7.1 Introduction
Lateral loads on structures are commonly caused by wind, earthquakes, and soil pressure, and less commonly from human activity, waves, or blasts. These loads are difficult to quantify with any degree of precision. However, following reasonable member and system proportioning requirements, coupled with prudent detailing, we can build reliable steel structures that effectively resist lateral loads.
What makes a structure perform well in a windstorm is vastly different than an earthquake. A heavy, squat structure, such as the Parthenon in Greece can easily withstand wind—even without a roof. Its mass anchors it to the ground. On the other extreme, a tent structure could blow away in a moderate storm. Conversely, the mass of the Parthenon makes is extremely susceptible to earthquakes (remember earthquake force is a function of weight), while the tent in a seismic event will hardly notice what is going on.
Looking at this closer, wind forces are dependent on three main variables:
- Proximity to open spaces such as water or mud flats
- Site exposure
- Building shape and height.
In contrast, earthquake forces are dependent on very different variables:
- Nature of the seismic event
- Building weight
- Rigidity of the structural system.
Because we operate in a world with gravity forces, we inherently understand the gravity load paths of the simple building shown in Figure 7.1a.
Downward loads enter the roof and floors and make their way to the walls, columns and eventually footings. Lateral loads can take more time to grasp. But we can think of them as turning everything 90 degrees; the structure acting as a cantilevered beam off the ground, illustrated in Figure 7.1b.
The magnitude and distribution of lateral loads drives the layout of frames and shear walls. These resist lateral forces, acting like cantilevered beams poking out of the ground.
We design lateral wind resisting members to not cause damage to the system. Conversely, because strong seismic loads occur much less frequently, we design their lateral systems to yield members. This absorbs significantly more energy, as illustrated in Figure 7.2, resulting in smaller member sizes. However, it leaves the structure damaged.
For design of seismic load resisting systems, we follow rigorous member proportioning and detailing requirements to ensure yielding occurs in the right places. This chapter focuses on design and detailing requirements from a conceptual point of view, and what lateral load resisting systems, elements, and connections should look like.
7.2 Lateral Load Paths
Following the path lateral loads travel through a structure is key to logical structural configuration and detailing. If the load path is not continuous from the roof to ground, failure can occur. Additionally, no amount of structural engineering can compensate for an unnecessarily complex load path.
When configuring the structure, visualize how lateral forces—and gravity forces—travel from element to element, and eventually to the ground. A well-planned load path will save weeks of design effort, substantially reduce construction cost, and minimize structural risk. Software can’t do this, but careful thought will.
Figure 7.2 Comparative energy absorption for high and low deformation behavior
Looking at lateral load paths further, Figure 7.3 shows how they enter a structure and find their way to the ground. Starting at point 1, wind induces pressure, or seismic accelerations cause inertial forces, perpendicular to the face of the building. Spanning vertically (point 2), the wall delivers a line or point load to a connection at the roof or floor level. The roof or floor picks up additional inertial seismic load. The roof (number 3) must resist lateral forces through diaphragm action—essentially a deep beam. The ends of the diaphragm (point 4) then deliver load into connections between a shear wall or frame. This occurs at each level (point 5). The lateral force works its way to the footing (point 6), which transfers the force to the soil through friction and passive pressure. Because the lateral forces are applied at a distance above the ground, they impart an overturning moment to the system. This causes tension and compression in the ends of shear walls and outside frame columns (point 7). The weight of the structure (point 8) helps resist this overturning moment; keeping it from tipping over.
Figure 7.3 Detailed lateral load path in structure
To review, lateral loads are applied perpendicular to walls or cladding. Bracing these are the roof and floor diaphragms, which transfer their loads to the walls parallel to the load. Walls are supported by the ground. The weight of the structure (and sometimes deep foundations) keeps the system from tipping over.
Connections are critical to complete load paths. We need to ensure the lateral loads flow from perpendicular wall and floor, into diaphragms, into walls parallel to the load, and down to the foundation. Each time the load enters a new element, there must be a connection.
7.3 Diaphragms
Lateral systems include horizontal and vertical elements. Horizontal systems consist of diaphragms and drag struts (collectors). Vertical elements consist of shear walls and frames. Horizontal systems transfer forces through connections to vertical elements, which carry the loads into the foundation.
Diaphragms may consist of concrete slabs, bare metal deck, and diagonal bracing. Diaphragms make possible large open spaces, without internal walls or braced frames—so long as there is adequate vertical support.
7.3.1 Forces
We can visualize diaphragms as deep beams that resist lateral loads, illustrated in Figure 7.4a. They experience maximum bending forces near their middle, and maximum shear at their supports (where they connect to walls or frames), as seen in Figure 7.4b.
