Masonry Magazine August 1992 Page. 25
For pier and panel and pilaster and panel wall systems, the panel is subject to three different deflection conditions: a horizontal simple span between piers or pilasters subject to wind or seismic load, a horizontal simple span between caissons subject to panel weight, and a vertical cantilever span subject to deflection of the pier or pilaster. If the panel is free to deflect both in-plane and out-of-plane, the moment due to simple spanning between piers or pilasters, Mpx, and the moment due to simple spanning between caissons, M are combined by vector addition to calculate the maximum design moment for the horizontal span of the panel. However, the panel must be flush with the ground to avoid noise penetration under the wall. Thus, the panel may, in fact, be supported along its entire length by the ground. This is significant, because the design moment in this case is solely Mpx, the moment about the weak axis of the panel. This condition will require the most amount of horizontal reinforcement for the panel. In the panel design examples that follow it is assumed that the ground supports the entire length of the panel.
Because of plate effects, Mpx will induce moment about the horizontal axis as well, denoted as Mpy. The strip solution does not and cannot calculate Mpy, as plate effects are ignored in this method. However, plate analysis shows that Mpy can be significant and that the ratio of Mpy to Mpx increases as the height to length ratio of the panel increases. As an approximation, Mpy is calculated as one tenth the height to length ratio times Mpx. Mpy is a maximum at the middle of the panel. However, moment due to vertical cantilever deflection of the wall is a maximum at the bottom of the panel. Thus, the design moment about the horizontal axis is the greater of: 1) the moment due to vertical cantilever deflection at the bottom of the panel, or 2) the sum of Mpy and the moment due to vertical cantilever deflection at the middle of the panel.
Vertical cantilever deflection of the panel is a function of the rigidity of the piers or pilasters. If the piers or pilasters are very rigid, cantilever deflection of the panel will be negligible. However, optimal flexural design may result in less rigid piers or pilasters with considerable deflection, especially when steel piers are used. Induced tensile stresses in the panel must be within allowable tensile stresses for unreinforced masonry if the panel cannot be reinforced in the vertical direction. Thus, deflection criteria will often govern pier and pilaster design.
Reinforced brick masonry pilaster and panel and pier and panel wall systems are typically very rigid, so deflections in many cases will be small. However, the deflection of the pilaster must be calculated considering the ratio of applied moment to cracking moment. Cracking moment is calculated using the gross moment of inertia of the pier or pilaster.
In the pilaster and panel design example that follows, a two span continuous panel is assumed. Thus, the pilaster-panel interface is assumed to be a fixed connection for the middle pilaster, and a simple connection for the two exterior supports. This allows for expansion joints at the simple supports to accommodate horizontal expansion of the panels.
Lastly, compression steel in the pilaster is usually ignored in design. If consideration of the increased compressive strength due to the compression steel is made, the steel must be properly confined within the pilaster with lateral or spiral ties.
DESIGN PROCEDURE
It is important to establish a set design procedure to ensure an accurate and comprehensive noise barrier wall design. The following nine steps are presented as a guide to the structural design of a brick masonry noise barrier wall. Additional criteria may be warranted for a particular wall design scheme.
1) Determine required wall height based upon acoustical considerations.
2) Determine critical lateral and axial load combinations on wall elements. Loads should be determined according to the recommendations of the local building code or as contained in the document Minimum Design Loads for Buildings and Other Structures (ASCE 7). For the examples that follow, inertial wall force due to seismic base shear is divided by wall surface area for comparison with wind loads.
3) To determine required reinforcement, assume j = 0.9:
As req'd = M/F jd
4) Calculate masonry compressive stresses and the steel tensile stress:
f = 2M/jkbd2
fa = P/bkd
f = M/Ajd
5) Check the allowable compressive stress in masonry and the tensile stress in steel (Table 1). Axial compression and buckling seldom govern design of noise barrier wall elements. However, axial compression must be included to calculate the maximum flexural compression. Note that allowable stresses for wind or seismic load conditions may be increased by one-third over those given in Table 1.
6) Calculate shear stress:
f = V/bjd
TABLE 1
Summary of ACI 530/ASCE 5/TMS
402 Allowable Stresses¹
Allowable Flexural Compressive Stress
F1/3 m
Allowable Shear Stress for Flexural Members
Where reinforcement is not provided to resist entire shear:
Fv-m
not to exceed 50 psi
Where reinforcement is provided to resist entire shear:
not to exceed 150 psi
F-30
Allowable Steel Stress
Grade 40 or 50 reinforcement
Grade 60 reinforcement
Wire reinforcement
F, 20 ksi
F - 24 ksi
F = 30 ksi
Allowable stresses for wind and seismic loading conditions may be increased
by one-third.