Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_193

⚡ Mecademy AIENG정역학 · ch5  Problem Statement As part of a preliminary design study, the effects of wind loads on a 900-ft building are investigated. For the parabolic distribution of wind pressure shown in the figure, compute the force and moment reactions at the base A of the building due to the wind load. The depth of the building (perpendicular to the paper) is 200 ft. Problem 5/193 (a) Resultant horizontal force reaction at the base A 1. Formula: The total wind force is the integral of the pressure over the surface area of the building. The load per unit height is , where is the depth. 2. Substitution: First, find the constant in the pressure distribution . Given at : Now substitute , , and : 3. Calculation: Perform the integration: Calculate 4. Result: Fp(x) w(x)=p(x)⋅DD R = A F= w (x)dx= ∫ 0 H p(x) D dx ∫ 0 H kp(x)=k x p= 12 lb/ft 2 x=900 ft 12=k = 90030k⟹k= = 30 12 0.4 lb/ft 2.5 p(x)=0.4 xD=200 ftH=900 ft R = A (0.4 )(200)dx= ∫ 0 900 x 80 x dx ∫ 0 900 1/2 R = A 80 = [ 3/2 x 3/2 ] 0 900 80⋅ 900 3 2 [ 3/2 ] 900= 3/2 ( )= 900 3 30= 3 27,000 R = A (27,000)= 3 160 160×9,000=1,440,000 lb R = A 1.44×10 lb 6 ● Final Conclusion: The horizontal force reaction at the base of the building is (or ). (b) Bending moment reaction at the base A 1. Formula: The total moment about the base is the integral of the moment arm times the differential force . 2. Substitution: Using and : 3. Calculation: Perform the integration: Calculate 4. Result: ● Final Conclusion: The bending moment react