We resolve the mid-span moments into a tension-compression couple, requiring boundary elements around their edges, such as beams. Often a few pieces of rebar in the slab can resist these forces, since the distance between these is large.
Shear forces are distributed throughout the length of the diaphragm in the direction of lateral force. Because many shear walls and frames do not go the length of the building, the transfer of shear forces between the diaphragm and vertical elements causes high stress concentrations at the ends of the wall or frame illustrated in Figure 7.5a. By adding drag struts (also called collectors), we gather the shear stresses into this stronger element, which can then deliver the force to the wall or frame. This reduces the stress concentration (Figure 7.5b) and ensures the diaphragm retains its integrity. Drag struts frequently consist of beams, joists, and slab reinforcing. Note that a structural element that acts as drag strut, will act as a diaphragm chord when the forces are turned and analyzed 90 degrees.
Figure 7.4 (a) Diaphragm forces and reactions, and (b) internal forces
7.3.2 Geometric Considerations
To ensure reasonable behavior of metal deck diaphragms, the ICC Evaluation Service reports1 limit diaphragm aspect ratios (L/W) to those in Table 7.1. The limitations vary depending on whether the wall is flexible (curtain wall), or rigid (concrete or masonry). Generally, flexibility factorsF are less than 70 for bare metal deck and less than 2 for concrete-topped diaphragms. We can use this table when laying out frame and shear walls, to ensure the diaphragms are well proportioned. Diaphragms that support concrete or masonry walls must meet additional span and deflection criteria.
Figure 7.5 Diaphragm stress distribution (a) without and (b) with drag struts
7.3.3 Analysis
To design a diaphragm, we need to know the shear and moment distribution in it—though often just the maximum shear and moment. We take these and find the unit shear and tension-compression couple. The steps are as follows, illustrated in Figure 7.6.
- Draw the diaphragm and dimensions L and W
- Apply forces from the walls and floor as a
line load w
Table 7.1 Metal deck diaphragm aspect ratio limits
Figure 7.6 Diaphragm load, shear and moment diagram, and design forces
-
Draw the shear and moment diagrams. For a simply supported diaphragm, the maximum shear and moment are shown in Equations 7.1 and 7.2:
(7.1) (7.2) where
Wu = uniform distributed load from walls and floors, lb/ft (kN/m)
L = span, ft (m).
- Calculate the unit shear vu by dividing the
shear force Vu by the depth W (Equation 7.3):
(7.3) - Convert the moment Mu to a
tension-compression couple as follows (Equation 7.4):
(7.4)
For the perpendicular direction, we follow the previous steps rotating the load and dimension labels 90 degrees.
7.3.3.1 Capacity
Knowing the diaphragm forces, we can size the chords. If we use beams we treat it as a combined axial and bending load, as discussed in Section 6.3. If we use reinforcing steel, we take the chord force and divide it by 0.9 Fy to get the required area, then select the necessary number of bars.
7.3.3.2 Detailing
Structural performance, particularly in earthquakes, depends on detailing. Figure 7.7 shows a typical building edge detail showing possible chords and shear transfer between the slab and beam. Figure 7.8 shows a chord detail across a column, where the beam-column connection doesn’t have the capacity to carry the force.
Figure 7.7 Detail of slab edge and chord
Figure 7.8 Chord splice across a column
7.4 Lateral System Types
There are as many variations in steel lateral systems as opinions on soccer clubs. The following sections discuss the most common: braced and moment frames. They can be configured in endless ways.
7.4.1 Braced Frames
Braced frames use axial strength and stiffness of braces, beams, and columns to resist lateral loads, illustrated in Figure 7.9. They act as cantilevered trusses. They are stiff and structurally efficient. However, they concentrate force to a few elements, which requires thoughtful consideration of connections and redundancy. The internal forces in a braced frame are illustrated in Figure 7.10.
Figure 7.9 Braced frame in architectural feature
The most common braced frame types are:
- Concentrically Braced Frames—where the loads are all transferred through the work points, and don’t induce bending into the members. Seismic energy is absorbed by brace yielding.
- Eccentrically Braced Frames—where the braces do not meet at work points, and induce bending moments in the beams. In earthquakes, this causes the beams to yield, and dissipate energy.
- Buckling Restrained Braced Frames—contain a steel core that yields equally in tension and compression. It is jacketed by concrete within a steel tube that keeps the core from yielding. They absorb seismic energy by core yielding.
