AISC/MBMA Steel Design Guide No. 16

Emmett Sumner is currently anAssistant Professor North CarolinaState University in Raleigh, NorthCarolina. He is working to com-plete his Ph.D. from Virginia Techand should receive his degree inMay 2003. In 1993, he received hisB.S. degree from the University ofNorth Carolina at Charlotte, and in1995, he received his M.S. degreefrom Virginia Tech.

Before returning to Virginia Techto pursue his Ph.D., he worked as an engineer in Columbia,South Carolina for the LPA Group, Inc., where he designedbridge and transportation structures. He later worked forStevens and Wilkinson of South Carolina, Inc., designingcommercial and industrial building structures. As a regis-tered professional engineer, he has been a consultant toindustrial corporations and engineering firms.

His research experience includes the design, analysis,and full-scale testing of steel roof systems, rigid knee joints,tapered members, end-plate moment connections, and rigidgable frames used in pre-engineered metal building sys-tems. The primary focus of his Ph.D. research is the analy-sis and design of end-plate moment connections subject toseismic forces.

He serves as a member of the Committee onConnections for the American Society of Civil Engineersand is an active member of several other professional organ-izations. During his tenure as a Ph.D. candidate at VirginiaTech, he has received several fellowships including theprestigious Via Ph.D. Scholar fellowship and the MetalBuilding Manufacturers Association fellowship.

W. Lee Shoemaker joined theMBMA Staff in February 1994 asthe Director of Research andEngineering. He received hisBachelor's Degree and Ph.D. inCivil Engineering from DukeUniversity and his Master's Degreein Civil Engineering from TulaneUniversity.

From 1975 through 1981, hewas a structural engineer withAvondale Shipyards in New

Orleans, Louisiana. From 1981 through 1983, he was aGraduate Teaching and Research Assistant at DukeUniversity in Durham, North Carolina. In 1983, Dr.Shoemaker joined the Civil Engineering Faculty at AuburnUniversity in Auburn, Alabama. In 1989, he returned to

2003 NASCC Proceedings Baltimore, MD – April 2-5 Session D7 – Page 1

AISC/MBMA STEEL DESIGN GUIDE NO. 16FLUSH AND EXTENDED MULTIPLE-ROW MOMENT END-PLATE CONNECTIONS

Tom Murray is Montague-BettsProfessor of Structural Steel Design,The Charles E. Via Jr. Department ofCivil and EnvironmentalEngineering at the VirginiaPolytechnic Institute and StateUniversity. He joined Virginia Techin 1987 after 17 years with theUniversity of Oklahoma, the lastyear of which was spent as aDistinguished Visiting Professor atthe U.S. Air Force Academy. After

receiving his BS degree from Iowa State University in 1962,he was employed as an Engineer Trainee with Pittsburgh-Des Moines steel company, Des Moines, Iowa. In 1966 hereceived his MS degree from Lehigh University, and in1970 he received a Ph.D. in Engineering Mechanics fromthe University of Kansas.

He has served on several national committees in theAmerican Society of Civil Engineers and number of otherprofessional organizations. In 1977, The American Instituteof Steel Construction presented him with a special citationfor contributions to the art of steel construction and in 1991with the T. R. Higgins Lectureship Award. Murray is amember of both the American Institute of SteelConstruction and the American Iron and Steel Institutespecification committees, as well as, the AISC Committeeon Manuals and Textbooks. He has excellence in teachingawards from both the University of Oklahoma and VirginiaTech. In February 2002, he was elected to the NationalAcademy of Engineering.

Thomas M. Murray

W. Lee Shoemaker

Emmett A. Sumner

industry as Chief Engineer at Cornell Crane Manufacturingin Woodbury, New Jersey and later was promoted to VicePresident of Manufacturing.

Shoemaker is a registered professional engineer in fourstates (LA, AL, NJ, PA). He was recognized by theAlabama Society of Professional Engineers as YoungEngineer of the year in 1986 and as Outstanding CivilEngineering Faculty by the Auburn students in 1985.

Shoemaker is a member of several technical committeesincluding ASCE 7 Committee on "Minimum Design Loadsfor Buildings and Other Structures", ASTM Committee E6on "Performance of Buildings", AISC SpecificationsCommittee, AISC Research Committee and AISICommittee on Specifications for the Design of Cold-Formed Steel Structural Members.


