TR12 General Dowel Equations For

ANSI/AWC NDS-2012 Approval Date: August 15, 2011

ASD/LRFD TECHNICAL REPORT 12 ®

NDS® National Design Specification for Wood Construction with Commentary

General Dowel 2012 EDITION Equations for Calculating Lateral Connection Values with Appendix A The American Wood Council (AWC) is the voice of North American traditional and engineered wood products. From a renewable resource that absorbs and sequesters carbon, the wood products industry makes products that are essential to everyday life. AWC’s engineers, technologists, scientists, and building code experts develop state-of-the-art engineering data, technology, and standards on structural wood products for use by design professionals, building officials, and wood products manufacturers to assure the safe and efficient design and use of wood structural components. TECHNICAL REPORT 12 General Dowel Equations for Calculating Lateral Connection Values with Appendix A

While every effort has been made to insure the accuracy of the information presented, and special effort has been made to assure that the information reflects the state-of- the-art, neither the American Wood Council nor its members assume any responsibility for any particular design prepared from this publication. Those using this document assume all liability from its use.

Table of Contents

Part/Title Page Part/Title Page 1 General Dowel Equations 3 Example Problems

1.1 Introduction 1 3.1 Bolted Connection with Gap 17 1.2 Lateral Connection Values 1 3.2 Lag Screw Connection 17 1.3 Reference Design Value 1 3.3 Lag Screw Penetration 20 1.4 Connection with Members of Solid 3.4 Steel Side Member to Wood Main Cross Section 1 Member – Tapered Tip Effects 22 1.5 Connections with Members of Hollow 3.5 Bolted Connection through Solid and Cross Section 1 Hollow Members – Double Shear 23 1.6 Dowel Bearing Strength and Fastener Bending Yield Strength 2 4 References 1.7 Notation 2 References 24 2 Equation Derivation Appendix A Dowel Bearing 2.1 Introduction 6 Strength and Fastener 2.2 Equation Derivation for Connections Bending Yield Strength with Members of Solid Cross Section 7 A.1 Introduction 25 2.3 Tapered Tip Equation Derivation 13 A.2 Notation 25 2.4 Equation Derivation for Connections A.3 Dowel Bearing Strength 25 with Members of Hollow Cross Section 14 A.4 Dowel Bending Yield Strength 28 A.5 References 29

List of Tables

1-1 General Dowel Equations for Solid Cross A1 Dowel Bearing Strength, Fe...... 27 Section Members...... 3 A2 Dowel Bending Yield Strength...... 29 1-2 General Dowel Equations for Solid Cross Section Main Members and Hollow Cross Section Side Member(s)...... 4 1-3 General Dowel Equations for Hollow Cross Section Main Member and Solid Cross Section Side Member(s)...... 5

List of Figures

2-1 Connection Yield Modes – Solid Cross 2-5 Single Shear Connection –Mode II...... 12 Section Members...... 6 2-6 Dowel Bearing with Tapered Tip 2-2 Connection Yield Modes – Solid and Connector...... 13 Hollow Cross Section Members...... 7 2-7 General Conditions of Dowel 2-3 General Conditions of Dowel Loading – Hollow Cross Section Members..15 Loading – Solid Members...... 8 A1 Dowel Bearing Strength Test Specimen...... 26 2-4 Connection Yield Modes Assumed A2 Dowel Bending Strength...... 28 Loading – Solid Members...... 11

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 1

PART 1. General Dowel Equations

1.1 Introduction 1.3 Reference Design Value

A generalized form of the National Design The reference design value, Z, is the minimum of ® ® Specification (NDS ) for Wood Construction (AWC, the calculated, P/Rd, for all yield modes as follows: 2012) yield limit equations applicable to dowel-type  P  fastener connections between members of solid cross Z Minmum= value of   (1)  Rd  section is provided in Table 1-1 of this report. Equations are also provided for connections with side where: or main members of hollow cross section, in Tables 1-2 Z = Reference lateral design value and 1-3, respectively. The variables for these tables are defined in Section 1.6. These general dowel equations P = Reference 5% offset yield value are applicable to NDS connection conditions, allow for Rd = NDS reduction term for dowel type fastener evaluation of connections with gaps between connected connections, see NDS Table 11.3.1B members, and include separate equation variables to better account for varying bearing and moment 1.4 Connections with Members of Solid resistances of fasteners having more than one diameter Cross Section along their length (such as threaded fasteners). Equations in Table 1-1 are applicable for 1.2 Lateral Connection Values calculation of reference 5% offset yield, P, for dowel type fastener connections where connected members Yield limit equations provided herein apply to are of solid cross section. The reference 5% offset calculation of lateral values for single fastener yield, P, is calculated for each applicable connection connections between wood-based members and yield mode, as depicted in Table 1-1. Example connections of wood-based members to steel and applications of equations in Table 1-1 are provided in concrete/masonry components. Design criteria for Part 3 of this report. dowel type fastener connections are provided in the NDS for Wood Construction and include the following 1.5 Connections with Members of Hollow considerations: Cross Section  fastener design limit states (e.g. tension, bearing, and shear); Equations in Table 1-2 are applicable for  fastener spacing, edge, and end distance; calculation of reference 5% offset yield, P, for dowel  connection fabrication and tolerances; type fastener connections where the main member is of  connection geometry; solid cross section and the side member(s) have a  multiple fasteners and group action; hollow cross section. Equations in Table 1-3 are  member strength at the connection; applicable for calculation of reference 5% offset yield,  adjustments for end use (e.g. load duration and P, for dowel type fastener connections where the main wet service) and fastener type (e.g. drift bolts member has a hollow cross section and the side and drift pins). member(s) is/are of solid cross section. The equations  member bearing strengths; in Tables 1-2 and 1-3 are based on the assumption that  fastener bending strengths; the dowel penetrates both walls of the hollow member  reduction factors, Rd, to adjust reference 5% and the thickness of each wall through which the dowel offset yield connection values, P, to reference penetrates, tws or twm, is the same. Connection yield allowable stress design values, Z. modes are depicted in Tables 1-2 and 1-3. Example applications of equations in Table 1-3 are provided in Part 3 of this report.

AMERICAN WOOD COUNCIL 2 GENERAL DOWEL EQUATIONS

1.6 Dowel Bearing Strength and Fastener Mbm = main member dowel bearing maximum Bending Yield Strength moment, in.-lbs Mbs = side member dowel bearing maximum

Dowel bearing strengths, Fe, and fastener bending yield moment, in.-lbs strengths, Fyb, are provided in Appendix A. Mds = side member dowel moment resistance, 3 Fyb(Ds /6), in.-lbs Mdm = main member dowel moment resistance, 1.7 Notation 3 Fyb(Dm /6), in.-lbs Ms = maximum moment developed in side D = dowel diameter, in. member at xs, in.-lbs Ds = dowel diameter at maximum stress in side Mm = maximum moment developed in main member, in. member at x, in.-lbs Dm = dowel diameter at maximum stress in main P = reference 5% offset yield lateral connection member, in. value for a single fastener connection, lbs Dr = fastener root diameter, in. p = dowel penetration, in. E = length of tapered dowel tip, in. qs = side member dowel-bearing resistance, FesD, Fe = dowel bearing strength, psi lbs./in. Fe‖ = dowel bearing strength parallel to grain in qm = main member dowel-bearing resistance, wood, psi FemD, lbs./in. Fe = dowel bearing strength perpendicular to t = thickness, in. grain in wood, psi tws = wall thickness in hollow side member, in. Fes = side member dowel bearing strength, psi twm = wall thickness in hollow main member, in. Fem = main member dowel bearing strength, psi vs = length of void space along the axis of the Ftu = tensile ultimate strength, psi dowel in hollow side member, in. Fu = specified minimum tensile strength, psi vm = length of void space along the axis of the Fy = specified minimum tensile yield strength, dowel in hollow main member, in. psi x = distance from shear plane to maximum Fyb = specified minimum dowel bending yield moment, in. strength of fastener, psi Rd = NDS reduction term for dowel type G = specific gravity fasteners g = gap between members, in. Z = reference lateral design value for a single Ls = side member dowel-bearing length, in. fastener connection, lbs Lm = main member dowel-bearing length, in. Zʹ = adjusted lateral design value for a single fastener connection, lbs

