Design Parameters for Steel Special Moment Frame Connections

12 Pages·2011·2.73 MB·English

by  Scott Adan

SEAOC 2011 CONVENTION PROCEEDINGS

Design Parameters for Steel Special Moment Frame
Connections

Scott M. Adan, Ph.D., S.E., SECB, Chair
SEAONC Structural Steel Subcommittee
Principal
Adan Engineering
Oakland, California
Abstract 2010a). Chapter E references requirements published in
ANSI/AISC 358, Prequalified Connections for Special and
Current seismic provisions for steel special moment frame Intermediate Steel Moment Frames for Seismic Applications,
connections require minimum moment ratios to theoretically (hereafter referred to as AISC 358 (AISC 2010b). Both the
force flexural yielding into attaching beams. In some cases, Provisions and AISC 358 contain references to ANSI/AISC
the provisions also require doubler plates to control column 360, Specification for Structural Steel Buildings (hereafter
panel-zone deformation. The same provisions require referred to as the Specification) (AISC 2010c).
continuity plates when the column web or flange may be
susceptible to local bending or yielding. The fit-up and These design and detailing requirements are intended to
welding associated with doubler and continuity plates can be achieve a strong-column/weak-beam condition and to enable
labor and cost intensive. For many practicing engineers, the ductile flexural response in regions where inelastic behavior
application of these concurrent provisions can be difficult to may occur.
distinguish from an economic standpoint. With consideration
of these parameters, this study, as part of the in progress Column-Beam Moment Ratio
SEAONC 2010 Special Projects Initiative, examines the
design aspects of steel special moment frame connections and In a single-story mechanism, inelastic response is dominated
develops visual aids to assist practicing engineers in the by the formation of a plastic hinge at the top and bottom of a
economical application of the provisions. single-story column. This undesirable phenomenon can
result in a significant concentration of drift and instability
Introduction within a frame. To avoid this, a strong-column/weak beam
formulation can promote multi-story mechanisms dominated
Steel special moment frames are often used as part of a by plastic hinges in the beams. The provision cannot
structure’s lateral resisting system in areas with high seismic guarantee that individual frame columns will not yield, but
risk. The frames provide structural stiffness and stability that yielding of the beams rather that the columns will
through the shear and bending of the beams and columns. predominate.
When subjected to earthquake motions, inelastic behavior is
intended to occur through the formation of plastic hinges at With some exceptions, Section E3.4a of the Provisions
beam-to-column connections and at the column bases. requires the relationship equation, E3-1, reproduced here, be
satisfied at beam-to-column connections:
As a result of material overstrength and strain hardening,
inelastic forces generated by earthquake motions can ΣM*
significantly exceed design requirements. The connections pc >1
ΣM*
must be proportioned and detailed to accommodate this pb

inelastic behavior.
It is permitted by equation E3-2a, reproduced here, to

The special requirements associated with the design and determine ΣM* as follows:
pc€
construction of moment frame connections for high seismic
applications are published primarily in Chapter E of ΣM* =ΣZ (F −P /A )
pc c yc uc g
ANSI/AISC 341, Seismic Provisions for Structural Steel

Buildings (hereafter referred to as the Provisions) (AISC €
where:
€
1
the summation of the moments at the column faces as
Z = plastic section modulus of the column, in.3 determined by projecting the expected moments at the plastic
c
F = F of the column, ksi hinge points to the column faces as follows:
yc y
P = required compressive strength using LRFD load
uc
combinations, kips (a positive number) ΣM
Ag = gross area of the column, in.2 Ru= d f −Vcol (4)
b

