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Hello I am going to start a new chapter on new module, that is tension member. So far,we have discussed about different type of connections, starting from bolted connections,welded connections and also eccentric connections. Now we will go one by one the memberdesign. Member means either it is a compression member or tension member or flexuralmember.Now unlike RCC structure here tension member plays an important role. In case of RCCstructure because of the dead load or self-weight, generally structure undergoes compressionsand may be rarely tension comes into but in case of some structures where tension occursfrequently, we have to use the steel member so that the steel can take tension.So in case of industrial building or bridges particularly trust members are subjected to tensionbecause of different type of loads including vehicle load for bridges and wind load,earthquake load for industrial structure etc. Therefore, we found that many membersundergoes axial tension.So we means we have when we will be learning the design means design of steel structureswe have to learn how to design a tension member. In case of RCC member many of us havenot learnt that design of tension member in RCC but in case of steel we need to know as weknow that wind when industrial structure is built when wind comes into picture or earthquakecomes into picture some columns goes compression and other columns under tension.Again, because of reverse direction again the columns which were in compression, willundergo tension and which were in tension earlier may undergo compression. So we have todesign the members for both tension and compression in case of industrial building orstructures. So those things we will see one by one and you know tension members can haveany type of cross sections it may be angle section, it may be circular section, it may be Isections any type of sections can be used.However generally we use circular section as a tension member or sometimes we use anglesections also because of its advantages geometrical properties.
So if we see that truss member, cables in suspension bridges, bracings for buildings, these areoften subjected to axial tensile forces which is be designed properly and as I told that anycross sectional configuration may be used where circular rods and rolled angle sections arecommonly used.
These are some application of tension member where in case of cable stayed bridge we needto design tension the stay cables and similarly in case of truss members few members are intension. In case of bracings we need to design the bracings which experience tensile force, sothe purlin, hanger supporting floor deck, etc we have to design for tension.
Now coming to tension member, we see that different type of section can be used, one iscircular sections, and we can use rectangular or square section. We can use angle sectionback-to-back angle section we can also use one angle and this is another angle which isconnecting with a gusset plate.Also we can see, this two angle sections are connected with a gusset plate with boltconnection or four angle sections are also connected, this is the way we can make some anglesections.
Then other type of configurations are like this, two channel sections back to back thatgenerally we use for column section means for compression member but sometimes we mayneed it for design of tension member also. Again, channel section face to face may beconnected and angle section making a box this may also can be connected. Angle sectionswith the use of gusset plate and other additional plates can be used for making a built ofsection which will be useful for tension member design.
Now we will discuss about various factors affecting the tensile strength. Therefore, if wehave a plate and if we make a connection with a hole then the net area of the section is goingto be reduced. For this reason we will be calculating the net area or the for calculation of thetensile strength we have to reduce the bolt hole area because this bolt hole cannot take tensionthat is why the strength will be decreased in the presence of hole.Then another factor is geometry factor. The ratio of gauge length (g) to diameter (d)represents geometry factor. A lower ratio of gauge length to its diameter gauge results incontentment of contraction at the net section and hence it is more efficient.Then another is ductility factor if the members become more ductile then it increases itsstrength because of even distribution of stress. Then residual strength, where fatigue isinvolved, we have to count the residual stresses also, how much it is present so accordingly ithas to be taken care.If spacing of fasteners are closer than relative to the diameter then block shear will lead intofailure so that has to be also taken care.
Next is the shear lag effect this is very important in case of tension member design.Sometimes the whole member are not connected to the gusset plate or to the system. So whenthe members are subjected to tension so all the portions of the element or the member are notdirectly under tension. Therefore, tension force are not distributed throughout its cross sectionproperly, so there is scope of shear lag effect. Because of shear lag effect the strength of themember gets reduced. Say suppose an angle is connected to a gusset plate. Now when thetension force is applied so this portion will be under tension directly as it is directlyconnected but in this portion, it will not occur there will be some lagging. So because of thatlagging shear lag effect will come into picture and because of shear lag effect the strength ofthe member will be reduced.
Now coming to net area calculation because in case of tensile member the net area playsimportant role because when we will find out the rupture of the section means the membermay undergo rupture along its critical section.So for that we have to find out the net area, net area means basically the total area minus thehole area because of the presence of bolt, holes are made so that hole cannot take tension. Sowhen we are going to calculate the net area we have to reduce that area. So we have tocalculate the different options and then we have to find out that which one is the most criticalsection and according to that critical section we have to find out the what is the strength dueto rupture. So, this is how we will make it.