AISC/MBMA Steel Design Guide No. 16 Flush and Extended Multiple-Row Moment End-Plate Connections

Thomas M. Murray1, W. Lee Shoemaker2, Emmett A. Sumner3, and Patrick N. Toney4

ABSTRACT

AISC recently published Design Guide No. 16, Flush and Extended Multiple-Row Moment End-Plate Connections, AISC (2002). The development of the Guide was co-sponsored by the Metal Building Manufacturers Association (MBMA), an industry that pioneered the use of moment end-plate connections in the United States. The Guide has design procedures for four flush and five extended end-plate configurations. Yield-line analysis is used to determine required plate thickness. Two methods are provided to determine the required bolt diameter. The “thick plate” method results in the smallest possible bolt size; whereas, the “thin plate” method results in a larger bolt and the thinnest plate possible. An overview of the Guide will be presented as well as typical example calculations.

OVERVIEW OF DESIGN GUIDE

The bolted connections covered in Design Guide 16 are typically used in the metal building industry between rafters and columns and to connect two rafter segments in typical gable frames with built-up shapes, as shown in Figures 1 and 2. However, the design procedures also apply to hot-rolled shapes of comparable dimensions to the tested parameter ranges.

The primary purpose of the Guide is to provide a convenient source of design procedures for the four flush end-plate connections and five extended end-plate connections that are shown in Figures 3 and 4. In addition, design considerations for the “knee area” of rigid frames are discussed. Both ASD and LRFD procedures are provided and either fully-tightened or snug-tightened bolts can be evaluated.

DESIGN PHILOSOPHIES

The end-plate connection design procedures presented in the Guide use yield-line techniques for the determination of end-plate thickness and include the prediction of tension bolt forces. The bolt force equations were developed because prying forces are important and must be considered in bolt force calculations. Moment-rotation considerations are also included in the design procedures.

1 Montague Betts Professor of Structural Steel Design, Charles E. Via Department of Civil Engineering,

Virginia Polytechnic Institute and State University, Blacksburg, VA. 2 Director of Research and Engineering, Metal Building Manufacturers Association, Cleveland, OH. 3 Assistant Professor, Department of Civil Engineering, North Carolina State University, Raleigh, NC. 4 Manager, Engineering Standards, Star Building Systems, Oklahoma City, OK.


M M

Tension Zone

(a) Beam-to-Beam Tension Zone

M

M

(b) Beam-to-Column Connection

Figure 1 Typical uses of flush end-plate moment connections

Tension Zone

Tension Zone

MM

M

M

Tension Zone

M

M

Tension Zone

M M

(a) Beam-to-Beam Connection

(b) Beam-to-Column Connection

Figure 2 Typical uses of extended end-plate moment connections

Tension Zone

Tension Zone

MM

M

M


(a) Two-Bolt Unstiffened (b) Four-Bolt Unstiffened

(c) Four-Bolt Stiffened with Web Gusset Plate Between the Tension Bolts

(d) Four-Bolt Stiffened with Web Gusset Plate Between the Tension Bolts

Figure 3 Flush end-plate connections.


(a) Four-Bolt Unstiffened (b) Four-Bolt Stiffened (c) Multiple Row 1/2 Unstiffened

(d) Multiple Row 1/3 Unstiffened (e) Multiple Row 1/3 Stiffened

Figure 4 Extended end-plate connections.


Yield Lines

Yield-lines are the continuous formation of plastic hinges along a straight or curved line. It is assumed that yield-lines divide a plate into rigid plane regions since elastic deformations are negligible when compared with plastic deformations. Although the failure mechanism of a plate using yield-line theory was initially developed for reinforced concrete, the principles and findings are also applicable to steel plates.

The procedure to determine an end-plate plastic moment strength, or ultimate load, is to first arbitrarily select possible yield-line mechanisms. Next, the external work and internal work are equated, thereby establishing the relationship between the applied load and the ultimate resisting moment. This equation is then solved for either the unknown load or the unknown resisting moment. By comparing the values obtained from the arbitrarily selected mechanisms, the appropriate yield-line mechanism is the one with the largest required plastic moment strength or the smallest ultimate load. Design Guide 16 provides the controlling yield-line mechanism for each of the nine end-plate connections considered.

Bolt Force Analysis

Yield-line theory does not provide bolt force predictions that include prying action forces. Since experimental test results indicate that prying action behavior is present in end-plate connections, a variation of the method suggested by Kennedy, et al. (1981) was adopted in the Guide to predict bolt forces as a function of applied flange force.

