PROCEDURE FOR DESIGN OF GLUED-LAMINATED

ORTHOTROPIC BRIDGE DECKS

U.S.D.A. FOREST SERVICE

RESEARCH PAPER

FPL 210

1973

U.S. Department of Agriculture • Forest Service • Forest Products Laboratory • Madison, Wis

ABSTRACT

The most recent improvement in timber bridge design is the verticallyglued-laminated panel deck, with the panels placed in a transversedirection to the stringers. Experimental evaluations showed its perform-ance to be superior to that of the conventional nailed-laminated deck.Design methods which consider the glued-laminated deck as an orthotropicplate accurately predict its behavior,

Since a laminated bridge deck is constructed from many relatively narrowpanels, it is necessary to install connectors which allow the deck to actas a continuous plate. Eight different connector systems were evaluatedand steel dowels are best suited for the purpose. Design criteria fordowel connectors, based on the theory of a beam supported on an elasticwood foundation, were developed.

The problem of dimensional stability was investigated by observingthe behavior of glued-laminated panels at a long term exposure site, andby observing bridges that have been in service for several years. Itwas found that creosote treatment greatly retards changes in moisturecontent and associated dimensional changes.

The design procedures for glued-laminated transverse decks and steeldowel connectors are presented as a set of easy-to-use graphs and tables.These should be of immediate use for designers of timber bridges.

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PROCEDURE FOR DESIGN OF

GLUED-LAMINATED ORTHOTROPIC BRIDGE DECKS

By WILLIAM J. McCUTCHEON, Engineer

and

ROGER L. TUOMI, Engineer

Forest Products Laboratory 1 Forest ServiceU.S. Department of Agriculture

INTRODUCTlON

Timber bridges have a long record of service in the secondary roadsystems of this country. In the National Forests alone approximately7,500 bridges are in use with more being built each year, and the railroads

have over 1,500 miles of timber bridges and trestles in service (3 ) .2

The most common type of timber bridge, by far, has longitudinalstringers with transverse timber decking. Typically, the decking con-sists of nailed-laminated 2-inch lumber where the material is through-nailed together and toenailed to the stringers. This system has a longrecord of use. Because of the close spacings of solid sawn stringers,the deck deflections were minimal and performance was adequate.

With the advent of glued-laminated stringers and the subsequentincrease in spacing, the inherent shortcomings of the nailed-laminateddeck have become apparent. The larger deck deflections and the swellingand shrinkage due to cyclic wetting and drying cause a gradual looseningof the nail connectors and of the entire deck. This shortens the servicelife of the bridge,

Ideally, the deck of a timber bridge should serve two purposes.First, it must be adequate structurally to carry the design load.Secondly, the deck should serve as a roof over the entire bridge struc-ture, protecting the supporting members and the deck itself from thedeteriorating effects of rain and snow.

The nailed-laminated deck fails to perform this second function.Differential displacements between the laminations and subsequent looseningof nails permits water to penetrate into the deck and stringers.

2Underlined numbers in parentheses refer to literature cited at end of

th is report .

1Maintained at Madison, Wis., in cooperation with the University of

Wisconsin.

By gluing, rather than nailing the lumber together, a deck can bemanufactured which meets both criteria. A glued-laminated deck is apanel constructed by gluing pieces of nominal 2-inch dimension lumbertogether using a waterproof adhesive. Since the panel will be loadedparallel to the wide face or glueline, this layup is referred to asvertically laminated construction. The panel is in effect a conventionalglued-laminated beam resting on its side. Unlike a beam, however, it isnot possible to strategically position high-quality material as is doneon tension laminations in beams. Therefore, it is best to use thesame grade material throughout the panel.

Glued-laminated panels can be manufactured in any desired length.The width is most commonly a multiple of 1.5 inches, the net width ofdimension lumber. A 32-lamination deck panel would thus have an overallwidth of 48 inches.

The thickness of a deck is controlled by the nominal sizes of lumber,which run in 2-inch increments from 4 to 16 inches. The finished thick-ness of the deck will be slightly less than the actual depth of thelumber since the deck is resurfaced on both sides after manufacture.Dimensions, as well as allowable stresses for various speciesare contained in “Timber Construction Standards,” as prepared by the AmericanInstitute of Timber Construction (1 ).

