Lecture 5 January 31 2006 In this Lecture
- Slides: 60
Lecture 5 January 31, 2006
In this Lecture n n Impulsive and convective base shear Critical direction of seismic loading Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 2
Base shear n Previous lectures have covered n Procedure to find impulsive and convective liquid masses n n Procedure to obtain base shear coefficients in impulsive and convective modes n n This was done through a mechanical analog model This requires time period, damping, zone factor, importance factor and response reduction factor Now, we proceed with seismic force or base shear calculations Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 3
Base shear n n Seismic force in impulsive mode (impulsive base shear) Vi = (Ah)i x impulsive weight Seismic force in convective mode (convective base shear) Vc = (Ah)c x convective weight (Ah)i = impulsive base shear coefficient (Ah)c = convective base shear coefficient n These are described in earlier lectures Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 4
Base shear n Now, we evaluate impulsive and convective weights n n n Or, impulsive and convective masses Earlier we have obtained impulsive and convective liquid mass Now, we consider structural mass also Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 5
Base shear : n Impulsive liquid mass is rigidly attached to container wall n n Ground supported tanks Hence, wall, roof and impulsive liquid vibrate together In ground supported tanks, total impulsive mass comprises of n n n Mass of impulsive liquid Mass of wall Mass of roof Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 6
Base shear : Ground supported tanks n Hence, base shear in impulsive mode mi = mass of impulsive liquid n mw = mass of container wall n mt = mass of container roof n g = acceleration due to gravity n Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 7
Base shear : Ground supported tanks n n This is base shear at the bottom of wall Base shear at the bottom of base slab is : Vi’ = Vi + (Ah)i x mb n n mb is mass of base slab Base shear at the bottom of base slab may be required to check safety against sliding Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 8
Base shear : Ground supported tanks n Base shear in convective mode n mc = mass of convective liquid Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 9
Base shear : Ground supported tanks n n n Total base shear, V is obtained as: Impulsive and convective base shear are combined using Square Root of Sum of Square (SRSS) rule Except Eurocode 8, all international codes use SRSS rule n Eurocode 8 uses absolute summation rule n i. e, V = Vi + Vc Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 10
Base shear : Ground supported tanks n In the latest NEHRP recommendations (FEMA 450), SRSS rule is suggested n Earlier version of NEHRP recommendations (FEMA 368) was using absolute summation rule n n FEMA 450, 2003, “NEHRP recommended provisions for seismic regulations for new buildings and other structures”, Building Seismic Safety Council, National Institute of Building Sciences, , USA. FEMA 368, 2000, “NEHRP recommended provisions for seismic regulations for new buildings and other structures”, Building Seismic Safety Council, National Institute of Building Sciences, , USA. Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 11
Bending moment: Ground supported tanks n n Next, we evaluate bending or overturning effects due to base shear Impulsive base shear comprises of three parts n n n (Ah)i x mig (Ah)i x mwg (Ah)i x mtg Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 12
Bending moment: Ground supported tanks n n n mw acts at CG of wall mt acts at CG of roof mi acts at height hi from bottom of wall n n If base pressure effect is not included mi acts at hi* n n If base pressure effect is included Recall hi and hi* from Lecture 1 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 13
Bending moment: Ground supported tanks n Bending moment at the bottom of wall n n Due to impulsive base shear Due to convective base shear n n hi = location of mi from bottom of wall hc = location of mc from bottom of wall hw = height of CG of wall ht = height of CG of roof Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 14
Bending moment: Ground supported tanks n For bending moment at the bottom of wall, effect of base pressure is not included n Hence, hi and hc are used Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 15
Bending moment: Ground supported tanks n Bending moment at the bottom of wall (Ah)imt (Ah)cmc hc hi (Ah)imw ht hw Ground level Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 16
Bending moment: Ground supported tanks n Total bending moment at the bottom of wall n SRSS rule used to combine impulsive and convective responses Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 17
Overturning moment: Ground supported tanks n Overturning moment n n This is at the bottom of base slab Hence, must include effect of base pressure n hi* and hc* will be used Ground level Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 18
