Bearing Walls Under Out-of-Plane Loads: A Design Overview
What are the typical loads?
Bearing walls are laterally supported and braced by the rest of the structure, and are mostly subjected to downward dead and live loads. In an interior bearing wall it’s unlikely that these loads are perfectly balanced at each side of the wall, therefore an eccentricity is usually considered. In an exterior wall the gravity loads are applied to one side of the wall only, therefore the load eccentricity is even larger. It’s common practice to apply the vertical loads in a hunch attached to the wall, as shown in the figure below.
An example of this condition occurs in warehouse buildings where a series of joists rest directly on the perimeter walls. Another example occurs in parking garage buildings, where a wall supports a series of double-Tee precast members.
In addition to the gravity uniform or concentrated loads, exterior walls may be subjected to the lateral out-of-plane wind pressure. Note that the worst case scenario occurs when the wind pressure is negative (suction), since the wind moments add up to the moments produced by the gravity loads.
Is the condition at the top important?
Typically the wall just rests on top of the footing and the base connection is considered pinned. The top condition is important in order to determine the shape of the moment diagram along the height of the wall. If it is a one-story building then the wall will be analyzed as a simply supported beam spanning vertically. On the other hand, if it’s a multistory building then the wall will be analyzed as a continuous beam, with a moment at the top support. Usually single story buildings have a parapet for architectural purposes. In this case the parapet will affect the shape of the moment diagram as well.
The image below shows schematically the effect of a parapet in the shape of the wall moment diagram.
What are the design options per the ACI?
According to the ACI, walls shall be designed in accordance with any of the following methods:
Walls designed as compression members using the strength design provisions for flexure and axial loads, like columns. Any wall may be designed by this method, and no minimum wall thickness is prescribed.
Empirical Design Method, which applies to walls with resultant loads for all applicable load combinations falling within the middle third of the wall thickness at all sections along the height of the wall. Wall thickness shall not be less than 1/25 of the unsupported height, nor less than 4″.
Alternate Design Method, applicable to simply supported axially loaded walls, with maximum moments and deflections occurring at mid-height. The wall cross section must be constant over the height of the panel. No minimum wall thickness is prescribed.
ASDIP CONCRETE performs the design of the wall per the first method, applying all the provisions for columns and the slenderness requirements in ACI Code. As with columns, the design of walls is usually difficult and cumbersome since it involves the generation of the interaction diagram, as shown in the image below.
It should be noted that in a typical wall the loads are grouped in the lower portion of the interaction diagram, indicating that the wall is much stronger under compression than it is under bending. Unless the wall is very short and thick, the flexural capacity will control the design. Considering this, ASDIP CONCRETE shows a blow-up view of the lower portion of the diagram for easier interpretation of the wall strength.
Walls must contain both horizontal and vertical rebars. The minimum reinforcement ratios are 0.0012 (vertical) and 0.0020 (horizontal) for rebars not larger than #5. The maximum spacing is 18″ or 3 * wall thickness, whichever is smaller. It should be noted that the ACI requires more reinforcement horizontally than vertically. This reflects the fact that vertical shrinkage stresses are dissipated by vertical compression stresses in the wall.
How is the slenderness effect accounted for?
The wall slenderness is defined in terms of its slenderness ratio kLu/r. The value of the effective length factor k is 1.0 for the pin-pin condition, and it’s slightly smaller for a continuous wall at the top. It may be conservatively considered as 1.0 in all cases.
Since the thickness of a typical wall is relatively small, the flexural transverse capacity is also limited. For this reason, most bearing walls are designed as “non-sway” members, meaning that the lateral stability of the structure is not dependent of the transverse capacity of the wall.
The ACI establishes the Moment Magnification procedure, where the moments computed from a first-order analysis are multiplied by a magnification factor to account for the second-order effects. ASDIP CONCRETE calculates the magnified moments for each load combination, as shown in the table below.
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Article originally posted on asdipsoft.com