Structurally, glued-laminated decks are superior in strength andstiffness to nail-laminated decks. These properties can reduce the re-quired deck thickness and also enhance the service life of a wearingsurface. But while the Standard Specifications for Highway Bridges ofthe American Association of State Highway Officials (2 ) contain designcriteria for nailed-laminated decks, they do not have criteria for glued-laminated. This report provides the background information from whichsuch glued-laminated design criteria can be developed.

The practical width of glued-laminated panels is probably not morethan 4 feet. This makes it necessary to install connectors which preventrelative displacements and rotations of adjacent panel edges. Therefore,a design procedure for steel dowel panel connectors is also presented.

EXPERIMENTAL METHOD

The bridge deck research program consisted essentially of two sepa-rate phases. First, physical tests were run on both glued-laminated decksand on various connectors to assess performance characteristics. Thesetests demonstrated the advantages inherent in certain systems and justifiedfurther research effort. The initial work consisted of comparing thestructural behavior of glued-laminated decks with nailed-laminated decks

and screening numerous connector systems.3 Next, research followed todevelop the theories that define the superior behavior characteristicsof select systems, and establish design procedures to implement them.Additional laboratory tests were required to support theoretical findings.

3Boland, L. B. 1969. Glued-Laminated Wood Panels for Highway BridgeDecks. M.S. Thesis, University of Wisconsin.

FPL 210 - 2 -

Species Selection

Most commercial timber bridge deck construction utilizes eithersouthern pine or Douglas-fir. Since a large percentage of National Foresttimber bridges occur in the western states, Douglas-fir L-2 grade wasselected for use in this study. Nearly identical structural qualitiesare available in the commercial grades of southern pine, and the resultsof this study should be applicable to both groups.

Test Loading

Static load tests were used throughout this study. A structuralframe was constructed (fig. 1) whereby the panels could be simply sup-ported over variable spans of 2 to 6 feet. Loads were applied by ahydraulic jack which could be positioned over any part of the panel.

In the first series of tests3 the load block was rectangular, rangingin size from 18 to 22 inches in the span direction and from 8.4 to 10.0inches in the other direction. A second series in 1971 utilized a square10- by 10-inch load block. The size of the load block influences stresses,as will be apparent later.

Although the frame was extremely stiff, some support deflection wasobserved under load. Also there was elastic deformation in the contactbearing area of the wood and some distortion in the pipe supports whichrested on the structural frame. This was corrected for by positioningdisplacement instrumentation on the top side of the panels along thecenterlines of the supports to measure the sum of deformations within theframe, wood, and pipe. Deflection measurements were obtained with 23LVDT's (linear variable differential transformers). The load-deflectiondata were fed into a 100-channel digital data aquisition system for rapidreduction.

Most bridges are comprised of three or more stringers, and the deckperforms as a continuous slab across the supports. However, for simplicityof testing, single spans were used throughout and the results will be some-what conservative. This factor is widely recognized in design, and it iscommon practice to reduce stresses by 20 percent for continuous spans.

Nailed Versus Glued Panels

The first objective of this study was to compare the structuraleffectiveness of glued-laminated panels with conventional nailed-laminatedpanels. This was accomplished by test loading panels equal in size andapproximate thickness for both types of construction. Both panel typeswere 7 by 7 feet and were built from nominal 6-inch lumber. This thick-ness was selected as the median of three common sizes: 4, 6, and 8 inches.The actual thicknesses were 5-5/8 inches for the nailed panels and 5-1/4inches for the glued panels. The panels were supported by solid-sawnstringers spaced on 6-foot centers attached to the structural frames.

The nailed-laminated panel was constructed from creosote-treatedDouglas-fir 2 by 6's which had been air dried to approximately the samemoisture content (12 pct.) as the glued-laminated slabs. In accordancewith U.S. Forest Service specifications for nailed-laminated decks, theboards were fastened together by through-nailing with thirtypenny nails,

- 3 -

spaced 18 inches apart. These intervals were alternated for repetitionin each fourth lamination. The deck was fastened to the stringers bytoe-nailing with twentypenny nails through alternate laminations. Sincestraight, dry material was used under laboratory conditions, the deckwas probably of higher quality than the typical site-built bridge deck.

Comparative deflection profiles, of both glued- and nailed-laminateddecks under 12,000-pound loads, are illustrated on figure 2. The longitudinaldeflection profile of the glued-laminated panel is a smooth bell-shapedcurve, demonstrating effective load distribution, while the nailed-laminated deck profile is extremely truncated with nearly all deflectionoccurring directly under the load block.

