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Introduction to Flexural Members

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Video 1
I am going to start a new chapter on flexural member i.e. beam. At the beginning, I will be giving a lecture on introduction to flexural member and beam is basically a structural member which is subjected to transverse loading, that means the load is perpendicular to its axis. And because of this transverse loading the members produces bending moment as well as shear force. So we have to design a beam against bending moment and shear force.Now in an anatomy of a structure we have seen that apart from compression member or tension members beams also exist and beam is an important member in a structural system which carries load which are basically transverse load and the loads from the super structure which are coming to the column, mainly from the floor and floor to beam and then beam to column. Therefore, we need to know how to design the beam against such type of forces like bending moment and shear force. In case of steel structure we will see the beam is not only failed due to bending or due to shear but also failed due to lateral buckling, due to local buckling, due to torsional moment, so many things will come into picture. Why we have not studied this since in case of RC structure because in case of RC structure generally we provide rectangular section, where such type of problems will not come. But in case of steel structure we provide certain rolled section where the thickness of the member is quite less means say for example I section the thickness of the flange the thickness web is quite less.
So there will be chances of local buckling of the flange, web which we need to take care, so all these aspects will be discussed in this chapter. Beams are basically two types, primary beam and secondary beam. So secondary beam are rested on the primary beam and in case of bridge structure, we often use a term girder and this bridge structures are designed considering beam as a plate girder, where the girder dimensions are decided on the basis ofthe bending moment and other forces.
• JOIST: A closely spaced beams supporting floors or roofs of building but notsupporting the other beams.• GIRDER: A large beam, used for supporting a number of joists.• PURLIN: Purlins are used to carry roof loads in trusses.• STRINGER: In building, beams supporting stair steps; in bridges a longitudinalbeam supporting deck floor & supported by floor beam.• FLOOR BEAM: A major beam supporting other beams in a building; also thetransverse beam in bridge floors.
• SPANDREL BEAM: In a building, a beam on the outside perimeter of a floor,supporting the exterior walls and outside edge of the floor• GIRT: A horizontal beam spanning the wall columns of industrial buildings used tosupport wall coverings is called a GIRT.• RAFTER: A roof beam usually supported by purlins.• LINTELS: This type of beams are used to support the loads from the masonry overthe openings .
Basically the nature of the force is transverse load and sections lie in the plane of symmetry that means say suppose a I section is there, now when loads are coming across its cross section it is considered that it is a symmetric loading. That means that there is no twisting and it follows that such a beam will be primarily subjected to bending accompanied by shear in the loading plane with no external torsion and axial force. Though in case of beam the axial force may come into picture sometimes and sometimes torsion also will also be there because of unsymmetrical loading.
Now the torsion cannot completely be avoided. If the beam section is symmetrical and load also act in a plane of symmetry then also torsion may occur due to the instability of compressive stress. The reason I am reading once again the reason is the instability caused by the compressive stresses. So such instability is defined as Lateral Buckling right and when it is involved only local components of a beam it is called Local Buckling. So while going for design of a beam member we need to design for lateral buckling and local buckling and this local buckling is a function of width to thickness ratio.
Primary modes of failure of beams are as follows:1. Bending failure2. Shear failure3. Deflection failure1. Bending failure: Bending failure generally occurs due to crushing of compressionflange or fracture of tension flange of the beam.2. Shear failure: This occurs due to buckling of web of the beam near location of highshear forces. The beam can fail locally due to crushing or buckling of the web near thereaction of concentrated loads.3. Deflection failure: A beam designed to have adequate strength may becomeunsuitable if it is not able to support its load without excessive deflections.
Video 2
So, in case of beam we may use different type of sections one is say solid section. We can use different type of rolled section like channel section, we can provide, again thin walled open section, I section can be provided, and sometime fabricated I sections are also provided. This is used frequently to fulfil the requirements and sometimes we provide the thin walled close section also. In addition, box section can be used sometimes, angle sections can be used, light weight transverse load angle sections may be provided, however for this case asymmetric load will come into picture which need to be taken care. Moreover, sometimes compounds sections also we provide.Compound sections means combination of two sections. Say for example this is a steel rolled I section and along with that say if the compression is quite high compared to tension then we may provide sometimes channel section at the top. So, this is called compound section which is made of two different section.Then also we use composite beam, composite beams mean made of steel and concrete say for example this is one case, this is I section and over the I section we provide the RCC slab or beam and connect with the shear connector. This has certain advantages in the sense we know the concrete are good in compression and steel are in tension.So when the beam members are subjected to gravity load/transverse load, then the compression occurs at the top and tension occurs at the bottom. So if we use such type of composite section, then compression will be taken care by the concrete section and tensionwill be taken care by the steel. So we can make advantageous use of the concrete properties and steel properties. Also sometimes we use encased beam, encased beams means we provide certain I section, then at periphery of the I section, we cast with concrete so this is alsosometimes used.
Another section we can use that is suppose a cantilever beam is there having certain UDL load bending moment will be maximum at the support and minimum at the free end. So we provide a section of same depth throughout the length then it will be uneconomical. We have to provide a particular section considering the maximum bending moment and throughout the section we use which will be uneconomical. So to make economical we can provide varying cross section.
So another section is called castellated beam. We take a I section and we cut through its web, web in this way. So this is a cut right, if we displace the upper section in this way then we can make a sections like this. So, the advantage of this kind of section is that if we slide these two, then the depth of the cross sectional will increase. If the depth of the cross section is increased then the moment of inertia will increase. If moment of inertia increase then we know stress will be decreased. So this type of beam is called Castellated Beam right.
Another way of making castellated beam is to insert a plate here right, with a certain thickness and depth right. So if we insert this then we can see the depth is becoming much higher than the original one, so through this I can achieve the moment of inertia to a large extent right and here we need to weld to make it monolithic. So this is one another example of castellated beam.
Another way of making castellated beam is to insert a plate here right, with a certain thickness and depth right. So if we insert this then we can see the depth is becoming much higher than the original one, so through this I can achieve the moment of inertia to a large extent right and here we need to weld to make it monolithic. So this is one another example of castellated beam.
Now another thing we have to see that different types of sections have certain limitations, like angles and T sections are weak in bending. So unless transverse load is less, generally we do not go for angle section or channel section or T sections. Then channels only be used under light loads that means when the length of the member is quite high but load is less, then in such case we can use channel section. The rolled steel channels and angle section are used in those cases where they can be designed and executed satisfactorily, so that has to be also keep in mind. Now, this is because the loads is not likely to be in the plane, which removes torsional eccentricity. So while using such type of section we have to keep in mind that torsional eccentricity may come into picture. Also, it is complicated to calculate the lateral buckling characteristics of these type ofsections. So, we have seen here certain demerits of using channel sections angle sections or T sections,later we can see that in case of flexural member I sections will be the best one , because I sections are symmetric and it can take both compression and tension equally. So , we will like to conclude here, we will see why I sections is better, and then will see what are the failures may come into picture and then how to develop a designmethodology. Thank you.