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Now I am going to discuss about certain steps which we should follow in case of design oftension member. So in last few lectures we have seen that how to calculate the designstrength of the tension member and we have seen that tension member may fail due to itsgross yielding, it may fail due to rupture of the net section, also it may fail due to block shear.So these three aspects we have to see as well as one another thing we have to that is theslenderness ratio means radius of gyration and allowable slenderness ratio.The member which we are going to consider whether it is exceeding its limiting value or notthat is necessary from serviceability criteria point of view. Therefore these four aspects wehave to keep in mind while designing the things. So if we can develop methodologymethodology means the steps that what are the steps we will follow whether we first calculatethe slenderness ratio and we will try to find out the section or we will calculate the designstrength due to block shear, then we will find out the section that we have to decide, right.So in today’s lecture I will give an overview of the steps to be followed and then I will cometo the some flow chart that how if I write a program then how flow chart can be developedand how algorithm we can develop at our own, so that we can make a program and we canmake it useful we can make it useful in the sense that we have seen that design calculationTds we have to calculate lot of things, lot of complicated expressions are there.So when we are going to design means it is a repetitive process repetitive process means wecan start with certain angle section or certain other section but that may fail or may beoverdesigned. So we may have to reiterate again, right. So doing all the things for everymember it is Tds job. So if we can develop a program at our own in an customized mannerthen it will be useful and easier and helpful for us for designing a tension member in aneconomic way and in a short time, right.
So if we come to the steps we will see that first step is we have to find out the gross areabecause the design because the load acting on the member is given that is Tu the ultimateload means the factor load that is given if the factor load is given then how do I decide themember, right. For a particular member if some factor load is given then how to start that canbe started with the use of gross yielding of the section from that we can find out aapproximate area because in our experience we have seen you can see in the previousexample also we have seen that the least strength comes generally due to yielding.So first we will try with yielding, we will try to find out the gross area then we will choose asection and then we will go for other sent criteria we will see whether it is fulfilling thecriteria of not if it is not fulfilling then we have to go for higher section otherwise we canmake use of it, right.So first we will find out the gross area to carry given factor load Tu considering the strengthin yielding from the following expression that is we know Tu is the means Tdg is the Agfy bygamma m0. So from that equation I can write that Ag is equal to Tu into gamma m0 by fy,right here Tu is the factor load that load coming in the member with certain factor.Then from this Ag the gross area we can find out the suitable shape of section means first wehave to design whether we are going for angle section, or channel section, or some othersection, right. So depending on the shape of section we will go to the IS handbook and thenwe will find out what is the gross area available for a particular section, right.
So first we will find out the shape of the section whether it is I section, or channel section, orangle section then we will find out what should be the section size, right. So that section sizecan be found from this gross area if we know the gross area then we will go to correspondingarea of that angle section or other section and then we will choose a section whose gross areais slightly more than the gross area obtained in step 1, right.So member what we will be choosing its gross area will be more than the gross area obtainedin step 1, because it has to satisfy this criteria, right and I mentioned already that usually ifminimum edge and pitch distance is maintained, strength in yielding gives least value, right.So design will be safe if gross area provided is greater than the gross area required so heregross area required is this and we will provide slightly higher gross area and accordingly wewill choose a particular section depending on the requirement, right.Then what we will do one section is chosen section is chosen means two things we arechoosing one is shape and its size, shape means whether it is angle section or channel section,or some built up section this is one thing and then size what should be the size, size of thesection should be in such a way its area should be more than this area required area, requiredgross area, right.And then we can find out the number of bolts or the welding length required and we canarrange the bolts.
