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Structural Steel Design
Rafael Sabelli, S.E. and Brian Dean, P.E. Originally developed by James R. Harris, P.E., PhD, Frederick R. Rutz, P.E., PhD and Teymour Manouri, P.E., PhD
- 6.1 INDUSTRIAL HIGH-CLEARANCE BUILDING, ASTORIA, OREGON Contents
- 6.1.1 Building Description
- 6.1.2 Design Parameters
- 6.1.3 Structural Design Criteria
- 6.1.4 Analysis
- 6.1.5 Proportioning and Details
- 6.2 SEVEN-STORY OFFICE BUILDING, LOS ANGELES, CALIFORNIA
- 6.2.1 Building Description
- 6.2.2 Basic Requirements
- 6.2.3 Structural Design Criteria
- 6.2.4 Analysis and Design of Alternative A: SMF
- 6.2.5 Analysis and Design of Alternative B: SCBF............................................................................
- 6.2.6 Cost Comparison
- 6.3 TEN-STORY HOSPITAL, SEATTLE, WASHINGTON
- 6.3.1 Building Description
- 6.3.2 Basic Requirements
- 6.3.3 Structural Design Criteria
- 6.3.4 Elastic Analysis
- 6.3.5 Initial Proportioning and Details................................................................................................
- 6.3.6 Nonlinear Response History Analysis
FEMA P-751, NEHRP Recommended Provisions: Design Examples
This chapter illustrates how the 2009 NEHRP Recommended Provisions (the Provisions ) is applied to the
design of steel framed buildings. The following three examples are presented:
- An industrial warehouse structure in Astoria, Oregon
- A multistory office building in Los Angeles, California
- A mid-rise hospital in Seattle, Washington
The discussion examines the following types of structural framing for resisting horizontal forces:
Ordinary concentrically braced frames (OCBF)
Special concentrically braced frames
Intermediate moment frames
Special moment frames
Buckling-restrained braced frames, with moment-resisting beam-column connections
The examples cover design for seismic forces in combination with gravity they are presented to illustrate
only specific aspects of seismic analysis and design—such as lateral force analysis, design of concentric
and eccentric bracing, design of moment resisting frames, drift calculations, member proportioning
detailing.
All structures are analyzed using three-dimensional static or dynamic methods. ETABS (Computers &
Structures, Inc., Berkeley, California, v.9.5.0, 2008) is used in Examples 6.1 and 6.2.
In addition to the 2009 NEHRP Recommended Provisions , the following documents are referenced:
AISC 341 American Institute of Steel Construction. 2005. Seismic Provisions for
Structural Steel Buildings , including Supplement No. 1.
AISC 358 American Institute of Steel Construction. 2005. Prequalified Connections
for Special and Intermediate Steel Moment Frames for Seismic Applications.
AISC 360 American Institute of Steel Construction. 2005. Specification for Structural
Steel Buildings.
AISC Manual American Institute of Steel Construction. 2005. Manual of Steel
Construction , 13th Edition.
AISC SDM American Institute of Steel Construction. 2006. Seismic Design Manual.
FEMA P-751, NEHRP Recommended Provisions: Design Examples
functions as a diaphragm for distribution of the effects of eccentric loading caused by the mezzanine floor
when the building is subjected to loads acting in the transverse direction.
The mezzanine floor at the east end of the building is designed to accommodate a live load of 125 psf. Its
structural system is composed of a concrete slab over steel decking supported by floor beams spaced at 10
feet on center. The floor beams are supported on girders continuous over two intermediate columns
spaced approximately 30 feet apart and are attached to the gable frames at each end.
The member sizes in the main frame are controlled by serviceability considerations. Vertical deflections
due to snow were limited to 3.5 inches and lateral sway due to wind was limited to 2 inches.
Figure 6.1- 1 Framing elevation and sections
(1.0 ft = 0.3048 m; 1.0 in. = 25.4 mm)
Chapter 6: Structural Steel Design
Earthquake rather than wind governs the lateral design due to the mass of the insulated concrete panels.
The panels are attached with long pins perpendicular to the concrete surface. These slender, flexible pins
isolate the panels from acting as shear walls.
