SMALL-SCALE SHAKE TABLE EXPERIMENTS AND COMPARISON TO ANALYTICAL PREDICTIONS

Transcription

1 SMALL-SCALE SHAKE TABLE EXPERIMENTS AND COMPARISON TO ANALYTICAL PREDICTIONS A PROJECT DEVELOPED FOR THE UNIVERSITY CONSORTIUM ON INSTRUCTIONAL SHAKE TABLES Develped by: Brenda E. Shnkwiler Thmas H. Miller Oregn State University This prject is supprted in part by the Natinal Science Fundatin Grant N. DUE

2 1.0 Overview This student manual cntains instructins fr a set f experiments t be perfrmed with the UCIST Shake Table. The ultimate gal is t cmpare results frm an earthquake simulatin n the UCIST Shake Table t analytical results using SAP 2000 sftware. 1.1 Intrductin This manual prgresses thrugh the necessary steps t run an earthquake simulatin n the UCIST Shake Table and t create the crrespnding SAP 2000 mdel. The manual starts with sme basic infrmatin abut the UCIST Equipment and explains hw t build a 3D mdel. It ges n t explain hw t determine prperties f the 3D mdel, including stiffness and damping. There is als a sectin n hw t determine the scale used by the UCIST Shake Table fr each earthquake. This is fllwed by explanatins n hw t determine acceleratins as a functin f time fr each flr and the maximum relative displacement f the tp flr. The manual ends with the steps fr develping the SAP 2000 mdel. 1.2 Cntents 1.0 Overview Intrductin Cntents UCIST Equipment and Table Specificatins D Mdel Specificatins Hw t Cnstruct the 3D Mdel Plan Views f 3D Mdel D Mdel Schematic D Mdel Material Prperties D Mdel Prperties Experiment Stiffness Experiment Damping Free Vibratin Test Earthquake Scale Determinatin UCIST Shake Table Experiments Shake Table Acceleratins Experiment Displacement Experiment SAP 2000 Mdel Oregn State University

3 2.0 UCIST Equipment and Table Specificatins The UCIST Shake Table is a uniaxial bench-scale shake table. This unit can be cntrlled by a Pentium cmputer r the Pendant (see figures belw). It is effective fr a wide variety f experiments fr civil engineering structures. The shake Table specificatins are as fllws: Table 1: Shake Table Specificatins (Dyke, Equipment page) Specificatin Design Paylad Peak Acceleratin Frequency Range Peak Velcity Sliding Table Dimensins Strke Weight f the Shake Table Value 25 lb f 1 g 0-20 Hz 20 in/sec 18 in x 18 in 6 in (+/- 3 in) Apprximately 100 lb f Figure 1: Shake Table Figure 2: Pentium Cmputer Figure 3: Pendant Figure 4: Universal Pwer Mdule 3 Oregn State University

4 3.0 3D Mdel Specificatins This sectin explains the prcess f building the 3D mdel, shws plan views f the 3D mdel, lists material prperties, and explains hw t determine prperties f the mdel (mass, dimensins, stiffness, and damping). Building the mdel is a necessary step t testing it n the UCIST Shake Table. Determining the prperties f the mdel must be dne befre creating the SAP 2000 cmputer mdel. 3.1 Hw t Cnstruct the 3D Mdel Purpse: This sectin explains hw t build the 3D mdel that will be tested n the UCIST Shake Table. Materials: in x 36 in f ¼ inch aluminum plate feet f 3/16 inch diameter rd (spring steel) 3. (16) Mdified tube fittings 4. (32) Allen blts 5. Epxy 6. Oil Prcedure: 1. Cut ¼ inch aluminum plate int (4) in x 18 in pieces. 2. Drill hles in each crner f each in x 18 in plate t insert mdified tube fittings (fur mdified tube fittings per plate). See Plan Views f 3D Mdel fr the lcatin f these hles. 3. Tap (2) hles in each pipe fitting t insert Allen blts. 4. Drill hles at 1.25 in n center in each plate as specified in Plan Views f 3D Mdel. 5. Drill hles in the base plate at 3.25 inches n center fr munting t the Shake Table. 6. Epxy pipe fittings t each plate (see Figure 5). 7. Insert rds int pipe fittings n each flr. 8. Oil each Allen blt (see Figure 6). 9. Insert (2) Allen blts int each pipe fitting. 10. Adjust height f each flr and tighten Allen blts against the rds t hld each flr in place. Flrs shuld be spaced at 11 inches n center. 4 Oregn State University