The nailed-laminated deck deflected over 50 percent more than the glued-laminated panel. A complete puncture failure developed in the nailedpanel under a load of 26,250 pounds. The glued-laminated deck sustaineda 38,000-pound load without apparent structural damage. This was themaximum capacity of the test apparatus in 1969. However, identical testswere performed on similar glued-laminated decks in 1972 to load levelsof 50,000 pounds, and again no structural damage was apparent.

Theoretical Versus ExperimentalPerformance of Glued-LaminatedPanels

Having demonstrated the structural superiority of glued-laminated con-struction, further tests were conducted to define load-deflection character-i s t i c s , In 1969, three tests were conducted on both the nominal 4-inch-

and nominal 6-inch-thick decks.3

The panels were loaded at their centers in 2,000- and 4,000-poundincrements and deflection measurements were obtained along the supportsand longitudinal and transverse centerlines. Panels were simply supportedover spans that varied from 30 to 72 inches. The load block which dis-tributed the force over a rectangular area similar to the contact surfaceof a pneumatic tire varied in size as previously noted.

The theoretical slab analysis followed the initial tests and the panelswere retested in 1971. This time four tests were run on each of the panelsand the load block was square (10 by 10 in.). The panels were also lineloaded along the longitudinal centerline to determine the moduli of elas-ticity by simple beam theory. These moduli were needed to computetheoretical deflections in the slab analyses.

Theoretical and measured maximum deflections for the 14 test runs

are presented in table 1.4 The load level was 12,000 pounds, which corre-sponds to the AASHO HS-20 wheel loading for timber bridges.

Agreement between maximum theoretical and measured deflections wasextremely good. The greatest difference occurred when the nominal 4-inch

panel was loaded to 12,000 pounds over a span of 72 inches. This is wellabove the allowable load for this span and thickness, and the deck may

have been stressed slightly beyond its proportional limit.

4 Symbols used in this paper are grouped in the List o f Symbols at the

back of this report.

FPL 210 - 4 -

Figure 1. --Structural frame and recording apparatus for static load tests.

(M 138 736)

Figure 2. --A comparison of deflection profiles for glued- andnailed-laminated decks.

(M 140 014)

- 5 -

Table 1 .--Comparison of maximum theoretical deflections versusmeasured deflections at 12,000-pound load

1 Deflection coefficient from fig. 17

2Ex for 3.25-in. and 5.25-in. panels was obtained by line-loading

panels and calculat ing modul i o f e last ic i ty f rom measured

d e f l e c t i o n s b y

FPL 210 - 6 -

A comparison of theoretical and measured deflections along thelongitudinal (parallel to stringers) and transverse centerlines is alsopresented in figure 3. The two profiles very nearly coincide over theirfull length.

Connector Systems

The initial search for suitable connectors preceded the developmentof the design theory for load transfer, which will be discussed later.Physical tests were first conducted on seven connector types as a screen-ing process to determine which were most effective. An eighth connectortype, steel pipe dowels, was tested by a different method and will bediscussed separately in the supplemental tests section.

There are two basic types of connectors -those with shear capacityonly and connectors with both shear and moment capabilities. In eachcase, two panels, 42 by 84 by 5-1/4 inches, were joined by each of theseven methods. These assemblies were simply supported over a 72-inchspan with the joints normal to the supports. A concentrated load wasapplied to one of the panels immediately adjacent to the joint at midspan.The deflection profile was recorded along the longitudinal centerline ofthe panels to assess load transfer capabilities of the system.

Shear connectors .--Five types of shear connectors were tested: woodsplines, single steel splines, double steel splines, tapered tongue-and-groove joints, and rectangular tongue-and-groove joints. The steelsplines were reasonably effective in reducing relative displacement acrossthe joint, but there was an abrupt discontinuity in the shape of thedeflection profile across the joint. There was relative displacementacross the interface of all the other joints followed by complete shearfailures along the joints. None of the above connectors was fully effec-tive and most of the load was absorbed by the loaded panel.

Shear and moment connectors .--Two shear-moment connectors, solidsteel dowels and hardwood oak dowels, were tested initially. Seven cold-rolled steel dowels, 10 inches long by 1 inch in diameter, were installedover the middle half of the span. The length and placement patterns forthe hardwood dowels were identical, but the diameter was 1-3/8 inches.Both were effective in transferring the combined loads across the joints.The panel pairs were loaded in 2,000-pound increments to a maximumconcentrated load of 38,000 pounds.

