Lateral Load example.pdf

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By : By :

Mohd Zamri Ramli Mohd Zamri Ramli

DESIGN EXAMPLES

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1. Linear-elastic analysis

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to determine the seismic effects and the effects

of the other actions considered

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may be performed using 2 planar models where

one is for main horizontal direction

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Two types of linear elastic can be used:

• Lateral force method of analysis

• Modal response spectrum analysis

Method 1

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2. Non-linear analysis

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an alternative to the linear method

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should be properly substantiated with regard to

seismic input, constitutive model used, method

of interpreting results of analysis and the

requirements to be met

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Two types of non-linear analysis:

• Non-linear static (push over) analysis

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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

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36 m 55 m 1 2 A B C D 3.3 m 3.3 m 3.9 m 9786 kN 8896 kN 7562 kN

(a) Plan view (b) Elevation view

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6

3.2.2.2 Horizontal elastic response spectrum 3.1.2 (1) Identification of ground types

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4.3.3.2.2 Base shear force

(d u a l s y s t e m - o t h e r s t r u c t u r e s )

T₁ = 0.05 (10.5 m) ¾

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T₁ = 0.29 sec

3.2.2.5 Design spectrum for elastic analysis

5.2.2.2 Behaviour factors for horizontal seismic actions q = 3.0 u/1= 3.0 (1.2) = 3.6 NA Tab. 3.7 Constant value, C=2.4 NA Fig. A2 TR 2500 years, a_g = 0.12g S_d (T₁) = 0.08

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Base Shear, F_b

 

. . 1 m T S F d b 

F_b= 0.08 (26,244) (0.85)

= 1,784.59 kN (taken into design)

m = 26,244 KN

λ = 0.85 (because T₁ < 2T_C, and > 2 storey)

Correction factor (Eq. 4.5) 3.3 m 3.3 m 3.9 m 9786 kN 8896 kN 7562 kN

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Level z_i m_i z_im_i z_im_i / z_jm_j F_i V_i M_i (m) (kN) (kNm) (kN) (kN) (kNm) 3 10.5 7,562 79,401 0.4372 780.20 780.20 2,574.66 2 7.2 8,896 64,051.2 0.3527 629.37 1,409.57 7,226.26 1 3.9 9,786 38,165.4 0.2101 375.02 1,784.59 14,186.16 S 26,244 181617.6 1.0000 1,784.59 Vertical Distribution: See Table 6.1 Overturning Moment: See Table 6.1 ) ( j j i i b m z m z F Fi  





    n j i j i i h h F Mi Table 6.1 : Example 6.1

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Fb = 1784.59 kN 375.02 KN 629.37 kN 780.20 kN 7.2 m 3.9 m 10.5 m

Figure 6.1 : Lateral force distribution based on EBD

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Assume the buildings have brittle material of non-structural elements d_r  0.005h 2nd_{and 3}rd_Floor: d_r  0.005(3300mm) = 16.5mm 1st_Floor: d_r  _{0.005(3900mm)} = 19.5mm

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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

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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

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A B C D 1 2 3 4 5 6 7 8 7 x 7.9 = 55.3 m 3 x 6 . 7 = 2 0 .1 m

Figure 6. 3: Typical Floor Framing Plan

1 2 3 4 5 6 7 8 9 10 11 12 3 x 6.7 = 20.1 m

Figure 6. 4: Transverse Section 3/A-D

4.9 m 1 1 @ 3 . 6 m

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6.2. 1 Lateral Seismic Design Force

Base Shear, F_b

 

T ₁ .m. S F d b 

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Floor Level Height m Story Weight kN z_im_i (W_xh_x) z_im_i / z_jm_j (C_vx) F_i (F_x) kN Roof 44.50 1,276.86 56,820.27 0.12 119.33 11.00 40.90 1,696.17 69,373.35 0.14 145.70 10.00 37.30 1,696.17 63,267.14 0.13 132.87 9.00 33.70 1,696.17 57,160.93 0.12 120.05 8.00 30.10 1,696.17 51,054.72 0.11 107.22 7.00 26.50 1,696.17 44,948.51 0.09 94.40 6.00 22.90 1,696.17 38,842.29 0.08 81.58 5.00 19.30 1,696.17 32,736.08 0.07 68.75 4.00 15.70 1,696.17 26,629.87 0.06 55.93 3.00 12.10 1,696.17 20,523.66 0.04 43.10 2.00 8.50 1,696.17 14,417.45 0.03 30.28 1.00 4.90 1,696.17 8,311.23 0.02 17.46 Total 19,934.73 484,085.49 1.00 1,016.67

Table 6. 3 : Design lateral force (Seismic load) in transversal direction 3/A-D

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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