Question 6.9: Determine the design seismic forces on the residential build......

• Step 1: Determine the seismic ground motion values from Flowchart 6.2.

Using the USGS Ground Motion Parameter Calculator, S_S = 0.27 and S_1 = 0.06 .

Using Tables 11.4-1 and 11.4-2, the soil-modified accelerations are S_{MS} = 0.44 and S_{M1} = 0.15 .

Design accelerations: S_{D S}={\frac{2}{3}}\times0.44=0.29 and S_{D1}={\frac{2}{3}}\times0.15=0.10

• Step 2: Determine the SDC from Flowchart 6.4.

From IBC Table 1604.5, the Occupancy Category is II.

From Table 11.6-1 with 0.167 < S_{DS} < 0.33 and Occupancy II, the SDC is B.

From Table 11.6-2 with 0.067 < S_{D1} < 0.133 and Occupancy Category II, the SDC is B.

Therefore, the SDC is B for this building.

• Step 3: Determine the response modification coefficients R in accordance with 12.2.3.1 for vertical combinations of structural systems.

The vertical combination of structural systems in this building is a flexible wood frame upper portion above a rigid concrete lower portion.

Thus, a two-stage equivalent lateral force procedure is permitted to be used provided the design of the structure complies with the four criteria listed in 12.2.3.1:

a. The stiffness of lower portion must be at least 10 times the stiffness of the upper portion.

It can be shown that the stiffness of the lower portion of this structure is more than 10 times that of the upper portion. O.K.

b. The period of the entire structure shall not be greater than 1.1 times the period of the upper portion considered as a separate structure fixed at the base.

Determine the period of the upper portion by Eq. 12.8-7 using the approximate period coefficients in Table 12.8-2 for “all other structural systems”:

T_{a}=C_{t}h_{n}^{X}=0.02(32)^{0.75}=0.27 sec

Determine the period of the lower portion in the N-S direction by Eqs. 12.8-9 and 12.8-10 for concrete shear wall structures:

T_{a}=\frac{0.0019}{\sqrt{C_{W}}}\,h_{n} \,

C_{W}={\frac{100}{A_{B}}}\sum_{i=1}^{X}\left\lgroup{\frac{h_{n}}{h_{i}}}\right\rgroup^{2}\frac{A_i}{\left[1+0.83\left\lgroup\frac{h_{i}}{D_{i}}\right\rgroup^{2}\right]}

where

A_B = area of base of structure = 118×80 = 9,440 sq ft

h_n = height of lower portion of building = 10 ft

h_i = height of shear wall i = 10 ft

A_i = area of shear wall i={\frac{10}{12}}\times30=\ 25 sq ft

D_i = length of shear wall i = 30 ft

Thus,

C_{W}=\frac{4\times100}{9,440}\frac{25}{\left[1+0.83\left\lgroup\frac{10}{30}\right\rgroup^{2}\right]}=0.97 \,

T_{a}={\frac{0.0019}{\sqrt{0.97}}}\times10=0.02 sec

The period of the lower portion in the E-W direction is equal to 0.01 sec.

The period of the combined structure is approximately 0.28 sec.^{18}

0.28 sec < 1.1× 0.27 = 0.30 sec O.K.

c. The flexible upper portion shall be designed as a separate structure using the appropriate values of R and ρ .

From Table 12.2-1 for a bearing wall system with light-framed walls with wood structural panels rated for shear resistance (system A13), R = 6.5 with no height limitation for SDC B.

For SDC B, ρ =1.0 (12.3.4.1).

d. The rigid lower portion shall be designed as a separate structure using the appropriate values of R and ρ . Amplified reactions from the upper portion are applied to the lower portion where the amplification factor is equal to the ratio of the R/ρ of the upper portion divided by R/ρ of the lower portion and must be greater than or equal to one.

From Table 12.2-1 for a building frame system with ordinary reinforced concrete shear walls (system B6), R = 5 with no height limitation for SDC B.

For SDC B, ρ =1.0 (12.3.4.1).

Amplification factor = (6.5/1)/(5/1) = 1.3.

Therefore, a two-stage equivalent lateral force procedure is permitted to be used.