The building is supported on spread footings based on moderately deep alluvial deposits (i.e., medium
dense sands). The foundation plan is shown in Figure 6.1-3. Transverse ties are placed between the
footings of the two columns of each moment frame to provide restraint against horizontal thrust from the
moment frames. Grade beams carrying the enclosing panels serve as ties in the longitudinal direction as
well as across the end walls. The design of footings and columns in the braced bays requires
consideration of combined seismic loadings. The design of foundations is not included here.
Figure 6.1- 2 Roof framing and mezzanine framing plan
(1.0 ft = 0.3048 m; 1.0 in. = 25.4 mm)
Chapter 6: Structural Steel Design
R = 4.
Cd = 4
East-west (E-W) direction:
Braced frame system = ordinary steel concentrically braced frame ( Standard Table 12.2-1)
R = 3.
Cd = 3.
6.1.2.2 Loads
Roof live load ( L ), snow = 25 psf
Roof dead load ( D ) = 15 psf
Mezzanine live load, storage = 125 psf
Mezzanine slab and deck dead load = 69 psf
Weight of wall panels = 75 psf
Roof dead load includes roofing, insulation, metal roof deck, purlins, mechanical and electrical equipment
that portion of the main frames that is tributary to the roof under lateral load. For determination of the
seismic weights, the weight of the mezzanine will include the dead load plus 25 percent of the storage
load (125 psf) in accordance with Standard Section 12.7.2. Therefore, the mezzanine seismic weight is
69 + 0.25(125) = 100 psf.
6.1.2.3 Materials
Concrete for footings: fc' = 2.5 ksi
Slabs-on-grade: fc' = 4.5 ksi
Mezzanine concrete on metal deck: fc' = 3.0 ksi
Reinforcing bars: ASTM A615, Grade 60
Structural steel (wide flange sections): ASTM A992, Grade 50
Plates (except continuity plates): ASTM A
Bolts: ASTM A
Continuity Plates: ASTM A572, Grade 50
FEMA P-751, NEHRP Recommended Provisions: Design Examples
6.1.3 Structural Design Criteria
6.1.3.1 Building configuration. Because there is a mezzanine at one end, vertical weight irregularities
might be considered to apply ( Standard Sec. 12.3.2.2). However, the upper level is a roof and the
Standard exempts roofs from weight irregularities. There also are no plan irregularities in this building
( Standard Sec. 12.3.2.1).
6.1.3.2 Redundancy. In the N-S direction, the moment frames do not meet the requirements of Standard
Section 12.3.4.2b since the frames are only one bay long. Thus, Standard Section 12.3.4.2a must be
checked. A copy of the three-dimensional model is made, with the moment frame beam at Gridline A
pinned. The structure is checked to make sure that an extreme torsional irregularity ( Standard Table
12.3-1) does not occur:
1.4( ) A
1.4⎛ ⎜ 4.17 in.2+ 6.1 in.⎞ ⎟ ⎠ = 7.19 in.≥ 6.1 in.
where:
∆A = maximum displacement at knee along Gridline A, in.
∆K = maximum displacement at knee along gridline K, in.
Thus, the structure does not have an extreme torsional irregularity when a frame loses moment resistance.
Additionally, the structure must be checked in the N-S direction to ensure that the loss of moment
resistance at Beam A has not resulted in more than a 33 percent reduction in story strength. This can be
checked using elastic methods (based on first yield) as shown below, or using strength methods. The
original model is run with the N-S load combinations to determine the member with the highest
demandcapacity ratio. This demand-capacity ratio, along with the applied base shear, is used to calculate
the base shear at first yield:
Vyield =⎜ ⎜ ⎟ V
⎝ ( D C / ) max ⎟ ⎠ base
Vyield =
1 ⎞^
⎟ ⎠ (223 kips)=^ 250.5 kips
FEMA P-751, NEHRP Recommended Provisions: Design Examples
Δ a /ρ = 0.025 hsx /1.0 in the N-S direction
At the roof ridge, hsx = 34 ft-3 in. and Δα = 10.28 in.
At the knee (column-roof intersection), hsx = 30 ft-6 in. and Δ a = 9.15 in.
At the mezzanine floor, hsx = 12 ft and Δ a = 3.60 in.
