general dowel equations for calculating lateral connection...

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GENERAL DOWEL EQUATIONSFOR CALCULATING LATERAL

CONNECTION VALUES

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TECHNICAL REPORT 12(ISSUES RELATED TO THE 1997 NDS®)

P

P/2 P/2

q m q m

q s q s

M s M sM m

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GENERAL DOWEL EQUATIONS FOR CALCULATING LATERAL CONNECTION VALUES i

TABLE OF CONTENTS

Part/Title Page Part/Title Page

Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Part I: General Dowel Equations1.1 Introduction . . . . . . . . . . . . . . . . . . . . . 11.2 Calculation of Lateral Connection

Values . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Input Parameters . . . . . . . . . . . . . . . . . 21.4 Other Considerations . . . . . . . . . . . . . . 31.5 Yield Mode -Actual Versus Predicted . 4

Part II: Example Problems2.1 Bolted Connection with Gap . . . . . . . . 92.2 Lag Screw Connection . . . . . . . . . . . . 102.3 Nailed Connection . . . . . . . . . . . . . . . 112.4 Nailed Connection with Reduced

Penetration . . . . . . . . . . . . . . . . . . . . . 11

Part III: Equation Derivation . . . . . . . 12

References . . . . . . . . . . . . . . . . . . . . . . . . . 18

LIST OF FIGURES

Figure Page Figure Page

1 Connection yield modes . . . . . . . . . . . . 5

2 General conditions of dowelloading . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Connection yield modes assumed loading . . . . . . . . . . . . . . . . 16

4 Single shear connection, Mode II . . . . 17

LIST OF TABLES

Table Page Table Page

1 General dowel equations . . . . . . . . . . . 6

2 Reduction terms adjustingP values to nominal design values . . 65%

3 Dowel bearing strengthestimates, F . . . . . . . . . . . . . . . . . . . . . 7e

4 Dowel bearing strengths, F ,e

for various connection materials . . . . . 7

5 Dowel bending strength estimates, F . . . . . . . . . . . . . . . . . . . . . 8b

6 Bending strengths, F , for b

dowel type fasteners . . . . . . . . . . . . . . . 8

Copyright © 1999American Forest & Paper Association, Inc.

ii TECHNICAL REPORT NO. 12

AMERICAN WOOD COUNCIL

Notation

D = dowel shank diameter, in. G = specific gravityD = dowel diameter at max. stress in side K = diameter coefficient for wood screw, nails

member, in. and spike connectionsD = dowel diameter at max. stress in main K = angle to grain coefficient for bolt and lagm

member, in. screw connectionD = fastener root diameter, in. M = side member dowel moment resistance, in.-r

F = dowel bending strength, psi lbs.b

F = proportional limit dowel bending M = main member dowel moment resistance, in.-b,pl

strength, psi lbs.F = 5% offset dowel bending strength, psi P = nominal lateral connection value, lbs.b,5%

F = ultimate dowel bending strength, psi P = nominal 5% offset lateral connection value,b,ult

F = dowel bearing strength, psi lbs.e

F = proportional limit dowel bearing strength, Z,Z’ = nominal and allowable lateral design valuee,pl

psi for a single fastener connection, lbs.F = 5% offset dowel bearing strength, psi fN = concrete compressive strength, psie,5%

F = ultimate dowel bearing strength, psi g = gap between members, in.e,ult

F = dowel bearing strength parallel to grain, psi R = side member dowel bearing length, in.e*

F = dowel bearing strength perpendicular to R = main member dowel bearing length, inez

grain, psi q = side member dowel-bearing resistance,F = side member dowel bearing strength, psi lbs./in.es

F = main member dowel bearing strength, psi q = main member dowel-bearing resistance,em

F = tensile strength, psi lbs./in.u

F = tensile yield strength, psi t = thickness, in.y

D

2

s

m

5%

c

s

m

s

m

GENERAL DOWEL EQUATIONS FOR CALCULATING LATERAL CONNECTION VALUES 1

AMERICAN FOREST & PAPER ASSOCIATION

PART I. GENERAL DOWEL EQUATIONS

1.1 Introduction

The yield limit equations specified in the National construction. This report covers calculation ofDesign Specification (NDS ) for Wood lateral values for single dowel type fastener® ®

Construction (AF&PA, 1997) for bolt, lag screw, connections using a generalized and expandedwood screw, nail, spike and drift pin connections form of the NDS yield limit equations. Theseprovide a mechanics-based approach for general dowel equations apply to NDS connectionconnection design. This approach, which was conditions, but also permit rational and consistentincorporated in the NDS for Wood Construction in treatment of gaps and fastener moment resistance,1991, permits the designer to determine effects of and consideration of various connection limitmember thickness, member strength, fastener size, states. General information is provided in Part I ofand fastener strength on lateral connection values this report. Part II contains example problems andfor the majority of connections found in wood Part III provides equation derivations.