5 Figure 5: Step 5 -Epxy Pipe Fittings t Flr Figure 6: Oil each Allen Blt Oil Epxy Figure 7: Cmpleted 3D Mdel Flr 3 Flr 2 Flr 1 Base 5 Oregn State University

6 3.2 Plan Views f 3D Mdel Figure 8: Plan View f 3D Mdel Flr in 7.75 in 1.25 in, TYP 18 in 15 in Drilled hle Hle fr pipe fitting 1.25 in, TYP 6 Oregn State University

7 Figure 9: Plan View f 3D Mdel Base in 18 in 15 in 7.75 in 3.25 in, TYP 1.25 in, TYP Drilled hle Hle fr rds Hle fr munting t UCIST Shake Table 1.25 in, TYP 3.25 in, TYP 7 Oregn State University

8 3.3 3D Mdel Schematic Figure 10: Basic Schematic m 3 m 3 K 3 11 in K 3 11 in m 2 m 2 K 2 11 in K 2 11 in m 1 m 1 K 1 11 in K 1 11 in 15 in 7-3/4 in 3.4 3D Mdel Material Prperties Rds: Spring Steel Specific Gravity γ = 489 lb/ft 3 Mdulus f Elasticity E = 29,000 ksi Shear Mdulus f Elasticity G = 11,000 ksi Pissn s rati ν = 0.30 Flr Plates: 6061 Aluminum Specific Gravity γ = 170 lb/ft 3 Mdulus f Elasticity E = 10,000 ksi Shear Mdulus f Elasticity G = 3,800 ksi Pissn s rati ν = Oregn State University

9 3.5 3D Mdel Prperties Experiment Purpse: The purpse f this exercise is t determine the mass and dimensins f the 3D mdel. This is required input data fr the SAP 2000 cmputer mdel. Equipment: 1. 3D Mdel 2. Ruler 3. Yardstick 4. Calipers 5. Scale (Mettler Pll-k) Prcedure: 1. Take 3D mdel apart. Nte: The mdified tube fittings can stay attached t each flr. 2. Measure and recrd the dimensins f each piece (see Figure 11 belw). 3. Weigh and recrd the mass f each piece (see Figure 12 belw) 4. Reassemble the mdel. Figure 11: Measuring the 3D Mdel (a) Plate Dimensins (b) Plate Spacing Figure 12: Weighing a Flr f the 3D Mdel 9 Oregn State University