So what we will do next that we can find out a particular bolt means we can choose adiameter of bolt and then we can find out the pitch, edge distance, right and then we can findout what is the shear strength of this bolt Vdsb shear strength of the bolt, then bearingstrength of the bolt Vdpb, right.So from this we can find out the bolt strength and then we can go to find the number of boltrequired, right and this number of bolt we can find out from the total load coming that Tu bythe shear strength, ok. So shear strength oh sorry strength of the bolt so say Vb, so if Vb is thestrength of the bolt and Tu is the factor load then I can find out the number of bolt if we aregoing to use bolt connection.And if we are going to use weld connection then also we have to find out the weld lengthassuming size of the weld, we can assume certain size of the weld depending on the platethickness or angle thickness we can assume certain size of the weld and according to the sizeof the weld we can find out the strength depending on the material properties of the weld weare using. And then we can find out the length required to withstand that much tensile loadthat is Tu, ok.So in second step what we can do sorry in third step what we can do we can find out thenumber of bolts and its positions that means how we are going to make it whether it is chainbolting or zig-zag bolting, so those things we will see and what will be its pitch distance,what will be edge distance, so all these things we will fix or if we go for weld connectionwhat will be the weld length distribution in top and bottom and what will be the size of weld,what will be the length of weld so everything will be decided, right.So in step three we have to do that because if we do not do that we will not be able tocalculate Anc value and Ago value, net area of the connected leg and gross area of theoutstanding length also we cannot find out the shear lag width unless we know shear lagwidth we cannot find out the factor beta then we cannot find out the strength due to rapturethat is Tdn, also later we cannot find out the block shear strength.
So to find those things we have to make detail of the connections, right. So once we do that instep 3 we can go further to step 4 that is in step 4 we can find out the yielding of the grosssection that means Tdg, then rapture at critical section we can calculate this also, thenstrength in block shear, right. So these three we will consider and we have to see the Tu valuethe load acting on the member the tensile load that should be less than these three, this Tdg,Tdn, and Tdb, ok this has to be less.That means so it has to be less if it is not less then what we will do we have to increase thesize of the section, right. So if any of the above strength become less than the factored tensileforce so so if if any of the strength become less than the factored shear force Tu then we haveto increase the size of the section, right if it is more than the Tu then find that means if designstrength is more than the applied load then it is fine otherwise we have to increase the size ofthe section and we have to repeat 3 step 3 we have to repeat, that means step 3 we will doagain and again we will go for step 4, right.So what we could see here that we have to find out the yielding of gross section, rapture ofcritical section and strength in block shear and these three strength should be greater than theTu otherwise we have to increase the section size and we have to repeat the steps so that thisthis criteria is fulfilled.
Next what we can do in step 6, that if we see the if the design strength that means minimumof these three in step 4, is too high compare to factored load then also we can decrease thesection size suitably and repeat from step 3. That means if we see the design strength is quitehigher than the applied load applied load means the Tu the axial tension if the design strengthis quite high design strength means least of Tdg, Tdn and Tdb that is the design strength, ifdesign strength is quite high then the Tu value that applied load then it will be a conservativedesign that means it will be uneconomic whatever section is required we have consider biggersection.So what we can do we have to means we can go with this one or if we make if we want tomake economic design then we have to reduce section size and again we have to follow fromstep 3, right.And once it is over we can check the slenderness ratio of the member and the limiting valueis given in table 3 of IS: 800-2007. Now if the value of slenderness ratio exceeds the value ofgiven in the code, then this is not ok that means what we have to do then we have to increasethe size of the section and redesign redesign means again we have to go to step 3 and we haveto check all the things, right. So these are the steps which we have to follow for designing atension member.
Next I will show uhh the flow chart diagram of the of the developed algorithm and I willshow some screenshot of the developed code and one program I will run and I will show howthe things are means outputs are coming and how we can make it useful, right. So it has beendeveloped in MATLAB program and also it is graphical user interface based program, so as itis GUI based so it will be user friendly means user can easily make useful of this programand they can find out the intended section due to a particular load.