Overturning moment: Ground supported tanks n Overturning moment in impulsive mode n Overturning moment in convective mode n tb = thickness of base slab Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 19
Bending moment: Ground supported tanks n Overturning moment is at the bottom of base slab n n n Hence, lever arm is from bottom of base slab Hence, base slab thickness, tb is added to heights measured from top of the base slab Total overturning moment Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 20
Example n Example: A ground-supported circular tank is shown below along with some relevant data. Find base shear and bending moment at the bottom of wall. Also find base shear and overturning moment at the bottom of base slab. Roof slab 150 mm thick mw = 65. 3 t, mt =33. 1 t, 10 m 4 m Wall 200 mm thick Base slab 250 mm thick Sudhir K. Jain, IIT Kanpur mi = 141. 4 t; mc = 163. 4 t mb = 55. 2 t, hi =1. 5 m, hi* = 3. 95 m, hc = 2. 3 m, hc* = 3. 63 m (Ah)i = 0. 225, (Ah)c = 0. 08 E-Course on Seismic Design of Tanks/ January 2006 21
Example Solution: Impulsive base shear at the bottom of wall is Vi = (Ah)i (mi + mw + mt) g = 0. 225 x (141. 4 + 65. 3 + 33. 1) x 9. 81 = 529. 3 k. N Convective base shear at the bottom of wall is Vc = (Ah)c mc g = 0. 08 x 163. 4 x 9. 81 = 128. 2 k. N Total base shear at the bottom of wall is Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 22
Example For obtaining bending moment, we need height of CG of roof slab from bottom of wall, ht. ht = 4. 0 + 0. 075 = 4. 075 m Impulsive bending moment at the bottom of wall is Mi = (Ah)i (mihi + mwhw + mtht) g = 0. 225 x (141. 4 x 1. 5 + 65. 3 x 2. 0 + 33. 1 x 4. 075) x 9. 81 = 1054 k. N-m Convective bending moment at the bottom of wall is Mc = (Ah)c mc hc g = 0. 08 x 163. 4 x 2. 3 x 9. 81 = 295 k. N-m Total bending moment at bottom of wall is Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 23
Example Now, we obtain base shear at the bottom of base slab Impulsive base shear at the bottom of base slab is Vi = (Ah)i (mi + mw + mt + mb) g = 0. 225 x (141. 4 + 65. 3 + 33. 1 + 55. 2) x 9. 81 = 651. 1 k. N Convective base shear at the bottom of base slab is Vc = (Ah)c mc g = 0. 08 x 163. 4 x 9. 81 = 128. 2 k. N Total base shear at the bottom of base slab is Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 24
Example Impulsive overturning moment at the bottom of base slab Mi* = (Ah)i [mi (hi* + tb) + mw(hw + tb) + mt(ht +tb) + mb tb/2]g = 0. 225 x [141. 4(3. 95 + 0. 25) + 65. 3(2. 0 + 0. 25) + 33. 1(4. 075 + 0. 25) + 55. 2 x 0. 25/2] x 9. 81 = 1966 k. N-m Convective overturning moment at the bottom of base slab Mc* = (Ah)c mc (hc* + tb) g = 0. 08 x 163. 4 x (3. 63 + 0. 25) x 9. 81 = 498 k. N-m Total overturning moment at bottom of base slab Notice that this value is substantially larger that the value at the bottom of wall (85%) Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 25
Base shear : n n n Elevated tanks In elevated tanks, base shear at the bottom of staging is of interest Ms is structural mass n Base shear in impulsive mode n Base shear in convective mode Total base shear Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 26
Bending moment: Elevated tanks n Bending moment at the bottom of staging n n Impulsive base shear comprises of two parts n n n Bottom of staging refers to footing top (Ah)i x mig Ah)i x msg Convective base shear has only one part n (Ah)c x mcg Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 27
Bending moment: Elevated tanks n n mi acts at hi* mc acts at hc* n n Bending moment at bottom of staging is being obtained Hence, effect of base pressure included and hi* and hc* are used Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 28
Bending moment: Elevated tanks n Structural mass, ms comprises of mass of empty container and 1/3 rd mass of staging n n ms is assumed to act at CG of empty container shall be obtained by considering roof, wall, floor slab and floor beams Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 29
Bending moment: Elevated tanks n Bending moment at the bottom of staging n hs = staging height n n Measured from top of footing to bottom of wall hcg = distance of CG of empty container from bottom of staging Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 30
Bending moment: Elevated tanks n Bending moment at the bottom of staging (Ah)i mig (Ah)c mcg (Ah)i msg hi * hc * hs hs hcg Top of footing Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 31
Bending moment: Elevated tanks n n Total bending moment For shaft supported tanks, M* will be the design moment for shaft Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 32
Bending moment: Elevated tanks n n n For analysis of frame staging, two approaches are possible Approach 1: Perform analysis in two steps Step 1: n n n Step 2: n n n Analyze frame for (Ah)imig + (Ah)imsg Obtain forces in columns and braces Analyze the frame for (Ah)cmcg Obtain forces in columns and braces Use SRSS rule to combine the member forces obtained in Step 1 and Step 2 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 33
