Now, I am going to discuss about different aspects of failure modes of the flexural members.We know in case of RCC structure the failure modes are basically the failure due to bending,due to shear and due to deflection, which is basically a serviceability criteria. However incase of steel structure as the structural sections are mainly hot rolled sections, it is not like arectangular section or like a compact section. Therefore, some other type of failure may alsooccur. The other types of failure are like local buckling of the cross section, local buckling ofthe web and failure of the flange, because of low thickness compared to its width. Lateraltorsional buckling also come into picture. So such type of failures may arise in case of steelstructure.Therefore, when we are going to design a flexural member, made of steel we have to considernot only the bending shear or deflection, we have to consider other sort of failures and designcriteria has to be satisfied from those points of view so that the local failure may be restricted.
So first kind of failure is excessive bending triggering collapse. When load is too high orspan is too long then maximum Bending moment will be huge at mid span in general.However, it may differ considering the support condition and loading condition as well. So,because of the excessive bending moment the collapse may occur due to bending.
Bending failure is the basic failure mode and in this case, the beam is prevented from lateralbuckling and the component elements are list compact so that they do not buckle locally. Sosuch beams will collapse due to plastic deformation. Another type of failure is lateraltorsional buckling, which is an important failure criteria for steel flexural member. So lateraltorsional buckling comes in picture when the beam is quite long.
Say for example, if an I-section have long length then it may fail due to lateral torsionalbuckling. So here, if load is acting in transverse direction and support conditions are therethen it may buckle laterally and this lateral buckling occurs due to combination of lateraldeflection and twist. The proportion of the beam support conditions and the load applied on itare the certain factors, which affect the failure due to lateral torsional buckling. say forexample, if the load is not concentric twisting will occur because of the torsional momentacross the section and because of that lateral torsional buckling take place.
The next category is failure by local buckling i.e. failure of flange in compression, failure ofweb due to shear and compression. These are the certain modes of failure, which come intothis category. Say for example, if we have a box section, then it may fail in its flange due tocompression. So, box sections may require flange stiffening to prevent premature collapse. Inaddition, it may fail due to web under shear and compression.
If we have a member under concentrated load then at the point of application of concentratedload the force is heavy, because load cannot disperse throughout it section. So therefore thefailure may occur due to compression. This can be overcome by the use of additional bearingplate, which will disperse the load.
Under Category 4, the basic failure modes are shear yield of web, crushing of web andbuckling of thin flange.
So local crushing of web means if we have a section and if it is under concentrated load thenit may fail due to local crushing. Sometimes the flange width is quite high compares to itsthickness. Therefore, it may buckle due to the very thin flange width. However, this type offailure may overcome, if we use additional plate at the flange by welding so that width tothickness ratio increase.
While choosing the most suitable section for beam we have to see certain things, we have toknow what a stress diagram along the cross section is; say for example, if we see rectangularsection then we know initially bending stress will develop. If the load is going to increasethen after certain period the bending stress will reach to its yield stress. Therefore, afterfurther increase of the load, it will start formation of plastic hinge. So the sections willundergoes under plastic deformation, right. So after certain time the section will become fullyplastic.Now we know bending stress developed is calculated by (M/I )×y. So if we increase the Ivalue then the development of stress at the extreme fiber can be reduced. So from theexperiment we see that, if I section are provided then compared to its cross sectional area orrequirement of material, its moment of inertia is quite high. Therefore, with lightweight, wecan achieve high amount of moment of inertia and as a result, we can reduce a major amountof stress. For this reason, I-section is the most suitable section.Now another thing is that in case of I section, it is symmetry in but if we use channel sectionor angle section then unsymmetric bending will come into picture for which, we have toagain consider the stress developed by unsymmetrical bending,. So, in case of high load orlarge length if we use I section then, because of the high moment of inertia we can reduce thedeflection as well as stress due to bending. Therefore, we generally choose I section mostpreferably.
