load iscoming 250 kN whereas we have done with the assume section here we got the load carryingcapacity as 308.7 kN. That means we have to repeat the design to get an economical sectionbecause if we use this section it will not be economic.So it is always better to make a program at our own and use that, if we make a program anddo it then we can find out the economic section, because in programming required amount ofiteration will be done automatically if we make the algorithm properly, so we do not have todo anything means once we develop a program then we can find out an economic section. Sothrough iteration it will search which one will be the best section to carry out that muchexternal load.
Video 3
So here I will just show a demonstration, here you see we have developed a program fordesign of compression member using MATLAB environment and it is graphical userinterface based program. So there is a problem has been demonstrated as followsExample: Design a single angle discontinuous strut to carry a factored load of 50 kN.Assume that the distance between its joints is 2 m. Use f y=250 Mpa.
So this is the GUI of the program in first page it will show you the different option here wehave made three options only one is single angle section, another is double angle section onsame side and double angle section on opposite side, for these three cases we have developedthe program for other cases we have to develop. So those who want to develop they can makethe algorithm in such a way that the different type of orientation of the angle sections can beused.So for this case as it is told that single angle section, so we have to click on single anglesection then it will show this type of section and then if we enter the input values then it willgo to next page.
In next page you can see that factor load it was actually 50 kN and effective length ofcompression member was given 2 meter which is 2000 millimetre, imperfection factor as pertable 7, then maximum effective slenderness ratio can be defined as per table 3, then thegusset plate thickness if we are going to use, double angle section then we have to providegusset plate thickness otherwise we can provide 0 because we are not using any gusset plate.Then we can opt whether it is equal angle section or unequal angle section, if unequal anglesection then again we have option that outstanding leg is larger or the connected leg is largermeans as we will be choosing according to that orientation will be done and calculation willbe made accordingly. Then according to table 5 the material strength means factor formaterial strength γm0 that will be calculated if we click here, if we give the check boxautomatically it will take the value, otherwise we can put our chosen value also.Similarly as Fe410 grade of steel if u use then automatically its ultimate tensile strength andyield strength will be shown otherwise u can provide at our own also. Then we have to go tonext.
So if we go to next then this type of page will come where the data whatever we haveprovided has been shown means now if we see that if some data are mistakenly done meansby mistake if we have given some data then we can go to back and we can provide the properdata, otherwise we can click on check a particular section means if we can click here it willshow different section available in SP: 6, so we can check a particular section for exampleISA 90 by 90 by 10.
Now if it is okay then it will show okay, otherwise it will show it is unsafe and if we click onfind economical section then it will start from the least one and it will go on increasing stageby stage for each case it will check whether it is okay or not, if it is not okay then it will gofor next higher section and then again it will check. So in this way lot of iteration will happenand finally it will find out the economic section, this is how the program runs.
So if we choose a particular section we can make then this is the output. Now if we u see herethat 75×75×6 section has been chosen and these are the inputs which has been given and inoutput it is shown that design compressive strength is coming 59.43 whereas the externalforce was 50 kN. So marginally higher value is coming and thus effective slenderness ratioalso coming 137 and allowable slenderness ratio was 180, so this is how one can find out thevalues.So from demonstration of this program what I wanted to say is writing a MATLAB code isvery easy if you know the design methodology, if you know how to calculate that designstrength of a compression member, then the same can be written in a program and then byproviding some loop we can try with different section and finally we can find out a suitablesection by trial and error method.So once if we develop such type of program then next we can just simply we can do not haveto do anything else, otherwise every time if you do not have program at our hand then wehave to calculate every type means those who are design engineer, those who are working indesign firm for then every time they have to calculate for designing a particular member butonce we develop a customized program then we do not need to give that much effort forevery time.So this is all about the design of compression member with respect to single compressionmember or single angle section or double angle section this is what we will do.