Design aid for seismic strengthening of reinforced concrete beams

Transcription

1 Design aid for seismic strengthening of reinforced concrete beams Arshad K. Hashmi Design for seismic strengthening of the existing doubly beam involves - analysis of the existing beam for assessing its current strength, and based on the current seismic demand posed on it, redesigning the beam for the required additional strength. In practice this is considered as lengthy, as procedure of iteration is mandatory in calculation of the ultimate moment capacity of doubly beam having arbitrary combinations of areas of compression and tension steel. The seismic strengthening of the existing non-seismic buildings is a vital need of time, given such cases are more in numbers so as its inhabitants. To facilitate these seismic strengthening formulations, analysis cum design aids for beams are presented in this paper and their use is demonstrated by means of an illustrative example which can fulfil the vital need of time. This will help to quickly identify the amount of steel (i.e. longitudinal and transverse) required for posed seismic demand on the RC beam member. INTRODUCTION Major stock of existing multi-storeyed buildings in urban India converts the seismic hazard in to seismic disaster as its vulnerability against seismic load is very huge. Past major earthquake event such as Bhuj (2001) exposed this fact. Even now, very few multi-storeyed buildings in urban India, are designed as earthquake resistant building based on current seismic design and detailing code i.e. IS: 1893 (2002) and IS: (1993) [1-2]. The seismic strengthening of these seismically deficient existing building is a vital need of time as its inhabitants are more compared to the newly constructed buildings designed as per relevant seismic codes [1-2]. On the other hand, the skilled human resources (i.e. engineers) for the seismic strengthening of these large numbers of seismically deficient existing buildings are very few in numbers [3]. To fill this discrepancy IS: (2013) provides simple methods for the seismic strengthening of the seismically deficient building structures [4]. Post seismic disaster of Bhuj (2001), many efforts were made in regard to seismic evaluation and strengthening of the existing building not designed for current seismic demands [5-7]. The present paper is also an effort in this direction, by providing design aids for the seismic strengthening of RC beams. Among various methods of retrofit, strengthening of members at local level with the help of jacketing is very much effective because of low cost, no obstruction in the functional use of area and adequacy in the experience of traditional RC construction [8]. Present paper deals with this strengthening option applied to the beams. Beam is a structural member, which is at the lowest level in strength hierarchy requirement for seismic load. As beams carry relatively very less or nearly no compression load compared to the columns, can be designed and detailed to be more ductile than columns [9]. Thereby beams can absorb large amount of energy through inelastic behaviour. Good ductility of the building at global level is achieved through sway mechanism which ensures the yielding of beams prior to columns. The ideal situation for seismic performance is that the damage should occur at the ends of the beams and should be distributed throughout the building height. Thus the ductile behaviour of each and every beam at its ultimate moment capacity sets the benchmark for the beginning of the ideal hinge formation in the building and thereby decides the lateral strength of the building at the global level. The primary requirement of ductile design of reinforced concrete (RC) beams is to ensure that ductile flexural failure should come before brittle failure such as shear failure (due to insufficient stirrups) and bond-slip failure (due to insufficient development length). The important condition of shear failure is normally not considered in design practices because of difficulty in finding out the ultimate moment capacity at both ends of beam that too under sagging and hogging conditions with arbitrary combination of The Indian Concrete Journal April

