 Welcome to the session, Ductility Provisions for Beams, Myself Chetanji Konapure, Assistant Professor, Department of Civil Engineering, Vulture Institute of Technology, Solapur. This is the learning outcome for this session, so student will be able to describe the ductility provisions for the beams, flexural members. Now, what are the ductility provisions and why it is important and what it covers? So, this ductility provision covers and applicable to monolithic construction and second the building or the structures which belongs to seismic zone 4 and 5. The member which is covered or the structural element which is covered in this session, that is the flexural member, this is the term from IS code, so beam which is a flexural member that will be detailed covered in this session. Now, let us see the flexural member, so this flexural member beam which is having breadth and width, so you can see here breadth and the width depth, so this is the cross section of the beam, most important thing in the design of the beam we are providing the sizes and the sizing of reinforcement also. So, geometrical dimensions, the first provision is regarding that whatever B by D, the breadth width by depth of the beam that is selected it must be always greater than 0.3, what why it is important because if we go for smaller width as compared to the depth provided that member or that beam will become very slender and slender beam leads to lateral buckling during earthquake excitation, this will be the problem that is why B by D must be greater than 0.3, so that proper provisioning is important. Next thing is what shall be B now, breadth of the section, breadth of the beam that must be greater than 200, minimum breadth of the beams must be selected 200, why it is important because the detailing whatever we are doing reinforcement detailing in the cross section of the beam it requires at least 200 mm width, so it is very difficult in detailing for smaller dimensions that is why 200 mm width is required. Now, let us go to now the reinforcement section, first is the longitudinal reinforcement, most important thing which is specified in IS 3920 that is regarding steel grade should not be greater than Fe415 that is because of as the strength of steel is increased provided that will be much brittle. So, carbon content of the steel will increase and it will be not that much ductility we will get, but right now in the market Fe500, Fe550 these types of steels are available, but the one more requirement is specified by the IS that it shall have elongation more than 14.5 percent, though you are using Fe500 and Fe550 elongation must be 14.5 percent more, we want ductility, we do not bother about strength of the steel. Next thing is that most important clause for this longitudinal reinforcement at least two bars on each face throughout the length of the member because this contributes to safety during reversible of stresses. Stress reversible that is the major problem in earth again it is happening. So, compression to tension, tension to compression these stress reversible possible at any phase of the beam. Now, next thing is regarding the minimum reinforcement, this is also regarding the longitudinal reinforcement or percentage of the steel, here the greatest of the concretes are specified as per IS 456 2000, minimum steel is 0.85 divided by FY and as per IS 3920 minimum steel is 0.24 fck or under root fck divided by FY and whatever formulations are given in these two course according to that for by IS 456 for m20 for 30 and 40 these are the percentage 0.21 percent is the minimum steel required. As per 3920 according to the grade this percentage of steel is increasing, here for m20 it is 0.26 for m30.32 and for m40.37 percent. Now, the longitudinal reinforcement what should be the maximum minimum we have specified in earlier slide it was tabulated also. So, to avoid over reinforced section and subsequent brittle failure if you go for over reinforced section your section will will not yield also. So, this will fail in the compression or compressive stresses will be very high and it will be the brittle failure. So, maximum steel ratio it shall not be greater than 2.5 percent at any phase. So, 2.5 percent is the maximum reinforcement in this section allow. Next is positive steel means steel for the positive bending moment siding bending moment generally it is at the bottom at any joint phase at least equal to half the negative steel. Negative steel means the steel which is calculated for hogging bending moment generally at the joint phase it is at the top. So, the meaning of this statement is the bottom reinforcement at joint phase of the beam must be at least half the top reinforcement at that joint phase this is the practical meaning of this statement. So, it takes care of again the reversible of stresses during earthquake motion. Okay now the one more clause is important regarding this longitudinal reinforcement that is steel on any phase at any section at least equal to one fourth of maximum negative steel. So, most important thing is this any section any phase it may be your bottom phase it may be lateral vertical phases this steel must be at least one fourth of maximum negative steel. Okay negative steel means the steel at the top at the joint or at the continuous end whatever negative steel you calculate steel at the top its one fourth must be present at bottom it one fourth must be present at least at the vertical phases of the beam. Next is redistribution of the moments not allowed for lateral loads. So, in case of earthquake load redistribution of the moment is not allowed. Basic philosophy of design is based on inelastic behavior this is the limitation for not considering the redistribution of the moments and most important note for you please note higher steel does not necessarily mean safety most important thing is that provision appropriate of appropriate quantity at appropriate location that is the only requirement in ductility most important point related to this longitudinal reinforcement is the joint phase beam column joint it may be internal joint it may be external joint now the figure for external joint is shown this is the beam and its reinforcement that is anchored in the column. So, top reinforcement of the beam is anchored bent actually and anchored in the column bottom reinforcement of this beam is bent and anchored at top or it is going in the column in upward direction this will develop the bond of this reinforcement in the column so that there will not be separation of this beam and column at joint phase how much it must be anchored this is given here external extension of longitudinal bar from inner phase of the column it must be measured from inner phase of the column here you start the measurement of this bar length by the amount ld development length of this bar plus 10 times the diameter of bar suppose this bottom bar is 12 mm diameter so development length for 12 mm bar shall be calculated plus 10 times the diameter of bar means 120 mm so this much must be the anchored length required in this external joint. So, bar bent to accommodate the length most important solution for this you go for larger width of the column automatically it will solve this anchor issue. Next thing is internal beam column joint so bars passed straight through the column to accommodate the length that is even most important provision for internal beam column joint. Now, in case of longitudinal reinforcement sometimes splicing is required lap is required so that splicing shall not be provided for this portion joint portion do not go for the splicing at a distance twice depth of this section from joint phase this is also not allowed and at a quarter length of the member so even one fourth length of the member beside the joint in the twice depth from the joint phase even the quarter length of the member it is not allowed where it is allowed best location is you can provide lap or splicing at mid span of the section. How much it is so lap length or splicing shall be done for the length which is having the develop or it must be greater than the development length of that bar and the hoop spacing shall be less than 150 for the plus splice portion. So, you can refer this figure to so lap length is shown here at the splice location this is the splice location and the transfer reinforcement hoop shall be maximum 150 not more than that and here in this lap you only 50 percent of bars shall be placed all the bars shall not be placed at one location this is the criteria most important criteria my question for all of you what is the maximum spacing of hoop in splice portion of the beam these are the four options all the video think of that give the answer the answer is 150 mm now this is about the transverse reinforcement wave reinforcement most important point in this that you should provide this 135 mm hook first bent 90 degree again one more bent of 45 degree so 90 plus 45 that is 135 hook is called this hook is called as 135 degree and it must be extended up to 6 times the diameter of this bar or 65 mm which minimum 65 mm is the anchor or 6 times the diameter of bar. So, it helps a gradual failure of the member and minimum diameter of hoop bar shall be 8 mm now the transfer reinforcement for it must be provided twice the depth of the section from each end the spacing shall not be greater than the depth of the section by 4 m 8 into diameter of smallest longitudinal bars spacing shall not be less than 100 mm. So, all these clauses are explained and we will see in detail in the sketch also. So, this is the sketch where the transfer reinforcement for flexural member is explained. So, this hoop spacing for twice D depth of the section from face here the hoop shall be D by 4 or 8 diameter bar whichever is lesser and at the middle portion the hoop spacing shall not be greater than D by 2 D is depth of the section all these provisions you can study in this sketch and according to that all the steel or reinforcement shall be provided. Now, these are the references for the sections session. Thank you.