It is also permitted by equation E3-3a, reproduced here, to
where:
determine ΣM* as follows:
pb
d = beam d€ep th, in.
b
ΣM* =Σ(1.1R F Z +M )
pb y yb b uv
The equation to determine the larger and smaller values of the
€
where: expected moment at the face of the column can be expressed
as follows:
R = rat€io of the expected yield stress to the specified
y
minimum yield stress, Fy (per Table A3.1 of the Mf = 1.1RyMp + VhSh (4)
Provisions)
Fyb = Fy of the beam, ksi Mf ′= 1.1RyMp + Vh′ Sh (5)
Z = plastic section modulus of the beam, in.3
b
The equation to determine the column shear can be expressed
The equation to determine the additional moment due to as follows:
shear amplification from the location of the plastic hinge to
the column centerline can be expressed as follows: ΣM
V = f (6)
col h
ΣM = (V +V′)(d/2+S ) (1)
uv h h c h
where:
where:
h = average sto€ry height above and below the joint, in.
d = column depth, in.
c
S = distance from the column face to the plastic hinge, in. In most instances, the nominal panel-zone shear strength, is
h
determined by Equation J10-11, reproduced here, of Section
The equations to determine the larger and smaller values of J10.6 of the Specification:
shear force at the plastic hinge can be expressed as follows:
 3b t2 
V = 2[1.1RM ]/L + w L /2 (2) φR =0.60Fd t 1 + cf cf 
h y p h u h v n y c w dbdctw
V′= 2[1.1RM ]/L – w L /2 (3)
h y p h u h
For Puc ≤ 0.75 Pc

Where:
where€:

M = FZ = nominal plastic flexural strength, kip-in.
p y
Lh = distance between plastic hinges, in. € φv =1.0 per Section E3.6e(1) of the Provisions
wu = uniform beam gravity load, kips per linear ft. dc = column depth, in.
tw = column web thickness, in.
Doubler Plates bcf = column flange width, in.
tcf = column flange thickness, in.
At the connection to a beam, the column panel-zone must Pc =FyA, axial yield strength of the column, kips
have adequate thickness to prevent excessive distortion or
shear buckling. If the thickness is insufficient, the panel-zone To identify the plastic panel-zone deformation contribution to
can be strengthened with the addition of a doubler plate. the shear strength, Equation J10-11 can be written as:

As defined by Section E3.6e.(1) of the Provisions, the φvRn = 0.6Fy dctwVpz (7)
required shear strength of the panel-zone is determined from
2
where: Example 1: Special Moment Frame Connection
Design
 3b t2  (8)
Vpz=1 +dbdcfctcwf Given:

Refer to the special moment frame connection J-1 shown in
The individual thickness of the column web and/or doubler
Figure 1. Determine the connection design parameters for the
plates, if required, is determined by Equation E3-7,
€
W14×257 column and W36×150 beam. The beam and
reproduced here, of Section E3.63.(2) of the Provisions:
column are both ASTM A992 wide-flange sections (Fy = 50
ksi, F = 65 ksi, E =29,000 ksi).
t ≥ (dz + wz)/90 u s

where: W14×257 d = 16.4 in. bf = 16.0 in. tw = 1.18 in.
tf = 1.89 in. Ag = 75.6 in.2 Zx = 487 in.3
t = thickness of column web or doubler plate, in.
dz = depth of the panel-zone between beam flanges, in. W36×150 d = 35.9 in. bf = 12.0 in. tw = 0.63 in.
w = width of panel-zone between column flanges, in. t = 0.94 in. A = 44.2 in.2 Z = 581 in.3
z f g x

With some exceptions Equation E3-7 can be written as:

t ≥ [(d -2t )+ (d-2t )]/90 (9)
b bf c cf

Continuity Plates

At the connection to a beam, the column flange must be
sufficiently rigid to prevent deformation or local bending.
The column web must also be sufficiently rigid to prevent
local yielding due to the corresponding high state of stress
concentrations. The installation of stiffeners or continuity
plates can address these local limit states. If the flange and
web thicknesses are sufficient, the concentrated beam flange

forces can be adequately transferred without the required

stiffening effects or secondary load path.
Figure 1. Special moment frame elevation for