Bending moment: Elevated tanks n n Approach 2: Apply horizontal force V at height h 1 such that n n n V x h 1 = M* V and M* are obtained using SRSS rule as described in slide nos. 26 and 32 In this approach, analysis is done in single step n Simpler and faster than Approach 1 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 34
Example n Example: An elevated tank on frame staging is shown below along with some relevant data. Find base shear and bending moment at the bottom of staging. A is CG of empty container A 2. 8 m mi = 100 t; mc = 180 t Mass of container = 160 t Mass of staging = 120 t hs = 15 m hi* = 3 m, hc* = 4. 2 m (Ah)i = 0. 08, (Ah)c = 0. 04 GL Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 35
Example Structural mass, ms = mass of container + 1/3 rd mass of staging = 160 + 1/3 x 120 = 200 t Base shear in impulsive mode = 78. 5 + 157 = 235. 5 k. N Base shear in convective mode Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 36
Example Total base shear Now, we proceed to obtain bending moment at the bottom staging Distance of CG of empty container from bottom of staging, hcg = 2. 8 + 15 = 17. 8 m Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 37
Example Base moment in impulsive mode = 78. 5 x 18 + 157 x 17. 8 = 4207 k. Nm Note: 78. 5 k. N of force will act at 18. 0 m and 157 k. N of force will act at 17. 8 m from top of footing. Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 38
Example Base moment in convective mode = 70. 6 x 19. 2 = 1356 k. Nm Note: 70. 6 k. N of force will act at 19. 2 m from top of footing. Total base moment Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 39
Example n Now, for staging analysis, seismic forces are to be applied at suitable heights n There are two approaches n n Refer slide no 33 Approach 1: n n n Step 1: Apply force of 78. 5 k. N at 18 m and 157 k. N at 17. 8 m from top of footing and analyze the frame Step 2: Apply 70. 6 k. N at 19. 2 m from top of footing and analyze the frame Member forces (i. e. , BM, SF etc. in columns and braces) of Steps 1 and 2 shall be combined using SRSS Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 40
Example n Approach 2: n Total base shear, V = 245. 8 k. N will be applied at height h 1, such that V x h 1 = M* 245. 8 x h 1 = 4420 h 1 = 17. 98 m n Thus, apply force of 245. 8 k. N at 17. 98 m from top of footing and get member forces (i. e. , BM, SF in columns and braces). Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 41
Elevated tanks: Empty condition n Elevated tanks shall be analysed for tank full as well as tank empty conditions n n Design shall be done for the critical condition In empty condition, no convective liquid mass n n Hence, tank will be modeled usingle degree of freedom system Mass of empty container and 1/3 rd staging mass shall be considered Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 42
Elevated tanks: Empty condition n n Lateral stiffness of staging, Ks will remain same in full and empty conditions In full condition, mass is more n n Hence, time period of empty tank will be less n n n In empty condition mass is less Recall, T = Hence, Sa/g will be more Usually, tank full condition is critical n However, for tanks of low capacity, empty condition may become critical Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 43
Direction of seismic force n n Let us a consider a vertical cantilever with rectangular cross section Horizontal load P is applied n n First in X-Direction Then in Y-direction (see Figure below) More deflection, when force in Y-direction Hence, direction of lateral loading is important !! P Y X Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 P 44
Direction of seismic force n On the other hand, if cantilever is circular n n n Direction is not of concern Same deflection for any direction of loading Hence, it is important to ascertain the most critical direction of lateral seismic force n Direction of force, which will produce maximum response is the most critical direction n In the rectangular cantilever problem, Y-direction is the most critical direction for deflection Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 45
Direction of seismic force n For frame stagings consisting of columns and braces, IS 11682: 1985 suggests that horizontal seismic loads shall be applied in the critical direction n IS 11682: 1985, “Criteria for Design of RCC Staging for Overhead Water Tanks”, Bureau of Indian Standards, New Delhi Clause 7. 1. 1. 2 Horizontal forces – Actual forces and moments resulting from horizontal forces may be calculated for critical direction and used in the design of the structures. Analysis may be done by any of the accepted methods including considering as space frame. Clause 7. 2. 2 Bending moments in horizontal braces due to horizontal loads shall be calculated when horizontal forces act in a critical direction. The moments in braces shall be the sum of moments in the upper and lower columns at the joint resolved in the direction of horizontal braces. Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 46