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 3

Table 1-1 General Dowel Equations for Solid Cross Section Members2

Yield Mode Single Shear Double Shear Description

Im P = qmLm P = qmLm

Is P = qsLs P = 2 qsLs

2 2 General equation for member bearing  B + B - 4 A C  B + B - 4 A C II-IV P= P= and dowel yielding 2 A A Inputs A, B, & C for Yield Modes II-IV 1 22 II 1 1 LLsm qqLLsm = A = + B = + g + C = -sm - 4 q 4 q 22 44 ms 1 2 IIIm Lm 1 1 B = g + qmLm = A = + 2 C = - M s - 2 q 4 qms 4 2 IIIs 1 1 Ls q = A = + B = + g s Ls 2 C = - - M m 4 q 2 qms 4

IV 1 1 B = g C = - M - M ms = A = + 2 q 2 qms 1 Yield Modes II and IIIm do not apply for double shear connections. 2See Section 1.6 for notation.

AMERICAN WOOD COUNCIL 4 GENERAL DOWEL EQUATIONS

Table 1-2 General Dowel Equations for Solid Cross-Section Main Member and Hollow Cross Section Side Member(s)2 Table 1-3 General Dowel Equations for Hollow Cross Section Main Member and Solid Cross Section Side Member(s)2

Yield Yield Mode Single Shear Double Shear Description Mode Single Shear Double Shear Description

Im P = qm Lm P = qmLm Im P = 2qm t wm P = 2qmt wm

Is P = P = 4 2qst ws qs tws Is P = qsLs P = 2 qsLs

2 2 2  2  General equation for member bearing  B + B - 4 A C  B + B - 4 A C General equation for member bearing B + B - 4 A C B + B - 4 A C P= P= P= P= and dowel yielding II-IV and dowel yielding II-IV 2 A A 2 A A Inputs A, B, & C for Yield Modes II-IV Inputs A, B, & C for Yield Modes II-IV 2 2 1 1 L 1 1 Lm 1 s qLss 1 B = t + v g + qLmm II A = + B = twm + v m  g + C = -q t() t v - II A = + ws s C = -qt t(  v) - m wm wm m sws ws s 4 q 4 qms 2 4 4 q 4 qms 2 4

1 1 2 1 1 1 IIIm A = +   1 Lm qLmm B = g + twm v m C = - M s -qm twm() twm v m IIIm A = + B = g + C = - - 2 q 4 q 2q 4 q M s ms ms 2 4 1 1 2 Ls qs Ls 1 1 IIIs A = + B = + g C = - - M m IIIs A = +  4 q 2 qms 2 4 B = tws v s + g C = -qts tws( ws  v s ) - M m 4 q 2 qms 1 1 IV A = + B = g C = - M - M ms 1 1 2 q 2 qms IV A = + B = g C = - M - M ms 2 q 2 q 1 ms Yield Modes II and IIIm do not apply for double shear connections. 2See Section 1.6 for notation. 1 Yield Modes II and IIIm do not apply for double shear connections. 2See Section 1.6 for notation.

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 5

Yield Yield Mode Single Shear Double Shear Description Mode Single Shear Double Shear Description

Im P = qm Lm P = qmLm Im P = 2qm t wm P = 2qmt wm

Is P = P = 4 2qst ws qs tws Is P = qsLs P = 2 qsLs

1 1 2 1 1 1 IIIm A = +   1 Lm qLmm B = g + twm v m C = - M s -qm twm() twm v m IIIm A = + B = g + C = - - 2 q 4 q 2 q 4 q M s ms ms 2 4 1 1 2 Ls qs Ls 1 1 IIIs A = + B = + g C = - - M m IIIs A = +  4 q 2 qms 2 4 B = tws v s + g C = -qts tws( ws  v s ) - M m 4 q 2 qms 1 1 IV A = + B = g C = - M - M ms 1 1 2 q 2 qms IV A = + B = g C = - M - M ms 2 q 2 q 1 ms Yield Modes II and IIIm do not apply for double shear connections. 2See Section 1.6 for notation. 1 Yield Modes II and IIIm do not apply for double shear connections. 2See Section 1.6 for notation.

AMERICAN WOOD COUNCIL 6 EQUATION DERIVATION

PART 2. Equation Derivation

2.1 Introduction between members are conservatively ignored. End fixity is the resistance to rotation provided at the The yield model used to develop the general end(s) of the dowel, such as under a nail head or bolt dowel equations considers effects of dowel moment nut and washer. The strength contribution of end fixity resistance and dowel bearing resistance on a is difficult to predict and may be dependent on several connection’s lateral strength. Based on the European factors including load level, fastener type and Yield Model (Soltis 1991), connection strength is installation, washer or fastener head size (e.g. nail or assumed to be reached when: (1) compressive strength screw head size), tensile forces that may develop in the of the member beneath the dowel is exceeded; or (2) fastener under lateral loading, and amount of one or more plastic hinges forms in the dowel. dimensional change in connected members. Frictional Behavior of the connection is assumed to be in resistance to slipping of connection members is not accordance with yield modes depicted in Tables 1-1, typically addressed in wood connection design 1-2 and 1-3. Dowel loading is assumed to be because the amount of frictional force is difficult to uniformly distributed and perpendicular to the axis of predict and in many instances may not exist as wood the dowel (e.g. ideally plastic deformation). Each yield shrinks or the connection relaxes. mode addresses a specific loading condition on the 2.1.2 Predicted Yield Mode dowel such that the dowel will remain in static Predicted yield modes for single fastener equilibrium. General dowel equations can be obtained connections are in agreement with yield modes by considering equilibrium of forces within a observed from connection tests where end and edge connection exhibiting behavior in accordance with distance, member cross section, and fastener size are yield modes I – IV as shown in Tables 1-1, 1-2 and 1-3, adequate to ensure development of yielding by and Figures 2-1 and 2-2. Applying this concept, a free- precluding occurrence of premature wood failures body diagram for each yield mode can be drawn, and such as those due to splitting, formation of a wood principles of statics can be used to develop the general shear plug, fastener failure or fastener withdrawal. dowel equations. These and other failure limit states are not specifically 2.1.1 End Fixity and Friction addressed by the yield mode equations. Potential increased strength due to effects of end fixity, tension forces in the fastener, and friction

Figure 2-1 Connection Yield Modes – Solid Cross Section Members Section Members

“m” denotes main member, “s” denotes side member

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 7

2.2 Equation Derivation for Connections simplifies equation derivation. These basic conditions with Members of Solid Cross Section are shown in Figure 2-3. In Case B, maximum moment is based on dowel bearing. In Case C, 2.2.1 Mode I maximum moment is based on dowel bending. Yield modes Im and Is model connections limited Maximum moments for both cases occur at points of by uniform bearing in the main and side member(s). zero shear. Maximum moment due to dowel bearing, Figure 2-3, Case A, shows that the maximum value for shown in Case B of Figure 2-3, represents a load shear, P, is determined by the following equations: condition where the dowel’s moment capacity is sufficiently large to prevent yielding of the dowel P = qmLm (2) (dowel bending). For calculation purposes, let q define

