Seismic Design Principles for RC Structures

Transcription

1 CE 490 Int. to Earthquake Engineering Seismic Design Principles for RC Structures H. Sucuoğlu

2 Introduction Seismic design of structural systems is essentially based on an inherent ductile response under strong ground excitation. Ductility can be defined as the capacity of undergoing large plastic deformations without reduction in strength, both at the material, component and system levels. Although ductility is not expressed explicitly in the analysis procedures of seismic codes, reduction of elastic earthquake forces relies on the premise of a ductile seismic response H. Sucuoğlu 2

3 Ductility in RC systems is considered in the global level in the Turkish Earthquake Code. It is described for three system categories with the related seismic response characteristics, expressed with the associated R factors. a) RC Systems with enhanced ductility (R = 6-8 in TEC 2008) b) RC Systems with ordinary ductility (R = 4 in TEC 2008) c) RC Systems with mixed ductility (R 5-7 in TEC 2008) H. Sucuoğlu 3

4 Systems with ordinary and enhanced ductility are essentially frame or frame-wall systems where both the frames and the walls have either ordinary or enhanced ductility, respectively. Systems with enhanced ductility satisfy strong column-weak beam condition at most of the joints (70% of story shear) Systems with ordinary ductility do not satisfy strong columnweak beam condition at most of the joints (less than 70% of story shear) Systems with mixed ductility are frame-wall systems composed of frames with ordinary ductility and walls with enhanced ductility (special rules for wall design). Enhanced or mixed ductility definitions should be satisfied in both earthquake directions H. Sucuoğlu 4

5 Capacity Design Special detailing rules are applied for the ordinary ductility level, leading to modest reductions in elastic forces (R = 4) Special «additional» detailing rules are applied for the enhanced ductility level, leading to larger reductions in elastic forces (R = 6-8). Enhanced ductility level in RC systems composed of ductile beams, columns and shear walls and strong connections, is provided by employing the Capacity Design Principles H. Sucuoğlu 5

6 Capacity design has two major implications, one at the member level, and the other at the system level. Member level: Flexural failure mode is ensured by suppressing shear failure (capacity shear principle in beams, columns, walls and joints). System level: The spreading of plastic regions that undergo flexural yielding follows a hierarchy for obtaining a more ductile system response (strong column-weak beam principle at the beam-column joints) H. Sucuoğlu 6

7 Ductility in Concrete Strength and deformation capacities of concrete fibers in the core region of columns and compression region of beams increase with the amount of lateral confinement reinforcement H. Sucuoğlu 7

8 Seismic Design of Ductile Beams Limitations on Tension Reinforcement: The minimum tensile reinforcement ratio controls cracking of concrete in service conditions whereas the maximum ratio controls ductility of the section H. Sucuoğlu 8

9 Minimum Compression Reinforcement The ratio of compression reinforcement to tension reinforcement at the support regions of beams should be at least 0.5 in seismic zones 1 and 2, and 0.3 in seismic zones 3 and 4. Compression reinforcement increases the ductility of a beam cross section significantly H. Sucuoğlu 9

10 Shear Design of Beams where H. Sucuoğlu 10

11 Ductile Beam Detailing 50 mm s k h k Beam confined end region = 2 h k Beam middle region (minimum lateral reinf. w.r.to TS-500) s k h k / 4 Beam confined end region = 2 h k s k 8 ( = smallest long. reinf. diameter) s k 150 mm H. Sucuoğlu 11

12 Seismic Design of Ductile Columns Limitations on Axial Stress: The moment capacity and stiffness increases with axial load up to N/No=0.4, but ductility decreases as shown below. Therefore the level of axial load or axial stress has to be limited such that ductile section response is ensured H. Sucuoğlu 12

13 Limitation on Longitudinal Reinforcement A ductile flexural column response requires that the minimum and maximum longitudinal reinforcement ratios are 1% and 4%, respectively H. Sucuoğlu 13