Figure 7.10 Braced frame internal forces and deflections
Figure 7.11 Braced frame configurations
There are many ways to configure braced frames. Figure 7.11 shows five configurations. The inverted V configuration is quite common, as it keeps the middle of the bay open for doors and windows. Flipping this, we get the V configuration. In seismic applications, these configurations create a large force imbalance, that the beam must carry. Two story braces eliminate this imbalance, and allow equally large openings. We configure eccentric braced frames with the link at the middle of the beam, or end, shown in the bottom two bays of Figure 7.11. We prefer avoiding K type bracing, shown in Figure 7.12, which puts high, horizontal forces into the columns.
Figure 7.12 K-type bracing worth avoiding
7.4.2 Moment Frames
Moment frames resist lateral loads through bending of beams and columns, with rigid connections between them. Internal forces and deflections of a moment frame are shown in Figure 7.13. Moment frames have high redundancy when compared to braced frames and shear walls, because of their many members and joints, shown in Figure 7.14.
Often moment frames are considered more expensive, when compared to braced frames. However, when we include the foundation costs in the analysis, they have similar costs. This is because moment frame foundations are lighter than braced frames, since they spread the load out over a greater area.
7.4.3 Dual Systems
We often use a combination of frame systems in buildings to resist lateral forces. For instance, core shear walls work well with typical office building layouts, and provide high strength and stiffness. When paired with perimeter moment or braced frames, the building has additional redundancy and torsional stiffness. When using dual systems, the code specifies seismic response modification factors R (see section 7.5.1) that consider the combined behavior of the two systems.
Figure 7.13 Moment frame internal forces and deformations
Figure 7.14 Moment frame in a commercial office building
7.5 Seismic Design Considerations
Seismic design centers on yielding specific members in the structure to absorb energy. This reduces member sizes and creates more economical structures. In concentric braced frames, we yield the braces; in eccentric braced frames and moment frames, we yield the beams. We avoid yielding columns, as these contribute to the gravity load capacity and stability of much larger areas than their counterparts. Connections must be designed to yield these members, without failure. We therefore design them based on expected member strength, rather than forces from structural analysis.
After the 1994 Northridge earthquake, structural engineers learned that some of their design, detailing, and construction practices were not adequate to ensure yielding of specific elements. This event started a decade of research and modification to steel seismic requirements, now found in AISC 341 Seismic Provisions for Structural Steel Buildings.2 These range from welding requirements to connection forces. We summarize key seismic provisions below.
7.5.1 Response Modification
Because we design seismic systems to yield, the building code permits us to reduce the design seismic force. We do this by dividing it by the Response Modification Factor R, which is a function of energy absorption. A higher R indicates a better performing seismic system. Table 7.2 provides these for various lateral force resisting systems.
Codes also limit the height of most lateral systems in high seismic regions. These limits are based on seismicity, which manifest themselves as seismic design categories B through F, and are listed in Table 7.2. Category D is the most common in regions of high seismicity. Categories E and F apply to very high seismicity, and buildings with higher societal importance.
7.5.2 Drift
For seismic forces, the code limits how much relative movement is permissible between floors—known as drift Δ. Think of it like a stack of dinner plates sliding off each other. Limiting drift helps reduce damage to cladding, partitions, mechanical ducts, and plumbing. Drift is determined from a structural analysis and compared to the limits shown in Table 7.3—which are a function of story height.
Drift in steel structures can have a substantial effect on how cladding joints are detailed. The joints need to accommodate the drift movement, without damaging the cladding. See Chapter 8 of Special Structural Topics in this series for additional guidance.
Table 7.2 Seismic lateral system R factors and maximum heights
7.5.3 Configuration Requirements
Building configurations that have horizontal jogs, vertical steps, large diaphragm openings, or large stiffness changes perform less effectively than their counterparts. This is because force concentrates in sharp changes of geometry, and the load path through these is inefficient. Examples of horizontal and vertical irregularities are shown in Figure 7.15 and Figure 7.16, respectively, along with potential options to avoid them.
Table 7.3 Drift limits for multi-story structures
Source: ASCE 7–10
hsx=Story height under level being considered, don’t forget to convert to inches or mm
Expanding further, horizontal structural irregularities include:
- Torsion occurs where there is a substantial difference in lateral system stiffness, such as a building with shear walls on three sides, with a moment frame on the fourth, illustrated in Figure 7.15.
- Reentrant Corners occur where there is an inside corner of the structure without frames or shear walls along them, shown also in Figure 7.15.
- Diaphragm Discontinuity happens where there
are large openings in the diaphragms.
Figure 7.15 (a) Common horizontal seismic irregularities and (b) their mitigation
Figure 7.16 Vertical seismic irregularities showing (a) soft story and (b) in-plane discontinuities, and their mitigation
- Out-of-Plane Offsets occur where the lateral system changes plane and the forces must be transferred through the diaphragm to the vertical frames or shear walls.
