FIAT LUX UNIVERSITY OF LIVERPOOL School of Engineering Department of Civil Engineering and Industrial Design CIVE342: Earthquake Engineering UNIVERSITY OF LIVERPOOL A three-storey residential (ordinary) building is shown in Figure 1, where the value next to each column indicates the corresponding lateral stiffness. The mass of each whole floor is 2000 tonnes. The building is situated in a region with a reference PGA of 25%g (TNCR = 475 years) and where seismic hazard is dominated by events with a surface wave magnitude less than Ms 5.5. The shear wave velocity of the site is estimated to be 510m/s. The sample structure is a shear-type building. Assume a damping ratio of 5% and a behaviour factor of 3.0. Determine: 3m 800kN/mm 600kN/mm 3m 700kN/mm 500kN/mm 4m 600kN/mm 400kN/mm TI Figure 1 - Shear-type multi-storey building (bay width 4.5m). Number and values of frequencies of vibration; - Modes of vibration and their shape; - Participating masses for modes of vibration. Using the equivalent static approach and the seismic input provided above, determine: - Seismic horizontal base shear; Seismic horizontal forces at each storey; Bending moment and shear distributions in beams and columns Inter-storey drifts at each storey. 2 Appendix. Excerpts from EN 1998-1:2004 3.2.2.2 Horizontal elastic response spectrum UNIVERSITY OF LIVERPOOL T 0≤T≤TB: Se(T) = ag · S + (n.2.5-1) (3.2) TB TB≤T≤Tc : Se(T)=αg·S⋅n·2.5 (3.3) Tc≤T≤TD: Se(T) =ag ·S.n.2.5 2.5√ (3.4) Tɲ≤T≤4s: Se(T) = ag · S · n ⋅ 2.5| TCTD (3.5) T2 n=10/(5+)≥0.55 (3.6) (= viscous damping ratio in percent) 3.2.2.5 Design spectrum for elastic analysis (For 5% damping) 0≤T≤TB: Sɖ(T) = ag · S 2 T 2.5 + (3.13) TB q TBST≤TC: Sa(T) = a 2.5 (3.14) q 2.5 TC ·S. Tc≤T≤Tp: Sd(T) = · q T (3.15) ≥ẞ-ag S 2.5 TcTo TD≤T: Sα(T) = 9T2 (3.16) ≥ẞ.ag 3 UNIVERSITY OF LIVERPOOL Table 3.1 Ground types Ground type Description of stratigraphic profile Parameters Vs,30 (m/s) NSPT Cu (kPa) (blows/30cm) A B Rock or other rock-like geological formation, including at most 5 m of weaker material at the surface. Deposits of very dense sand, gravel, or very stiff clay, at least several tens of metres in thickness, > 800 360-800 > 50 > 250 characterised by a gradual increase of mechanical properties with depth. C Deep deposits of dense or medium dense sand, gravel or stiff clay with thickness from several tens to many hundreds of metres. 180-360 15-50 70-250 Ꭰ Deposits of loose-to-medium cohesionless soil (with or without some soft cohesive layers), or of < 180 < 15 < 70 predominantly soft-to-firm cohesive soil. E S₁ A soil profile consisting of a surface alluvium layer with vs values of type C or D and thickness varying between about 5 m and 20 m, underlain by stiffer material with vs > 800 m/s. Deposits consisting, or containing a layer at least 10 m thick, of soft clays/silts with a high plasticity index (PI > 40) and high water content S2 Deposits of liquefiable soils, of sensitive clays, or any other soil profile not included in types A – E or Si < 100 (indicative) 10-20 Table 3.2 Values of the parameters describing the recommended Type 1 elastic response spectra Ground type S TB (S) Tc (s) TD (S) A 1.0 0.15 0.4 2.0 B 1.2 0.15 0.5 2.0 C 1.15 0.20 0.6 2.0 D 1.35 0.20 0.8 2.0 E 1.4 0.15 0.5 2.0 Table 3.3 Values of the parameters describing the recommended Type 2 elastic response spectra Ground type S TB (S) Tc (s) TD (s) A 1.0 0.05 0.25 1.2 B 1.35 0.05 0.25 1.2 C 1.5 0.10 0.25 1.2 D 1.8 0.10 0.30 1.2 E 1.6 0.05 0.25 1.2