So in flow chart if we see the flow of the program will be like this this is basically based onthe steps whatever I have discussed in earlier slides that is first what we will do is thecalculation of cross section require that is from the gross yielding we can find out what is thegross area require that is Ag once that is find out then what we can do we can decide meanswe can we have to decide whether we are going for bolt connection or weld connection.So from gross area we can find out the smallest angle with cross section area greater than thecross section area calculated or taken before and thickness of length of connected leg largerthan taken before, ok.So as per the requirement with there we are going for bolt connections or for weld connectionthe program will flow accordingly if we go for (weld) bolt connection then we have to seewhether length connected leg is bigger enough to fit the bolt if not then we have to go and wehave to again increase the section size otherwise we can go for calculation of number of bolt,ok.So after that we will go for calculation of design strength of angle due to net section rapture.So (net) rapture of net section we can calculate the design strength in other way also we canstart with welding. So from that we can find out the minimum weld length require and welddistribution also we have to do then we will find out the rapture strength. That means oncethe section is selected either we will go for weld connections or we will go for boltconnections accordingly number of bolts and its distribution can be decided and then rapturestrength can be calculated or if we use weld connection then also we can distribute therequirement of weld length properly and then we can find out rapture strength.So as per the necessity we will follow the path, that means when we will right the programwe will right in such a way that as per the choice of the user it will flow the path.
Next is we will calculate that is angle safe in next section of rapture that means the rapturestrength we calculated in earlier step. Now if rapture strength is less than the applied forceapplied tensile force then we have to go to the earlier step to increase the section size, right. Ifit is not less than we will go for either welding or bolting as we have decided, that means if itis bolt then what we will do that we will find out the gauge distance and other things to findout the block shear so we will calculate the block shear.And then if block shear due to block shear it is going to fail then what we can do we canchange the gauge distance and we can redesign it, right means without changing the size ofthe section otherwise if it is not going to fail then we will go next step. Similarly here also incase of welding we check for block shear then if angle is safe then fine if not then either wewill increase the length of the weld and then we will recheck or we will go for higher sectionwhatever we feel we can do and if it is safe then we will go to next step next step means forbolt case also we will go to next step, for weld also we can go to next step.
So in next step so what we have seen that the strength due to block shear, strength due torapture is more than the the applied load, if it is so then it has come to this step, if it is no thenit has gone to the earlier step to increase the section size, so once it is over the strengthcalculation is over we will go for check for slenderness ratio. So the slenderness ratio limitwe know from the codal provisions and if the slenderness ratio is less than the allowable thenit is fine if it is no then we have to go for increase of the section size, so that the slendernessratio is becoming more, right.And if slenderness ratio is less than allowable then we can say that angle is ok. So in this wayone can flow its program so that he can write the program and find out the intendedcalculations.
Now I will show some snapshot of the developed program as I told that develop program wasdone using MATLAB and in MATLAB you have options so this programs were developed bysome of my students during summer summer intensive course. So in fact you can develop inother way means according to your requirement in the industry or in your case, so you candecide what should be the GUI and what are the options you want, right. Here we have givencertain options like if you see option is that one is single angle section with bolt connectionsand single angle section with weld connections that means according to our option chosen wecan find out the design calculation, so one is the single angle section with bolt connections orsingle angle section with weld connections.Another option is two angle sections placed back to back on the same side of gusset plate,right and two angle sections placed back to back on the opposite side of gusset plate. So theseare four options at that time we have considered you can choose any other type also like hereonly we have considered the angle sections, you can consider channel sections and you canfind out its design strength also, you can consider any other sections also as you wish, just fordemonstration purpose we have used this and then once you choose a particular type then youclick on this give input values. So once if you click then you can go to next one, right.
So here another snapshots I have shown that is if you choose this one that is that is if youchoose two angle sections placed back to back, so it will be like this on the same side ofgusset plate. Again if the angle sections are chosen on the opposite side of gusset plate it willbe like this. So for different options different pictures have been given, so that the user canunderstand properly.