There was no indication of differential displacement of panels whenusing steel dowels, nor was there any apparent structural damage. how-ever, upon dismantling the panels connected with wood dowels, a crackwas found along the line of dowels in the loaded panel (fig. 4).

After the dowel theory was finalized, it became apparent why failure

occurred with the wood dowels and not with the steel dowels. The wood

dowels, being more flexible and of greater diameter, deflected nearly

50 percent more and imposed stresses in the wood approximately 60 percent

higher. The stress under the wood dowels was more than seven times theproportional limit stress. In general, for wood and steel dowels of equaldiameter and of sufficient length for maximum efficiency, the stress underwood dowels will be 2 to 4-1/2 times the stress imposed by steel dowels.

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Figure 3.--Comparison of theoretical and measured deflections alonglongitudinal and transverse centerlines.

(M 140 536)

Figure 4.--Crack along centerline of hardwood dowels,

(M 134 801)

FPL 210- 8 -

One further drawback with wood dowels is dimensional stability. Thewood dowels for this study were turned on a lathe to precisely 1-3/8-inchdiameter. Ten days later, the dowels had swelled to the extent that theyno longer fit the predrilled panel holes. They required sanding beforethe connection could be made.

A comparison of deflection patterns across a joint for shear-onlyand shear-moment connectors is shown in figure 5. The shear connectorsare obviously unsatisfactory. The flexibile hardwood dowels develop highstresses in the panels, but the Steel dowels perform satisfactorily.

THEORETICAL ANALYSES

Orthotropic Plate Analysis

A glued-laminated wood bridge deck can be analyzed as an orthotropicplate. The differential equation for such a plate in the x-y plane is( 5 ,6) :

where

In general, this equation is not amenable to direct solution. Oneproblem for which solutions are obtainable, however, is that of aninfinite strip ( f ig . 6) .

- 9 -

Figure 5. --A comparison of centerline deflection patterns of panels joinedby shear connector (spline) and shear-moment connectors (dowels).

(M 138 845)

Figure 6. --Bridge deck analyzed as an infinite stripunder uniform rectangular load.

(M 140 540)FPL 210 -10-

The wheel load P is uniformly distributed over an a-by-b rectangulararea centered at (x,y) = (ξ,0) (fig. 6). It is assumed that the edgesx = 0 and x = s are simply supported by the bridge stringers and thatthe slab extends indefinitely in the positive and negative y-directions.Thus, the deflections, moments, and shears must approach zero as y approaches± infinity. Although a glued-laminated bridge deck is, of course, offinite dimensions, the fact that the stiffness is much greater in thex-direction than in the y-direction causes the deflections, etc., to diminishvery rapidly away from the loaded area. Thus, modeling the bridge deckas an infinite strip gives a very close approximation to the true solution.

First considering the case of a line load along the x-axis (i.e.,b = 0), the load is expressed as a Fourier series:

where, in this case:

If H < as is the case for wood, the solution for the portion

of plate where y > 0 is (6):

where

(1)

- 1 1 -

From the above solution for deflection, the moments and shears per unitwidth can also be obtained in series form, since:

forOnce the solution for a line load is known (eq. 1), the solutiona rectangular loaded area (b > 0) can be found by integration

f(y) defines the plate response (deflection, moment, or etc.) to a 1ine

load on the x-axis, then f , the response at y = y to the distributedload, is :

(2)

where

when First, rewrite equation (2) as:

Since the line load solution is valid only for y > 0, it isnecessary to consider the symmetry, or asymmetry, of-the response

FPL 210 -12-

When f is an even, or symmetric, function (i.e., when f (–y) = f (y)), asfor deflection, then

and it follows that:

If f is odd (i.e., f (-y) = -f(y)), as it is for Qy , then

and

Thus, from the series solution for a line load (eq. 1), the solu-tion can be obtained for a strip uniformly loaded over a rectangulararea (eqs. 3 and 4). This approach gives results which agree veryclosely with experimental data (fig. 3).

Steel Dowel Analysis

Due to fabrication, transportation, and erection limitations, aswell as consideration of possible contraction and expansion, a glued-laminated bridge deck is normally constructed from fairly narrow panels(usually not wider than 4 ft.). In order for the panels to act as acontinuous, uninterrupted slab, it is necessary to provide connectorswith the structural capacity to prevent relative displacements androtations between adjacent panels. The earlier tests have shown thatsteel dowels are well suited for this purpose. The dowels are installedat the midthickness of the panels and are embedded to half their lengthin each of the panels being joined.