10 3.6 Stiffness Experiment Purpse: This experiment was designed t measure the inter-stry stiffnesses f the threedimensinal mdel that was built t g with the UCIST Shake Table. Stiffness is nt directly entered int the SAP 2000 mdel, but shuld be checked t ensure accuracy f the SAP 2000 mdel. Equipment: 1. 3D Mdel Figure 13: Stiffness Experiment Set-up 2. Wd platfrm 3. Level 4. (6) L-shaped brackets 5. (12) screws 6. (1) nut and blt 7. Magnetic tl hlder 8. Magnetic base fr dial indicatr 9. (6) C-clamps 10. Dial Indicatr (A) 2 inch x inch, Brand: Teclck AI-9510 (B) 1 inch x inch, made in China 11. Lad Cell (Brand: Interface, Mdel: SSM2-250, Serial #: B95621) 12. Lad Indicatr (Brand: Dillan, Mdel: WI-120D, Serial #: ) 13. (2) Strips f Velcr 14. (2) Bungee crds 15. Mveable cart Prcedure: 1. Calibrate Lad cell (Figure 15). 2. Cnstruct wd platfrm. Level the platfrm and screw it t the wall using tw brackets. Be sure t screw int a clumn r stud (Figure 16). 3. Screw ne bracket int the wall just abve each flr level (Figure 17). 4. Place the 3D mdel n the wd platfrm clse enugh t the wall t clamp each flr t the brackets. 5. Clamp 3D mdel t the wd platfrm with (2) C-clamps. 6. Screw the magnetic tl hlder int the wall using (2) screws. 7. Attach the dial indicatr t the magnetic base. 8. Cnnect the lad cell t the lad indicatr. 9. Attach the bungee chrds t the lad cell using a Velcr lp. 10. Attach the ther end f the bungee chrds t the mveable cart. 11. Determine K1 (the stiffness between the base and Flr 1). a. Blt a bracket t Flr 1. Cart Lad Indicatr Lad Cell 10 Oregn State University

11 b. Psitin the rd and dial indicatr alng the metal strip just abve r belw the level f Flr 1, s the dial indicatr presses against the bracket n Flr 1 and reads displacements f that flr (Figures 18 and 19). c. Attach a clamp t the end f Flr 1 (the end away frm the wall). d. Attach the lad cell t the clamp using a Velcr lp (Figure 20). e. With the mdel base clamped t the wd platfrm, incrementally pull n Flr 1 (see Figure 21) f. Recrd displacements (read frm dial indicatr) and pull (read frm lad indicatr) at apprximately 2 pund increments. 12. Determine K2 (the stiffness between Flr 1 and Flr 2). a. Clamp Flr 1 t the bracket at that level, using a shim between the flr and the bracket. b. Repeat the steps (a) thrugh (d) in part 11 fr Flr 2 instead f Flr 1. c. With the mdel base clamped t the wd platfrm and Flr 1 clamped t the wall, incrementally pull n Flr 2. d. Recrd displacements (read frm dial indicatr) and pull (read frm lad indicatr) at apprximately 2 pund increments. 13. Determine K3 (the stiffness between Flr 2 and Flr 3). a. Clamp Flr 2 t the bracket at that level, using a shim between the flr and the bracket. b. Repeat the steps (a) thrugh (d) in part 11 fr Flr 3 instead f Flr 1. c. With the mdel base clamped t the wd platfrm and Flr 1 and Flr 2 clamped t the wall, incrementally pull n Flr 3 (Figure 22). d. Recrd displacements (read frm dial indicatr) and pull (read frm lad indicatr) at apprximately 2 pund increments. 14. Unscrew everything frm the wall and put the equipment away. Figure 14: Schematics f Set-up Flr 3 Flr 2 Flr 1 K 3 K 2 Base K 1 K 1 K 2 K 3 11 Oregn State University

12 Figure 15: Lad Cell Calibratin Figure 16: Platfrm Set-up Figure 17: Bracket at Each Flr Figure 18: Magnetic Base Attached t Magnetic Tl Hlder Figure 19: Dial Indicatr Psitin Figure 20: Attachment f Lad Cell Figure 21: K 1 Set-up Figure 22: K 3 Set-up 12 Oregn State University

13 3.7 Damping Free Vibratin Test Purpse: This experiment is designed t determine the damping rati f the 3D mdel. The damping rati is imprtant input in the SAP 2000 mdel. Equipment: 1. Vide Camera (Sny) 2. Yardstick with 1/10 inch scales 3. (2) Ring-stands 4. Masking tape 5. (4) Clamps (t clamp t ring-stand and hld yardsticks) 6. (2) C-clamps (t secure mdel t a stable surface) 7. Ladder 8. Spt light if rm lighting nt sufficient 9. 3D Mdel 10. VCR that will play vides frame-by-frame 11. Televisin Prcedure: 1. Place the ring-stands n either side f the shake table. 2. Tape the 1/10 inch scale rulers t the yardsticks. See Figure 26 fr samples that can be cut-ut and used. 3. Place the yardstick just belw Flr 3 f the mdel. 4. One persn climbs up the ladder and prepares t vide tape the shake table (Figure 23). Be sure that bth 1/10 inch scales can be clearly read thrugh the camcrder. 5. The ther persn pulls the structure and releases (Figure 24). Figure 23: Persn n Ladder Figure 24: Pulling and Releasing Structure 13 Oregn State University