1.2 Calculation of Lateral Connection Values

The general dowel equations in Table 1 apply to Property estimates of dowel bearingcalculation of lateral values for single dowel-type resistance and dowel moment resistance should befastener connections between wood-based based on the limit state being investigated. In thismembers and connections of wood-based members Technical Report, proportional limit load is theto steel and concrete/masonry components. Dowel load at which the load-deformation curve deviatesbearing resistance, dowel bearing length, and from a straight line fitted to the initial lineardowel moment resistance are explicitly considered portion of the load-deformation curve. The 5%in the general dowel equations for calculation of offset load is the load at which the load-lateral connection values. Additional variables that deformation curve intersects a line represented byinfluence lateral connection values include: the initial tangent modulus offset 5 percent of theC fastener type; fastener diameter. The 5% offset load isC fastener failure modes (e.g. tension, intermediate between proportional limit and

bearing, and shear); ultimate loads and represents the nominal yieldC fastener spacing, edge, and end distance; value for dowel bearing strengths and fastenerC connection fabrication and tolerances; bending strengths in the NDS. The ultimate loadC connection geometry; limit state is synonymous with the limit state atC multiple fasteners and group action; maximum load. Note that failure load, which isC member strength at the connection; and typically less than ultimate load and whichC adjustments for end use. generally occurs after ultimate load has beenGuidelines and recommended practice for the reached, is not a limit state that can be modeled byabove variables are provided in the NDS for Wood the general dowel equations.Construction. The term “nominal” is used to designate

1.2.1 Nominal Limit State Values

Nominal lateral connection values at various limitstates (see ASTM D 5652, Figure 4) such asproportional limit, 5% offset, and ultimate(maximum) load are obtained by taking theminimum calculated value, P, using all yield modeequations in Table 1.

values that have not been modified by design“adjustment” factors, such as load duration, wetservice, etc., as shown in NDS Table 7.3.1.

1.2.2 Nominal Design Value

The nominal design value, Z, is the minimum ofthe calculated 5% offset strength, P , for all yield5%

2 TECHNICAL REPORT NO. 12


mode equations in Table 1 divided by applicable moment resistance, and dowel bearing length). Forreduction terms in Table 2. lag screw and wood screw connections, identical

In the NDS, reduction terms are integral values result when the dowel moment resistance inwith the yield limit equations and appear in the the main member is set to 75% of the doweldenominator of each of the available yield mode moment resistance in the side member (M = 0.75equations (See 1.2.2.1 and Table 2). These terms M ). Nominal design values for drift bolt and driftadjust nominal yield values (based on the 5% pin connections equal 75% of the nominal designoffset yield point) to values representative of value for bolts of the same diameter.nominal proportional limit based design values ofearly editions of the Specification. In thisTechnical Report, reduction terms and calculationof yield mode values are separated to permit directcalculation of limit state values of proportionallimit, 5% offset and ultimate load. When usingthis Technical Report to calculate nominal lateraldesign values from the NDS, 5% offset propertyestimates of dowel bearing resistance and fastenerbending yield strength should be used. Note thatfastener bending yield strengths and dowel bearingstrengths appearing in the NDS are based on 5%offset property estimates and are identical to 5%offset property estimates presented in this report.

Nominal design values, Z, are identical toNDS yield limit values for bolt, nail and spikeconnections provided equivalent input parametersare used (e.g. dowel bearing resistance, dowel

m

s

1.2.2.1 Reduction Terms for P Values5%

Reduction terms in Table 2, which adjust P5%

values to nominal design values are identical tothose used in the NDS yield limit equations. Table2 also provides guidance on reduction terms foryield modes not covered in the NDS due tosimplifying assumptions used to develop the NDSyield limit equations. Reduction terms adjustingultimate or proportional limit values to nominaldesign values have not been established.Proportional limit and ultimate values of fastenerbending strength and dowel bearing strength,however, are provided (see 1.3.1 and 1.3.2) todemonstrate the applicability of the general dowelequations at various limit states.

1.3 Input Parameters

Basic information needed to calculate lateralconnection values includes dowel-bearingresistance, dowel moment resistance, dowelbearing length, and gap distance.

1.3.1 Dowel bearing resistance

Dowel diameter and dowel bearing strength areused to determine dowel bearing resistance, q ands

q , in the side and main member respectively. Form

wood-based members, dowel bearing strengthestimates based on dowel bearing strength of thematerial should be used and are generally based ontest methods outlined in ASTM D 5764. Table 3provides guidance for estimating dowel bearingstrengths. Table 4 contains specific dowel bearingstrengths including 5% offset dowel-bearingstrengths assumed for tabulated NDS connectionvalues.

1.3.2 Dowel moment resistance

Dowel bending strength and applicable sectionmodulus are used to determine dowel momentresistance, M and M , in the side and mains m

member respectively. Dowel bending strengths aregenerally based on test methods outlined in ASTMF 1575, estimates of dowel tensile strength asdetermined by ASTM F 606, or tabulated tensilevalues for the dowel material. A guide forestimating bending strength is outlined in Table 5.Table 6 contains specific dowel bending strengthsincluding 5% offset dowel bending strengthsassumed for tabulated NDS connection values.

1.3.3 Dowel bearing length

Dowel bearing lengths, R and R , represent thes m

length of dowel bearing in the side and mainmember, respectively. For double shearconnections, the minimum length of bearing ineither of the side members should be used. Thetapered tip of a lag screw should not be included indetermination of bearing length (See NDS



Appendix L for typical lag screw dimensions). Formost wood-to-wood and wood-to-metal boltedconnections, where the longitudinal axis of the boltis perpendicular to the faces of connectedmembers, the dowel bearing length in the side andmain member equals the side and main memberthickness respectively. For wood-to-concreteconnections, embedment length in the concreteshould be used as the dowel bearing length in theconcrete member.

1.3.4 Gap distance

Gap distance, g, is the distance measured betweenadjacent faces of connected members. Gapdistance equals zero for connected members withadjacent faces in contact.