Example 1.
Section E3.6f of the Provisions requires continuity plates

unless the column flange thickness satisfies equations E3-8
Assume the factored uniform distributed load on the beam, w
u
and E3-9, reproduced here:
= 1.0 kips/ft and the factored axial load on the column, P =
uc

100 kips. Also, assume the beam-to-column connection is a
t ≤0.4 1.8b t FybRyb prequalified welded unreinforced flange-welded web (WUF-
cf bf bf F R W) per AISC-358 and that both the beam and column are
yc yc
highly ductile members per Section D1.1b of the Provisions.

b
t ≥ cf In the beam-to-column connection, per Section 8.7 Step 2 of
cf 6
€ AISC 358, the plastic hinge location is taken to be at the face

of the column. That is, S = 0in.
where: h

Solution:
€
b = beam flange width, in.
bf
t = beam flange thickness, in.
bf Step 1: Determine the connection moment ratio.
t = minimum required thickness of column flange when no
cf
continuity plates are provided, in.
Determine the sum of projections of the nominal flexural
F = F of the column, ksi
yc y strengths of the columns per Eq. E3-2a of the Provisions:
R = R of the beam (per Table A3.1 of the Provisions)
yb y
Ryc = Ry of the column (per Table A3.1 of the Provisions) ΣM *= 2(487in.3)(1ft./12in.)(50ksi-100kips/75.6in.2)
pc
3
Check that the required column axial compressive strength is
ΣM *= 3951kip-ft. less than or equal to the axial yield strength per Eq. J10-11 of
pc
the Specification:
Determine the distance between plastic hinges, L ′:
h
Puc ≤ 0.75(50ksi)(75.6) = 2835kips o.k.
L ′= 30ft.-16.4in.(1ft./12in.) = 28.6ft.
h
Therefore, determine the plastic panel-zone deformation
Determine the expected shear force at the plastic hinge using contribution to the shear strength using Eq. (8):
Eq. (2): €
 3(16in.)(1.89in.)2 
Vh = 2[1.1(1.1)(50ksi)(581in.3)(1ft./12in.)/(28.6ft.)] Vpz=1 +(35.9in.)(16.4in.)(1.18in.) =1.25
+1.0 kip/ft.(28.6ft.)/2

Determine the nominal panel-zone shear strength of the
V = 218.9kips
h column using Eq. (7):
€

Because the connection is single sided, V ′= 0 kips.
h φR = 0.60(50ksi)(16.4in.)(1.18in.)(1.25)
v n

Determine the additional moment due to shear amplification
φR = 726kips < 770kips n.g.
from the location of the plastic hinge to the column centerline v n

using Eq. (1):
Therefore, determine the required panel-zone thickness, t ,
pz
using the following equation:
ΣM = (218.9kips)(16.4in.)(1ft./12in.)/2) = 149.6kip-ft.
uv

t ≥ t R /φR (10)
Determine the sum of the projections of the expected flexural pz cw u v n

strength of the beam per Eq. E3-3a of the Provisions:
t ≥ (1.18in.)(770kips)/(1.0)(726kips) = 1.25in.
pz

ΣM *=(1.1)(1.1)(50ksi)(581in. 3)(1ft./12in.)+149.6kip-ft.
pb Determine the required doubler plate thickness, t , using Eq.
dp
(9):
ΣM *= 3079kip-ft.
pb

t ≥ {[35.9in.-2(0.94in.)]+ [16.4in.-2(1.18in.)]}/90
Determine the moment ratio of the connection per Eq. E3-1 dp

of the Provisions:
t ≥ 0.53in.
dp

3051kip-ft./3079kip-ft.=1.3 > 1.0 o.k.
Therefore, try a 5/8 in. doubler plate, t = 0.63in., and check
dp
if the doubler plate provides adequate panel-zone thickness
Step 2: Determine if a doubler plate is required.
using the following equation:

Determine the expected moment at the face of the column
t + t ≥ t (11)
using Eq. (4): cw dp pz

1.18in.+ 0.63in.= 1.81in. > 1.25in. o.k.
M = 1.1(1.1)(50ksi)(581in.3)(1ft./12in.) = 2929kip-ft.
f

Therefore, a 5/8 in. doubler plate is adequate.
Determine the column shear using Eq. (6):

Step 3: Determine if a continuity plate need not be
2(2929kip− ft.)
V = =209kips provided.
col 2(14ft.)