14 6. Recrd the mtin f the structure with the camcrder (Figure 25). Figure 25: Videtaping Damped Mtin 7. If the camcrder des nt recrd nt a VHS videtape, transfer the vide t a VHS tape. 8. View the vide frame-by-frame and recrd displacement values. 9. Determine V n and V n+1 frm recrded data. V Displacement, V V 1 V 2 Time, t 10. Cmpute δ = Ln (V n / V n+1 ). When damping is very small (as it shuld be in this case), use δ = ( 1 / m ) Ln (V n / V n+m ). 11. Cmpute damping rati, ξ = δ / 2π. Nte: Mst VCR s will stp playing frame-by-frame after a cuple f minutes. This makes it difficult t cllect data. Suggestin: Use a stpwatch with time displayed at 1/100 f a secnd in the vide. 14 Oregn State University

15 Figure 26: 1/10 inch Scales 15 Oregn State University

16 4.0 Earthquake Scale Determinatin Purpse: The purpse f this exercise is t determine what scale factr was used fr scaling each earthquake. Thery: Let the scale factr be S. When scaling an earthquake, acceleratin data is scaled at a 1:1 rati. Time is scaled at a 1: S rati. (See Figure 27) Equipment: 1. UCIST Shake table (Table and Universal Pwer Mdule) 2. Cmputer (with WinCn, MatLab, and Micrsft Excel) Prcedure: 1. Chse the earthquake t use. 2. Start WinCn, g t pen mdel, and select the earthquake s wcl file. (i.e., select Elcent.wcl) 3. Open a scpe fr Accel R. 4. Start the earthquake. 5. Save the plt as a MatLab file. (In the Scpe s screen, g t File, Save as, and select Save as an M-file.) 6. Cpy the Accel R data frm the M-file, save it as a text file, and paste it int an Excel file (r ther spreadsheet prgram). 7. Open the MatLab file cntaining the earthquake s riginal data. This shuld be stred n the UCIST Cmputer. 8. Cpy riginal earthquake data frm the M-file, save it as a text file, and paste it int the Excel file frm step Plt the riginal and the scaled earthquake acceleratin data versus time. The plts shuld appear similar. The acceleratin values shuld be f the same magnitude, but the duratin f the scaled earthquake shuld be shrter than that f the riginal earthquake. 10. If there is a perid f time at the beginning f the earthquake data where the acceleratin is essentially zer, exclude this data frm the analysis. 11. Find the duratin (frm the start f acceleratins t the end f acceleratins) fr each set f earthquake data (scaled and riginal). 12. Use the knwledge that time is scaled as a functin f S t back calculate the scale factr, S. Time factr = S. Therefre, S = (Time Factr) Reprt the scale factr as a 1: S rati. 16 Oregn State University