P = qsLs (3) member bearing resistance (lb/in.) (q = FeDb), L, define member bearing length (in.), and let x represent Similarly, considering the geometry of a double the location of zero shear (x = L – 2a). The resulting shear connection, the maximum value for shear, P, is maximum moment due to dowel bearing, Mb, equals determined by: qa2. Recognizing that a = (L – x)/2 and x = P/q and 2 P = qmLm (2) substituting results in Mb = (q/4)(L – P/q) for single shear connections. P = 2qsLs (4) Subscripts s and m indicate side and main member 2.2.2 Modes II-IV in the following equations for maximum moment due For modes II-IV, considering conditions where to dowel bearing: limiting or maximum moments act on the dowel

Figure 2-2 Connection Yield Modes – Solid and Hollow Cross Section Members

“m” denotes main member, “s” denotes side member

AMERICAN WOOD COUNCIL 8 EQUATION DERIVATION

Single Shear: 3 Fyb Ds = (8) 2 M ds q P 6 s (5) MLb s = s - 3 4 qs Fyb Dm M dm = (9) 2 6  qm P MLb m = m - (6) Assumed solid section loading conditions for each 4 qm of the yield modes I-IV is provided in Figure 2-4. Double Shear: Each mode consists of an interaction of dowel bearing and dowel bending as shown in Figure 2-3. 2  Considering equilibrium of the dowel for each qs P MLb s = s - (7) particular yield mode (by summing moments about a 42qs fixed point on the dowel), and using relationships for maximum moment defined above, characteristic

equations for the maximum load, P, can be determined Maximum moment due to dowel bending is shown as follows: in Case C of Figure 2-3. In this case, maximum moment is limited to the moment provided by the dowel in bending which is represented by a concentrated moment acting at the point of zero shear (x = P/q). Moment resistance of the dowel, assuming ideally plastic behavior, is expressed as follows:

Figure 2-3 General Conditions of Dowel Loading – Solid Members

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 9

Single Shear: Single Shear:

2 11  2 qs P P  + + P g - (MMsm + ) = 0 (10) b s = s - (5) 22qq ML sm 4 qs

Double Shear: 2 q P = m - (6) 2  MLb m m P 1 1 P g 4 qm  + + - (MMsm + ) = 0 (11) 42qqsm 2 2 Substituting Mbs and Mbm into the characteristic equation for Ms and Mm results in the following where: quadratic equation expressed in terms of known

Ms = maximum moment developed in the side properties for dowel-bearing resistance (qs and qm), dowel-bearing length (Ls and Lm), and the gap between member at xs members (g), and a single unknown variable, P. Mm = maximum moment developed in the main member at xm Single Shear:

g = gap distance (assumed to be equal for  2 2 2 11 LLsmqsmLs q Lm double shear connections) P  + + P  + g + -  + = 0 (12) 44qqsm  2 2 4 4 Variables Ms and Mm represent values of maximum moment due to dowel bearing or dowel 2.2.4 Mode IIIm bending depending on the mode being considered. An Mode IIIm models a connection limited by dowel example single shear connection with assumed loading bearing in the main member and dowel bending in the for yield mode II is provided in Figure 2-5. Shear and side member. The maximum load, P, is determined by moment diagrams are also provided. As shown in solving the characteristic equation for P:

Figure 2-5, maximum moments, Ms and Mm for mode II occur at distance xs and xm from connected faces, Single Shear: and are based on moments Mbs and Mbm due to dowel 2 bearing.  qm P Derivation of the general dowel equations assumes MLb m = m - (13) 4 q that critical stresses in the dowel occur at locations of m maximum induced moment. This is appropriate for dowels having a constant diameter in the side and and:

main member. Dowel diameters in the side and main Mds = side member dowel moment resistance member, however, do not need to be equal. For connections where dowel diameter is not constant Substituting Mds and Mbm into the characteristic within a member, it is conservative to assume that the equation for Ms and Mm results in the following least diameter occurs at the location of maximum quadratic equation expressed in terms of known moment. Alternatively, critical stress in the dowel can properties for dowel-bearing resistance (qs and qm), be determined by considering the applicable moment dowel-bearing length (Lm and Lds), and the gap between and dowel section properties along the length of the members (g), and a single unknown variable, P. dowel. Yield modes II and IIIm are not possible for double Single Shear: shear connections, as the assumed symmetry of double  2 shear connections does not permit these modes to 2 11 Lm qmLm  + + P g + - ds + = 0 (14) occur. PM 24qqsm 2 4 2.2.3 Mode II 2.2.5 Mode IIIs Yield Mode II models a connection limited by Mode IIIs models a connection limited by dowel dowel bearing in the side and main members. The bearing in the side member(s) and dowel bending in the maximum induced moment was previously determined main member. The maximum load, P, is determined by as follows: solving the characteristic equation for P.

AMERICAN WOOD COUNCIL 10 EQUATION DERIVATION

Single Shear: Double Shear: 2 2  2 q P PL11 Ps qs Ls s  + + + g - + M m = 0 (16) MLb s = s - (5)  44qqsm 2 22 4 4 qs 2.2.6 Mode IV and: Mode IV models a connection limited by dowel bending in the main and side member(s). The Mm = dowel bending moment in the main maximum load, P, is determined by solving the member characteristic equation for P: Double Shear: where: 2  Mds = side member dowel moment resistance qs P MLb s = s - (7)

42qs Mdm = main member dowel moment resistance

Substituting Mds and Mdm into the characteristic and: equations (equations 10 and 11) for Ms and Mm results in the following quadratic equations expressed in

Mdm = main member dowel moment resistance terms of known properties for dowel-bearing resistance (qs and qm), dowel-bearing length (Ms and Mm), and the Substituting Mbs and Mdm into the characteristic gap between members (g), and a single unknown equations (equations 10 and 11) for Ms and Mm results variable, P. in the following quadratic equation(s) expressed in terms of known properties of qs, qm, Ls, Mm, and g, and a single unknown variable, P. Single Shear:  2 11 Single Shear: P  + + P g -  MMds + dm = 0 (17) 22qqsm  2 2 11 Ls qs Ls PM  + + P  + g -  + dm = 0 (15) 42qqsm  2 4 Double Shear:

P2 1 1 P g  + + -  M ds + Mdm = 0 (18) 42qqsm 2 2

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 11

Figure 2-4 Connection Yield Modes Assumed Loading – Solid Members

AMERICAN WOOD COUNCIL 12 EQUATION DERIVATION

Figure 2-5 Single Shear Connection - Mode II

Single Shear Dowel Joint

Single Shear Dowel Joint with Uniform Loading

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 13

2.3 Tapered Tip Equation Derivation 2 2 P PLssq Ls M b s =  (22) 4q 24 Equations considering effect of a tapered fastener s tip are based on connections composed entirely of 2  p2 2  solid-cross section members but with bearing P  Ep   pE 5E  M b m = P   qm   (23) resistance in the penetrated member based on a   qm  24   44 4 48  combination of full diameter bearing and reduced diameter bearing of the tapered fastener tip. The maximum moment due to dowel bending is 2.3.1 Mode I limited to the moment provided by the dowel in bending which is represented by a concentrated The bearing resistance of the fastener with a moment acting at the point of zero shear (x = P/q). tapered tip can be calculated as the combination of Moment resistance of the dowel, Mds and Mdm, bearing resistance provided by the full diameter assuming ideally plastic behavior, is expressed in portion of the fastener plus the bearing resistance equations 8 and 9. provided by the tapered tip which is modeled as having diameter vary linearly from full diameter to a Figure 2-6 Dowel Bearing with Tapered Tip point over the length of the tapered tip, E. Maximum load P is determined by: Connector 1 P = q  p  qE E (19) m 2 m

The Mode Im equation can be further simplified to:

 E  P =  pq -  (20) m  2  For single shear connections, bearing in the side member is based on diameter, D. Maximum load P is determined by the characteristic equation:

P = qss L (3) Considering the geometry of a double shear connection, where the tip is in the side member, maximum load, P, is determined by:

P = qmm L (2) E P = qs 2Ls  (21) 2 2.3.2 Modes II-IV Figure 2-6 illustrates a general dowel bearing scenario with a tapered tip connector. For calculation purposes, let q define member bearing resistance (lb/in.) determined by the equation q = FeDb, p define penetration length (in), E define the length of taper (in), and let x represent the location of zero shear (x = p-a-b-E). The resulting maximum moment due to Substitution of values of maximum bearing 2 2 resistance and maximum moment resistance as dowel bearing, Mb, equals qa + qE /24. Recognizing applicable for the yield mode into characteristic that am = p/2 – xm/2 – E/4 and x = P/q results in the following equations for maximum moment due to equation for single shear (equation 10) and for double dowel bearing: shear (equation 11) result in equations the maximum load, P, as follows:

AMERICAN WOOD COUNCIL 14 EQUATION DERIVATION

Mode II 2.4 Equation Derivation for Connections Single Shear: with Members of Hollow Cross Section  2 11 Ls pE P  + + P  + g +  Following the approach for connections composed 44qq  2 24 sm (24) entirely of members having solid cross sections, 2 22 equations for connections composed of a combination qsmmLs qqp pE q m5 E -  +  = 0 of members having solid and hollow cross section can 4 4 4 48 be developed as shown in Section 2.4 for yield modes depicted in Tables 1-2 and 1-3. Equations in Section Mode IIIm 2.4 are based on assumed connection configurations Single Shear: composed entirely of hollow cross section members for both side and main members. 11 pE P2  + + P  g +  24qq 2 4 2.4.1 Mode I sm (25) Yield modes Im and Is model connections limited 22 qqmmp pE q m5 E by uniform bearing in the main and side member(s). - M s +  = 0 4 4 48 Figure 2-7, Case A, shows that the maximum value for shear, P, is determined by the following equations:

Mode IIIs P = 2qmtwm (30) Single Shear: P = 2qstws (31)  2 2 11 Ls qs Ls PM  + + P  + g -  + dm = 0 (26) Similarly, considering the geometry of a double 42qqsm  2 4 shear connection, the maximum value for shear, P, is determined by the equations: Double Shear: P = 2qmtwm (30) 2 11 Pq 2 PLs s Ls (27)  + +  + g -  + M dm = 0 P = 4qstws (32) 44qqsm 2 22 4 2.4.2 Modes II-IV Mode IV For modes II-IV, considering conditions where Single Shear: limiting or maximum moments act on the dowel simplifies equation derivation (see Figure 2-7). In  2 11 Case B, maximum moment is based on dowel bearing. P  + + P g -  MMds + dm = 0 (28) 22qq In Case C, maximum moment is based on dowel sm bending. Maximum moments for both cases occur at Double Shear: points of zero shear. Parsons (2001) showed that for hollow cross section members, the controlling load 2 1 1 P g cases show that all dowel yielding occurs in the wall P (29)  + + -  M ds + Mdm = 0 next to the shear plane, therefore only these cases are 42qqsm 2 2 considered in this document. For double shear where side member penetrations Maximum moment due to dowel bearing, shown in are unequal, Ls shall be taken as the minimum bearing Case B of Figure 2-7, represents a load condition length in either of the two side members. where the dowel is sufficiently large to prevent yielding of the dowel (dowel bending). For calculation 2.3.3 NDS Assumption purposes, let q define member bearing resistance For connectors with a tapered tip, the NDS (lb/in.) (q = FeDb), tw define member wall thickness specifies that bearing length is permitted to be (in.), and let x represent the location of zero shear (x = calculated as L = p – E/2. Example 2.4 in Part 3 of this 2(tw – a)). report shows that the NDS requirement closely The resulting maximum moment due to dowel approximates results from the more detailed evaluation 2 bearing, Mb, equals qa + 2qav – qtwv. Recognizing of a tapered tip on bearing resistance in accordance that a = tw – x/2 and x = P/q, and substituting, results with the foregoing derivations. 2 2 in Mb = P/(4q) – P(tw + v) + qtw + qtwv in the member.

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 15

Subscripts s and m indicate side and main member ideally plastic behavior, is expressed in equations 8 in the following equations for maximum moment due and 9. to dowel bearing: Following the method established in Section 2.2, the maximum load, P, can be determined using the Single Shear: same characteristic equations used for solid members

2 (equations 10 and 11). P 2 Similar to solid members, yield modes II and IIIm = P    qvt  qt t v (33) M b s ws ss ws s ws s are not possible for double shear connections, as the 4qs assumed symmetry of double shear connections does 2 not permit these modes to occur. P 2 b m =  P t  v q t  q t v (34) M wm m s wm m wm m 2.4.3 Mode II 4qm Yield Mode II models a connection limited by Double Shear: dowel bearing in the side and main members. The maximum induced moment was previously determined 2 tv P ws s 2 (equations 33 and 34). Substituting Mbs and Mbm into M b s =  P  qs t ws  q s t ws v s (35) 16qs  2 2 the characteristic equation for Ms and Mm results in the following quadratic equation, expressed in terms of Maximum moment due to dowel bending is shown known properties for dowel-bearing resistance (qs and in Case C of Figure 2-7. In this case, maximum qm), dowel-bearing length (Ls and Lm), and the gap moment is limited to the moment provided by the between members (g), and a single unknown variable, P. dowel in bending which is represented by a concentrated moment acting at the point of zero shear (x = P/q). Moment resistance of the dowel, assuming

Figure 2-7 General Conditions of Dowel Loading – Hollow Cross Section Members

Single Shear:  (36) 2 11 P  + + P  tws v s + g t wm + v m  44qqsm AMERICAN WOOD COUNCIL 22 -  qs t ws q s t ws q m t wm  q m t wm v m  = 0 16 EQUATION DERIVATION

properties for dowel-bearing resistance (qs and qm), dowel-bearing length (Ls), dowel moment resistance 2.4.4 Mode IIIm (Mdm) and the gap between members (g), and a single Mode IIIm models a connection limited by dowel unknown variable, P. bearing in the main member and dowel bending in the side member. Dowel bending will occur in the member wall closest to the shear plane. Substituting Single Shear: Mds (equation 8) and Mbm (equation 34) into the  characteristic equation (equations 10 and 11) for Ms 2 11 P  + + P  tws v s + g and Mm results in the following quadratic equation 42qqsm (38) expressed in terms of known properties for dowel- 2 bearing resistance (qs and qm), dowel-bearing length -  qs t ws q s t ws v s + M dm  = 0 (Lm), dowel moment resistance (Mds) and the gap between members (g), and a single unknown variable, Double Shear: P. 2  P 11 P  + +  tws v s + g 4 42qq 2 Single Shear: sm (39) 2 -  qs t ws q s t ws v s + M dm  = 0 11 2 + + P g + t v P wm m 2.4.6 Mode IV 24qqsm (37) Mode IV models a connection limited by dowel 2 bending in the main and side member(s). Substituting - M ds +qm t wm q m t wm v m  = 0 Mds and Mdm (equations 8 and 9) into the characteristic 2.4.5 Mode IIIs equations for Ms and Mm yields the same quadratic Mode IIIs models a connection limited by dowel equations developed for solid sections (equations 17 bearing in the side member(s) and dowel bending in and 18). the main member. Substituting Mbs (equations 33 and An alternative, energy based derivation, 35) and Mdm (equation 9) into the characteristic producing the same results in different equation equation for Ms and Mm results in the following format, is provided in Parsons (2001). quadratic equation(s) expressed in terms of known

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 17

PART 3. Example Problems

Example 3.1 Bolted Connection with Gap

Problem Statement: Determine the reference design Given: Both side and main member thicknesses are value, Z, for a wood-to-wood single shear bolted 1.5 in. Each connection uses a single ½ in. diameter connection. Compare values for gap distance, g, equal bolt (SAE J429 Grade 1). to 0 in., ¼ in., and ½ in. Connection end and edge Ls = Lm = 1.5 in. distances are assumed to be in accordance with D = 0.5 in. applicable NDS provisions. Fyb = 45,000 psi Fell = 4800 psi, Fe = 2550 psi g = 0, 0.25, 0.5 in.