Determine if the thickness of the column flange satisfies Eqs.
Determine the required panel-zone shear strength using Eq.
E3-8 and E3-9 of the Provisions:
(4):

€

50ksi(1.1)
2929kip− ft. t ≤0.4 1.8(12.0in.)(0.94in.)
Ru=35.9in.(1ft./12in.)−209kips=770kips cf 50ksi(1.1)

€ €
4
= 1.80in. < 1.89in. o.k.
Beam Load, S , Column Moment Varia-
h
t ≥12.0in. Span, wu, in. Height, Ratio tion
cf 6 ft kips/ft h, ft

20 1.0 0.0 14 1.25 0.98
=2.0in. > 1.89in. n.g.
30 1.0 0.0 14 1.28 1.00
€ Therefore, continuity plates must be provided. 40 1.0 0.0 14 1.30 1.02

20 2.0 0.0 14 1.25 0.98
Visual Aids
30 2.0 0.0 14 1.28 1.00

40 2.0 0.0 14 1.30 1.02
With consideration of the calculated parameters associated
with moment ratios, doubler, and continuity plates, visual 20 1.0 0.0 16 1.25 0.98
representations of the requirements for most highly ductile 30 1.0 0.0 16 1.28 1.00
single-sided W14 columns are presented herein. The visual 40 1.0 0.0 16 1.30 1.02
aids are shown in Figures 2 through 25. In the even
20 1.0 12 14 1.12 0.88
numbered figures, the moment ratios and continuity plate
30 1.0 12 14 1.19 0.93
requirements are displayed. In the odd numbered figures, the
required double plate thicknesses are displayed. The specific 40 1.0 12 14 1.22 0.95
beam-to-column connection design parameters associated 20 1.0 24 14 0.98 0.76
with Example 1 are displayed in Figures 16 and 17. 30 1.0 24 14 1.10 0.86

40 1.0 24 14 1.15 0.90
The figures are limited to multi-story connections (column

above and below the joint) and were developed with the
Table 1. Moment ratio parameter variation
assumptions indicated in Example 1, including the following:
summary. Example 1 parameters shown bold.

• Beam span =30ft.
• Average column height =14ft. Beam Load, Sh, Column Panel Varia-
• Factored uniform beam load = 1kip/ft. Span, wu, in. Height, Zone, tpz, tion
• Factored axial column load = 100kips ft kips/ft h, ft in
• Plastic hinge location at the column face. 20 1.0 0 14 1.25 1.00
• Beam flanges not reduced.
30 1.0 0 14 1.25 1.00

40 1.0 0 14 1.25 1.00
In order to determine the effect of these assumptions, a series
of parametric studies were performed. For example, as 20 1.0 12 14 1.41 1.13
shown in Tables 1 and 2, beam spans of 20 and 40 ft. were 30 1.0 12 14 1.36 1.08
shown to have only a slight influence on modifying moment 40 1.0 12 14 1.33 1.06
ratios and required panel-zone thicknesses, assuming other
20 1.0 24 14 1.60 1.28
parameters remained constant. Likewise as shown in Table
30 1.0 24 14 1.47 1.18
1, an increase in the uniform load or column height did not
significantly influence the moment ratios. As the variation 40 1.0 24 14 1.41 1.13
for the uniform load and column heights were negligible for
required panel-zone thicknesses, they were not included in Table 2. Panel-zone thickness parameter variation
Table 2. summary. Example 1 parameters shown bold.