2 compressive and tensile steel because of its iterative nature of analysis. This paper addresses issues pertaining to flexural, shear strengthening design and provide simple design aids to facilitate the calculation of the design of longitudinal and transverse steel. DESIGN FOR SEISMIC STRENGTHENING OF BEAMS Design for seismic strengthening of existing doubly beam involves assessing the strength of existing beam (i.e. analysis part) and then based on applied seismic demand (i.e. in terms of shear forces and moments) redesigning the beam (i.e. design part) for the required additional steel. Analysis part involves determination of ultimate moment and ultimate shear capacity of the existing beams, whereas design part involves determination of additional longitudinal steel and stirrups as per the seismic demand (i.e. in terms of ultimate moments and ultimate shear force). Following steps are involved in the procedure of design for seismic strengthening of beams Estimation of ultimate moment of resistance (Mur) of the existing doubly Beam. Determination of longitudinal top steel and bottom steel to achieve the applied ultimate moment capacity (Mua). Determination of feasible combination of top and bottom steel in the beam and estimation of ultimate moment capacity of designed strengthened beam (Murs). Determination of shear force due to uniform gravity load (i.e 1.2 times of dead and live load) at both ends, (Vu) Determination of the shear force developed by the formation of plastic hinge at both ends of the proposed strengthened beam (Vus e ) Estimation of total applied shear force (Vus) i.e. summation of shear force due to gravity load (Vu) and shear force due to formation of plastic hinges at both ends (Vus e ) Estimation of the stirrups required for strengthened beam Difficulties encountered in the computations of design for seismic strengthening of beams If the beam section is balanced, the calculations of ultimate moment capacity (Mur) of the doubly section is relatively simple. But in practice, the probability of section being exactly balance is very rare or near to negligible. Beam sections are generally kept under-reinforced to achieve ductility. In some cases there are chances of beams sections, turn out to be over-reinforced because of poor design or limited choice of available longitudinal steel diameter. If the section is under reinforced, iteration is required to correctly arrive at the stress in the compression steel (fsc). If the section is over-reinforced the stress in the tension steel (fst) is likely to be less than the permissible value of stress i.e. 0.87fy and its exact value can be determined only through an iterative procedure [10]. Thus in either situation (i.e. under-reinforced or over-reinforced) the process of iteration is mandatory. This iteration process involves determination of depth for neutral axis, satisfying conditions such as equilibrium, compatibility and constitutive relationship. As in handbooks such as SP16 [11], no design aids are provided to facilitate such calculations (i.e. analysis of doubly beams for arbitrary combination of compressive and tensile steel), in design practice such iteration process are normally ignored. Although the formulations for calculations in above steps of design for seismic strengthening of beams appear to be simple, step 1 and 3 (i.e. estimating the Mur for existing and Murs for strengthening beam) requires iteration procedure. Again it is mandatory to arrive at four values of Mur and Murs each in step 1 and 3 respectively for every single beam (i.e. for sagging and hogging ultimate moment capacities at the two beam end sections). Thus the process of design for seismic strengthening of single beam, needs determination of Mur or Murs for eight times, thereby it is needed to do iteration calculation eight times. This is not difficult in computation but considered as laborious in practicing environment. Hence there is clear need of design aids to facilitate the rapid calculations of the design for seismic strengthening of beams. Present paper is an effort in this direction to provide the design aids and illustrate its use for nearly all the steps involved in the design for seismic strengthening of beams. Estimation of design shear force in strengthening beams The requirement of ductile seismic design code, specify that the shear force to be resisted by the stirrups of the strengthening beam (Vus) should be at least equal to shear force due to formation of plastic hinge at both ends of the strengthening beam plus shear force due the factored gravity loads on the span [2]. This is due to the prospect that, at the instant of plastic hinges at the both ends of the strengthening beam, it should be able to carry gravity load without shear failure. Again, this is to ensure that at the sections of 94 The Indian Concrete Journal April 2016