1.4 Other Considerations

1.4.1 Penetration Effects

The NDS penetration depth factor is applicablewhen lateral capacity is based on checking yieldmodes considered in the NDS for nail, spike, woodscrew and lag screw connections only. Itconservatively reduces available NDS yield modevalues to account for yield modes not explicitlyaddressed.

When checking all six yield modes usingthe general dowel equations, it is not necessary toreduce calculated lateral values by the NDSpenetration depth factor, C . To do so would yieldd

very conservative design values, since the effect ofmain member bearing length on connectioncapacity is rationally addressed by considering allconnection yield modes (See Figure 1).

When nail, spike or wood screwpenetration, including tip, is reduced below 10D(10 fastener diameters) the impact of neglecting thereduction in bearing capacity due to the reducedfastener tip diameter can become significant. Forpenetration less than 10D, the user should excludethe fastener tip length from their assumed dowelbearing length (Note: Tip lengths of diamondpoint nails, such as common and box nails, rangefrom approximately 1.3 to 2.0 nail diameters inlength). In all cases, limiting minimum penetrationdepths in accordance with NDS minimums (e.g.6D for nails and spikes, 4D for wood screws andlag screws) should be maintained.

1.4.2 End Fixity

End fixity refers to resistance to rotation providedat the end(s) of the dowel. This action is notspecifically addressed in the derivation of the NDSyield limit equations nor in the general dowelequations. Contribution of end fixity is dependanton several factors including load level, fastener

type and installation, washer or fastener head size(e.g. nail or screw head size), and amount ofdimensional change in connected members. Singleshear connections exhibiting yield mode II, III , ors

III , shown in Figure 1, are prone to be influencedm

by end fixity. For double shear, connectionsexhibiting mode III behavior are prone to bes

influenced by end fixity. These yield modes areprone to be influenced by end fixity because theyare limited by dowel bearing resistance as thedowel rotates. The moment resistance contributedby end fixity tends to force fastener yielding in aconnection otherwise controlled by wood bearing.In all cases, it is necessary for the washer orfastener head to maintain contact with the memberin order to realize the contribution of end fixity.As a result, consideration of dimensional changesresulting from wood shrinkage, influence of loadlevel, wood bearing beneath the washer or fastenerhead, and fastener type should be addressed beforeaccounting for end fixity in design. End fixity isconservatively ignored in the development ofgeneral dowel equations and the NDS yield limitequations.

1.4.3 Friction

The effect of friction between members is largelydependant on type of fastener, condition of wood,amount of shrinkage, and relaxation of the woodmember. Friction is usually not accounted for inwood connection design because the amount offrictional force is difficult to predict and in manyinstances may not exist as wood shrinks or theconnection relaxes. Frictional resistance toslipping of connection members is conservativelyignored in the development of the general dowelequations and the NDS yield limit equations.



1.5 Yield Mode Actual Versus Predicted

The general dowel equations and the NDS yield single fastener connections with sufficient end andlimit equations assume that the connection yields edge distances are indicative of connectionin accordance with one of the yield modes depicted yielding up to ultimate load but do not representin Figure 1 and as described in Part III - Equation damage observed at failure. Wood splitting alongDerivation. Predicted yield modes at various limit a line of fasteners, formation of a shear plug,states up to ultimate load are in agreement with fastener shear, and fastener withdrawal are typicalyield modes observed from connection tests. It failures observed in connections tested beyondshould be noted that predicted yield modes for ultimate load.

Mode I

Mode I

Mode II

Mode III

Mode III

Mode IV

m

s

m

s

Single Shear Connections Double Shear Connections



Figure 1 Connection Yield Modes

P ' qmRm P ' qmRm

P ' qsRs P ' 2qsRs

P'& B % B 2 & 4 AC

2AP'

& B % B 2 & 4ACA

A '1

4qs

%1

4qmB '

Rs

2%g%

Rm

2C ' &

qsR2s

4&

qmR2m

4

A '1

2qs

%1

4qmB ' g%

Rm

2C ' & Ms&

qmR2m

4

A '1

4qs

%1

2qmB '

Rs

2%g C ' &

qsR2s

4& Mm

A '1

2qs

%1

2qm

B ' g C ' &Ms& Mm



Table 1 General Dowel Equations

Yield Mode Single Shear Double Shear Description

I Main member bearingm

I Side member bearings

General equation for member bearingII-IV and dowel yielding

Inputs A, B, & C for Yield Modes II-IV

II Side and main member bearing1

III Main member bearing and dowelm1,2

yielding in the side member

III Side member bearing and dowels2

yielding in the main member

IV Dowel yielding in the side and main2

member

Notes:P = nominal lateral connection value, lbs. g = gap between members, in.R = side member dowel bearing length, in. D = dowel shank diameter, in.s

R = main member dowel bearing length, in. F = dowel bending strength, psi m

q = side member dowel-bearing resistance= F D, lbs./in. D = dowel diameter at max. stress in side member, in.s es

q = main member dowel-bearing resistance= F D, lbs./in. D = dowel diameter at max. stress in main member, in.m em

F = side member dowel-bearing strength, psi M = side member dowel moment resistance , in-lbs. = F (D /6)es

