Staircase Stringer Design
Edward
According to the U.S. Consumer Product Safety Commission (CPSC) National Electronic Injury Surveillance System (NEISS), during 2008 through 2011, there were an estimated 10,000 instances nationally where an individual visited an emergency room with injuries related directly to a structural failure of wooden stairs. A cursory review of these instances reveals that the majority of those are related to wood tread failure and the minority related to wood-framed stringer failure. This article focuses on the design and construction of wood-framed stair stringers, through a review of current code requirements and rules-of-thumb; common structural performance issues; structural analysis considerations and examples; and, recommendations for mitigating this common construction deficiency.
The ICC family of codes, the IRC and International Building Code (IBC), contain very few provisions regarding wood-framed stair stringer design and construction. Live loading is specified as 40 pounds per square foot for residential applications and 100 pounds per square foot for other applications (IBC Table 1607.1). The majority of the code provisions address dimensional restraints, such as width, rise/run, and vertical clearance. Table 1 provides a summary of code requirements as well as some carpentry and building construction handbook recommendations for the dimensional restraints of stair rise and run.
Perhaps the most critical structural issue of wood-framed stair construction is the connection of the stair stringer to the supporting structure. More often than not, the lower end of a set of stringers is in direct bearing contact with its supporting structure and issues tend not to arise. Typical construction employs the use of a thrust/kicker block to prevent axial movement. More often, the most important connection is at the upper end of the stairs where the stringers are typically flush-framed to a header. Failure of this connection is often sudden and catastrophic, resulting in severe injuries. One recently documented instance resulted in serious injuries to several firefighters who were carrying an injured resident out of the home (Hench D., 2010).
Prescriptive fastening schedules in the IRC and IBC offer connection specifications for similar situations, such as a joist flush-framed to a header or girder (IRC Table R602.3(1) and IBC Table 2304.9.1). These connections entail face-nailing or toe-nailing; however, these connections cannot be directly applied to the upper connection of stair stringers because of their sloped grain condition. Another method of construction employs the use of a ledger to provide direct bearing for the stringers. This method can be suitable, but prescriptive provisions do not exist and need to be provided. With the widespread use of mechanical connectors in other aspects of modern wood-framed construction, it makes good sense that these could be used for this situation. Sloped sawn lumber face-mount hangers are common, simple to install, field adjustable, and capable of safely handling the connection forces from most wood-framed stringer applications.
The overcutting of notches at the tread/riser intersection during the construction of stair stringers is a common problem with unskilled or careless carpenters, as shown in Figure 1. In this instance the notches are overcut by three-quarters of an inch and unnecessarily reduce overall stringer strength. A less common, but largely more effective approach is to drill a one-quarter inch hole at the notch corner and cut to the hole with a handsaw or skillsaw. In both instances, the effective throat of the stringer is less than the theoretical throat. However, the drilled hole and careful cutting minimize the strength reduction and provides relief for the stress concentration created as a result of notching.
Deflection of stair stringers is largely ignored in typical construction, but code required limits should be applied. While prescriptive provisions of the IRC provide no explicit restrictions on deflection, the IBC provides deflection limits (Table 1604.3) for various situations. From this table, the most applicable limits for stair stringers are L/360 for live loads and L/240 for total load. Total load can be used as the live load plus half of the dead load for wood with moisture content below 16% at the time of installation (IBC Table 1604.3 note d). These limits are intended to reduce serviceability issues due to cracking of finishes and improve perception of structural performance among other things. As an example, Figure 2 shows cracking of a taped drywall joint beneath a set of underperforming stair stringers. Drywall directly applied to the bottom of the stringers has moved excessively, causing a failure of the joint and an unsightly crack. Figure 3 shows recent failure of a caulked joint between a tread and drywall of the same set of stairs. This finishing detail is common in lower-end construction. However, excessive deflection is less noticeable in typical higher-end construction where molding is attached to treads and specifically not attached to walls. Damage to finishes can be temporarily fixed, but will reappear without addressing the root of the problem, which is insufficient stringer stiffness.