3 strengthening beam ends, it should be able to reach their full ultimate moment capacities (Mur), without any premature shear failure which is brittle in nature. Shear strength of concrete i.e. due to longitudinal tensile steel and concrete is to be ignored in the computation, because of cyclic loading which creates adverse effects of severe cracking. Thus there are two components to be considered in the calculation of Vus, shear force due to gravity that is deal and live load (Vu d+l ) assuming partial load factor of 1.2 and shear force associated with the formation of plastic hinges at the two ends of the strengthening beams, Vus e,under seismic loading. Where is shear force due to gravity load and is illustrated in Figure 1(a) for uniformly distributed dead and live load. is shear force developed in the beam at the ultimate moment of resistance of the beam. The calculations of is depends upon the direction of sway and its value is shown in Figure 1(b) and 1(c). The ultimate moment of resistance in hogging (Mur H ) and sagging (Mur S )are to be calculated by following IS: 456 (2000) requirements for the given arbitrary combination of top and bottom steel at each end of the beam [12]. Ultimate moment of resistance (Mur) for strengthening beams To find out the ultimate moment of resistance (Mur) for doubly beam with the given arbitrary combination of top and bottom steel, Chugh R. and Menon D. has developed design aids in terms of charts [13]. These charts provides the coefficient of ultimate moment of resistance, Ru (i.e. Mur/bd 2 ) for the given random combination of tensile steel (Pt) and compressive steel (Pc). These charts are applicable for any rectangular beam section. A typical design charts is shown in Figure 2. The solid diagonal line in the Figure 2 represent balance section condition for the given combination of compressive and tensile steel. Chugh R. and Menon D. illustrated charts for (d /d) i.e. ratio of cover to effective depth of beam as 0.05 and 0.15 [13]. In the present paper, the author has developed and presented the chart for (d /d) as 0.1. Illustrative example The use of design charts are illustrated by using an example which is shown in Figure 3. The needed additional The Indian Concrete Journal April

4 Table 1. Governing applied ultimate moments on the beam considering seismic loading (Mua) Section at Tension at Governing applied ultimate moment considering seismic load, Mua (knm) Coefficient of applied ultimate moment, Ru req = Mua/bd 2 (N/mm 2 ) A Top A Bottom B Top B Bottom Table 2. Calculations of Mur Section at Action Tension at Percentage of tensile Pt Percentage of compressive Pc Coefficient of ultimate moment, Ru = Mur/bd 2 Rur (N/mm 2 ) Mur = Rubd 2 (knm) A Hogging Top A Sagging Bottom B Hogging Top B Sagging Bottom longitudinal steel (i.e. at top and bottom) and additional stirrups for the posed seismic demand (i.e. in Table 1) are found out. Input Data : b = 300 mm, D = 550 mm, d = 500 mm, d = 50 mm, M20, Fe415, amount of steel is as shown in Figures 3(b) and 3(c) Step 1. Estimation of ultimate moment of resistance (Mur) of the existing doubly beam The Mur is to be found out at the both ends under hogging and sagging action [Figures 1(b) and 1(c)]. With the help of amount of steel provided as shown in Figures 1(b) and 1(c), the percentage of steel in tension, Pt and compression, Pc can be found out. This is illustrated in 2. By using Pt and Pc for every joint (i.e. A and B) and under every action (i.e. sagging and hogging), the Ru can be found out very easily using Figure 4. The values of Ru and Mur are presented in Table 2. Step 2. Determination of longitudinal top steel and bottom steel to achieve the applied ultimate moment capacity. Once the ultimate moment of resistance, Mur of the existing beam is known under sagging and hogging action, it should be compared it with respective applied ultimate moment (Mua). If the governing applied ultimate moment, Mua (Table 1) on the existing beam is greater than the respective ultimate moment of resistance, Mur (Table 2), strengthening of the beam is needed. Strengthening of the existing beam can be done by providing the supplementary strength through adding compressive and tensile steel. Based on the governing applied ultimate moment, Mua the coefficient of applied ultimate moment Ru req can be found out as illustrated in Table 3. This value of Ru req can be round off on conservative side to suit with analysis aid (i.e. Figures 3 to 5). At section A, for applied ultimate hogging moment 96 The Indian Concrete Journal April 2016