Bearing length, in. & Z1, lbs grain direction P5%/Rd, lbs

Main Side Im Is II IIIm IIIs IV

Gap distance, g = 0 in.

1- ½ll 1- ½ll 900 900 414 550 550 663 414 720 383 250 380 324 442 250 1- ½ll 1- ½ 383 383 176 289 289 387 176 1- ½ 1- ½

Gap distance, g = ¼ in.

1- ½ll 1- ½ll 900 900 370 482 482 576 370 720 383 224 341 284 393 224 1- ½ll 1- ½ 383 383 157 258 258 349 157 1- ½ 1- ½

Gap distance, g = ½ in.

1- ½ll 1- ½ll 900 900 333 426 426 501 333 720 383 202 307 250 350 202 1- ½ll 1- ½ 383 383 142 231 231 315 142 1- ½ 1- ½

Example 3.2 Lag Screw Connection

Problem Statement: Determine the reference design other threaded fasteners such as bolts and wood value for a wood-to-wood single shear lag screw screws by accounting for specific attributes (diameter, connection. Compare values for different connection root diameter, dowel bending strength) of those conditions described in Cases 1–4. The main member fastener types. is loaded parallel to grain for all cases. Connection end and edge distances are assumed to be in accordance Given Data: with applicable NDS provisions. Parallel and perpendicular to grain dowel bearing strengths: Note: This example illustrates the application of TR12  equations to account for varying bearing and moment Fell = 5600 psi, Fe = 3650 psi resistances of lag screws in a wood-to-wood Fyb = 45,000 psi connection. A similar approach can be applied to Ls = 1.5 in.

AMERICAN WOOD COUNCIL 18 EXAMPLE PROBLEMS

Lm = 3 in. Case 3 (Figure 3-2C): Moment resistance is based on fastener root diameter, Dr, and bearing resistance is D = 0.375 in., based on D.

Dr = 0.265 in. Side Member: g = 0 in. qs = FesD

Case 1 (Figure 3-2A): Moment resistance, side 3 member bearing, and main member bearing are based FDy br Ms  on fastener root diameter, Dr. Note: These are the 6 assumptions used to develop the NDS tabular values. Main Member: Side Member: qm = FemD qs = FesDr 3 3 FDy br FD Mm  M  y br 6 s 6 Case 4 (Figure 3-2D): Fastener moment resistance Main Member: and bearing resistance are based on diameter, D (e.g. connection with unthreaded shank extending deep into qm = FemDr the main member). Additional calculations will 3 determine the required length of unthreaded shank FDy br Mm  penetration into the main member. 6 Case 2 (Figure 3-2B): Moment resistance and side Note: Where unthreaded shank penetration into the member bearing are based on fastener root diameter, main member is not adequate to enable development of the moment resistance of the fastener based on Dr. Bearing resistance in the main member is based on D. diameter D, the fastener rood diameter, Dr, is the appropriate diameter for calculation of fastener Side Member: moment resistance in the main member.

qs = FesDr Side Member: 3 FDy br qs = FesD Ms  6 3 FDy b Ms  Main Member: 6

qm = FemD Main Member: 3 FDy br qm = FemD Mm  6 FD3 M  y b m 6

AMERICAN WOOD COUNCIL

TECHNICAL REPORT NO. 12 19

Figure 3-2 Wood-to-wood single shear lag screw comparison of different diameter and thread location conditions.

Reduced body Reduced body diameter lag diameter lag screw, Dr screw, Dr (A) Case 1 (B) Case 2

Full body Full body diameter lag diameter lag screw, D screw, D (shear (shear plane plane cuts cuts threads) shank)

Bearing length, in. Z1, lbs & grain direction P5%/Rd, lbs

Side Im Is II IIIm IIIs IV Case 1 (NDS Tabular Basis)2

1- ½ll 1113 557 420 478 260 201 201 1- ½ 890 290 304 353 153 143 143 Case 2

1- ½ll 1575 557 548 629 275 218 218 1- ½ 1260 290 400 457 160 152 152 Case 3

1- ½ll 1575 788 595 671 357 239 239 1- ½ 1260 411 431 495 207 170 170 Case 4

1- ½ll 1575 788 595 697 406 403 403 1- ½ 1260 411 431 513 249 286 286

1Connection values have not been adjusted for end use conditions such as load duration, wet service, and temperature. Z is the minimum of P5%/Rd for each yield mode. The controlling yield mode value is underlined. 2Case 1 represents assumptions used to develop NDS tabular values. Since the NDS equations utilize only a single diameter in calculation of reference design value, the least diameter (e.g. Dr) is conservatively used to estimate moment and bearing resistances. In this example, Cases 2-4 demonstrate that more efficient designs can be achieved by considering the varying moment and bearing resistances of the fastener in lieu of the least diameter assumption.

AMERICAN WOOD COUNCIL 20 EXAMPLE PROBLEMS

Example 3.3 Lag Screw Penetration

Problem Statement: Determine the minimum 5.0 5.0 required length of shank penetration in the main  M   395 5.  a  22  max   2   .0 87 in. member to ensure that fastener moment resistance in  q   2100  the main member is limited by diameter, D, of the  m  shank rather than root diameter, Dr, at the threads. The fastener moment diagram in the main member Connection end and edge distances are assumed to be from 0 ≤ x1 ≤ 2a can be constructed from the alternate in accordance with applicable NDS provisions. load condition in Figure 2.3C.

Note: This example utilizes a lag screw connection to For 0 < x1 ≤ a: illustrate an approach for determining minimum 2 required length of shank penetration to ensure m xq 1 MM max  fastener moment resistance in the main member is 2 limited by diameter, D. A similar approach can be applied to other threaded fasteners such as bolts and Substituting Mreduced for M, distance x1 from the point of maximum moment to the point of reduced moment wood screws by accounting for specific dimensions (diameter, root diameter, dowel bending strength) of can be calculated as: those fasteners. 5.0  (2  MM )    max reduced  x1   Given: The 3/8" diameter lag screw connection in  qm  Figure 3.3A has a reference design value of 403 lbs (Mode IV) based on diameter, D (see Case 4 of Distance x2 from the shear plane to the point of Example 3.2). reduced moment can be calculated as: P = (Reference design value)(Rd) 5.0 = (403 lbs)(3.2) = 1289.6 lbs P  (2  MM )    max reduced  x2   qm  qm  qm = FemD = (5600psi)(0.375 in.) = 2100 lb/in. For a < x1 ≤ 2a Fastener moment resistance at shank: aq 2  xq  FD3 MM m   aq  m 1 x D = yb,5% = 395.5 in.-lbs max 2  m 2  1 6 Fastener moment resistance at root: Substituting Mreduced for M, distance x1 from the point 3 FDyb,5% r of maximum moment to the point of reduced moment Dr = = 139.6 in.-lbs 6 can be calculated as: Solution: 5.0  2M  The basic dowel loading condition for Mode IV is   reduced  1 2ax   shown in Figure 3.3B. Since the reference value is  qm  based on Mode IV yield, the maximum moment is equal to the moment resistance of the dowel (e.g. Mmax Distance x2 from the shear plane to the point of = 395.5 in.-lbs based on the moment resistance reduced moment can be calculated as: provided by shank diameter, D). Zero shear and 5.0 maximum moment occur at distance, xm, from the P  2M  x  2a   reduced  shear plane: 2 q  q  m  m  P 1289.6 x    0.61in. m Minimum penetration length qm 2100 The value of Mreduced is taken as 139.6 in.-lbs which To estimate moment beyond xm an alternate loading equals the moment resistance at the root diameter, Dr. condition can be constructed for the dowel as shown in For Mreduced = 139.6 in.-lbs, a < x1 ≤ 2a and the Figure 3.3C. The length of bearing needed to develop minimum required shank penetration, x2, equals 1.12 the maximum moment is calculated as: in.