The Kennedy method is based on the split-tee analogy and three stages of plate behavior. At the lower levels of applied load, the flange behavior is termed “thick plate behavior”, as plastic hinges have not formed in the split-tee flange. As the applied load is increased, two plastic hinges form at the centerline of the flange and each web face intersection. This yielding marks the “thick plate limit” and the transition to the second stage of plate behavior termed “intermediate plate behavior.” At a greater applied load level, two additional plastic hinges form at the centerline of the flange and each bolt. The formation of this second set of plastic hinges marks the “thin plate limit” and the transition to the third stage of plate behavior termed “thin plate behavior.”

For all stages of plate behavior, the Kennedy method predicts a bolt force as the sum of a portion of the applied force and a prying force. The portion of the applied force depends on the applied load, while the magnitude of the prying force depends on the stage of plate behavior. For the first stage of behavior, or thick plate behavior, the prying force is zero. For the second stage of behavior, or intermediate plate behavior, the prying force increases from zero at the thick plate limit to a maximum at the thin plate limit. For the third stage of behavior, or thin plate behavior, the prying force is maximum and constant.


Borgsmiller and Murray (1995) proposed a simplified version of the modified Kennedy method to determine tension bolt forces with prying action effects, which was adopted in Design Guide 16. The bolt force calculations are reduced because only the maximum prying force is needed, eliminating the need to evaluate intermediate plate behavior prying forces. The primary assumption in this approach is that the end-plate must substantially yield to produce prying forces in the bolts. Conversely, if the plate is strong enough, no prying action occurs and the bolts are loaded in direct tension. This simplified approach also allows the designer to directly optimize either the bolt diameter or end-plate thickness as desired.

Specifically, Borgsmiller and Murray (1995) examined 52 tests and concluded that the threshold when prying action begins to take place in the bolts is at 90% of the full strength of the plate, or 0.90Mpl. If the applied load is less than this value, the end-plate behaves as a thick plate and prying action can be neglected in the bolts. Once the applied moment crosses the threshold of 0.90Mpl, the plate can be approximated as a thin plate and maximum prying action is incorporated in the bolt analysis. This simplification results in two design alternatives (1) thick end-plate and smaller diameter bolts, or (2) thin end-plate and larger diameter bolts.

Stiffness Criterion

Connection stiffness is the rotational resistance of a connection to applied moment. This connection characteristic is often described with a moment versus rotation or M-θ diagram. The initial slope of the M-θ curve, typically obtained from experimental test data, is an indication of the rotational stiffness of the connection, i.e. the greater the slope of the curve, the greater the stiffness of the connection.

Since rigid frame construction is typically assumed in the frame analysis, the nine end-plate connections were tested to determine if they could carry an end moment greater than or equal to 90% of the full fixity end moment and not rotate more than 10% of the simple span rotation, as traditionally required for Type 1 (ASD) or FR (LRFD) connections. It was found that 80% of the full moment capacity of the four flush connections and 100% of the full moment capacity of the five extended connections could be used to limit the connection rotation at ultimate moment to 10% of the simple span beam rotation. Therefore, the required factored moment for the four flush end-plate designs must be increased 25% and is incorporated in the design procedure.

Verification of Design Procedures

The design procedures for the four flush and five extended moment end-plate connections used in Design Guide 16 were developed at the University of Oklahoma and Virginia Polytechnic Institute. Over 60 tests of the nine end-plate


connections were conducted. These results were presented in 12 research reports that are referenced in Design Guide 16.

DESIGN PROCEDURE 1: Thick End-Plate and Smaller Diameter Bolts

The following procedure results in a design with a relatively thick end-plate and smaller diameter bolts. The design is governed by bolt rupture with no prying action included, requiring “thick” plate behavior. The design steps are:

1.) Determine the required bolt diameter assuming no prying action,

( )=nt

ureqdb dF

Mdπφ

2, (1)

where,

φ = 0.75 Ft = bolt material tensile strength, specified in Table J3.2, AISC (1999),

i.e. Ft = 90 ksi for A325 and Ft = 113 ksi for A490 bolts. Mu = required flexural strength dn = distance from the centerline of the nth tension bolt row to the center

of the compression flange.

2.) Solve for the required end-plate thickness, tp,reqd,

YFM

tpy

npp,reqd

b

r)11.1(φ

φγ= (2)

where,φb = 0.90 γr = a factor, equal to 1.25 for flush end-plates and 1.0 for extended end-

plates, used to modify the required factored moment to limit the connection rotation at ultimate moment to 10% of the simple span rotation.