F = main member dowel-bearing strength, psi M = main member dowel moment resistance , in-lbs.= F (D /6)em

b

s

m

s b s2 3

m b m2 3

Yield Modes II and III are not applicable to double shear connections.1m

For proportional limit values, M = F (BD /32) and M = F (BD /32).2 3 3s b,pl s m b,pl m

Table 2 Reduction Terms Adjusting P Values to Nominal Design Values5%

Fastener Type Yield Mode Reduction TermBolts, drift pins I , I 4 Km s

II 3.6 KIII , III , IV 3.2 Km s

2

2

2

Lag screws I , I 4 Km s†

II ,III , III 2.8 K† †m s

IV 3 K

2

2

2

Nails, spikes I , I , II , III , III , IV Km s m s† †

D

Wood screws I , I , II , III , III , IV Km s m s† † †

D

Notes: K = 1 + 0.25(2/90) K = 2.2 for D# 0.17”2

2 = maximum angle of load to grain (0 #2#90 ) K = 10D + 0.5 for 0.17” < D < 0.25”E E

for any member in a connection K = 3.0 for D$ 0.25” D = fastener shank diameter

D

D

D

Yield modes and corresponding reduction terms are not provided in the NDS.†



Table 3 Dowel Bearing Strength Estimates, Fe

Material Proportional limit, F 5% Offset, F Ultimate, Fe,pl e,5% e,ult

Wood-based1

parallel-to-grain 0.67 F F F perpendicular-to-grain 0.50 F F F

e,ult

e,ult

e,5%

e,5%

e,ult

e,ult

Metal2

0.024” # t < 0.1875” 0.67 F F 3F t $ 3/16” 0.67 F F 1.5F

u

u

u

u

u

u

Concrete 2.5 fN 3fN 5fN3c c c

Notes: t = thickness, in.fN = compressive strength, psic

F = tensile strength, psiu

5% offset and ultimate dowel bearing strengths for wood-based products are based on test methods outlined in 1

ASTM D 5764.F based on AISC (1989) and AISI (1996).2

e,ult

F based on Vintzeleou (1986). Experimental verification of F (Biolzi, 1990) based on concrete compressive 3e,ult e,ult

strength, fN , of 2700 psi. F , F , and F estimates should be limited to concrete compressive strengthsc e,pl e,5% e,ult

of 2700 psi or less.

Table 4 Dowel Bearing Strengths, F , for Various Connection Materialse

(Tabulated Nds Connection Values Are Based on F )e,5%1,4

Material F (psi) F (psi) F (psi)2e,pl e,5% e,ult

Lumber (bolt, drift pin, lag screw) parallel-to-grain 7862G /D 11200G 11735G /D perpendicular-to-grain 3178G /D 6100G /D 6355G /D

Lumber (nail, wood screw) - 16600G -

1.07 0.17

1.15 0.51

3

1.45 0.5

1.84

1.07 0.17

1.15 0.51

3

Steel ASTM A653 Grade 33 (0.036”<t<3/16”) 30,150 45,000 135,000 ASTM A36 (t>3/16”) 38,860 58,000 87,000

Concrete (fN = 2000 psi) 5,000 6,000 10,000c

Notes: G = specific gravity (Oven dry weight and volume) fN = compressive strength, psic

D = fastener shank diameter, in t = thickness, in

Calculation of connection values using NDS yield limit equations or general dowel equations is not limited to 1

materials or dowel bearing strength values provided in this table.F for lumber based on Wilkinson (1991). Data from Wilkinson report on dowel bearing strength was used to 2

e,5%

derive other F values for lumber.e

F and F for nails and spikes are 80% of the values for bolts of equivalent diameter.3e,pl e,ult

See Additional References for information on dowel bearing strength, F , of panel products. 4e



Table 5 Dowel Bending Strength Estimates, Fb

Fastener Type Proportional limit, F 5% Offset, F Ultimate, Fb,pl b,5% b,ult

Bolts, lag screws, drift pins F F /2 + F /2 F

Common nails, box nails, spikes, lag 0.6F F Fscrews (D# 3/8”), wood screws1

y

b,ult

y u

b,5%

u

b,ult

Notes: D = fastener shank diameter, in. F = fastener tensile yield strength, psiy

F = fastener tensile strength, psi F = dowel bending strength, psiu b

Bending strengths are generally based on fastener bending tests outlined in ASTM F 1575.1

Table 6 Bending Strengths, F , for Dowel Type Fasteners (Tabulated NDSb

Connection Values Are Based On F )b,5%1

Fastener Type F (psi) F (psi) F (psi)b,pl b,5% b,ult

Bolt, lag screw, drift pin 36,000 45,000 60,0002

Common nail, box nail, spike, lag screw,wood screws3

0.099 # D # 0.142 78,000 100,000 130,0000.142 < D # 0.177 69,000 90,000 115,0000.177 < D # 0.244 54,000 80,000 90,0000.244 < D # 0.273 48,000 70,000 80,0000.273 < D # 0.344 42,000 60,000 70,0000.344 < D # 0.375 36,000 45,000 60,000

Threaded hardened steel nail4

0.120 # D # 0.142 - 130,000 -0.142 < D # 0.192 - 115,000 -0.192 < D # 0.207 - 100,000 -

Notes: D = fastener shank diameter, in. F = dowel bending strength, psib

Calculation of connection values using NDS yield limit equations or general dowel equations are not limited to 1

fastener bending strength values provided in this table.Bolt, lag screw, drift pin - SAE J429-Grade 1 with F = 36,000 psi and F = 60,000 psi. Use of the dowel2

y,min u,min

bending strength estimate outlined in Table 5 results in a F equal to 48,000 psi, however, 45,000 psi hasb,5%

been assumed for consistency with the bending strength assumption used for tabulated values in the NDS.Common nail, box nail, spike, wood screw, lag screw (D# 3/8”) with low to medium carbon steel. See Loferski 3