Without a published or publically accepted method for analysis of wood-framed stair stringers, the method of analysis used for the purposes of this article will be to ignore any contribution of stringer material outside the effective depth. Without performing an extensive finite-element analysis of the notched profile, it is believed that very little integrity is added from the notched material.
In a theoretical three stringer configuration, one may be tempted to apply twice the tributary load to the center stringer as to the exterior stringers. Doing so would result in an unreasonably stout center stringer and does not lend itself easily to prescriptive provisions. However, when considering the contribution of the riser and in a lesser part the tread to load distribution, it is feasible to assume that the stringers may bear an equal share. By isolating the riser as shown in Figure 4, analysis demonstrates this equal share in a common situation. In theory this equal distribution does not occur, but with a sufficiently stiff riser the distribution can be assumed uniform and therefore more conducive to prescriptive provisions.
Because stair stringers are typically axially restrained at each end, it is prudent to review the comparison of the sloping beam method and the horizontal plane method. With the sloping beam method, the uniform load is resolved into components of load perpendicular to the longitudinal axis of the beam (bending) and parallel to the longitudinal axis of the beam (compression), and the span length is to be considered the inclined span. With the horizontal plane method, uniform load is applied directly to the horizontal span of the inclined beam. It has been shown that the two methods result in very similar bending moment and shear values (Breyer et. al., 2003), but also that the axial compression portion of the sloping beam method is insignificant when considering the interaction of compression and bending. For the purposes of this article, the horizontal plane method will be used due to its simplicity, popularity, and relative accuracy.
The following analysis demonstrates results of a typical wood-framed stair stringer configuration as well as several similar configurations. Consider 15 risers at 7-inch tall with 10-inch wide treads and stringers cut from SPF No. 1/No. 2 2x12s. This configuration results in an effective throat depth of approximately 5 inches for a horizontal span of 12 feet and 3 inches. For a residential loading of 10 pounds per square foot dead and 40 pounds per square foot live and a one-foot tributary width (3-foot width with 3 stringers), the allowable bending strength ratio is 145% and the shear strength ratio is 50%. Live load deflections and total load deflections are 0.93 inches and 1.05 inches respectively, which are 127% and 72% more than the allowable limits of 0.41 inches and 0.61 inches. As discussed previously, excessive deflections are demonstrated and can be exacerbated by being exposed to the elements and experiencing a moisture content above 16% during construction. In which case, the total load deflection would increase to 1.16 inches which is 90% above the allowable limits.
In an effort to mitigate one of the remaining all-too-common life safety issues in wood-framed construction, a concerted effort should be put forth to provide additional prescriptive provisions. The following action items are recommended:
Christopher Fournier, P.E., SECB, M. SEI, M.ASCE is Vice President and Lead Structural Engineer with HEB Engineers, Inc. Chris is also on the SEI Professional Activities Committee and the SEI Structural Engineering Licensure Rationale Task Committee.
The stair calculator calculates stair rise and run, stair angle, stringer length, step height, tread depth, and the number of steps required for a given run of stairs. For convenience and flexibility, this stair stringer calculator comes in two forms: automatic and manual. Click on the [?] icons to determine the best calculator for your stairs.
Adding solid risers to your stairs will not change the results of the Stair Calculator, so long as you properly attach the risers before you add the treads, as shown in the Stairs with Solid Risers and 2x12 Treads diagram below.
Before cutting your stringers, double-check all of your measurements, and carefully plan how you will attach (or not attach) a solid riser at the upper connection point of your stringer. Depending on your design, you may need to adjust the depth of your stringer's top step.
For example, if you are not planning to add a riser to the last rise up to your deck or landing, you may need to subtract the thickness of one riser from the calculated Tread Depth [B] on the top step of the stringers. Using the diagram below, picture the top step without the last riser installed. Without the riser, the last tread would either have a gap on the back side or the nose of the tread would not have the same overhang as the other treads. Consider all of the possibilities before cutting your first stringer.
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