Footnote c in Standard Table 12.12-1 permits unlimited drift for single-story buildings with interior walls,
partitions, etc., that have been designed to accommodate the story drifts. See Section 6.1.4.3 for further
discussion. The main frame of the building can be considered to be a one-story building for this purpose,
given that there are no interior partitions except below the mezzanine. (The definition of a story in
building codes generally does not require that a mezzanine be considered a story unless its area exceeds
one-third the area of the room or space in which it is placed; this mezzanine is less than one-third of the
footprint of the building.)
6.1.3.6 Seismic weight. The weights that contribute to seismic forces are:
E-W direction N-S direction
Roof D = (0.015)(90)(180) = 243 kips 243 kips
Panels at sides = (2)(0.075)(32)(180)/2 = 0 kips 437 kips
Panels at ends = (2)(0.075)(35)(90)/2 = 224 kips 0 kips
Mezzanine slab and 25% LL = 360 kips 360 kips
Mezzanine framing = 35 kips 35 kips
Main frames = 27 kips 27 kips
Seismic weight = 889 kips 1,102 kips
The weight associated with the main frames accounts for only the main columns, because the weight
associated with the remainder of the main frames is included in the roof dead load above. The computed
seismic weight is based on the assumption that the wall panels offer no shear resistance for the structure
but are self-supporting when the load is parallel to the wall of which the panels are a part. Additionally,
snow load does not need to be included in the seismic weight per Standard Section 12.7.2 because it does
not exceed 30 psf.
6.1.4 Analysis
Base shear will be determined using an ELF analysis.
6.1.4.1 Equivalent Lateral Force procedure. In the longitudinal direction where stiffness is provided
only by the diagonal bracing, the approximate period is computed using Standard Equation 12.8-7:
T Cha = r nx =(0.02)(34.250.75 )=0.28 sec
where hn is the height of the building, taken as 34.25 feet at the mid-height of the roof. In accordance
with Standard Section 12.8.2, the computed period of the structure must not exceed the following:
Chapter 6: Structural Steel Design
Tmax = C Tu a =(1.4)(0.28)= 0.39 sec
The subsequent three-dimensional modal analysis finds the computed period to be 0.54 seconds. For
purposes of determining the required base shear strength, Tmax will be used in accordance with the
Standard ; drift will be calculated using the period from the model.
In the transverse direction where stiffness is provided by moment-resisting frames ( Standard Eq. 12.8-7):
T Cha = r n
x
)=0.47 sec
and
Tmax = C Tu a =(1.4)(0.47)= 0.66 sec
Also note that the dynamic analysis finds a computed period of 1.03 seconds. As in the longitudinal
direction, Tmax will be used for determining the required base shear strength.
The seismic response coefficient ( Cs ) is computed in accordance with Standard Section 12.8.1.1. In the
longitudinal direction:
SDS 1.0 0.
CS = = =
R I / 3.25/1.
but need not exceed:
S
D 1 0.6 0.
CS = = =
T
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ RI 0.39⎛ ⎜ ⎝ 3.251.0 ⎞ ⎟ ⎠
Therefore, use Cs = 0.308 for the longitudinal direction.
In the transverse direction:
SDS 1.0 0.
CS = = =
R I / 4.5/
Chapter 6: Structural Steel Design
It is not immediately clear whether the roof (a 22-gauge steel deck with conventional roofing over it) will
behave as a flexible, semi-rigid, or rigid diaphragm. For this example, a three-dimensional model was
created in ETABS including frame and diaphragm stiffness.
6.1.4.2 Three-dimensional ELF analysis. The three-dimensional analysis is performed for this example
to account for the following:
The differing stiffness of the gable frames with and without the mezzanine level
The different centers of mass for the roof and the mezzanine
The flexibility of the roof deck
The significance of braced frames in controlling torsion due to N-S ground motions
The gabled moment frames, the tension bracing, the moment frames supporting the mezzanine and the
diaphragm chord members are explicitly modeled using three-dimensional beam-column elements. The
tapered members are approximated as short, discretized prismatic segments. Thus, combined axial
bending checks are performed on a prismatic element, as required by AISC 360 Chapter H. The collector
at the knee level is included, as are those at the mezzanine level in the two east bays. The mezzanine
diaphragm is modeled using planar shell elements with their in-plane rigidity being based on actual
properties and dimensions of the slab. The roof diaphragm also is modeled using planar shell elements,
but their in-plane rigidity is based on a reduced thickness that accounts for compression buckling
phenomena and for the fact that the edges of the roof diaphragm panels are not connected to the wall
panels. SDI’s Diaphragm Design Manual is used for guidance in assessing the stiffness of the roof deck.