14 Minimum Lateral Reinforcement Moment-curvature relationships of two typical rectangular column sections are shown below. Two columns are identical except the amount of lateral reinforcement. The lower curve is for a column with inadequate lateral reinforcement. The upper curve is for a column with minimum lateral reinforcement according to TEC Even minimum lateral reinforcement improves the curvature ductility of the column cross section enormously H. Sucuoğlu 14

15 Strong Column Weak Beam Principle Flexural plastic hinges inevitably form at the ends of frame members under design ground motions which are reduced with R 1. A plastic hinge formed on a beam is less critical than a plastic hinge on a column or shear wall, because vertical members may loose their stability under gravity loads when plastic hinges form. Accordingly, plastic hinge hierarchy requires formation of plastic hinges first on beams, then at the base of first story columns. A plastic hinging hierarchy can be imposed in design by proportioning the flexural capacities of beam and column ends at a joint H. Sucuoğlu 15

16 Strong Column Weak Beam Strong column-weak beam principle leads to a ductile collapse strategy under increasing lateral earthquake forces H. Sucuoğlu 16

17 Let s consider a three story, single bay frame which obeys strong column-weak beam design. It is loaded with increasing lateral forces until collapse. This type of inelastic analysis is called the pushover analysis in earthquake engineering H. Sucuoğlu 17

18 If we plot the base shear force versus the roof displacement, we obtain the capacity curve in (b). The progress of plastic hinges at different stages of loading are marked on both figures. It can be observed that the frame exhibits significant ductility before collapse under lateral forces. Formation of plastic hinging at the column (or wall) bases is inevitable at the later stages of loading since they become cantilever columns after all the beams spanning to the columns yield (c) H. Sucuoğlu 18

19 If columns are weaker than beams, then a soft story may develop. Plastic hinges form at the first story columns first where the moments are maximum (a). When plastic hinges develop both at the bottom and top ends of the first story columns, a soft story forms since the instantaneous lateral stiffness becomes very low, even zero when there is no strain hardening (b). Then lateral deformations increase quickly under increasing lateral loads, and the frame looses its stability under gravity loads (collapse) H. Sucuoğlu 19

20 Shear Design of Columns Let s consider a column which reaches its flexural capacity (with strain hardening) at both top and bottom ends under double flexure (Fig. a). This eq. is valid when columns are weaker than beams. However, columns are stronger than beams. Hence beam ends yield before column ends around a connection (Fig. b) The sum of beam end plastic moments are distributed to columns in proportpion to their moments from elastic analysis H. Sucuoğlu 20

21 Short Column Effect H. Sucuoğlu 21

22 Beam-Column Joints Confined joint conditions b w1 and b w2 3/4 b b w3 and b w4 3/4 h b w2 b w3 V a A s1 1.25A s1 f C yk 2 C 1.25A s2 f 1 yk A s2 V ü V kol = min (V a, V ü ) b w1 b 1 b b 2 h b w4 V = 1.25 f ( A A ) V e yk s1 s2 kol Confined joints: V e 0.60 b j h f cd Unconfined joints: V e 0.45 b j h f cd EQ direction If b w1 and b w2 b: b j = b If b w1 and b w2 < b: b j = 2 min (b 1, b 2 ) b j (b w1 + h) (for b w1 < b w2 ) H. Sucuoğlu 22

23 Seismic Design of Ductile Walls Design EQ Moment Design EQ Moment H w H w H cr Analysis EQ Moment H cr Analysis EQ Moment Wall System Frame-Wall System H H cr w cr H /6 w Constant moment distribution along H cr is due to tension shift H. Sucuoğlu 23

24 Capacity Design Procedure 1. Analyze the system under, assuming flexural behavior. 2. Design the beams for flexure under the analysis moments M d and design for shear under beam capacity shear V e. 3. Calculate column moments from strong column-weak beam inequality. Perform flexural design under these moments and shear design under column capacity shear. 4. Design shear walls for flexure under design moment distribution with tension shift, and design for shear under wall capacity shear V e. 5. Design the capacity of joints for joint capacity shear H. Sucuoğlu 24