So basically net area means gross area minus hole area, so this is the formula which we canuse are in chain bolting,
Say we know the when two plates are in connections and under tension say P, boltconnections are made with a chain bolting. So there will be chance of failure along thisdirection say, 1-1. So in this direction, along this path the net section area will be less, if Iconsider here, if the width of the plate is b and thickness is t then gross area will be b × t,right but the net area along these sections will be less. And that will be gross area minus holearea means if diameter of the hole is dh and if t is the thickness then net area is b- dh × t × n.Therefore, this is how One can calculate the net area for chain bolting.
However, in case of staggered bolt we have different formula.
Where,b , t = width and thickness of the plate respectively.dh= diameter of the bolt hole (2 mm in addition to the diameter of the hole, in case thedirectly punched holes).g = gauge length between the bolt holes.ps= staggered-pitch length between line of bolt holes.n = number of bolt holes in the critical section.i = subscript for summation of all the inclined legs.In case of staggered or zig-zag bolt, the bolts are not in a particular line it is distributed in azig-zag manner so we need to know how to calculate the net area and we have to see how it isgoing to fail. t So here we can see that suppose the bolt connections is like this then it mayfail in this way say I can give a name that 1-2-3-4.So failure may occur along 1-2-3-4, againfailure may occur in this direction also if this is 5, this is 6 means 1-2-5-6. So it may fail inthe direction 1-2-5-6 also it may fail along 1-2-5-3-4. So three alternatives are there throughwhich the failure may occur. So what we need to know we need to find out what is the netarea along this three alternatives route and the least one will be the most critical one, so thefailure will happen first on that line so that is what we have to calculate.
Now if the gauge distance and staggered pitch distance are different then there is amodification in the formula,
So for example, this case where two plates are connected with a lag joint. P is the tensileforce acting and there is a bolt here, this is another bolt, this is another bolt, that means it mayfail along this 1-2-3, this is one case. There are other three failure cases, these are 1-2-4-5-6 /1-2-5-6/1-2-4-7.
So now, I will show the same thing in this picture to give the summary of the things whateverI have discussed. We can say that the net area Anet , we can calculate as (b - ndh )×t where, t isthe thickness of the plate, dh is the gross diameter of the plate, b is the width of the plate, andn is the number of bolts in one line. Therefore, this is what number of bolts in one line meansin this line how many bolts are there. Therefore, in this case it will be 3.So, for chain bolting I can easily find out the net area, but the problem start when we have tocalculate the net area for zig-zag bolting.
So in case of zig-zag bolting we have discussed two things one is when staggered pitchdistance () are same and gauge distance (g) are equal. In addition, I told that failure mayoccur along 1-2-3-4 or 1-2-5-6 or 1-2-5-3-4. Therefore, if I consider failure along 1-2-5-3-4then n will be 3, because number of bolt holes in critical section is 3 so n will be 3. So in thisway we can calculate.
So, the parameter name I have told that the variables like n is equal to number of bolt holes inthe critical section means which sections I am passing according to that I can find out numberof bolt holes. And ps is the staggered pitch length between line of bolt holes as shown in thefigure and g is the gauge length between the bolt holes and as shown in the figure earlier. Anddh is the diameter of bolt hole and b and t is the width and thickness of the plate respectivelytherefore the net area can be calculated.
Now if the staggered pitch is different for different cases say for example this case. So in thiscase this we see here s1 and s2 are different that means these bolts are not in the same linemeans, in 1-2-3 it is not situated.So in this case we have to calculate net area considering individual staggered distance. So if Iconsider the net area along 1-2- 4-5-6, so there is two inclined line so I have to make thisps2^2/4g2 and ps1^2/4g1 and net area I can find out in this way. Failure may occur in differentway and so for calculation of net area I have to find out the critical path or the net area for 1-2-3, 1-2-4-5-6, 1-2-5-6 and 1-2-4-7. So, I will calculate the net area for these four cases andthe minimum one will be the critical one through which the failure will occur, right. So byseeing we cannot tell that in which line it is going to fail, so I have to calculate and then Ihave to find out which one will be the most critical one.So with this I would like to conclude todays lecture as time is not permitting. So next day Iwill go through one example and we will show how the net area is going to be calculatedthank you.
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