DESIGN EXAMPLES
By : Mohd Zamri Ramli
1. Linear-elastic analysis – to determine the seismic effects and the effects of the other actions considered – may be performed using 2 planar models where one is for main horizontal direction – Two types of linear elastic can be used: Method 1
Method 2
• Lateral force method of analysis • Modal response spectrum analysis
2. Non-linear analysis – an alternative to the linear method – should be properly substantiated with regard to seismic input, constitutive model used, method of interpreting results of analysis and the requirements to be met – Two types of non-linear analysis: • •
Non-linear static (push over) analysis Non-linear time history (dynamic) analysis
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1 A three-story concrete shear wall office building are determined using Eurocode 8 to design seismic forces. It is located in Penang Malaysia on rock with a shear wave velocity of 900 m/s. The story heights are 3.9 m for the first floor and 3.3 m for the
second and third floors. The story dead loads are 9786 kN, 8896 kN and 7562 kN from the bottom up. The plan dimensions are 55 m by 36 m. The walls in the direction under
consideration are 36 m long and are without opening. The shear walls do not carry vertical loads.
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1
36 m
7562 kN
A
8896 kN B
55 m
3.3 m
3.3 m 9786 kN
C
3.9 m
D
1
(a) Plan view
2
(b) Elevation view
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1
3.1.2 (1) Identification of ground types
3.2.2.2 Horizontal elastic response spectrum
For type 1, the parameters of ground type A recommended in MS1555
6
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1 4.3.3.2.2 Base shear force
T1 = 0.05 (10.5 m) ¾ = 0.29 sec.
(dual system - other structures) 7
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1 5.2.2.2 Behaviour factors for horizontal seismic actions
q = 3.0u/1 = 3.0 (1.2) = 3.6 T1 = 0.29 sec 3.2.2.5 Design spectrum for elastic analysis
NA Tab. 3.7 Constant value, C=2.4 NA Fig. A2 TR 2500 years, ag = 0.12g
Sd (T1) = 0.08
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1 7562 kN
8896 kN
3.3 m
3.3 m 9786 kN
Base Shear, Fb
Fb Sd T1 .m.
Correction factor (Eq. 4.5) λ = 0.85 (because T1 < 2TC, and > 2 storey)
3.9 m
m = 26,244 KN
Fb = 0.08 (26,244) (0.85) = 1,784.59 kN (taken into design)
6.2
Method 1 - Eurocode 8 Based Design (EBD) Example 1
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1
Vertical Distribution: Fi Fb (
z i mi ) z jmj
See Table 6.1
Overturning Moment: See Table 6.1
Mi Fi hi h j n
i j
Table 6.1 : Example 6.1 Level
zi
mi
zimi
(m)
(kN)
(kNm)
3
10.5
7,562
79,401
2
7.2
8,896
1
3.9
S
zimi / S zjmj
Fi
Vi
Mi
(kN)
(kN)
(kNm)
0.4372
780.20
780.20
2,574.66
64,051.2
0.3527
629.37
1,409.57
7,226.26
9,786
38,165.4
0.2101
375.02
1,784.59
14,186.16
26,244
181617.6
1.0000
1,784.59
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1
780.20 kN 10.5 m 629.37 kN 7.2 m
375.02 KN 3.9 m
Fb = 1784.59 kN
Figure 6.1 : Lateral force distribution based on EBD
6.1
Method 1 - Eurocode 8 Based Design (EBD) Example 1 Assume the buildings have brittle material of non-structural elements
dr 0.005h 2nd and 3rd Floor: dr 0.005(3300mm) = 16.5mm 1st Floor: dr 0.005(3900mm) = 19.5mm
6.2
Method 1 - Eurocode 8 Based Design (EBD) Example 2
Design Example for 12-Story (Frame-Shear Wall Building) •
The application of earthquake resistance design provisions of this Seismic Design Guidelines with respect to design loads and EC 2 relating to proportioning and detailing of members will be illustrated for representative elements of a 12 reinforced concrete story frame, located in Penang.
•
The typical framing plan and section of the structure considered are shown in Figure 6.3 and Figure 6.4, respectively. The columns and structural walls have constant cross sections throughout the height of the building. The floor beams and slabs also have the same dimensions at all floor levels
6.2
Method 1 - Eurocode 8 Based Design (EBD) Example 2 Other pertinent design data are follows: 1) Dimension : - Exterior columns : 560 x 560 mm, interior columns : 660 x 660 mm - Beam : 500 x 600 mm - Height = 4.9 + 11(3.6) = 44.5 m 2) Material properties: - Concrete fc’ = 27600 kN/m2 - Reinforcement fy = 413685 kN/m2 - E concrete - E steel
3) Loading for 2D frame in transverse direction - Dead Load (slab + beam + superimposed dead Load) is 55.95 kN/m - Live load (roof) is 7.58 kN/m - Live load (floor) is 28.44 kN/m - Total load per story: - Roof : 1276.86 kN - Each story: 1696.17 kN
6.2
Method 1 - Eurocode 8 Based Design (EBD) Example 2 12
A
11
C
9
[email protected]
3 x 6.7 = 20.1 m
B
10
8 7 6 5 4
D
3 2 1
2
3
4
5
6
7
8
1
4.9 m
7 x 7.9 = 55.3 m 3 x 6.7 = 20.1 m
Figure 6. 3: Typical Floor Framing Plan Figure 6. 4: Transverse Section 3/A-D
6.2 Method 1 - Eurocode 8 Based Design (EBD) Example 2 6.2. 1 Lateral Seismic Design Force
Base Shear, Fb
Fb Sd T1 .m.
6.2
Method 1 - Eurocode 8 Based Design (EBD) Example 2
Table 6. 3 : Design lateral force (Seismic load) in transversal direction 3/A-D Floor Level
Height m
Story Weight kN
zimi (Wxhx)
zimi / S zjmj (Cvx)
Fi (Fx) kN
Roof
44.50
1,276.86
56,820.27
0.12
119.33
11.00 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00
40.90 37.30 33.70 30.10 26.50 22.90 19.30 15.70 12.10 8.50 4.90
1,696.17 1,696.17 1,696.17 1,696.17 1,696.17 1,696.17 1,696.17 1,696.17 1,696.17 1,696.17 1,696.17
69,373.35 63,267.14 57,160.93 51,054.72 44,948.51 38,842.29 32,736.08 26,629.87 20,523.66 14,417.45 8,311.23
0.14 0.13 0.12 0.11 0.09 0.08 0.07 0.06 0.04 0.03 0.02
145.70 132.87 120.05 107.22 94.40 81.58 68.75 55.93 43.10 30.28 17.46
19,934.73
484,085.49
1.00
1,016.67
Total
6.2
Method 1 - Eurocode 8 Based Design (EBD) Example 2 119.33
145.70
132.87
120.05
107.22
94.40
81.58
68.75
55.93
43.10
30.28
17.46