AMERICAN WOOD COUNCIL

TECHNICAL REPORT NO. 12 21

Figure 3-3A Figure 3-3C

D = 3/8” (full body diameter lag screw) qm V

1 ½” P M qm x a a x2 Shear plane P P x1

Shear, V x

Mmax

Figure 3-3B Mreduced

Moment, M

qm V

M x Mm

Shear plane

AMERICAN WOOD COUNCIL 22 EXAMPLE PROBLEMS

Example 3.4 Steel Side Member to Wood Given: Dowel bearing strength is 4700 psi. Side Main Member – Tapered Tip Effects member is 16 gage ASTM A653, Grade 33 steel. Nail diameter is 0.131" and is of adequate length to Problem Statement: Compare reference design accommodate the given penetrations. Tapered tip values, Z, for a single shear nail connection at 12D, length, E, is equal to 2D. Main member is loaded 10D, 8D, 6D, and 4D penetrations. Connection end and parallel to grain. edge distances are assumed to be in accordance with applicable NDS provisions. Ls = 0.06 in.

For “EYM tip derivation” case: D = 0.131 in. Lm = p E = 0.262 in. Use tapered tip equations 24 through 29 Fem = 4700 psi

For “NDS” case: Fes = 61,850 psi

Lm = p – E/2 Fyb = 100,000 psi Use general dowel equations in Table 1-1 g = 0 in.

EYM Tip derivation NDS (Lm = p-E/2) Penetration Z1 Controlling Z1 Controlling Depth (p) (lbs) Mode (lbs) Mode 12D (1.57") 97 IIIs 97 IIIs 10D (1.31") 97 IIIs 97 IIIs 8D (1.05") 97 IIIs 97 IIIs 6D (0.79") 79 II 78 II

1Connection values have not been adjusted for end use conditions such as load duration, wet service, and temperature. Z is the minimum of P5%/Rd for each yield mode.

AMERICAN WOOD COUNCIL

TECHNICAL REPORT NO. 12 23

Example 3.5 Bolted Connection through Given: Main member is an HSS 3x3x¼, side members Solid and Hollow Members – Double Shear are 1.5" thick. A single ½" diameter SAE J429 Grade 1 bolt is used to make the connection. Problem Statement: Using equation in Table 1-3, determine the reference design value, Z, for a double twm = 0.233 in. shear bolted connection with a hollow section main member and solid cross section side members shown vm = 2.534 in. in Figure 3.5. Connection end and edge distances are Ls = 1.5 in. assumed to be in accordance with applicable NDS provisions. D = 0.5 in.

Fem = 87,000 psi Figure 3-5 Fes = 4800 psi

Fyb = 45,000 psi g = 0 in.

qm = FemD = 87,000 psi(0.5 in.) = 43,500 lb/in.

qs = FesD = 4800 psi(0.5 in.) = 2400 lb/in.

3 3 FDyb 45,000psi 0.5in. Mm = Ms =  = 937.5 in.-lb 66

1 P5%/Rd, lbs Z , lbs

Im Is IIIs IV

5068 1800 1413 1825 1413

AMERICAN WOOD COUNCIL 24 REFERENCES 24

PART 4. References

ANSI/AWC NDS-2012 National Design Specification (NDS) for Wood Construction. American Wood Council, Leesburg, VA, 2012.

Parsons, W.R. (2001). Energy-based modeling of dowel-type connections in wood-plastic composite hollow sections. Masters Thesis, Washington State University. Pullman WA.

Soltis, L.A. European Yield Model for Wood Connections. New York, NY: American Society of Civil Engineers, Proceedings of Structures Congress 1991, Indianapolis, IN 60-63; 1991.

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 25

Appendix A. Dowel Bearing Strength and Fastener Bending Yield Strength

A.1 Introduction A.3 Dowel Bearing Strength

This Appendix provides dowel bearing strengths, Dowel bearing strengths, Fe, for wood, steel, alumi-

Fe, and fastener bending yield strengths, Fyb, for use in num, and concrete used in calculation of lateral connection calculation of reference lateral design values, Z, using design values, Z, are summarized in Table A1. Technical Report 12 (TR12) General Dowel Equations for For wood, dowel bearing strengths are determined Calculating Lateral Connection Values. Dowel bearing from dowel bearing tests in accordance with methods strengths and fastener bending yield strengths provided outlined in ASTM D5764 Standard Test Method for herein are identical to values established in the National Evaluating Dowel-Bearing Strength of Wood and Wood- Design Specification® (NDS®) for Wood Construction for Based Products [2, 3]. These tests are used to define the materials included in connection design value tables [1]. specific gravity-based relationships for wood members in Additional information on dowel bearing strengths and Table A1. Dowel bearing strengths for structural compos- fastener bending yield strengths is provided including in- ite lumber are specific to each manufacturer’s product and formation on dowel bearing strengths of aluminum and are typically reported on the basis of an equivalent specif- stainless steel, and bending yield strengths for stainless ic gravity, Geqv, using equivalency methods described in steel nails. ASTM D5456 Standard Specification for Evaluation of Structural Composite Lumber Products [4]. The bearing A.2 Notation strength and associated equivalent specific gravity may vary by product grade, fastener type, diameter, and ori- D = dowel diameter, in. entation. The equivalent specific gravities are generally f′c = specified concrete compressive strength, psi not equivalent or correlated to the actual product density.

Fe = dowel bearing strength, psi For wood structural panels, a value of specific grav-

Fe|| = dowel bearing strength parallel to grain in wood, psi ity, G, is provided that establishes the appropriate Fe for

Fe⊥ = dowel bearing strength perpendicular to grain in use in calculating lateral connection design values, Z, but wood, psi generally does not represent the actual product density.

Ftu = tensile ultimate strength, psi For example, the specific gravity applicable for deter-

Fu = specified minimum tensile strength, psi mination of Fe for wood structural panels, plywood and

Fy = specified minimum tensile yield strength, psi oriented strand board (OSB), with D ≤ ¼ inch is based on

Fyb = dowel bending yield strength of fastener, psi results of dowel bearing strength tests. A value of specific G = specific gravity of wood (oven dry weight and gravity is derived from testing to establish the appropri- oven dry volume) ate bearing strength when used in the applicable bearing

Geqv = test-based equivalent specific gravity of structural strength equation [5]. For plywood used in bolted joints, composite lumber where fastener diameter is greater than ¼ inch, the use t = thickness, in. of dowel bearing strength of 5600 psi regardless of ply- Z = reference lateral design value for a single fastener wood species and direction of face grain has been shown connection, lb. to result in conservative design values when compared to Z′ = adjusted lateral design value for a single fastener the tested strength of bolted plywood joints [6]. connection, lb. An illustration of a typical half-hole dowel bearing test specimen used to determine dowel bearing strength of a wood specimen is shown in Figure A1.