Vertical structural irregularities include:
- Soft Stories occur where there is a drastic change in stiffness between levels. For example, a braced frame sitting on a moment frame, shown in Figure 7.16.
- Weak Stories exist where there is a large change in strength between levels.
- Mass irregularities occur where the adjacent story is 50% heavier than the adjacent stories.
- Geometric irregularities happen when the horizontal dimension of the lateral system changes more than 30% longer than an adjacent story.
- In-Plane Discontinuities occur where the lateral system changes locations horizontally, creating overturning forces in the members below, illustrated in Figure 7.16.
Each irregularity comes with specific, and sometimes exhaustive code requirements. Some of these are not permitted for seismic design categories D through F. Any lateral system with these irregularities will have financial and environmental costs, as these systems always require more material to carry the required loads. Additionally, no amount of analysis or detailing will make these structures perform as well as buildings without them.
7.5.4 Seismic Force Amplifications
There are a handful of cases where the code requires that the basic seismic forces be amplified. These include low redundancy conditions, structural irregularities, and protection of certain lateral frame elements.
Redundancy is the ability of a structure to sustain damage without becoming unstable. If failure of a key element of the lateral force resisting system results in a reduction of story shear strength of greater than 33%, the seismic force must be increased by 30%. More, smaller frames or walls will result in a less expensive, better performing seismic system.
When we have structural irregularities, as discussed in the previous section, we must increase the forces in elements that will be affected by these. The amount depends upon the irregularity and member, but ranges from 25% to 300%.
7.5.5 Material Requirements
As a class of steel becomes stronger it loses deformation capacity and fracture toughness. AISC therefore limits the yield stress of structural steels used in seismic applications to 50 k/in2 (345 MN/m2) for intermediate and special systems, and 55 k/in2 (379 MN/m2) for ordinary systems.
Heavy sections and welds have Charpy toughness requirements to ensure they can absorb sufficient seismic energy. Heavy sections are defined as rolled shapes with flanges thicker than 1 1/2 in (38 mm) and plate 2 in (51 mm) and thicker.
Table 7.4 Representative wide flange shapes that qualify as highly ductile for use in seismic systems
7.5.6 Member Compactness
AISC 341 requires that members meet compactness criteria to ensure sufficient deformation in the members—and therefore sufficient energy dissipation. They define two ductility levels, moderate and high, which correlate to limiting width to thickness ratio (b/t) and web length to thickness ratio (h/tw). These are like those discussed in Section 2.4.2, but more restrictive. Ordinary and Intermediate seismic detailing requires the members to meet moderate ductility requirements, while those in the Special category must meet the highly ductile requirements. Boiling these requirements down, we see a limited number of available shapes for seismic systems. Table 7.4 and Table 7.5 lists shapes from Appendix 1, that qualify as highly ductile seismic sections for select lateral systems.
7.5.7 Protected Zone
To ensure large deformation capacity, and therefore energy absorption, certain portions of seismic connections and members are considered protected zones, shown in Figure 7.17. No connections or notches can be made in these areas, including connections for non-structural items.
Figure 7.17 Seismic protected zones for (a) concentric braced frames, (b) eccentrically braced frames, and (c) moment frames
Table 7.5 Representative HSS sections that qualify as highly ductile for use in seismic systems
| Section (Imperial) | SCBF Brace | EBF Brace | Section (Metric) |
| HSS16 × 16 × 3/8 | HSS406.4 × 406.4 × 9.5 | ||
| HSS14 × 14 × 3/8 | HSS355.6 × 355.6 × 9.5 | ||
| HSS12 × 12 × 3/8 | HSS304.8 × 304.8 × 9.5 | ||
| HSS10 × 10 × 5/8 | HSS254 × 254 × 15.9 | ||
| HSS10 × 10 × 3/8 | HSS254 × 254 × 9.5 | ||
| HSS8 × 8 × 5/8 | HSS203.2 × 203.2 × 15.9 | ||
| HSS8 × 8 × 3/8 | HSS203.2 × 203.2 × 9.5 | ||
| HSS7 × 7 × 5/8 | HSS177.8 × 177.8 × 15.9 | ||
| HSS7 × 7 × 3/8 | HSS177.8 × 177.8 × 9.5 | ||
| HSS7 × 7 × 1/4 | HSS177.8 × 177.8 × 6.4 | ||
| HSS6 × 6 × 5/8 | HSS152.4 × 152.4 × 15.9 | ||
| HSS6 × 6 × 3/8 | HSS152.4 × 152.4 × 9.5 | ||
| HSS6 × 6 × 1/4 | HSS152.4 × 152.4 × 6.4 | ||
| HSS5 × 5 × 3/8 | HSS127 × 127 × 9.5 | ||
| HSS5 × 5 × 1/4 | HSS127 × 127 × 6.4 | ||
| HSS4 × 4 × 3/8 | HSS101.6 × 101.6 × 9.5 | ||
| HSS4 × 4 × 1/4 | HSS101.6 × 101.6 × 6.4 | ||
| HSS3 × 3 × 1/4 | HSS76.2 × 76.2 × 6.4 | ||
| HSS3 × 3 × 1/8 | HSS76.2 × 76.2 × 3.2 |
Source: AISC Seismic Design Manual, 2nd Edition
| indicates highly ductile section | |
| Blank | indicates section insufficiently compact |
7.5.8 Connections
Good detailing is at the heart of safely performing buildings. For wind forces, we design the connections for the actual wind force. However, for seismic connections, we must ensure a part of the structure yields. This leads to larger connections and more demanding material requirements.
