CE-REF.COM
Design of Unreinforced Masonry WallGeneral: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:
Stresses in concrete masonry wall:
Design requirements:When the wall, pilaster, and column is subjected to axial compression and flexure.
fa/Fa + fb/Fb £ 1 (ACI 530 Eq. 2-10) Where, fa is compressive stress from axial load, fb is compressive stress from flexure; Fa and Fb, Fv are allowable compressive stress and tensile stress calculation from equation below: For member with h/r £ 99: Fa = (1/4) fm’ {1-[h/(140r)]2} (ACI 530 2-12) For member with h/r > 99: Fa = (1/4) fm’ (70r/h)2 (ACI 530 2-13) 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) fm’ (ACI 530 2-14)
P£ (1/4) Pe (ACI 530 Eq. 2-11) Where Pe is calculated as Pe = [p2EmI/h2][1-0.577*e/r)2 (ACI 530 2-15) Where Em is
elastic modulus of masonry, I is moment of inertia, h is the
height of wall, column or plaster, e is eccentricity of
axial load, r is radius of gyration.
Allowable flexural tension stress for hollow core concrete masonry unit, psi.
Design data:
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
Requirement:
Check if an 8 in unreinforced masonry wall is adequate
Solution:
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: Mc =
1200*0.8/12 = 80 lb/ft
Seismic moment: Ms =
5 psf * (12ft)2/8 = 90 lb-ft/ft
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
in2.
Moment of inertia: I = 330.9
in4.
Section modulus: S = 86.8 in3.
Radius of gyration: r = 2.78
in
Check flexural tensile
stress: fb =
M/S = 170*12/86.8 = 23.5 psf
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: fa =
(P+W)/A = 35.8 psi/ft
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, fm’ = 1500 psi Fa = (1/4) fm’ {1-[h/(140r)]2} = 323.7 psi
Allowable flexural strength: Fb = (1/3) fm’ = 500 psi Combined stress equation: fa/Fa + fb/Fb = 0.158 < 1 O.K. Check axial force:
Elastic modulus, Em = 900 fm’ = 1.35x106 psi Pe = [p2EmI/h2][1-0.577*e/r)2= 1.23x105 lb
(1/4) Pe =
3.09 x 104 lb
> 1200+330 = 1530 lb O.K. |