As indicated in Tables 1 and 2, the parameter that did connections such as the reduced beam section (RBS), bolted
significantly influence the both the moment ratio and the end plate (BEP), bolted flange plate (BFP), or Kaiser bolted
required panel zone thickness was the distance to the plastic bracket (KBB), the plastic hinge forms at a set distance away
hinge, S . The increasing plastic hinge distance lowered the from the column face. Therefore, for connections with larger
h
moment ratios and increased the required panel zone plastic hinge distances, additional verification on a case-by-
thicknesses proportionally. As stated in the example, the case basis may be a consideration. This study did not
WUF-W plastic hinge is assumed to form at the face of the consider the influence of flange width reduction, consistent
column (AISC 2010b). However, in other prequalified with the RBS, on any of the parameters.

5
Figure 2. Moment ratios for a single-sided W14x132 Figure 3. Doubler plate thickness of a single-sided
column. Gray shaded circles indicate the beam size W14x132 column. Assumes local buckling of the
where continuity plates are required for that and all doubler plate is not prevented per Section E3.6e(2) of
heavier sections in the series. the Provisions.

Figure 4. Moment ratios for a single-sided W14x145 Figure 5. Doubler plate thickness of a single-sided
column. Gray shaded circles indicate the beam size W14x145 column. Assumes local buckling of the
where continuity plates are required for that and all doubler plate is not prevented per Section E3.6e(2) of
heavier sections in the series. the Provisions.

6
Figure 6. Moment ratios for a single-sided W14x159 Figure 7. Doubler plate thickness of a single-sided
column. Gray shaded circles indicate the beam size W14x159 column. Assumes local buckling of the
where continuity plates are required for that and all doubler plate is not prevented per Section E3.6e(2) of
heavier sections in the series. the Provisions.

Figure 8. Moment ratios for a single-sided W14x176 Figure 9. Doubler plate thickness of a single-sided
column. Gray shaded circles indicate the beam size W14x176 column. Assumes local buckling of the
where continuity plates are required for that and all doubler plate is not prevented per Section E3.6e(2) of
heavier sections in the series. the Provisions.

7
Figure 10. Moment ratios for a single-sided Figure 11. Doubler plate thickness of a single-
W14x193 column. Gray shaded circles indicate the sided W14x193 column. Assumes local buckling of
beam size where continuity plates are required for that the doubler plate is not prevented per Section E3.6e(2)
and all heavier sections in the series. of the Provisions.

Figure 12. Moment ratios for a single-sided Figure 13. Doubler plate thickness of a single-sided
W14x211 column. Gray shaded circles indicate the W14x211 column. Assumes local buckling of the
beam size where continuity plates are required for that doubler plate is not prevented per Section E3.6e(2) of
and all heavier sections in the series. the Provisions.

8
Figure 14. Moment ratios for a single-sided Figure 15. Doubler plate thickness of a single-
W14x233 column. Gray shaded circles indicate the sided W14x233 column. Assumes local buckling of
beam size where continuity plates are required for that the doubler plate is not prevented per Section E3.6e(2)
and all heavier sections in the series. of the Provisions.

Figure 16. Moment ratios for a single-sided Figure 17. Doubler plate thickness of a single-sided
W14x257 column. Gray shaded circles indicate the W14x257 column. Assumes local buckling of the
beam size where continuity plates are required for that doubler plate is not prevented per Section E3.6e(2) of
and all heavier sections in the series. the Provisions.

9
Figure 18. Moment ratios for a single-sided Figure 19. Doubler plate thickness of a single-
W14x283 column. Gray shaded circles indicate the sided W14x283 column. Assumes local buckling of
beam size where continuity plates are required for that the doubler plate is not prevented per Section E3.6e(2)
and all heavier sections in the series. of the Provisions.

Figure 21. Doubler plate thickness of a single-sided
Figure 20. Moment ratios for a single-sided
W14x311 column. Assumes local buckling of the
W14x311 column. Gray shaded circles indicate the
doubler plate is not prevented per Section E3.6e(2) of
beam size where continuity plates are required for that
the Provisions.
and all heavier sections in the series.

10