Forces vs. Walls
Robert Grupe / February 2021
Q: Can you describe the difference between material and geometric properties relating to the structural capacity of wall systems?
A: The structural capacity of any product or system is a function of the product’s physical shape and its inherent material properties. In wall design, the material properties determine if the product or system can withstand compressive or tensile forces. These are the two forces that, when applied to the product or material, try to crush or buckle the product or conversely tear it apart. Materials can be very good under the one load direction and poor in the other. Gypsum and concrete both have the capacity to withstand compressive forces but are poor when subjected to tensile loads. Steel, on the other hand, does extremely well when subjected to tension loads.
Material can be considered either elastic or brittle in nature. A brittle material can take load with little or no apparent deformation. At some point as a load is increased, it will exceed the material’s capacity and failure occurs. This failure can be very sudden and catastrophic in nature. Materials that are examples of brittle behavior include cement plaster and masonry. Elastic behavior is the opposite: When a material deforms under load, it retains its structural capacity up to its yield point. If that load is removed, the material returns to its original shape. A yield point occurs when there is a permanent “set” or yielding, and the material remains deformed after the load is removed. Material that has yielded still has the capacity to carry load, but as loads increase, the deformations increase eventually exceeding the capacity of the material, and failure occurs. Steel is an example of a material that exhibits this behavior.
Another way of looking at this is if three different products were made, but all three had the exact same shape. One product was made of concrete, one of steel, and one was wood. The shape of all three was the same, 2 inches in breadth and 4 inches in height. Intuitively, all three will behave differently under an applied load. This is due to differing material properties.
In wall design, there are two prime structural considerations. One is the stiffness of the wall, and the other is the wall’s strength. The stiffness governs how much the wall will move under load or how much it will deflect. Deflection limits are placed on the wall to control cracking of the finish materials. The more brittle the finish material is, the less the wall is allowed to move. Plaster and tile are examples of brittle finish materials whereas gypsum panels fall into the more elastic category and are allowed to deflect more. The cracking of finish materials is a serviceability issue and does not imply a structural failure of the wall itself. Wall strength governs the load capacity of the system. These loads can be axial loads as in bearing walls or lateral loads as in wind forces on exterior curtain walls. The dimensions of a wall that is governed by strength will generally exceed the deflection limits for both brittle and elastic finishes.
The material property that predicts stiffness is MOE, or Modulus of Elasticity. The higher the MOE number, the greater the elastic response. Steel has the highest value of the three examples of wood, steel and gypsum board. Gypsum board has the lowest, and for wood it varies with the species. The MOE of steel is approximately 20 times that of wood and 100 times that of gypsum board. The property relating to the geometric shape that predicts stiffness is Moment of Inertia signified by “I.” The deeper the framing member, the greater its resistance to deflection. That can be seen in the calculation to determine the “I.” The formula for a rectangular shape is bh3/12, where “b” is the breadth (width) and “h” is the height (depth) of the member. The higher the value of “I,” the greater the resistance to deflection, resulting in the height (depth) of the member having the most impact.
Exceeding the strength limits on the wall does consider the structural failure of the wall itself. In this case, the material property that is considered is called yield stress. This is the measure of a material’s ability to handle an applied load without permanent deformation. Steel has the highest yield strength of the three materials given in the prior example. Wood will vary with the species and whether the lumber is “dimensional” or engineered. The property relating to the geometric shape that predicts strength of the product or a component is its Section Modulus or “S.” The calculation to determine “S” is based on the shape’s “I.”
Robert Grupe is AWCI’s director of technical services. Send your questions to email@example.com, or call him directly at (703) 538.1611.