(1991) for bending yield strength of nails.Threaded hardened steel nail with medium carbon steel.4



PART II. EXAMPLE PROBLEMS

Example problems are based on the application of For each example problem, connectionthe general dowel equations to single fastener values in parenthesis represent yield mode valuesconnections. Connection values for all yield calculated using NDS yield limit equations. Notemodes are provided for each example and that NDS connection provisions are not directlyminimum values for each configuration are applicable for several of the conditions and limitunderlined. Connection values have not been states covered in the Example problems and thatadjusted for conditions of end use such as load certain yield modes are excluded fromduration, wet service, and temperature. Connection consideration. For cases where NDS connectionend and edge distances are assumed to be in provisions apply, values from the general dowelaccordance with applicable NDS provisions. equations and NDS yield limit equations are

identical provided equivalent inputs are used.

Example 2.1 - Bolted Connection With Gap

Problem Statement: Determine the nominaldesign value for a single shear bolted connectionbetween sawn lumber members. Compare thevalues for gap distance (g) equal to 0 inch, ¼ inch,and ½ inch.

Given: The parallel and perpendicular to graindowel bearing strengths are equal to 4800 psi and2550 psi, respectively. Both side and mainmember thicknesses are 1-1/2 inches. Each

connection uses a single ½ inch diameter bolt(SAE J429 Grade 1), and the load is appliedparallel and perpendicular to grain.

R ,R = 1.5 inchess m

D, D , D = 0.5 inchs m

F = 45,000 psib,5%

F = 4800 psi, F = 2550 psie ez*

g = 0, 0.25, 0.5 inch

Bearing length, in. & Yield mode value, lbsgrain direction

Main Side I I II III III IVm s m s

Gap distance, g = 0 in.

1-½ 1-½ 900 (900) 900 (900) 414 (414) 550 (550) 550 (550) 663 (663)*

1-½ 1-½z 720 (720) 383 (383) 250 (250) 380 (380) 324 (324) 442 (442)*

1-½z 1-½z 383 (383) 383 (383) 176 (176) 289 (289) 289 (289) 387 (387)

*

Gap distance, g = ¼ in.

1-½ 1-½ 900 900 370 482 482 576*

1-½ 1-½z 720 383 224 341 284 393*

1-½z 1-½z 383 383 157 258 258 349

*

Gap distance, g = ½ in.

1-½ 1-½ 900 900 333 426 426 501*

1-½ 1-½z 720 383 202 307 250 350*

1-½z 1-½z 383 383 142 231 231 315

*

Underlined values represent nominal design values. Connection values in parentheses represent yield modevalues calculated using the NDS yield limit equations.



Example 2.2 - Lag Screw Connection

Problem Statement: Determine the nominaldesign value for a single shear lag screwconnection between sawn lumber members.Compare values assuming that fastener momentresistances in the side and main member are:

1) equal and based on the fastener root diameter,D (e.g. connection with fully threaded lag screw); Given: The parallel and perpendicular to grainr

2) unequal with fastener moment resistance in the 2950 psi, respectively. Side member thickness ismain member equal to 75% of the fastener moment 2-1/2 inches and lag screw bearing length in theresistance in the side member, M = 0.75 M where main member is 6 inches. Each connection uses am s

M is based on the unthreaded shank diameter, D single 3/4 inch diameter lag screw.s

(e.g. connection with unthreaded shank slightlyextended into the main member); and R = 2.5 inches, R = 6 inches

3) equal and based on the unthreaded shank F = 45,000 psidiameter, D ( e.g. connection with unthreaded F = 6150 psi, F = 2950 psishank extending deep into the main member). g = 0 inch

Consider side member loading parallel andperpendicular to grain and main member loadingparallel to grain. Case 2 handling of fastenermoment resistance is consistent with the treatmentof fastener moment resistance in the NDS yieldlimit equations for lag screws and wood screws.

dowel bearing strengths are equal to 6150 psi and

s m

D = 0.75 inch, D = 0.579 inchr

b,5%

e ez*

Bearing length,in. & grain Yield mode value, lbsorientation

Side I I II III III IVm s m s

Case 1

2-½ 6919 2883 (2226) 3311 3381 1573 (1210) 1222 (1004)*

2-½z 5535 1106 (854) 2297 2325 763 (585) 787 (647)

Case 2

2-½ 6919 2883 (2883) 3311 3480 1693 (1693) 1685 (1685)*

2-½z 5535 1106 (1106) 2297 2389 867 (867) 1085 (1085)

Case 3

2-½ 6919 2883 (2883) 3311 3480 1793 (1693) 1801 (1685)*

2-½z 5535 1106 (1106) 2297 2389 952 (867) 1160 (1085)

Underlined values represent nominal design values. Connection values in parentheses represent yield mode valuescalculated using the NDS yield limit equations.



Example 2.3 - Nailed Connection

Problem Statement: Determine the nominaldesign, proportional limit, 5% offset, and ultimatevalues for a single shear nailed connection betweensawn lumber members.