We typically design members using the lowest strength they will have coming from the mill—Fy and Fu. In practice, the material may be stronger. This is usually helpful until we design seismic connections, which must force the member to yield. If the actual strength is higher than we expect, the required force increases, and our connection may be undersized. To account for this, we factor the yield and ultimate strengths up by the expected strength factors when calculating connection demand. Yield strength is multiplied by Ry and ultimate strength by Rt. These values are provided in Table 7.6.
For concentric braced frames, yielding occurs in the braces and we design the connections to develop the tensile capacity of the brace. This leads to rather large connections, such as those in Figure 7.18.
Table 7.6 Expected strength adjustment factors
| ASTM Specification |
Yield Ry |
Ultimate Rt |
| Structural Shapes and Bars | ||
| A36 | 1.5 | 1.2 |
| A53 | 1.6 | 1.2 |
| A500 | 1.4 | 1.3 |
| A572 Gr 50 | 1.1 | 1.1 |
| A913 | 1.1 | 1.1 |
| A992 | 1.1 | 1.1 |
| A588 | 1.1 | 1.1 |
| Plate | ||
| A36 | 1.3 | 1.2 |
| A572 Gr 50 | 1.1 | 1.2 |
Source: AISC 341–10
Figure 7.18 Special concentric braced frame connection at (a) beam mid-span, and (b) base plate
In eccentric braced frames the yielding occurs in the link beam, between braces. Such a connection is shown in Figure 7.19. For moment frames, we proportion the beam to yield. Common seismic moment connections are shown in Figure 7.20. In the bolted connection, the flange plate and bolts are sufficient to yield the beam in bending. In the welded connection, the beam section is reduced to yield, but keep the weld stresses elastic. In both, the shear connection in the web must be able to develop the expected strength of the beam, at the opposite end.
Bolts in seismic connections must be slip critical. This is to reduce drift and increase energy dissipation.
For welds, an entire book can be written on their requirements, and indeed has. AWS D1.8 Structural Welding Code–Seismic Supplement3 provides the US code requirements for welds in seismic systems—also known as demand critical welds.
A key to successful welds is the access hole where the flange meets the web of a wide flange shape, shown in Figure 7.21. Proper configuration of this hole reduces constraint in the joint and allows the welder to properly make the weld.
7.6 Where We Go From Here
Figure 7.19 Eccentrically braced frame connection detail
Figure 7.20 (a) bolted and (b) welded moment frame connection
This chapter has introduced the general concepts of lateral design. From here, we estimate lateral forces on a structure, and through structural analysis, determine their distribution into diaphragms, frames, and shear walls. This yields internal forces, from which we proportion member sizes. We then detail the structure, paying attention to the seismic requirements discussed above.
Figure 7.21 Seismic weld access hole geometry
Seismic lateral design has become increasingly sophisticated in the past two decades. Prescriptive code requirements are giving way to performance-based design (PBD). This allows the owner and designer to pair the earthquake magnitude and structural performance that is consistent with the function of the building. Additionally, engineers are using performance-based design for more traditional, code-based buildings to reduce material consumption, as discussed in the Special Structural Topics volume of this series.
Notes
1 ICC-ES, Vulcraft Steel Deck Panels, ESR-1227 (Brea, CA; ICC Evaluation Service, 2016)
2 AISC, Seismic Provisions for Structural Steel Buildings, AISC 314 (Chicago: Research Council on Structural Connections, 2016).
3 AWS, Structural Welding Code-Seismic Supplement, AWS D1.8 (Miami: American Welding Society, 2016).