The analytical model includes elements with one-tenth the stiffness of a plane plate of 22 gauge steel.
The ELF analysis of the three-dimensional model in the transverse direction yields an important result:
the roof diaphragm behaves as a rigid diaphragm. Accidental torsion is applied at the center of the roof as
a moment whose magnitude is the roof lateral force multiplied by 5 percent of 180 feet (9 feet). A
moment is also applied to the mezzanine level in a similar fashion. The resulting displacements are
shown in Table 6.1-2.
Table 6.1- 2 ELF Analysis Displacements in
N-S Direction
Grid Roof Displacement (in.)
A 4.
B 4.
Table 6.1- 2 ELF Analysis Displacements in N-S
Direction
Grid Roof Displacement (in.)
C 4.
FEMA P-751, NEHRP Recommended Provisions: Design Examples
D 4.
E 4.
F 4.
G 4.
H 4.
J 4.
K 3.
The average of the extreme displacements is 4.45 inches. The displacement at the centroid of the roof is
4.51 inches. Thus, the deviation of the diaphragm from a straight line is 0.06 inch, whereas the average
frame displacement is approximately 75 times that. Clearly, then, the diaphragm flexibility is negligible
and the deck behaves as a rigid diaphragm. The ratio of maximum to average displacement is 1.1, which
does not exceed the 1.2 limit given in Standard Table 12.3-1 and torsional irregularity is not triggered.
The same process needs to be repeated for the E-W direction.
Table 6.1- 3 ELF Analysis Displacements in
N-S Direction
Grid Roof Displacement (in.)
The ratio of the maximum to average displacement is 1.07, well under the torsional irregularity threshold
ratio of 1.2.
The demands from the three-dimensional ELF analysis are combined to meet the orthogonal combination
requirement of Standard Section 12.5.3 for the columns:
E-W: (1.0)(E-W direction spectrum) + (0.3)(N-S direction spectrum)
N-S: (0.3)(E-W direction spectrum) + (1.0)(N-S direction spectrum)
6.1.4.3 Drift. The lateral deflection cited previously must be multiplied by Cd = 4 to find the transverse
drift:
δ x = Cd δ e = ( 4 )(4.51) =18 in.
I 1.
FEMA P-751, NEHRP Recommended Provisions: Design Examples
θ= (1,336 kips)(4.51 in.) = 0.083< 0.
(187 kips)(32.375 ft)
The three other stability coefficients were all determined to be less than θmax, thus allowing P-delta effects
to be excluded from the analysis.
6.1.4.5 Force summary. The maximum moments and axial forces caused by dead, live and earthquake
loads on the gable frames are listed in Tables 6.1-3 and 6.1-4. The frames are symmetrical about their
ridge and the loads are either symmetrical or can be applied on either side on the frame because the forces
are given for only half of the frame extending from the ridge to the ground. The moments are given in
Table 6.1-4 and the axial forces are given in Table 6.1-5. The moment diagram for the combined load
condition is shown in Figure 6.1-4. The load combination is 1.4 D + L + 0.2 S + ρ QE , which is used
throughout the remainder of calculations in this section, unless specifically noted otherwise.
The size of the members is controlled by gravity loads, not seismic loads. The design of connections will
be controlled by the seismic loads.
Forces in the design of the braces are discussed in Section 6.1.5.5.
Table 6.1- 4 Moments in Gable Frame Members
D
Location
(ft-kips)
L (ft-
kips)
S QE
(ft-kips) (ft-kips)
Combined *****
(ft-kips)
1 - Ridge 61 0 128 0 112 (279)
2 - Knee 161 0 333 162 447 (726)
3 - Mezzanine 95 83 92 137 79
4 - Base 0 0 0 0 0
- Combined Load = 1.4 D + L + 0.2 S + ρ QE (or 1.2 D + 1.6 S ). Individual maxima are not
nec same frame; combined load values are maximum for any frame.
1.0 ft = 0.3048 m, 1.0 kip = 1.36 kN-m.
