Masonry Magazine August 1992 Page. 24
P Design axial load, lb
P Reinforcement ratio, A,/bd
r Radius of gyration, in.
t Thickness of wall or panel, in.
V Design shear force, Ib
Vn Nominal shear strength, lb
Vpx Shear due to spanning between piers, Ib
V Ultimate shear strength, Ib
W Lateral load, lb/ft
X Width of footing, ft
y Depth of footing, ft
Δ Deflection, in.
Φ Resistance factor
SELECTION OF A WALL SYSTEM
As discussed in Technical Notes 45, there are three typical brick masonry noise barrier wall systems: cantilever walls, pier and panel walls, and pilaster and panel walls. Preliminary consideration of design parameters can help select the wall system that is most appropriate and efficient without having to develop and compare three separate designs.
Cantilever Noise Barrier Walls
A cantilever wall system is better suited for shorter noise barriers, i.e. walls that are 12 ft (3.7 m) or less in height. In most instances, taller cantilever walls are less desirable because strip footings become too massive. Cantilever walls are more efficient for shorter heights because they are likely the easiest and most economical to construct, and will require the least quality control and inspection. This is because construction techniques used are similar to building wall construction familiar to mason contractors.
Pier and Panel Noise Barrier Walls
Pier and panel wall systems are best for quick site erection. Brick panels can be prefabricated on or off site, or laid in place. Also, pier caissons are typically constructed faster and require less concrete than strip footings. Strip footings under the panel are not required, as the panel can span from pier to pier. Material costs for pier and panel wall systems will typically be the least of the three systems. Disadvantages of the pier and panel system include increased construction supervision and inspection, tight construction tolerances for pier-to-panel connections, and increased costs to install the panels.
Pilaster and Panel Noise Barrier Walls
Pilaster and panel walls, like pier and panel walls, typically utilize caissons for quick foundation construction. Wall construction is done on site, as the panel is built integral with the pilaster. This requires panel support between caissons during construction. Supervision and inspection are required to ensure proper construction. However, construction tolerances are more liberal than those for pier and panel systems. Generally, pilaster and panel wall systems permit longer pier spacing and taller wall height. A pilaster and panel wall assembly is structurally more efficient than a pier and panel wall assembly, as a fixed condition may be developed at the pilaster-panel connection.
DESIGN ASSUMPTIONS
It has been widely accepted that masonry stress-strain behavior is similar to that of concrete. Thus, design assumptions made for masonry under working stress and strength conditions are analogous to assumptions made in concrete design. Figure 1 depicts the assumed stress-strain relationship for masonry in flexure under working loads. In all cases, the principles of equilibrium and compatibility of strains of masonry materials are assumed to apply. Assumptions made following a working stress design are as follows: 1) plane sections before bending remain plane after bending, 2) moduli of elasticity of masonry and steel remain constant, 3) reinforcement is completely bonded to masonry, and 4) in cracked masonry members, the tensile capacity of masonry is neglected.
In this Technical Notes, a number of additional assumptions will be made to facilitate design. It is assumed that the brick masonry will be reinforced. Most noise barrier wall applications demand tall slender walls to meet acoustic requirements and minimize material costs and land use. Reinforcing is required for brick masonry to meet these criteria. Additional assumptions placed on both material properties and wall behavior are as follows.
Material Properties
Grout and concrete are assumed to have compressive strength equal to or greater than the masonry compressive strength, and elastic moduli of the masonry and the grout are assumed to be equal. The method of transformation of areas may be used in lieu of these assumptions.
Wall Behavior
Masonry walls are plate structures. Thus, a masonry wall loaded perpendicular to its plane will experience strain along its length and its height. However, the traditional masonry wall design approach is to use the strip method. In this method, a one foot wide section of wall is designed considering one span direction. Strains perpendicular to the strip span direction are ignored. For cantilever walls, this method is nearly exact, as plate effects are negligible. Pier and panel and pilaster and panel walls, however, exhibit wall behavior which can make plate effects significant. This does not mean a rigorous plate analysis is necessary for these walls. Rather, a few simple observations and assumptions can be made to simplify design.