AMERICAN WOOD COUNCIL 26 DOWEL BEARING STRENGTH AND FASTENER BENDING YIELD STRENGTH

Figure A1. Dowel Bearing Strength Test Specimen a) Dowel bearing strength half-hole specimen, and b) illustration of 5% diameter offset yield limit state for dowel bearing strength.

Yield

Proportional Limit Loading block

Fastener Dowel bearing specimen 5% of diameter Load (lbs.) Load

FRONT VIEW SIDE VIEW Deformation (in.) a) b)

For steel designed in accordance with AISC-360 steel by 1.6 when calculating the lateral connection design Specification for Structural Steel Buildings, the nomi- value, Z, is intended to apply to steel of other thicknesses, nal bearing strength is 2.4Fu when deformation at the with other specified minimum tensile strengths, and that bolt hole is a design consideration [7]. The result- vary from ASTM A36 and ASTM A653 steel, for which ing nominal bearing stress is 139 ksi for ASTM A36 steel design standards are applicable. steel with Fu = 58 ksi [8]. In the NDS, tabulated design For stainless steel [11,12] designed in accordance values for wood-to-steel connections using these steel with AISC Design Guide 27 Structural Stainless Steel bearing stresses are divided by 1.6, providing a dowel for hot-rolled structural stainless steel, the nominal bear- bearing strength, Fe, of 87,000 psi. While the 1.6 factor ing strength is limited to maximum value of 1.25Fu when is intended to permit use of load duration increases for deformation at the bolt hole is a design consideration calculation of the adjusted lateral design value, Z′, per [13]. Dividing this bearing stress value by 1.6 for consis- the NDS, it is not intended to supersede requirements tency with the bearing strength approach for carbon steel, for design of metal parts in accordance with accepted provides a dowel bearing strength, Fe, of 1.25Fu/1.6. For engineering practice (see NDS 10.2.3). cold-formed structural stainless steel designed in accor- For steel designed in accordance with AISI S100 dance with SEI/ASCE 8-02 Specification for the Design North American Specification for the Design of Cold- of Cold-Formed Stainless Steel Structural Members, the Formed Steel Structural Members, the nominal bearing nominal bearing strength for single shear connections stress is determined by the expression (4.64t + 1.53)Fu, with a washer under the bolt head and nut is 2.0Fu [14]. which is applicable where deformation around a bolt Dividing this bearing stress value by 1.6 for consistency hole is a design consideration [9]. The resulting ASTM with the bearing strength approach for carbon steel, pro-

A653 [10] nominal bearing stress for steel with Fu = 45 vides a dowel bearing strength, Fe, of 2.0Fu /1.6. ksi ranges from 76 ksi to 119 ksi for thicknesses rang- For bolts bearing on aluminum designed in ac- ing from 0.036 to 0.239 inches, respectively. In the NDS, cordance with ADM-1 Aluminum Design Manual, the tabulated design values for wood-to-steel connections are nominal bearing stress on bolts is 2Ftu [15]. Dividing this based on 2.2Fu divided by 1.6, providing a dowel bearing bearing stress value by 1.6 for consistency with the bear- strength, Fe, of 61,850 psi. The use of 2.2Fu for the range ing strength approach for steel, provides a dowel bearing of steel thicknesses addressed in NDS wood-to-steel strength, Fe, of 2Ftu /1.6. connection design value tables for ASTM A653 steel is Theoretical modeling of dowel bearing strength of based on bearing stress provisions in prior editions of concrete and dowel bearing tests in concrete with maxi-

AISI S100 in lieu of more recent AISI S100 provisions mum f′c = 2700 psi are the basis of the relationship 3f′c that adjust bearing stress based on steel thickness. representing the approximate 5% offset limit state value This bearing strength derivation approach for steel, for concrete dowel bearing strength [16, 17]. Information which includes dividing the nominal bearing stress for on design of dowels in concrete pavements suggests

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 27

dowel bearing strength of concrete in this range, and design of concrete or anchors in concrete in accordance also dependence on dowel diameter with larger bearing with accepted practice [19] (see NDS 10.2.4). strengths associated with dowels of smaller diameter NDS reference values of dowel bearing strength,

[18]. For the design of wood-to-concrete connections, a Fe, in Table A1 and in NDS Table 12.3.3 are rounded concrete dowel bearing strength of 7500 psi is considered values and are generally associated with smaller and applicable for concrete with a minimum compressive larger values than would result from the direct use of strength of 2500 psi. The use of a dowel bearing strength the equations. The rounded values of Fe are used to cal- of concrete for calculation of lateral connection design culate the lateral connection design values, Z, tabulated values, Z, is not intended to supersede requirements for in the NDS.

Table A1. Dowel Bearing Strength, Fe

NDS Dowel Nominal Bearing Strength, NDS Reference

Material Bearing Stress Fe, Equation (psi) Value, Fe (psi) Wood members3 (for D ≥ ¼″)

Parallel to grain (Fe‖) 11200 G NDS Table 12.3.3 1.45 0.5 Perpendicular to grain (Fe⊥) 6100 G /D NDS Table 12.3.3 Wood members3 (D < ¼″) 1.84 Parallel and perpendicular to grain (Fe) 16600 G NDS Table 12.3.3 Wood Structural Panels Plywood (for D ≤ ¼″) Structural 1, Marine (G= 0.5) 16600 G1.84 4650 Other Grades (G = 0.42) 16600 G1.84 3350 (Note: Use G = 0.42 when species of the plies is not known. When species of the plies is known, specific gravity listed for the actual species and the corresponding dowel bearing strength may be used, or the weighted average may be used for mixed species.) Plywood (for D > ¼″) All Grades (G = 0.5) 11200 G 5600 Oriented Strand Board (for D ≤ ¼″) All Grades (G = 0.5) 16600 G1.84 4650 1 Concrete (f′c = 2500 psi) 3f′c 7500 Steel2

ASTM A36 (Fu = 58 ksi, t > ¼″) 2.4Fu 2.4Fu/1.6 87,000

ASTM A653 (Fu = 45 ksi, t < 0.239″) (4.64t + 1.53) Fu 2.2Fu/1.6 61,850 Stainless Steel2

ASTM A240 (hot-rolled, t ≥ ⅛″) 1.25Fu 1.25Fu/1.6

ASTM A240 (cold-formed) 2.0 Fu 2.0 Fu/1.6

ASTM A240 specified Fu

Type 304: Fu = 75 ksi -

Type 304L: Fu = 70 ksi -

Type 316: Fu = 75 ksi -

Type 316L: Fu = 70 ksi - 2 Aluminum 2Ftu 2Ftu/1.6 -

1 Design of concrete parts shall also be in accordance with accepted practices (see NDS 10.2.4). For f ′c values greater than or equal to 2500 psi,

the dowel bearing strength, Fe, is limited to 7500 psi. 2 Design of metal parts shall also be in accordance with applicable metal design procedures (see NDS 10.2.3). 3 For structural composite lumber, an equivalent specific gravity, Geqv, is used to derive the dowel bearing strength instead of the actual product specific gravity, G.

AMERICAN WOOD COUNCIL 28 DOWEL BEARING STRENGTH AND FASTENER BENDING YIELD STRENGTH

A.4 Dowel Bending Yield Strength F1575 Standard Test Method for Determining Bending Yield Moment of Nails for determination of the 5% offset

Dowel bending yield strengths, Fyb, for bolts, lag limit state value [20, 21]. A typical fastener bending test screws, wood screws, and nails for use in calculation specimen is shown in Figure A2. Stainless steel nails of reference lateral design values, Z, are summarized in have been shown to display similar bending strength to Table A2. comparably sized carbon steel fasteners [22]. For either For nails and small-diameter wood screws and lags carbon steel nails or stainless steel nails, bending yield screws, the value of Fyb increases with reduced diameter values are evaluated in accordance with supplementary and depends on the hardness of the steel. The empiri- requirements of ASTM F1667 Standard Specification for cal relationships are based on testing of carbon steel Driven Fasteners: Nails, Spikes, and Staples for engi- nails in accordance with procedures outlined in ASTM neered construction [23].

