Question

The walls are 10 in. thick with an allowable compressive stress of 300 psi (pounds per square inch). A 3 ft wide vertical strip of wall currently supports both a roof load of 1.5 kips and 11 floor loads of 2.0 kips per floor. Each story is 12 ft tall from floor to floor. The density of the masonry wall is 130 pcf (pounds per cubic foot).

What is the maximum total force support by a 3ft wall segment for the existing 12 story building (include self weight of the wall)? What is the stress in the wall for this load?

How many additional floors can be added to the existing building? Assume that the existing roof will be demolished and replaced with a new floor. The final building construction will only have one roof.

Answer 1

Ans a) Given,

Load of roof = 1.5 kips

Load of floors = 2 kip/floor x 11 floor = 22 kips

Self weight of wall = Volume of wall x Unit weight of wall x number of walls

Volume of wall = 12 ft x 3 ft x 10/12 ft = 30 ft³

Unit weight of wall = 130 pcf (given)

=> Self weight of wall = 130 lb/ft³ x 30 ft³ x 11 = 42900 lbs or 42.9 kips

Total load supported by wall = 1.5 kips + 22 kips + 42.9 kips = 66.4 kips

Now, Stress = Load / Area

Cross sectional area of wall = (3 x 12) in x 10 in = 360 in²  

=> Stress = 66400 lb / 360 in² = 184.44 psi

Ans b) Now, suppose there are total 'n' floors ,then

  Load of floors = 2 kip/floor x n floor = 2 n kips

Roof load = 1.5 kip

Self weight of of wall = 3.9 kips x n walls = 3.9 n kips {from part (a)}

Total load = 2 n + 1.5 + 3.9 n = = (5.9 n+ 1.5) kips

Allowable stress = 300 psi

Also, stress = load / area

=> 300 lb/in² = (5.9 n + 1.5) kip x 1000 lb/kip  / 360 in²

=> 108000 = (5.9 n + 1.5) x 1000

=> 5.9 n + 1.5 = 108

=> n = 18.05 18 floors

Hence, the walls can support total 18 floors

Additional floor that can be constructed = total floors - existing floors = 18 - 11 = 7 floors