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Design of Laterally Supported Beams

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Video 1
Now, I am going to discuss the design procedure of a laterally supported beam. So in lastlecture we have discussed how to calculate the design bending strength of a laterallysupported beam, design shear of a laterally supported beam. So in today’s lecture first, I willgo through very quickly the design steps for laterally supported beam and then I will gothrough one workout example
So in first step, we can find out the load acting on the beam and then we can calculate theappropriate load by multiplying the partial load factor. In the second step, we can find out thebending moment distribution and shear force along the beam length and from that we canfind out maximum bending moment at shear force, because I have to design the beam againstthe maximum bending moment and maximum shear force.In the third step, on that basis of max. BM we can find out a trial plastic section Zp
where Md is the maximum bending moment, which we have calculated, Fy is the yield stressof the material and γm0 is a material safety factor. So from this in the fourth step, we can findout the trial plastic section and from the plastic section modulus we can find out acorresponding section whether we are going for ISMB or ISLB depending on that we canfind out the section whose plastic section modulus is greater than the calculated plasticsection modulus.
Then in the 5th step, we can classify the section as plastic or compact or semi-compact fromtable 2, IS 800: 2007. Once it is done then I can find out the design shear strength Vd which iscalculated by
So design shear strength Vd can be calculated from this and then we should check whether itis high shear or low shear. If the maximum shear force is less than 0.6Vd then the beam is inlow shear and if it is more than 0.6Vd then beam is in high shear.So considering high shear or low shear, the formula will be different for calculating designbending strength. So if it is in low shear then I can find out Md as,For low shear:value as this that is beta b into Zp Fy by gamma m0, right. So now for a particular section weknow Zp value and depending on the type of section whether it is plastic, compact or semicompact, I can find out the βb value and γm0 value we know.
Now if we see that M is greater than Md then we have to increase the section size and repeatfrom step 5, right. That means if the design bending strength is less than the actual momentthen I have to increase the section size and then I have to repeat from step 5 otherwise if it issatisfying then we can go to step 9.So from step 5 to 8 will be repeated till the design bending strength is more then the bendingmoment developed bending. Once it is satisfied then we have to calculate the design shearstrength Vd and it should be greater than the maximum factored shear force developed due to
external load. So maximum factor shear V has been already calculated. If this is fine then wecan go to next step otherwise if V is greater than then Vd then we have to redesign the sectionNext step is that we have to check for deflection, which is also another important aspect. Thebeam has to be checked for deflection as per table 6, IS 800:2007. In table 6, the limitingdeflection criteria has been given and the maximum deflection can be calculated from thegiven boundary conditions and the loading conditions. So from that we can find out themaximum deflection and maximum deflection has to be less than the limiting deflectiongiven in table 6, if it is okay then fine otherwise we have to again increase the section.
Now we have to check for web buckling. Ifdtw≤ 67ϵ for web without stiffeners, then theweb is assumed to be safe in web buckling and we do not need to check. So the shear strengthof the web is governed by plastic share resistance. But the web should be checked forbuckling, in case of high shear even if this limit is satisfied and the web buckling strength canbe calculated by, fwb= Ab × fcd . Here, Ab = area of the web at the neutral axis of the beam =Btw and fcd = design compressive stress which can be found from table 9C, as it is bucklingclass C. The web buckling strength should be greater than the design shear force.So if web buckling strength is greater than the design shear strength then fine otherwise wehave to increase the bearing plate length, either we have to increase the bearing plate lengthor we have to increase the section size to increase the web buckling strength. So once it isokay then we will go for checking web crippling. Web crippling strength can be calculated
So web crippling strength Fwc can be found from this formula and it has to be more than theshear force coming on that section. So if it is satisfying this criteria then fine otherwise againwe have to increase the section size or we have to increase the bearing length to make thesection safe from the web crippling. So these are the steps which we need to follow to designa beam with laterally supported.
Video 2
Example:A cantilever beam of length 4.5 m supports a dead load (including self weight) of 18 kN/mand a live load of 12 kN/m. Assume a bearing length of 100 mm. Design the beam.Solution:Step 1: Calculation of loadDead load = 18 kN/mLive load = 12 kN/mTotal load = (18 + 12) = 30 kN/mTotal factored load =1.5 (18 + 12) = 45 kN/m
Step 2: Calculation of BM and SFBM = w l22=45× 4.522= 456 kN-mSF = w×l = 45×4.5 = 202.5 kNStep 3: Choosing a trial section
Video 3
So from this what we can see that we have to design the beam stage by stage. So the steps arediscussed earlier, so according to these steps, we have gone through and we have checkedevery step that we found that the assumed section is safe against moment, against shear,against deflection, against buckling and against crippling. So all the checks are satisfied, sothe sections which are assumed is okay.