• Step 4: Determine the design seismic forces on the upper and lower portions of the structure using the equivalent lateral force procedure.

1. Use Flowchart 6.8 to determine the lateral seismic forces on the flexible upper portion of the structure.

a. The design accelerations and the SDC have been determined in Steps 1 and 2 above, respectively.

b. Determine the response modification coefficient R from Table 12.2-1.

The response modification coefficient was determined in Step 3 as 6.5.

c. Determine the importance factor I from Table 11.5-1.

For Occupancy Category II, I = 1.0.

d. Determine the period of the structure T.

It was determined in Step 3 that the approximate period of the structure T_a = 0.27 sec.

e. Determine long-period transition period T_L from Figure 22-15.

For Philadelphia, PA, T_L = 6 sec > T_a = 0.27 sec.

f. Determine seismic response coefficient C_s .

The seismic response coefficient C_s is determined by Eq. 12.8-3:

C_{S}={\frac{S_{D1}}{T(R/I)}}={\frac{0.10}{0.27(6.5/1.0)}}=0.06

The value of C_s need not exceed that from Eq. 12.8-2:

C_{S}={\frac{S_{D S}}{R/I}}={\frac{0.29}{6.5/1.0}}=0.05

Also, C_s must not be less than the larger of 0.044S_{DS} I = 0.013 (governs) and 0.01 (Eq. 12.8-5).

Thus, the value of C_s from Eq. 12.8-2 governs.

g. Determine effective seismic weight W in accordance with 12.7.2.

The effective weights at each floor level are given in Table 6.19. The total

weight W is the summation of the effective dead loads at each level.

h. Determine seismic base shear V.

Seismic base shear is determined by Eq. 12.8-1:

V=C_{s}W=0.05\times761=38 kips

i. Determine exponent related to structure period k .

Since T = 0.27 sec < 0.5 sec, k = 1.0.

j. Determine lateral seismic force F_x at each level x .

F_x is determined by Eqs. 12.8-11 and 12.8-12. A summary of the lateral forces F_x and the story shears V_x is given in Table 6.19.

2. Use Flowchart 6.8 to determine the lateral seismic forces on the rigid lower portion of the structure in the N-S direction.

a. The design accelerations and the SDC have been determined in Steps 1 and 2 above, respectively.

b. Determine the response modification coefficient R from Table 12.2-1.

It was determined in Step 3 that the response modification coefficient R = 5.

c. Determine the importance factor I from Table 11.5-1.

For Occupancy Category II, I = 1.0.

d. Determine the period of the structure T.

It was determined in Step 3 that the approximate period of the structure  T_a = 0.02 sec in the N-S direction.

e. Determine long-period transition period T_L from Figure 22-15.

For Philadelphia, PA, T_L = 6 sec > T_a = 0.02 sec.

f. Determine seismic response coefficient C_s .

The seismic response coefficient C_s is determined by Eq. 12.8-3:

C_{s}={\frac{S_{D1}}{T(R/I)}}={\frac{0.10}{0.02(5/1.0)}}=1.0

The value of C_s need not exceed that from Eq. 12.8-2:

C_{s}={\frac{S_{D S}}{R/I}}={\frac{0.29}{5/1.0}}=0.06

Also, C_s must not be less than the larger of 0.044S_{DS} I = 0.013 (governs) and 0.01 (Eq. 12.8-5).

Thus, the value of C_s from Eq. 12.8-2 governs.

g. Determine effective seismic weight W in accordance with 12.7.2.

The effective weight W is equal to 1,458 kips for the lower portion.

h. Determine seismic base shear V.

Seismic base shear is determined by Eq. 12.8-1:

V=C_{s}W=0.06\times1,458=88 kips

i. Determine total lateral seismic forces on the lower portion.

For the one-story lower portion, the total seismic force is equal to the lateral force due to the base shear of the lower portion plus the amplified seismic force from the upper portion:

V_{t o t a l}=88+(1.3\times38)=137 kips

Since the base shear is independent of the period, the total seismic force in the E-W direction is also equal to 137 kips.

The distribution of the lateral seismic forces in the upper and lower parts of the structure is shown in Figure 6.11.

^{18} The period of the combined structure was obtained from a commercial computer program.