5 Table 3. Determination of Top and Bottom Steel to achieve Applied Ultimate Moment, Mua Section at Action Tension at Mua (knm) Coefficient of applied ultimate moment, Ru req = Mua/bd 2 Round off on conservative side for Ru req (N/mm 2 ) Required percentage of tensile Pt req Required percentage of compressive Pc req A Hogging Top A Sagging Bottom B Hogging Top B Sagging Bottom The Indian Concrete Journal April

6 Table 4. Calculation of Ultimate Moment of Resistance for strengthening beam, Murs Section at Action Tension at Additional steel Percentage of tensile Pts Percentage of compressive Pcs Coefficient of ultimate moment, Rus = Mur/bd 2 Rur Murs = Rubd 2 (knm) A Hogging Top 2-25Φ A Sagging Bottom 1-25Φ B Hogging Top 2-25Φ B Sagging Bottom 1-25Φ 1-16Φ (330 knm) and sagging moments (210 knm), the required top and bottom steel can be found out using Figure 5. The procedure for the same is illustrated as below The Ru (Table 2) under hogging action for the existing beam with Pt (0.862) and Pc (0.628) can be found out as 2.8 The Ru req (Table 3) under hogging action is 4.5, so Pt can be increased to attain Ru req 4.5, at this point the top steel need is 1.5% Further, changing the top steel from 1.5% to 1.4% will not change any bottom steel percentage, i.e. 0.92% as determined in step 3. So the iteration can be stopped. Similar procedure has been done for section at B and the results are presented in Table 3. Step 3. Determination of feasible combination of top and bottom steel in the beam and estimation of ultimate moment resistance of designed strengthened beam (Murs) This top steel (i.e. 1.5%) will become compressive steel under sagging action which has Ru req (Table 3) as 3.0. To attain this, bottom tensile steel will be required as 0.92% New updated bottom steel is 0.92% and not 0.628% which was in step 1. So assuming bottom compressive steel as 0.92%, the Ru req (4.5) can be attained with the help of top steel as 1.4%. In practice we cannot provide exact amount of required percentage of steel due to constrains such as limited range in the diameter of rebar. Thus a feasible combination of top and bottom steel is selected to attain the respective applied ultimate moment capacity, Mua which is illustrated in Table 4. Repeating the step 1 using Figure 4, we can find out the ultimate moment capacity of strengthening beam, Murs which is also illustrated in Table The Indian Concrete Journal April 2016

7 Step 4. Determination of shear force due to uniform gravity load (i.e 1.2 times of dead and live load) at both ends, Vu The span of the beam is 4m and summation of dead and live load is 27kN/m. Following curve for 4m span and uniform gravity load 27kN/m in Figure 6, the shear force at each end of the beam for the gravity load will be 64.8 kn. Step 5. Determination of the shear force developed by the formation of plastic hinge at both ends of the proposed strengthened beam (Vus e ) For the sway in right direction Vus e = 1.4(M ura S + M urb H )/L (M ura S + M urb H ) = ( ) = kNm Following the Figure 7(a), Vus e for sway in right direction is kN For the sway in left direction Vus e = 1.4 (M ura H + M urb S )/L (M ura H + M urb S ) = ( ) = Following the Figure 7(b), Vus e for sway in right direction is Kn Step 6. Estimation of total applied shear force (Vus) i.e. summation of shear force due to gravity load (Vu) and shear force due to formation of plastic hinges at both ends (Vus e ) It is the summation of Vu (step 4) and Vus e (step 5). The total applied shear force in the stirrups is given by For right sway Vus = Vu + Vus e Vus = = kn For left sway Vus = Vu + Vus e Vus = = kn As values for total applied shear, Vus at both ends are very close to each other, same stirrups can be provided for both ends (i.e. for kn) The Indian Concrete Journal April