17 Figure 27: Scaling Infrmatin (Sabnis, 495) 17 Oregn State University

18 5.0 UCIST Shake Table Experiments The fllwing tw experiments are designed t cllect the necessary data fr cmparisn t SAP Shake Table Acceleratins Experiment Purpse: The purpse f this experiment is t determine the seismic respnse f the threedimensinal mdel when shaken by the scaled El Centr earthquake. Equipment: 1. UCIST Shake table (Table, Universal Pwer Mdule, and Cmputer) 2. 3D Mdel Prcedure: 1. Securely attach the 3D mdel t the UCIST Shake Table. 2. Start WinCn and pen El Centr earthquake wcl file. 3. Open Accel T, Flr 1, and Flr 2 scpes. 4. Cnnect accelermeters (ne n each flr f the 3D mdel and ne n the table) t the Universal Pwer Mdule (UPM). Nte: Accel T plts the accelermeter cnnected t S1 n the UPM, Flr 1 plts S2, and Flr 2 plts S3. 5. Run El Centr Earthquake (scaled). 6. Save each scpe as an M-File. 7. Run the earthquake enugh times t cllect at least 3 sets f acceleratin data fr each flr f the mdel (Table, Flr 1, Flr 2, and Flr 3). If yu nly have 3 accelermeters available, mve the accelermeters arund fr each test. Sample test series: Test Accel T (S1) Flr 1 (S2) Flr 2 (S3) 1 Table Flr 1 Flr 3 2 Table Flr 1 Flr 3 3 Table Flr 2 Flr 3 4 Flr 1 Flr 2 Flr 3 5 Table Flr 1 Flr 2 8. Cpy data frm M-Files int Micrsft Excel (r ther spreadsheet prgram). 9. Plt each graph t check cnsistency and t make cmparisns. 18 Oregn State University

19 5.2 Displacement Experiment Purpse: The purpse f this experiment is t determine the maximum displacements f the tp flr (Flr 3) relative t the bttm flr (Base) when running the scaled El Centr earthquake n the UCIST Shake Table. The data cllected in this experiment will be cmpared t SAP 2000 results. Equipment: 1. UCIST Shake table (Table, Universal Pwer Mdule, and Cmputer with WinCn and MatLab) 2. 3D Mdel 3. (2) Yardsticks 4. (2) 1/10 inch scale rulers 5. (2) Ring-stands 6. (4) Clamps (t clamp t ring-stand and hld yardsticks) 7. Masking tape 8. Ladder 9. Camcrder (Sny) 10. Spt light if rm lighting is nt sufficient 11. VCR that will play a vide frame-by-frame 12. TV t view vide Prcedure: 1. Securely attach the 3D mdel t the UCIST Shake Table. 2. Place the ring-stands n either side f the shake table. 3. Tape the 1/10 inch scale rulers t the yardsticks. See Figure 26 fr sample 1/10 in scales that can be cut-ut and used. 4. Place ne yardstick just belw the Shake Table base and ne just belw Flr 3 f the mdel. 5. One persn climbs up the ladder and prepares t vide tape the shake table. Be sure that bth 1/10 inch scales can be clearly read thrugh the camcrder. 6. The ther persn pens and runs the El Centr Earthquake wcl file, while the persn n the ladder recrds the mtins n the camcrder. 7. If the camcrder des nt recrd nt a VHS videtape, transfer the vide t a VHS tape. 8. View the vide frame-by-frame and recrd the maximum relative displacement between Flr 3 and the Base f the mdel. Nte: Mst VCR s will stp playing frame-by-frame after a cuple f minutes. This makes it difficult t cllect data. Suggestin: Use a stpwatch with time displayed at 1/100 f a secnd in the vide. 19 Oregn State University

20 6.0 SAP 2000 Mdel Purpse: The purpse f this exercise is t develp data frm a cmputer analysis (using structural analysis sftware), s these results can be cmpared t experimental results fund with the UCIST shake table. Equipment: 1. Cmputer 2. SAP 2000 Sftware r similar cmputer prgram 3. Printer t print results Prcedure: 1. Input gemetry and material prperties f 3D mdel. (See 3D Mdel Schematic and 3D Mdel Material Prperties fr input values.) 2. Input scaled El Centr earthquake using Time Histry analysis feature. 3. Run SAP 2000 mdel. 4. Display and print acceleratin as a functin f time fr each flr f the mdel. 5. Display and print displacement f the tp flr as a functin f time. Nte the value f the maximum displacement and at what time the maximum displacement ccurred. 6. Cmpare these results t thse fund with the UCIST Shake table (see Shake Table Experiment ). 20 Oregn State University