Question

Suppose I have a rectangular building with five floors, each 10 feet high, 50 feet long in the x direction and 30 feet wide in the y direction. Suppose x is the direction perpendicular to the wind and y is the direction parallel to the wind. Suppose coordinate (0,0) is at the lower left side of the building facing the wind. If I know the wind pressures at each floor level, what would be the coordinates of the resultant wind pressures at each floor level relative to the (0,0) coordinate. No need to calculate wind pressures. Suppose wind pressures are 100 psf at floor 1, 102 psf at floor 2, 103 psf at floor 3, 104 psf at floor 4 and 105 psf at floor 5. The wind blows from north to south.

Answer 1

Given dimension of building perpendicular to wind direction is 50 ft

Since the pressure is uniform along this dimension, loads at all levels will act at x coordinate of 50/2=25 ft

Each floor height is 10 ft

Pressure at fift floor=105 psf

Tributtary height=10/2=5 ft

Force at fifth floor=105*5*50/1000=26.25 kips

Coordinate=(25,15,50)

Pressure at fourth floor=104 psf

Tributtary height=10 ft

Force at fourth floor=104*10*5/1000=52 kips

Coordinate=(25,15,40)

Pressure at third floor=103 psf

Tributtary height=10 ft

Force at third floor=103*50*10/1000=51.5 kips

Coordinate=(25,15,30)

Pressure at second floor=102 psf

Tributtary height=10 ft

Force at second floor=102*50*10/1000=51 kips

Coordinate=(25,15,20)

Pressure at first floor=100 psf

Tributtary heigjt=10 ft

Force at first floor=100*50*10/1000=50 kips

Coordinate=(25,15,10)

Total force=26.25+52+51.5+51+50=230.75 kips

Z coordinate of resultant force=(26.25*50+52*40+51.5*30+51*20+50*10)/230.75=27.98 ft

Coorof resultant force=(25,15,27.98)