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## Design of Unreinforced Masonry Wall## General:Unreinforced masonry walls are often
used as load bearing or non-loading interior wall in one
story building. Although it is called “unreinforced”, the
masonry wall still needs to be reinforced with joint
reinforcements. In
addition, ordinary and detailed plan masonry walls are
allowed as shear walls in seismic design category A & B. But
it still needs to meet code required minimum reinforcement
requirements. By
definition of ACI 530 Section 1.6, the tensile strength of
masonry is considered, but the strength of reinforcing steel
is neglected. ## Load on masonry walls:
- Vertical dead load, live load, snow load, etc.
- Lateral load from wind, seismic, earth pressure etc.
## Stresses in concrete masonry wall:- Compressive stress from vertical load
- Compressive stress from flexural moment due to lateral load.
- Tensile stress from flexural moment due to lateral load, eccentric moment, etc.
## Design requirements:When the wall, pilaster, and column is subjected to axial compression and flexure. - The maximum compression stress shall satisfy the following equation
f Where, f For member with h/r £ 99: F For member with h/r > 99: F Where h is effective height of wall, column or pilaster, r is radius of gyration, fm’ is compressive strength of masonry Allowable compressive stress from flexure: Fb = (1/3)
f - The maximum axial force P shall satisfy the following equation
P£ (1/4)
P Where Pe is calculated as P Where E - The tensile stress due to flexure shall not exceed the value listed in ACI 530 Table 2.2.3.2. as shown below:
Allowable flexural tension stress for hollow core concrete masonry unit, psi.
Roof dead load: 20 psf
Roof live load: 20 psf
Tributary width: 30 ft
Height of wall: 12 ft
Normal width of wall: 8 in
Assume minimum eccentricity:
0.8 in
Seismic load from ASCE 7: 4
psf
Axial load per foot width of
wall from roof, P = (20 psf+20 psf)*30 psf = 1200 lb/ft
Eccentricity: e = 0.8 in
Eccentric moment: M
Seismic moment: M
Moment per foot width of
wall, M = (80 + 90) lb-ft/ft = 170 lb-ft/ft
Width of wall: 7.625 in
Cross section area: A = 42.8
in
Moment of inertia: I = 330.9
in
Section modulus: S = 86.8 in
Radius of gyration: r = 2.78
in
Check flexural tensile
stress: f
Less than allowable tensile
stress 25 psi for ungrouted hollow unit O.K.
Check compressive stress:
Weight of wall at mid-height:
W = 55 psf * 6 ft = 330 lb/ft
Axial compressive stress: f
Slenderness ratio: h/r =
12*12/2.78 = 51.7 <
99
Use 1900 psi concrete masonry
units with type S mortar,
Compressive strength of
concrete masonry, f
F
Allowable flexural strength:
Fb = (1/3)
f Combined stress equation:
f Check axial force:
Elastic modulus, Em = 900 fm’ = 1.35x10
P
(1/4) P |