Now coming to conventional use of various sections, we generally use channel or anglesection, in case of PURLIN. Generally, PURLINS are subjected to light load. So, for suchtype of member we use either angle section or channel section. I sections are preferred in caseof LINTEL. Double angles, T sections or sometimes also ISJB sections are also used. Forlarge spans and light loads, where the deflection may come huge, we have to increase the Ivalue, so CASTELLATED BEAM is preferred in this type of situation.
There are few criteria’s we should follow to select a beam section. The first is the usualmethod of selecting a beam section, by using a section modulus (Z) which is equal to I /Y,because maximum bending stress is equal to (M/Z). The criterion of economy is weight ratherthan section modulus, because sometimes, if the section modulus is high, weight may be lessor may be high also. So but if we consider to make section economical then lighter weightsection should be chosen however that may not be achieved always. Therefore, we have tosee the section modulus and sometimes deflection and occasionally shear may be thenecessary criteria for selection of section. This is very rare, when we have to consider thedeflection criteria where deflection is quite high and we have to arrest the deflection and forsuch type cases we may have to go for castellated beams and sometimes shear may be theguiding criteria, so for that also we have to consider corresponding section.And, if we have a similar section modulus of different kind of section then among thoselighter section should be chosen.
Primarily design criteria is based on these three aspects, these are based on deflection, basedon stress due to bending and due to shear. However, other criteria has also to be fulfilled likethe torsional buckling, local buckling, web buckling, flange buckling. Then web cripplingalso will come into picture, which has to be overcome by providing certain measurement.Now the maximum deflection depends on the span length, moment of inertia of the section,load distribution and modulus of elasticity and support condition. So these are the five factorson which, the maximum deflection depends. So depending on that we will try to find outwhat is the maximum deflection coming into the member and what is the limiting deflection,depending on those we have to decide the section size.
In general the maximum deflection in beam is given byδ=K W L3EIWhere,W Total load on the spanL Effective span lengthE Modulus of elasticityI Moment of inertia of the sectionK a coefficient depends upon the distribution of loading & end support of the beamThe value of the coefficient K for different loading conditions and support conditions arelisted below.
Limiting deflection is given in table 6 of IS 800-2007 and maximum deflection for differentsupport and loading condition should not exceed the limiting deflection. Effective length forlateral torsional buckling can be found from table 15. Effective length for lateral torsionalbuckling will be required for calculation of design bending moment.
So few of them are shown here, which are given in table 15 and in clause 8.3.1 of IS
So in today’s lecture, the last thing we like to discuss is about the design procedure. So designprocedure can be divided into 3 parts, one is structural; another is secondary effect andpractical limitations. So, basically the design of the member will be done due to bendingmoment, due to shear force, due to deflection and due to stability. So first we will see, what isthe maximum bending moment coming into the member and for that what will be the size ofthe section whether, it is capable of carrying, this much bending moment or not. Then we willcheck whether the developed shear force can be carried by the section. If the design shearforce is more than the external shear force then it is fine otherwise we have to increase thesection size to withstand the shear force coming from the load.Then the maximum deflection can be calculated for the given load and the support and wewill check whether the maximum deflection is exceeding the limiting deflection or not. If it isexceeding the limiting deflection then we have to increase the section size and we have toredo all the things, otherwise we can go ahead. Another thing is stability; lateral torsionalbuckling may come into picture. So from that point of view also we have to consider whetherthe structure is safe or not. So these are the structural aspects which has to be taken care fordesign.Another is the local buckling. So local buckling means buckling of the web, crippling of theweb or the buckling of the flange, because of thin flange, flange may also buckle. So theseare the some secondary effects, which has to be also taken care and we have to check whetherit is safe against local buckling, against secondary forces or not and also we have to check theconnections whether it is okay or not and then we will go to the practical limitations.Practical limitations means we have to consider the durability, fabrication tolerances anderection strategy. Erection strategy means we have to see that the given section which iscoming, is possible to be erected properly or not that we have to see and we have to make aerection strategy so that the given sections can be erected properly in the site.So in short, the main thing that we have discussed is the failure criteria of the member andwhat are the type of failure may come into picture and because of that failure how to takeproper measurement, how to go through design that will be discussed in next class.
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