Table 6.1- 5 Axial Forces in Gable Frame Members
essarily on the
Location
D L S ρ QE
(ft-kips) (ft-kips) (ft-kips) (ft-kips)
Combined *****
(ft-kips)
1 - Ridge 14 3.5 25 0.8 39
2 - Knee 16 4.5 27 7.0 37
3 - Mezzanine 39 39 23 26 127
4 - Base 39 39 23 26 127
Chapter 6: Structural Steel Design
- Combined Load = 1.4 D + L + 0.2 S + ρ QE. Individual maxima are not necessarily on the same frame; combined
load values are maximum for any frame.
1.0 ft = 0.3048 m, 1.0 kip = 1.36 kN-m.
Figure 6.1- 4 Moment diagram for seismic load combinations
(1.0 ft-kip = 1.36 kN-m)
6.1.5 Proportioning and Details
The gable frame is shown schematically in Figure 6.1-5. Using the load combinations presented in
Section 6.1.3.4 and the loads from Tables 6.1-4 and 6.1-5, the proportions of the frame are checked at
the roof beams and the variable-depth columns (at the knee). The mezzanine framing, also shown in
Figure 6.1-1, was proportioned similarly. The diagonal bracing, shown in Figure 6.1-1 at the east end of
the building, is proportioned using tension forces determined from the three-dimensional ELF analysis.
112 ft - kips
447 ft - kips
53 ft - kips
40 ft - kips
0.7 D - ρ
1.4 D + 0.2 S + QE ρ
QE
53 ft - kips
Chapter 6: Structural Steel Design
6.1.5.1 Frame compactness and brace spacing. According to Standard Section 14.1.3, steel structures
assigned to Seismic Design Category D, E, or F must be designed and detailed per AISC 341. For an
intermediate moment frame (IMF), AISC 341, Part I, Section 1, “Scope,” stipulates that those
requirements are to be applied in conjunction with AISC 360. Part I, Section 10 of AISC 341 itemizes a
few additional items from AISC 360 for intermediate moment frames, but otherwise the intermediate
moment frames are to be designed per AISC 360.
AISC 341 requires IMFs to have compact width-thickness ratios per AISC 360, Table B4.1.
All width-thickness ratios are less than the limiting λ p from AISC 360, Table B4.1. All P-M ratios
(combined compression and flexure) are less than 1.00. This is based on proper spacing of lateral
bracing.
Lateral bracing is provided by the roof joists. The maximum spacing of lateral bracing is determined using
beam properties at the ends and AISC 341, Section 10.8:
E
Lb max , ≤ 0.17 ry
Fy
Lb max ,≤ 0.17 1.46( in.)⎛ ⎜ ⎝ 2900050 ksi ksi ⎞ ⎟ ⎠ =148 in.
Lb is 48 inches; therefore, the spacing is OK.
Also, the required brace strength and stiffness are calculated per AISC 360, Equations A- 6 - 7 and A- 6 - 8:
0.02 M Crd
Pbr =
ho
1 ⎛ 10 M Crd ⎞
β br =φ⎜ ⎝ L hb o ⎟ ⎠
where:
M RZFr = y y
Cd =1.
FEMA P-751, NEHRP Recommended Provisions: Design Examples
ho = distance between flange centroids, in.
Lb = distance between braces or Lp (from AISC 360 Eq. F2-5), whichever is greater, in.
M
r =(1.1 309)( in. 3 )(50 ksi)=16,992 in.-kip =1,416 ft-kip
Pbr = 0.02 16,992( in.-kip)(1.0)
(36 in.−5/8 in.
Pbr =9.61 kips
Lp =1.76 ry
Lp =1.76 1.46( in.
β br = (0.751 )⎛ ⎜ ⎜ ⎝ 10 16,992(( 62
in.)( in.-kip35.375 in.)(1.0) )⎞ ⎟ ⎟ ⎠
β br =104 kips/in.
Adjacent to the plastic hinge regions, lateral bracing must have additional strength as defined in
AISC 341 10.
0.06 Mu
Pu =
ho
Pu = 0.06 16992( in kip‐ )
(35.375 in.)
Pu = 28.8 kips
y
E
F
29 ,000 ksi 62 in. 50 ksi