Now when we go next we can see that different inputs are asked by the program, one is thefactor load in kilonewton, ok so you have to provide certain factor load, right. Then length ofthe tension member that is effective length effective length also you have to consider and youhave to put the allowable slenderness ratio that is available in code. So allowable slenderness ratio in particular case what is the allowable slenderness ratio that (())(25:37) also enter bythe user, right. So these three inputs you have to give, one is the factor load and then effectivelength and also the allowable slenderness ratio, right.So next the properties of steel we have to enter, properties of steel means what type of whatgrade of steel we are going to use what grade of steel means you can use that ultimate tensilestress that is fu, what is the value of fu in MPa and yield stress in MPa, right. So these two wehave to enter or what we can do if we check this box if we make a tick to this box thenautomatically it will take the ultimate tensile strength value of Fe410 grade of steel. So oneautomatic value is given otherwise if you want other type of properties you can enter this.Then again partial safety factor partial safety factor can be chosen as per the IS code in table5 whatever given if we choose this then partial safety factor can be obtained automaticallyotherwise we can provide our own partial safety factor gamma m1 and gamma m0 is here, inplace of 1.25 and 1.1 we can provide other partial safety factor also, right. So to make itgeneralize it has been made.Next is the properties of bolt, if bolt connections are there then these these things will come,if it is not bolt connection then this screen will not come, right. So properties of bolt either wecan use 4.6 grade bolt or 8.8 grade bolt these are means if you can choose this radio buttonthen automatically its properties will be taken, otherwise we have to provide the tensilestrength in MPa here that option is also available, right.Then diameter of bolt you have to choose a particular diameter of bolt which you are going touse and then you can provide the pitch distance and edge distance pitch, distance and edgedistance can be taken different way that is either you can provide the pitch distance meansuser can make definition of means make some value of pitch distance and edge distance or itcan allow the program to calculate the values or means that is P is equal to 2.5d and 1.5d,right as per IS code it can take.Then partial safety factor gamma mb of the bolt, partial safety factor also as per table 5 youcan choose or you can customize means in place of gamma mb 1.25 you can provide someother value also, ok that is also possible. Then as we have chosen angle section because thisprogram are developed only for angle section, so in case of angle section we have to definewhether it is equal angle or unequal angle. If equal angle fine otherwise if it is unequal anglethen you have two options that outstanding leg will be larger or outstanding leg will be smaller because which leg is being connected depending on that its shear lag width will becalculated and other things also will be calculated accordingly that is why you have to giveinput to the program here that outstanding leg is larger or smaller and then you can go tonext, ok.
So after putting the value you can go to next so in next you can see that some values havebeen put here like factor load 180 kilonewton we have given, effective length we have given2500 in millimeter, allowable stress we have given. Then we have check the that we haveused the Fe410 grade steel, so it has come accordingly means ultimate tensile stress and yieldstress has come accordingly.And partial safety factor also has been consider as per the IS code and 4.6 grade bolt has beenconsider, so accordingly the ultimate tensile strength has been obtained. Then diameter ofbolt then as per IS code we have consider pitch value. So in this way we have consider theinput values, right like here we have told that connected leg larger, so connected leg is largerwe have considered, right. So once these inputs are given you can go back to means you cango to next ok.
If you put next so all the data whatever we have put is giving here, ok all the data. Also sodata means that what are the load and length, so partial safety factor and stresses, boltproperties, so everything is given and section is means which one is going to be connectedlarger leg or smaller leg, ok. So these are already given.Now another option we have to tell that design for economical section or check for aparticular section that means if you tell that check for a particular section then you have togive a particular section size say 90 by 60 by 6, if you give that then it will means programwill tell you whether this section is safe or not, ok. And if you say design for economicsection then the program will start with the minimum one and it will go on increasing then itwill give you the just the section size which was which is going to pass, that means theminimum section size which is safe that will be given, which is called economic section.So the beauty of this program is you can find out a economic section and you do not have todo manual calculations means n number of iterations you do not have to go program will doautomatically and accordingly you can find out the most suitable section in terms ofeconomy, ok. Or if a particular sections you have to provide you do not have other optionyou have you should you have to know only only that particular section which is availablewhether it is safe or not, that also can be done by giving this option, right.