8 Step 7. Estimation of the stirrups required for strengthened beam Following Figure 8, the needed stirrups can be found for the applied shear force Vus at the beam ends. Figure 8 illustrates the comparison of applied shear force per unit depth (Vus/d) against spacing of 2 legged stirrups for different diameters of stirrups. As applied shear force (Vus) is of value kn, (Vus/d) can be found out as (Vus)/d = 286.6/0.5 = kn/m Assume 10 mm diameter 2 legged stirrups. Figure 8 illustrates that, as (Vus/d) is kn/m, the needed spacing for 2 legged 10 mm φ stirrups is 100 mm c/c. Number of additional stirrups can now be uniformly placed in between the existing stirrups in the beam (i.e. 10mmφ@250mm c/c) so the total stirrups provided will be 10mmφ@100mm c/c. DISCUSSION The present paper illustrates a quick procedure for design of seismic strengthening of existing doubly beams with arbitrary combination of top and bottom steel. Presented analysis aid evades the iteration procedure required to find out the ultimate moment of resistance of existing beam as well as strengthened beam. Further these design aids can be used as an easy tool for the seismic strengthening of large stock of seismically deficient beams. References 1. Criteria for Earthquake Resistant Design of Structures. Part 1 General Provisions and Buildings, IS: 1893, Bureau of Indian Standard, 2002, New Delhi 2. Ductile Detailing of Reinforced Concrete Structures Subjected to Seismic Forces- Code of Practice, IS: 13920, Bureau of Indian Standard, 1993, New Delhi 3. Hashmi A.K. Preliminary seismic evaluation aid for reinforced concrete framed structures based on IS: (2013) guidelines The Indian concrete journal, 89(9), 2005,pp Seismic Evaluation and Strengthening of Existing Reinforced Concrete Building- Guidelines, IS: 15988,Bureau of Indian Standard, 2013, New Delhi 5. Durgesh C. Rai Seismic Evaluation and Strengthening of Existing Buildings IITK-GSDMA-EQ06-V4.0, Draft Final Report-A Earthquake Codes, IITK-GSDMA, Project on Building Codes, 2005, Kanpur 6. Anand S. Arya, Seismic Evaluation and Strengthening of Existing Reinforced Concrete Building prepared under GOI-UNDP Disaster Risk Management Programme, Indian Institute of Technology, 2006, Roorkee 7. Durgesh C. Rai, Review of Documents on Seismic Evaluation of Existing Buildings. IITK-GSDMA-EQ03-V1.0, Interim Report 1-A Earthquake Codes, IITK-GSDMA, Project on Building Codes, 2005, Kanpur 8. Handbook of Seismic Retrofit of Building, Central Public Works Department and Indian Building Congress inassociation with Iindian Institute of Technology Madras, 2007, Chennai. 9. Murthy C.V.R., Goswami Rupen, Vijayanarayan A.R., and Mehta V.V., Some Concepts in Earthquake Behaviour of Buildings,Gujarat State Disaster Management Authority, Government of Gujarat, 10. Pillai S.U. and Menon, D., Reinforced concrete design, Second Edition, Tata McGraw Hill Publication CO, New Delhi, Design aids for reinforced concrete to IS: 456 (1978), Special Publication, SP16 (1980), Bureau of Indian Standard, New Delhi. 12. Plain and Reinforced Concrete, Code of Practice, IS: 456, Bureau of Indian Standard, 2000, New Delhi 13. Chugh R. and Menon D., Design Aids for Estimation of Shear in Seismic Design of RC Beams, The Indian concrete journal, 79(3), 2005, pp Dr. Arshad K. Hashmi holds a BE (civil engineering) from Swami Ramanand Teerth Marathwada University, Nanded, Maharashtra; ME (structural engineering) from University of Pune; PhD in structural engineering from IIT Delhi. He is an Associate Professor in the Department of Civil Engineering, MGM s College of Engineering, Nanded, Maharashtra. His areas of research interest are structural dynamics and vibration control, earthquake engineering, performance based seismic engineering, structural optimization, masonry infills. 100 The Indian Concrete Journal April 2016