Direction of seismic force n n Section 4. 8 of IITK-GSDMA Guidelines contains provisions on critical direction of seismic force for tanks Ground-supported circular tanks need to be analyzed for only one direction of seismic loads n n These are axisymmetric Hence, analysis in any one direction is sufficient Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 47
Direction of seismic force n Ground-supported rectangular tanks shall be analyzed for two directions n n Parallel to length of the tank Parallel to width of the tank Stresses in a particular wall shall be obtained for seismic loads perpendicular to that wall Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 48
Direction of seismic force n RC circular shafts of elevated tanks are also axisymmetric n n Hence, analysis in one direction is sufficient If circular shaft supports rectangular container n Then, analysis in two directions will be necessary Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 49
Direction of seismic force n For elevated tanks on frame staging n n n Critical direction of seismic loading for columns and braces shall be properly ascertained Braces and columns may have different critical directions of loading For example, in a 4 - column staging n n n Seismic loading along the length of the brace is critical for braces Seismic loading in diagonal direction gives maximum axial force in columns See next slide Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 50
Direction of seismic force n Critical directions for 4 - column staging Bending Axis Critical direction for shear force in brace Sudhir K. Jain, IIT Kanpur Critical direction for axial force in column E-Course on Seismic Design of Tanks/ January 2006 51
Direction of seismic force n For 6 – column and 8 – column staging, critical directions are given in Figure C-6 of the Guideline n n See next two slides More information available in Sameer and Jain (1994) n Sameer, S. U. , and Jain, S. K. , 1994, “Lateral load analysis of frame staging for elevated water tanks”, Journal of Structural Engineering, ASCE, Vol. 120, No. 5, 1375 -1393. (http: //www. nicee. org/ecourse/Tank_ASCE. pdf) Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 52
Direction of seismic force n Critical directions for 6 - column staging Bending Axis Critical direction for shear force and bending moment in columns Sudhir K. Jain, IIT Kanpur Critical direction for shear force and bending moment in braces and axial force in columns E-Course on Seismic Design of Tanks/ January 2006 53
Direction of seismic force n Critical directions for 8 - column staging Bending Axis Critical direction for shear force and bending moment in braces Sudhir K. Jain, IIT Kanpur Critical direction for shear force, bending moment and axial force in columns E-Course on Seismic Design of Tanks/ January 2006 54
Direction of seismic force n As an alternative to analysis in the critical directions, following two load combinations can be used n 100 % + 30% rule n n Also used in IS 1893(Part 1) for buildings SRSS rule Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 55
Direction of seismic force n 100%+30% rule implies following combinations n n ELx + 0. 3 ELY + 0. 3 ELx is response quantity when seismic loads are applied in X-direction ELY is response quantity when seismic loads are applied in Y-direction Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 56
Direction of seismic force n 100%+30% rule requires n Analyze tank with seismic force in X-direction; obtain response quantity, ELX n n Response quantity means BM in column, SF in brace, etc. Analyze tank with seismic force in Y-direction; obtain response quantity, ELY Combine response quantity as per 100%+30% rule Combination is on response quantity and not on seismic loads Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 57
Direction of seismic force n Important to note that the earthquake directions are reversible n Hence, in 100%+30% rule, there are total eight load combinations Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 58
Direction of seismic force SRSS rule implies following combination n n Note: n n n ELx is response quantity when seismic loads are applied in X-direction ELY is response quantity when seismic loads are applied in Y-direction Hence, analyze tank in two directions and use SRSS combination of response quantity Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 59
At the end of Lecture 5 n n This completes seismic force evaluation on tanks There are two main steps n n Evaluation of impulsive and convective masses Evaluation of base shear coefficients for impulsive and convective modes SRSS rule is used to combine impulsive and convective responses Critical direction of seismic loading shall be properly ascertained n Else, 100%+30% or SRSS rule be used Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 60