Figure A2. Dowel Bending Strength a) Nail bending specimen, and b) illustration of 5% diameter offset yield limit state for bending yield strength.

LOAD

Yield

Proportional Limit

5% of diameter

CL (lbs.) Load Deformation (in.) a) b)

For bolts and lag screws with diameter of ⅜ inch NDS reference values of fastener bending yield and greater, Fyb = 45 ksi is associated with the equation strength, Fyb, in Table A2 are rounded values. The rounded

Fyb = Fy /2 + Fu /2 for bolts having Fy = 36 ksi and Fu = values of Fyb are used to calculate lateral connection design 60 ksi. This bending yield strength equation applies for values, Z, tabulated in the NDS. In some cases, such as steel fasteners for which steel design standards are ap- for nails of 0.344 to 0.375 inches in diameter as well as plicable, including both carbon steel and stainless steel hardened nails greater than 0.192 inch, the equations pro-

[24, 25, 26]. duce slightly greater values of Fyb than used as the basis of lateral connection design values, Z, tabulated in the NDS.

AMERICAN WOOD COUNCIL TECHNICAL REPORT NO. 12 29

Table A2. Dowel Bending Yield Strength, Fyb

NDS Dowel Bending Yield NDS Reference

Fastener Strength, Fyb, Equation (psi) Value, Fyb (psi) Bolt, lag screw (with D ≥ ⅜″), drift pin

SAE J429 Grade 1: Fy = 36 ksi, Fu = 60 ksi Fy/2 + Fu/2 45,000 ASTM A320, Class 1, Type B8 and B8M:

Stainless Steel S30400: Fy = 30 ksi, Fu = 75 ksi -

Stainless Steel S30403: Fy = 25 ksi, Fu = 70 ksi -

Stainless Steel S31600: Fy = 30 ksi, Fu = 75 ksi -

Stainless Steel S31603: Fy = 25 ksi, Fu = 70 ksi - Common, box, or sinker nail, spike, lag screw, wood screw (low to medium carbon steel) 130,400 – 213,900D 0.099″ ≤ D ≤ 0.142″ 100,000 0.142″ < D ≤ 0.177″ 90,000 0.177″ < D ≤ 0.236″ 80,000 0.236″ < D ≤ 0.273″ 70,000 0.273″ < D ≤ 0.344″ 60,000 0.344″ < D ≤ 0.375″ 45,000 Hardened steel nail (medium carbon steel) including post- 169,500 – 278,000D frame ring shank nails 0.120″ ≤ D ≤ 0.142″ 130,000 0.142″ < D ≤ 0.192″ 115,000 0.192″ < D ≤ 0.207″ 100,000

A.5 References [6] APA E825E, Fastener Loads for Plywood – Bolts, APA – The Engineered Wood Association, Tacoma, [1] ANSI/AWC NDS-2012 National Design Washington, 1997. Specification (NDS) for Wood Construction. American Wood Council, Leesburg, VA, 2012. [7] AISC 360-10 Specification for Structural Steel Buildings. American Institute of Steel Construction, [2] ASTM D5764-97a (2013) Standard Test Method for Inc., Chicago, IL, 2010. Evaluating Dowel-Bearing Strength of Wood and Wood- Based Products. ASTM, West Conshohocken, PA, 2013. [8] ASTM A36-12, Standard Specification for Carbon Structural Steel. ASTM, West Conshohocken, PA, 2012. [3] Wilkinson, T.L., Dowel Bearing Strength. Forest Products Laboratory Research Paper FPL-RP-505. [9] AISI S100-2007. North American Specification for Madison, WI: U.S. Department of Agriculture, Forest the Design of Cold-Formed Steel Structural Members. Service, Forest Products Laboratory, 1991. American Iron and Steel Institute, Washington, DC, 2007.

[4] ASTM D5456-11a, Standard Specification for [10] ASTM A653-13, Standard Specification for Steel Evaluation of Structural Composite Lumber Products. Sheet, Zinc-Coated (Galvanized) or Zinc Iron Alloy- ASTM, West Conshohocken, PA, 2011. Coated (Galvannealed) by the Hot-Dip Process. ASTM, West Conshohocken, PA, 2013. [5] APA D510, Panel Design Specification, APA – The Engineered Wood Association, Tacoma, Washington, 2012. [11] ASTM A240-14, Standard Specification for Chromium and Chromium-Nickel Stainless Steel Plate, Sheet, and Strip for Pressure Vessels and for General Applications. ASTM, West Conshohocken, PA, 2014.

AMERICAN WOOD COUNCIL 30 DOWEL BEARING STRENGTH AND FASTENER BENDING YIELD STRENGTH

[12] ASTM A480-14b, Standard Specification for [19] ACI 318-14. Building Code Requirements for General Requirements for Flat-Rolled Stainless and Structural Concrete and Commentary. American Heat-Resisting Steel Plate, Sheet, and Strip. ASTM, Concrete Institute, Farmington Hills, MI, 2014. West Conshohocken, PA, 2014. [20] Loferski, J.R. and McLain, T.E., "Static and Impact [13] AISC Design Guide 27, Structural Stainless Steel. Flexural Properties of Common Wire Nails," Journal American Institute of Steel Construction, Inc., Chicago, of Testing and Evaluation, JTEVA, Vol. 19, No. 4, July IL, 2013. 1991, pp. 297-304.

[14] SEI/ASCE 8-02 Specification for the Design of [21] ASTM F1575-03 (2013) Standard Test Method for Cold-Formed Stainless Steel Structural Members. Determining Bending Yield Moment of Nails. ASTM, American Society of Civil Engineers, Reston, VA, 2002. West Conshohocken, PA, 2013.

[15] AA ADM-1 2010. Aluminum Design Manual, 2010 [22] Rammer, D.R., and Zelinka, S.L., "Withdrawal Edition. Aluminum Association, Washington, D.C, Strength and Bending Yield Strength of Stainless Steel 2010. Nails," Journal of Structural Engineering, July 2014.

[16] Vintzeleou, E.N., Tassios, T.P., "Mathematical [23] ASTM F1667-11a Standard Specification for Models for Dowel Action Under Monotonic and Cyclic Driven Fasteners: Nails, Spikes, and Staples. ASTM, Conditions." Magazine of Concrete Research: Vol. 38, West Conshohocken, PA, 2011. No. 134: March 1986. [24] SAE J429, Mechanical and Material Requirements [17] Biolzi, L., and Giuriani, E., "Bearing Capacity for Externally Threaded Fasteners, Society of of a Bar Under Transversal Loads," Materials and Automotive Engineers, Warrendale, PA, 1999. Structures, V. 23, n 138, Nov., 1990, pp. 449 456, University di Udine, Udine, Italy, 1991. [25] ASTM A320-14, Standard Specification for Alloy- Steel and Stainless Steel Bolting for Low-Temperature [18] Snyder, M.B., Guide to Dowel Load Transfer Service. ASTM, West Conshohocken, PA, 2014. Systems for Jointed Concrete Roadway Pavements. National Concrete Consortium, Ames, IA, 2011.

AMERICAN WOOD COUNCIL American Wood Council

AWC Mission Statement To increase the use of wood by assuring the broad regulatory acceptance of wood products, developing design tools and guidelines for wood construction, and influencing the development of public policies affecting the use and manufacture of wood products. American Wood Council 222 Catoctin Circle, SE Suite 201 Leesburg, VA 20175 www.awc.org 10-15 [email protected]