Masonry Magazine August 1992 Page. 26
7)
Check the allowable shear stress in masonry (Table 1). If exceeded, member must be reinforced for shear and the shear stress checked.
8)
Design the pier or pilaster, if applicable. If the pier or pilaster is made of reinforced masonry, design will follow steps 3 through 7. If a steel pier is used, follow the design recommendations given in the Load and Resistance Factor Design Manual of Steel Construction. Flexural tensile stresses developed in unreinforced masonry panels due to pier or pilaster deflection may not exceed the allowable flexural tensile stresses given in Table 2.
9)
Calculate overturning and resisting moments, and sliding resistance (Fig. 2). These are functions of the wall, footing, and caisson dimensions, as well as the soil pressure resistance. The factor of safety is the ratio of resisting moment, Mr, to the overturning moment, M. A factor of safety of 2 or greater is recommended.
TABLE 2
ACI 530/ASCE 5/TMS 402
Allowable Flexural Tension Stress for
Unreinforced Masonry, psi¹
| Direction of Stress | Masonry Type | Mortar Type |
|---|---|---|
| | | Masonry cement and air entrained |
| | | Portland portland |
| | | cement/lime cement/lime |
| | | M or S N M or S N |
| Normal to bed joints | Solid units | 40 30 24 15 |
| | Hollow units | | | | |
| | Ungrouted | 25 19 15 9 |
| | Fully grouted? | 68 58 41 26 |
| Parallel to bed joints in running bond | Solid units | 80 60 48 30 |
| | Hollow units | | | | |
| | Ungrouted & partially grouted | 50 38 30 19 |
| | Fully grouted | 80 60 48 30 |
¹Allowable stresses for wind and seismic loading conditions may be increased by one-third.
²For partially grouted masonry allowable stresses shall be determined on the basis of linear interpolation between hollow units which are fully grouted or ungrouted and hollow units based on amount of grouting.
DESIGN EXAMPLES
Design Example #1: Hollow Brick Cantilever Noise Barrier Wall
Type S portland cement/lime mortar, f'm = 3600 psi, Em 3.0 x 106 psi
Wall dimensions shown in Fig. 3, running bond, face shell bedding
Grade 60 reinforcement, E, 29 × 106 psi, n = 9.7
Loads: wind 20 psf, wall weight = 73 psf
W
TOE
SHEAR
SOIL PRESSURE
Wall/Footing Forces
FIG. 2
Step 1: Based on acoustical considerations, the wall height shall be 10 ft minimum.
Step 2: Critical load combinations result in the following design values (per ft of wall):
M = (0.5)(W)(h)2 = (0.5)(20 psf) (10 ft)2 = 1000 ft-lb
V = (W)(h) = (20 psf) (10 ft) = 200 lb
P = (wall weight)(h) = (73 psf) (10 ft) = 730 lb
Step 3: Calculate required reinforcement.
As req'd = M / Fajd = 1000 ft-lb (12 in./ft) / (4/3)(24 ksi)(0.9)(7.63 in./2) = 0.109 in.2
Try #5 bars @ 32 in. o.c., A, 0.115 in.2 per foot of wall (Table 3).
pn = An / bd = (0.115 in.2)(9.7) / (12 in.)(7.63 in./2) = 0.0244
k = √(pn)2 + 2pn - pn =√(0.0244)2 + 2(0.0244) - (0.0244) = 0.198
j = 1-k/3 = 0.934
kd = (0.198)(7.63 in./2) = 0.755 in. < 1.5 in., within face shell, OK
Step 4: Calculate the masonry compressive stress and the steel tensile stress.
f = 2M / jkbd2 = 2(1000 ft-lb)(12 in./ft) / (0.934)(0.198)(12 in.)(7.63 in./2)2 = 744 psi