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I am going to discuss about the design procedure of the laterally supported beam. So,beam can be designed on the basis of laterally supported or laterally unsupported. So today,we will discuss only about the laterally supported beam where, its web is supported laterallyso that the lateral torsional buckling may be prevented.
The design criteria of such beam is given in clause 8.2.1 of IS 800-2007, the detail has beendiscussed where the design bending strength can be calculated in two cases, one is for lowshear another is for high shear. When the shear force is less than the 0.6 times that designshear strength then it is called low shear, that means if Vd is the design shear strength of thecross section and V is less than 0.6Vd then it is a case of low shear. So in case of low shear wecan find out the design bending strength simply by from this formula
To avoid irreversible deformation under serviceability loads, following conditions are to besatisfied.
Where,βb = 1.0 for plastic and compact sections;βb = Ze / Zp for semi-compact sections;Zp, Ze = plastic and elastic section moduli of the So once we find the value of Md then we can go ahead for next; however if we see that theshear force is more than the 0.6 times design shear strength of the beam section then we canuse this formula,Md = MdvWhere, Mdv is the design bending strength under high shear and it is calculated as,(a) Plastic or compact section
Vd = design shear strength as governed by web yielding or web buckling = Av f vfv = design shear strengthAv = shear area = Dtw for rolled sections= dtw for welded/built up sectionsV = factored shear force
Md = plastic design moment of the whole section disregarding high shear force effect andconsidering web buckling effects.Mfd = plastic design strength of the area of the cross section excluding the shear area So after designing for bending we will go for design for shear. Clause 8.4, IS 800:2007describes the criteria. In clause 8.4, it says that the factored design shear force should satisfy,
Now shear areas (Av) can be calculated as given in clause 184.108.40.206, IS 800:2007 for differenttypes of section.
Next, in case of web buckling we can see that the web behaves like a column if placed underconcentrated load. If we have I-section say for example, a concentrated load, the web maybuckle depending on the type of member. So if the web is thin then it may buckle orsometimes it may cripple also.
So for calculating web buckling, the effective depth for different cases has been given say forexample, when the web is restrained against lateral deflection and rotation, the effective depthis considered as d1/2, right where d1 is a depth of the web; if it is restrained against lateraldeflection, but not against rotation then the effective depth will be 2/3d1. If the retrainedagainst rotation, but not against lateral deflection then effective depth will be d1 and if notrestrained against rotation and lateral deflection the effective depth will be 2d1. So this isrequired to calculate the compressive stress of the web.
So for calculation of web buckling strength we need to find out how the bearing plate shouldbe provided to prevent the web buckling. Say for example, if a member is subjected toconcentrated load at certain point then also there is a chance of web buckling here and underthe support, because of the reaction at the support. Therefore, at support and the point whereconcentrated load is applied we need to provide bearing plate. If we provide the bearing platethen the load will be dispersed with 45-degree angle. This is the flange and if this is neutralaxis depth, then the width for which we have to calculate is B=b+2n1 where n1 is the lengthfrom dispersion at a 45 degree angle to the level of neutral axis, b is the width of the bearingplate. At support the width for which the buckling load should be calculated is B1=b+n1.So the web buckling strength can be calculated by,
Now here the when we are going to calculate the design compressive stress fcd we need toknow what is the value of slenderness ratio.
Once the slenderness ratio is found and for bucking class C, for a particular grade of steel wecan find out the value of fy, we can find out the fcd value from this parameters.
Now we will discuss about the web crippling for which it may fail. Web crippling occur whena member is under concentrated load, say for example, we have a support condition here wehave a support condition here, so it may fail at the root like this. So web crippling may occurdue to concentrated force at the support due to concentrated force, otherwise in other casealso, it may fail at the point of concentrated load.Web crippling strength can be found as,
WhereFwc = web crippling strengthb1 = bearing length= b+2n1 under concentrated load= b+n1 under reactions at supportMinimum bearing length = 100 mmn1 = dispersion through the flange to the flange-to-web connection at a slope of 1:2.5to the plane of the flange i.e. n1=2.5(tf+R1)tw= thickness of the webfyw = design yield strength of the webSo, if this web crippling strength is more than the load coming into the member at that pointthen it is fin otherwise we have to increase the section or increase the web width so that webcrippling can be avoided.So, we have discussed that a beam is designed for bending moment then depending ontwo cases; low shear and high shear. Once design bending strength is calculated we will gofor calculation of the shear strength. Then we should check the strength against web bucklingand web crippling. Of course we have not discussed about that deflection criteria, which alsoneed to be fulfilled that means we we will find out what is that maximum deflection comingon the member due to the load and support condition avoiding limiting deflection and if thecriteria is satisfying then fine otherwise again we have redo.
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