Given: Proportional limit; 5% offset; and ultimatedowel bearing strength are equal to 4088 psi, 4637psi, and 6093 psi respectively. The side memberthickness is 1-1/2 inches and penetration into themain member is 2 inches (p = 2.0 inches). Asingle 16d (0.162 inch diameter x 3-1/2” long)common nail is used in the connection. The load

direction for both side and main members isparallel to grain.

R = 1.5 inchess

R = 2.0 inchesm

D, D , D = 0.162 inchs m

F = 4083 psi, F = 69,000 psie,pl b,pl

F = 4637 psi, F = 90,000 psie, 5% b, 5%

F = 6093 psi, F = 115,000 psie,ult b,ult

g = 0 inch

Yield mode, lbs

I I II III III IVm s m s

Nominal design value 683 512 (512) 252 208 (242) 190 (190) 141 (141)

Proportional limit value 1323 992 488 455 350 195

5% offset value 1502 1127 554 532 417 310

Ultimate value 1974 1481 728 698 546 401

Underlined values represent nominal values for the given limit state. Connection values in parentheses representyield mode values calculated using the NDS yield limit equations.

Example 2.4 - Nailed Connection With Reduced Penetration

Problem Statement: Determine the nominaldesign value for a single shear nailed connectionbetween sawn lumber members.

Given: Side and main member thickness equals 1-1/2 inches, and have a dowel bearing strengthequal to 4637 psi. A single 16d (0.162 inch

diameter x 3-1/2” long) common nail is usedto make the connection.

R = 1.5 inches, R = 1.5 inchess m

D, D , D = 0.162 inchs m

F = 4637 psi, F = 90,000 psie, 5% b, 5%

g = 0 inch

Yield mode, lbs

Nail Size I I II III III IVm s m s

16d common 512 512 (395) 212 190 (146) 190 (146) 141 (109)(0.162" dia. x 3 ½")

The underlined value of 141 lbs. represents the nominal design value calculated in accordance with the generaldowel equations and recommendations for treatment of fastener bearing length in the main member. Connectionvalues in parentheses represent yield mode values calculated using the NDS yield limit equations multiplied bythe NDS Penetration Depth Factor, C , of 0.77.d

Mb s 'qs

4Rs&

Pqs

2

Mb m 'qm

4Rm&

Pqm

2

Mb s 'qs

4Rs&

P2qs

2



PART III. EQUATION DERIVATION

The yield model used to develop the general dowel R = side member bearing length, in.equations considers effects of dowel moment F = side member dowel bearingresistance and dowel bearing resistance on a strength, psiconnection’s lateral strength. Based on the F = main member dowel bearingEuropean Yield Model (Soltis 1991), connection strength, psistrength is assumed to be reached when: (1) D = dowel shank diameter, in.compressive strength of the member beneath thedowel is exceeded; or (2) one or more plastichinges forms in the dowel. Behavior of theconnection is assumed to be in accordance withyield modes depicted in Figure 1. Dowel loadingis assumed to be uniformly distributed andperpendicular to the axis of the dowel (e.g. ideallyplastic deformation). Effects of end fixity, tensionforces in the fastener, and friction betweenmembers is ignored.

Each yield mode addresses a specificloading condition on the dowel such that the dowelwill remain in static equilibrium. General dowelequations can be obtained by consideringequilibrium of forces within a connectionexhibiting behavior in accordance with yieldmodes I - IV. Applying this concept, a free-bodydiagram for each yield mode can be drawn, andprinciples of statics can be used to develop thegeneral dowel equations.

Mode I = (q/4)(R-P/q) .Yield modes I and I model connections limited Subscripts s and m indicate side and mainm s

by uniform bearing in the main and side member in the following equations for maximummember(s). Figure 2 Case A, shows that moment due to dowel bearing:maximum load, P, is determined by the followingequations: Single Shear:

P = q Rm m

P = q Rs s

Similarly, considering the geometry of a doubleshear connection, maximum load, P, is determinedby:

P = q Rm m

P = 2q R Double Shear:s s

where,q = side member dowel bearings

resistance = F D, lbs./in.es

q = main member dowel bearingm

resistance = F D, lbs./in.em

R = side member bearing length, in.s

m

es

em

Modes II-IVFor modes II-IV, consideration of conditions wherelimiting or maximum moments act on the dowelsimplifies equation derivation. These basicconditions are shown in Figure 2. In Case B,maximum moment is based on dowel bearing. InCase C, maximum moment is based on dowelbending. Note that maximum moments for bothcases occur at points of zero shear.

Maximum moment due to dowel bearing,shown in Case B of Figure 2, represents a loadcondition where the dowel is sufficiently large toprevent yielding of the dowel (dowel bending).For calculation purposes, let q define memberbearing resistance (lb/in) determined by theequation q = F D, R define member bearing lengthe

(in), and let x represent the location of zero shear(x = R-2a). The resulting maximum moment due todowel bearing, M , equals qa . Recognizing that ab