Fpy = end-plate material yield strength Y = yield-line mechanism parameter defined for each connection in the

"summary tables" in Chapter 3 of the Guide for flush end-plates and Chapter 4 of the Guide for extended end-plates.

φMnp = connection strength with bolt rupture limit state and no prying action

DESIGN PROCEDURE 2: Thin End-Plate and Larger Diameter Bolts

The following procedure results in a design with a relatively thin end-plate and larger diameter bolts. The design is governed by either the yielding of the end-plate or


bolt rupture when prying action is included, requiring “thin” plate behavior. The design steps are:

1.) Determine the required plate thickness,

YFMt

pyb

urp,reqd φ

= (3)

2.) Select a trial bolt diameter, db, and calculate the maximum prying force.

For flush end-plate connections and for the interior bolts of extended end-plate connections, calculate Qmax,i as follows:

2

22

, 34 ′

′−

′=

p

ipy

i

pimax tw

FFatw

Q (4)

where,

( )16/12/ +−=′ bp dbw (5)

085.062.33

−=b

pi d

ta (6)

if

tbpPyp

i p

Fdwb

FtF

,

32

48

80.02

85.0 π+′+=′ (7)

For extended connections, also calculate Qmax,o, based on the outer bolts as follows:

22

2

34 ′

′−

′=

p

opy

o

pmax,o tw

FFatw

Q (8)

where,

ofext

b

p

o

ppdt

a

,

3

min

085.062.3

−

−= (9)

of

tbppyp

o p

Fdwb

FtF

,

32

48

80.02

85.0 π+′+=′ (10)


If the radical in either expression for Qmax (Equations 4 and 8) is negative, combined flexural and shear yielding of the end-plate is the controlling limit state and the end-plate is not adequate for the specified moment.

3.) Calculate the connection design strength for the limit state of bolt rupture with prying action as follows:

For a flush connection:

)])((2[)])((2[

21

2

max ddTddQP

Mb

1,imaxtq +

+−=

φφ

φ (11)

For an extended connection:

)](2[)](2))((2[

)](2)(2[]2))((2)(2[

max 3210b

20b31max,it

321b0max,ot

2b31max,it0max,ot

q

ddddTddTddQP

dddTdQPdTddQPdQP

M

++++++−

+++−++−+−

=

φφφφ

φ (12)

where,φ = 0.75

4/2tbt FdP π=

di = distance from the centerline of each tension bolt row to the center of the compression flange (Note: For rows that do not exist in a connection, that distance d is taken as zero).

Tb = specified pretension in Table J3.7 of AISC ASD or Table J3.1 of AISC LRFD.

4.) Check that φMq > Mu. If necessary, adjust the bolt diameter until φMq is greater than Mu.

ADDITIONAL ASSUMPTIONS AND CONDITIONS

Design Guide 16 includes a summary table for each of the nine connections with the relevant design information. An example of one of these tables is shown below.

Design Guide 16 should be consulted for additional assumptions and conditions for using the design procedures.


Geometry Yield-Line Mechanism Bolt Force Model

End-Plate

Yield

YtFMM ppybplbn2φφφ ==

[ ])(22

sphgs

1p1h

bY f1

f1

p +++= Note: Use pf = s, if pf > s

gbs p21= φb = 0.90

Bolt Rupture

w/Prying Action [ ][ ]1b

1maxtqn dT

dQPMM

)(2)(2

max φφ

φφ−

== φ = 0.75

Bolt Rupture

No Prying Action [ ]1tnpn dPMM )(2φφφ == φ = 0.75

EXAMPLESThe required end-plate thickness and bolt diameter for a two bolt flush end-plate

connection is to be determined for a required factored moment of 600 k-in. The end-plate

material is A572 Gr 50, the bolts are snug-tightened A325, and the connection is to be

used in rigid frame construction as assumed in the frame analysis. Both design

procedures are illustrated.

Geometric Design Data

bp = bf = 6 in.

ble

4.2

Summ

ary of

Four-

Bolt

Exten

ded

Unstif

fened

Mome

nt

End-

Plate

Analy

sis

Geometry Yield-Line Bolt Force Model

tw

ptg

h

pf

b p t f

s

h 1

Mq1d

2(P - Q )t max


tf = 1/4 in. g = 2 3/4 in. pf = 1 3/8 in. h = 18 in.