So according to the requirement either you can choose a section, right then if you click onthis check then it will tell you that whether it is ok or not, means when you are giving aparticular section and if you are putting a check means you can click in check then it will giveyou a dialogue of check that section is safe or section is unsafe, ok if it is unsafe again youcan click another section then you can try that whether it is you check if it is ok fine, if it isnot ok then you can go for again next one.So by this way you can check for particular section and we can find out, right and you seehere in drop box different sections are given as available in the IS code as SP6 as available inthe SP6 we have made in database means all the properties of the say angle sections orchannel sections are fit in database so all the things will come if you select a particularsection is all properties are as per the codal provisions or properties are stored that will beused in the program, right.And if you say that economic section then it will find out the economic section particulareconomic section then again you may act means you may want to find out what is theintermediate calculation, right. So what are the calculations happen that can be found if youuse this the open output file if you open output file then the number of iterations the what arethe things have been done all outputs will be is written in the program, means in the outputfile so all outputs will be displayed there, right in a file in a word file. So in word file you canget the output and you can check manually or means one or two you can check to getconfidence that program is ok, right.
And also help file is there where if you click you will get the theory whatever has been usedhow it has been used all the things it has been made and if you are not satisfied with this, thenyou can go to again redesign means if you go to redesign then the earlier page will show andyou have to change the design parameter, if you change the design parameter, then again ifyou redo then you can find out the new sections and you can make it.
So this is a sample input and output if you see this we have done in the program, these are the(output) means input we have taken if you remember the screen we used this as input, right.So after providing this input one can get the output.
Output means so step by step this intermediate calculations should be shown like requiredarea of the section as per the applied load that has been given, then it has started with this thesection 65 by 45 by 8, so whose sectional area is 817 millimeter square and if you(remember) if you see we want this one and we have just given 817 that means just next tothis value, right. So what computer has that means the algorithm has done that it has searchedthe value which are more than 792 section, ok. So according to that it could find that ISA 65by 45 by 8 is coming immediately above this 792 millimeter square.Then it has calculated the shearing strength and bearing strength of the bolt and then numberof bolt also it could find out, right and then the gross yielding of the section it could find ifyou see 185 where 180 was the Tu value that applied load. Then check for net section in caseof net section it has calculated that has number of bolts are 4, so alpha value has been takenas 0.8, so An value Tdn value has been calculated and it has seen that Tdn is 167 kilonewtonthat means it is less than the value given Tu that is 180. So as it is less than 180, so section isnot safe that means it is going to next section, right.
So it will go to next section next higher section is sorry next higher section is this one the 70by 45 by 8 and its gross sectional area is 858 that means just for next higher section it hascalculated all all the things and then it found that Tdn value is coming 178 kilonewton thatmeans still it is not ok that means we have to go again next higher section, right.
So for next higher section in test case 3 Tdn value is coming 192, which is more than 180 thatmeans this time it is ok. So every time it is iterating all those calculations, repeating all thosecalculations and then finding the value, right. So in this case Tdn value it is getting 192, sowhat it can go it can go for next calculation that is Tdb block shear strength, ok.
So block shear failure calculation should be done, so for block shear again Avg, Atg, Avn, Atnall these things should be calculated and then it is calculating the Tdb2 value is coming just180, right so this is ok just 180.329, ok. That means from here we can see that the justminimum section which is required has been found, right and then slenderness ratio point ofview also it is ok that means this is (ok) this section is safe, right. So it is the optimum sections or economic section and under present load and configuration this is the best suitablesections we can tell, ok.Now we can means we can imagine that if we have to do calculations of all manually itwould take lot of time, right to get the economic sections because we do not know whichsection is going to be safe. So we have to try with different sections, so for so manyrepetitions it takes lot of time so that can be saved if once we can develop a algorithm, if oncewe can provide a program then means while writing a program it will take little time but onceit is written and tested then n number of times we can use it without wasting any time andconfidently we can make it useful, right.
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