2

= (R-x)/2 and x = P/q and substituting results in Mb2

Ms 'Fb D 3

s

6

Mm 'Fb D 3

m

6

Ms 'B Fb,p l D

3s

3 2

Mm 'B Fb,p l D

3m

3 2

P 2 12qs

%1

2qm

%Pg& (ML s%MLm) ' 0

l

q

C a s e A

S h e a r , V

M o m e n t , M

M m a x

P

P

ba

q

q

C a s e B

x

M m a x

P

M o m e n t , M

S h e a r , V

ba

q

M

C a s e C

x

M

V

M

V

M

V

S h e a r , V

M o m e n t , M

M l

P

P

x

l l

P = V = q lM = q l / 2l

2P = V = q xM = q a

2m a x

P = V = q xM = Mm a x d o w e l



Maximum moment due to dowel bending, is where,shown in Case C of Figure 2. In this case, F , F = dowel bending strengthmaximum moment is limited to the moment D = dowel diameter atprovided by the dowel in bending which is maximum stress in siderepresented by a concentrated moment acting at the memberpoint of zero shear (x = P/q). Moment resistance D = dowel diameter atof the dowel assuming ideally plastic behavior is maximum stress in mainexpressed as follows: member

If elastic behavior is assumed, such as when relationships for maximum moment defined above,estimating values at proportional limit, the moment characteristic equations for the maximum load, P,resistance of the dowel can be expressed as can be determined as follows:follows:

b b,pl

s

m

Assumed loading conditions for each ofthe yield modes I-IV is provided in Figure 3.Each mode consists of an interaction of dowelbearing and dowel bending as shown in Figure 2.Considering equilibrium of the dowel for eachparticular yield mode (by summing momentsabout a fixed point on the dowel), and using

Single Shear:

Figure 2 General Conditions of Dowel Loading

P 2

41

2qs

%1

2qm

%Pg2& (ML s%MLm) ' 0 Mb s '

qs

4Rs&

Pqs

2

Mb m 'qm

4Rm&

Pqm

2

P 2 14qs

%1

4qm

% PRs

2%g%

Rm

2&

qsR2s

4%

qmR2m

4' 0

Mb m 'qm

4Rm&

Pqm

2

P 2 12qs

%1

4qm

% P g%Rm

2& Ms%

qmR2m

4' 0



Double Shear: Single Shear:

where,M = maximum moment developed inLs

the side member at xs

M = maximum moment developed inLm

the main member at x Substituting M and M into the characteristicm

g = gap distance (assumed to be equal equation for M and M results in the followingfor double shear connections) quadratic equation expressed in terms of known

Variables, M and M , represent values unknown variable, P.Ls Lm

of maximum moment due to dowel bearing ordowel bending depending on the mode being Single Shear:considered. An example single shear connectionwith assumed loading for yield mode II is providedin Figure 4. Shear and moment diagrams are alsoprovided. As shown in Figure 4, maximummoments, M and M for mode II occur atLs Lm

distances x and x from connected faces and ares m

based on moments, M and M , due to dowelbs bm

bearing.Derivation of the general dowel equations

assumes that critical stresses in the dowel occur atlocations of maximum induced moment. This isappropriate for dowels having a constant diameterin the side and main member. Dowel diameters inthe side and main member, however, do not needto be equal. For connections where doweldiameter is not constant within a member, it isconservative to assume that the least diameteroccurs at the location of maximum moment.Alternatively, critical stress in the dowel can bedetermined by considering the applicable momentand dowel section properties along the length ofthe dowel.

Yield modes II and III are not possible form

double shear connections as the assumed symmetryof double shear connections does not permit thesemodes to occur.

Mode II Single Shear:Yield Mode II models a connection limited bydowel bearing in the side and main members. Themaximum induced moment was previouslydetermined as follows:

bs bm

Ls Lm

properties of q , q , R , R , and g, and a singles m s m

Mode IIImMode III models a connection limited by dowelm

bearing in the main member and dowel bending inthe side member. The maximum load, P, isdetermined by solving the characteristic equationfor P where:

Single Shear:

M = dowel bending moment in the sides

member

Substituting M and M into the characteristics bm

equation for M and M results in the followingLs Lm

quadratic equation expressed in terms of knownproperties of q , q , R , M , and g, and a singles m m s

unknown variable, P.

Mb s 'qs

4Rs&

Pqs

2

Mb s 'qs

4Rs&

P2qs

2

P 2 14qs

%1

2qm

% PRs

2%g &

qsR2s

4% Mm ' 0

P 2

41

4qs

%1

2qm

%P2

Rs

2%g &

qsR2s

4% Mm ' 0

P 2 12qs

%1

2qm

% Pg& Ms% Mm ' 0

P 2

41

2qs

%1

2qm

%Pg2

& Ms% Mm ' 0



Mode IIIsMode III models a connection limited by dowels

bearing in the side member(s) and dowel bendingin the main member. The maximum load, P, isdetermined by solving the characteristic equationfor P where:

Single Shear: Mode IV

M = dowel bending moment in the main M = dowel bending moment in them

member side member(s)

Double Shear: main member

M = dowel bending moment in the mainm

member

Substituting M and M into the characteristicbs m

equation for M and M results in the followingLs Lm

quadratic equation(s) expressed in terms of knownproperties of q , q , R , M and g, and a singles m s m,


Single Shear:

Double Shear:

Mode IV models a connection limited by dowelbending in the main and side member(s). Themaximum load, P, is determined by solving thecharacteristic equation for P where:

s

M = dowel bending moment in them

Substituting M and M into the characteristics m

equations for M and M results in the followingLs Lm

quadratic equations expressed in terms of knownproperties of q , q , M , M , and g, and a singles m s m


Single Shear:

Double Shear:

P

P

q m

P

P

q s

P

P

qm

qmqs

q s

P

P

q m

q mq s

Ms

P

P

q m

q s

Ms

Mm

P

P

qm

qs

qs

Mm

P

P/2 P/2

qm

P

P/2 P/2

q s q s

P

P/2 P/2

q m q m

q s q s

Ms MsMm

P

P/2 P/2

q m q m

qs qs

qs qs

Mm

Mode II

Mode IV

Mode Im

Mode Is

Mode IIIm

Mode IIIs

Single Shear Connections Double Shear Connections



Figure 3 Connection Yield Modes Assumed Loading

g

Dowel

P

P

Side member

Main member

gap

q

q

a b

R

xm

xs

Single Shear Dowel Joint

s

s

s

s

m

qm

qs

Shear Diagram, V

Moment Diagram, M

P

P

M max

Rm

Single Shear Dowel Joint with Uniform Loading



Figure 4 Single Shear Connection, Mode II



References Additional ReferencesAF&PA. 1997. National Design Specification (NDS ) AF&PA. 1999. Commentary on the National Design® ®

for Wood Construction. American Forest & Paper Specification (NDS ) for Wood Construction, 1991Association, Washington, DC. Edition with Addendum on 1997 Provisions. American

AISC. 1989. Manual of Steel Construction, AllowableStress Design, ninth edition. American Institute of APA. 1996. Bearing Strength of OSB to be Used forSteel Construction, Inc. Chicago, IL. The EYM Design Method. APA The Engineered Wood

AISI. 1996. Cold Formed Steel Design Manual.American Iron and Steel Institute. Washington, DC. Aune, Petter; Patton-Mallory, Marcia. Lateral load-

ASTM D5652-95 Standard Test Methods for Bolted theory: Theoretical Development. Res. Pap. FPL 469.Connections in Wood and Wood-Base Products. Madison, WI. U.S. Department of Agriculture, ForestVolume 4.10 Wood. ASTM, West Conshohocken, PA. Service, Forest Products Laboratory; 1986. 20 p.

ASTM D5764-97 Standard Test Method for Evaluating Aune, Petter; Patton-Mallory, Marcia. Lateral load-Dowel-Bearing Strength of Wood and Wood-Base bearing capacity of nailed joints based on the yieldProducts. Volume 4.10 Wood. ASTM, West theory: Experimental verification. Res. Pap. FPL 470.Conshohocken, PA. Madison, WI. U.S. Department of Agriculture, Forest

ASTM F606-95b Determining the MechanicalProperties of Externally and Internally Threaded Ehlbeck, J., Nailed Joints in Wood Structures. No. 166.Fasteners, Washers, and Rivets. Volume 15.08 Blacksburg, VA. Virginia Polytechnic Institute andFasteners. ASTM. West Conshohocken, PA 1995. State University Wood Research and Wood

ASTM F1575-95 Standard Test Method forDetermining Bending Yield Moment of Nails. Volume Karacabeyli, E., Lateral Strength of Bolted15.08 Fasteners. ASTM, West Conshohocken, PA. Wood-to-Concrete Connections, 1997, Forintek Canada

Biolzi, L., and Giuriani, E., Bearing Capacity of a BarUnder Transversal Loads, Materials and Structures, V. McLain, T.E., Soltis, L.A., Pollock, D.G., Wilkinson,23, n 138, Nov., 1990, pp. 449-456, University di T.L., LRFD For Engineered Wood Structures-Udine, Udine, Italy. Connection Behavioral Equations, ASCE Structures

Loferski, J.R. and McLain, T.E., Static and ImpactFlexural Properties of Common Wire Nails, Journal of McLain, T.E., Strength of Lag-Screw Connections,Testing and Evaluation, JTEVA, Vol. 19, No. 4, July Journal of Structural Engineering, Vol, 118, No. 10,1991, pp. 297-304. October, 1992.

Soltis, L.A. European Yield Model for Wood Soltis, L.A., and Wilkinson, T.L. (1987). BoltedConnections. New York, NY: American Society of Connection Design. General Tech. Rep. FPL-GTR-54.Civil Engineers, Proceedings of Structures Congress Madison, WI. U.S. Deptartment of Agriculture, Forest‘91, Indianapolis, IN 60-63; 1991. Service, Forest Products Laboratory; 1987. 21p.

Vintzeleou, E.N., Tassios, T.P. 1986. MathematicalModels for Dowel Action Under Monotonic and CyclicConditions. Magazine of Concrete Research: Vol. 38,No. 134: March 1986.

Wilkinson, T.L. 1991. Dowel Bearing Strength.Forest Products Laboratory Research Paper FPL-RP-505. Madison, WI: U.S. Department of Agriculture,Forest Service, Forest Products Laboratory.

® ®

Forest & Paper Association, Washington, DC.

Association, Tacoma, Washington.

bearing capacity of nailed joints based on the yield

Service, Forest Products Laboratory; 1986. 29 p.

Construction Laboratory; September 1979. 148 p.

Corp., Western Region, Vancouver, B.C.

Journal, Vol. 119(10) 3024-3028, Oct. 1993.

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The American Wood Council (AWC) is the wood productsdivision of the American Forest & Paper Association (AF&PA).AF&PA is the national trade association of the forest, paper,and wood products industry, representing member companiesengaged in growing, harvesting, and processing wood andwood fiber, manufacturing pulp, paper, and paperboardproducts from both virgin and recycled fiber, and producingengineered and traditional wood products. AF&PA represents asegment of industry which accounts for over 8% of the totalU.S. manufacturing output.

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