A three story police station is shown in the building elevat

A three story police station is shown in the building elevation below. The lateral frame is constructed using a steel eccentrically braced frame. Seismic Weights and ground accelerations are: enel . W roof 1000 kips W 3rd 2850 kips 2nd = 3000 kips · SDs 0.58 SD10.62 (S1 is less than 0.6g) Determine the following using ASCE 7-10: o7 Base shear of the building Vertical distribution of forces. lo a. b. 15\' 16 2 18\' 1

Solution

Solution:-

Base shear (V_B) = A_h*W

A_h = Z/2 * I/R * S_a/g

A_h = 0.24/2 * 1.5/5 * 2.5

A_h = 0.09

Where

Time period(T ) = 0.085* (h)^0.75

Height of building (h) = 14.935 meter

T = 0.085 * (14.935)^0.75

T = 0.645 second

For this time period

S_a/g = 2.5

Weight of building (W) = 3000 + 2850 + 1000 = 6850 kips

V_B = A_h * W

V_B = 0.09 * 6850

Base shear (V_B ) = 616.5 kips   Answer

Vertical Distribution of base shear

Q₂ = V_B * W₂ * (h₂)²/(W₂h₂² + W₃h₃² + W_Rh_R²)

Q₂ = 616.5 *3000 * 18²/(6.6676 *10⁶)

Q₂ = 90 kips Answer

Q₃ = 616.5 * 2850 *34²/(6.6676 * 10⁶)

Q₃ = 304.62 kips     Answer

Q_R = 616.5 * 1000 * 49²/(6.6667 * 10⁶)

Q_R = 222 kips   Answer