Calculate: d1 = 18 – 0.25 – 1.375 – (0.25/2) = 16.25 in. h1 = 16.375 in. γr = 1.25 for flush connections

Design Procedure 1 (Thick End-Plate and Smaller Diameter Bolts):

1.) Solve for the required bolt diameter assuming no prying action,

( )( )

( )( )( ).in59.0

25.169075.060022

,

=

==ππφ nt

ureqdb dF

Md

Use db = 5/8 in.

2.) Solve for the required end-plate thickness, tp,reqd,( ) .in03.275.20.6

21

21 === gbs p

pf = 1.375 in. ≤ s ∴use pf = 1.375 in.

[ ])(2112

sphgsp

hb

Y f1f

1p +++=

( )[ ] in.5.10003.2375.1375.1675.22

03.21

375.11375.16

20.6

=++

+=

( ) ( ) k6.274/90625.04/ 22 === FdP tbt

( )[ ].ink673

)]25.16)(6.27(2[75.02

−=

== ntnp dPM φφ

( ) ( )( )( )( )( )

.in45.0

5.1005090.067325.111.111.1 r

,

=

==YFM

tpyb

npreqdp φ

φγ

Use tp = 1/2 in.


Design Procedure 2 (Thin End-Plate and Larger Diameter Bolts):

1.) Determine the required plate thickness, ( )

( )( ) .in41.05.1005090.0

60025.1, ===

YFMtpyb

urreqdp φ

γ

Use tp = 7/16 in.

2.) Select a trial bolt diameter, db, and calculate the maximum prying force, Qmax,i.

Try db = 0.75 in.

( ) ( ) ( ) in.19.216/175.02/0.616/12/ =+−=+−=′ bp dbw

( ) ( )in.65.0

085.075.0/4375.0682.3085.0/682.3 33

=

−=−= bpi dta

if

tbppyp

i p

Fdw

bFt

F,

32

4

880.0

285.0 +′+

=′

( ) ( ) ( )

)375.1(48

9075.019.280.020.685.0504375.0

32 ++

= = 10.2 k

22

2

34 ′

′−

′=

p

ipy

i

pmax,i tw

FF

atw

Q

( )( ) ( ) ( )

k49.7

4375.019.22.10350

65.044375.019.2

22

2

=

−=

3.) Calculate the connection design strength for the limit state of bolt rupture with prying action,

[ ][ ]1b

1maxtq dT

dQPM

)(2)(2

max φφ

φ−

=

( ) ( ) k8.394/9075.04/ 22 === FdP tbt

For snug-tight bolts, Tb is 50% of Table J3.1 pretension = 0.50(28) = 14 k

Summary: tp = 1/2 in. db = 5/8 in.


( )( )[ ].ink341])25.16)(14(2[75.0

.ink78825.1649.78.39275.0

max --

M q ==−

=φ

4.) Check that φMq > Mu. If necessary, adjust the bolt diameter until φMq is greater than Mu.

600788 >=qMφ k-in. so the trial bolt, 3/4 in dia. is ok.

Note: A check (not shown) of 5/8 in. bolt confirms that 3/4 in. is required.

Comparison of Results for the Two Design Procedures

Design Procedure 1End-Plate: A572 Gr 50 material tp = 1/2 in. Bolts: A325 db = 5/8 in.

Design Procedure 2End-Plate: A572 Gr 50 material tp = 7/16 in. Bolts: A325 db = 3/4 in.

As expected, Design Procedure 1 results in a thicker end-plate and smaller diameter bolts than Design Procedure 2. Either design is acceptable.

REFERENCES

AISC, (1999) Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL.

AISC, (2002) Flush and Extended Multiple-Row Moment End-Plate Connections, Steel Design Guide Series No. 16, American Institute of Steel Construction, Chicago, IL.

Borgsmiller, J. T. and Murray, T. M., (1995) “"Simplified Method for the Design of Moment End-Plate Connections,” Research Report CE/VPI-ST-95/19, Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, November, 1995.

Kennedy, N.A., Vinnakota, S. and Sherbourne, A.N. (1981) “The Split-Tee Analogy in Bolted Splices and Beam-Column Connections”, Proceedings of the International Conference on Joints in Structural Steelwork, 2.138-2.157.

Summary: tp = 7/16 in. db = 3/4 in.

Documents

AISC/MBMA Steel Design Guide No. 16