To design such a connector system, it is possible to employ a

technique which has been used by Kuenzi (4 ) and Stluka5 to predict thebehavior of nailed and bolted joints. The dowel is considered to be abeam supported by an elastic foundation. The perpendicular-to-graincompression stress in the wood foundation is proportional to the deflectionof the beam (dowel) induced by the shear and moment in the deck (fig. 7).

5Stluka, R. T. Theoretical Design of a Nailed or Bolted Joint Under LateralLoad. M.S. Thesis, University of Wisconsin. 1960.

-13-

(3)

(4)

The joint is designed so that the stresses in both the dowel andthe wood are at or below their proportional limits.

The length of the dowel is of major importance. If too short, itwill act as a rigid body, causing excessively high stresses in the wood.Making the dowel excessively long will not enhance its performance andwill result in material waste.

Associated with the dowel length is a constant, λ, which isdefined as:

where

k = kod;

ko = foundation modulus (pounds per cubic inch), see appendix:

d = dowel diameter (inch); and

EI = flexural stiffness of dowel (pound-square inch).

Thus, λ has units of inch -1 and represents the inverse of acharacteristic length. For satisfactory transfer of load between thedowel and the wood foundation, with minimum stresses, it is necessarythat λ 3. Coefficients for the foundation deflection and for the

bending moment along the length of the dowel5

with = 3 are shownin figures 8 and 9.

From figure 8, the maximum total deflection under the dowel is:

The stress in the wood foundation is equal to the deflection, z, timesthe foundation modulus, k

o, and may not exceed the proportional

limit stress. Because the foundation stress is perpendicular to thegrain, a “diameter factor,” f, (8) is applied to Thus, the

deflection may not be greater than and the interaction equation

which defines the limiting combinations of shear and moment is:

FPL 210 -14-

Figure 7.--Dowel considered to be a beam supportedby an elastic foundation.

(M 140 528)

Figure 8.--Coefficients for elasticfoundation deformation due to shearand moment loads.

(M 140 537)

Figure 9.-- Coefficients for dowelmoment due to shear and momentloads.

(M 140 535)

-15-

Similarly, from figure 9, the maximum moment in the dowel is:

The dowel moment is limited to that which causes the steel elastic limitstress to be reached, MEL. Therefore,

(6)

gives the combinations of joint shear and moment which produce yieldingof the dowel. Usually, the stresses in the wood will control thedesign, and the dowel stress need be computed only as a check.

DESIGN CHARTS AND TABLES

Deck Design

The theoretical slab analysis presented earlier is, obviously, notamenable to simple hand calculations. Therefore, a digital computer wasprogramed to perform the necessary computations, and the results havebeen reduced to a set of easy-to-use design charts which cover the practicalrange of design problems. The charts are presented in terms of dimensionlessparameters. The following relationships between elastic properties, whichare reasonable for most wood species, have been assumed (8 ) :

With the above parameters, design charts were developed to defineforces (bending moments and vertical shears) in the two principaldirections. Primary denotes the span or x-direction which coincideswith the longitudinal grain of the wood. Secondary forces are thoseacting parallel to the supports (y-direction) or perpendicular tograin. All unit forces are a maximum when the wheel load is centered( i . e . , when ξ/s = 0.5, fig. 6) except for primary shear. The maximumshear occurs under the wheel edge nearest to the support, and its magni-tude increases as the load approaches the support. In calculating shearin beams, there are many different rules which are used for positioning

FPL 210 -16-

the load. Therefore, multiple graphs are presented for primary shear,each graph corresponding to a different load position.

Bending stresses can be computed from the unit bending moment (M)

and are equal to 6M/t2. Using the common assumption of a parabolicdistribution of shear stresses across the depth, the horizontal shearstress (which is equal to the vertical shear stress) is 3Rx/2t, where

Rx denotes the primary vertical unit shear force. Secondary shear, R ,

acts perpendicular to grain (rolling shear), and stresses can bey

calculated in the same manner.

The curves of figure 10 are used to determine the maximum primaryunit bending moment, Mx (inch-pound per inch). The abscissa is the

ratio of tire width to span, a/s, and the ordinate gives the ratio ofbending moment to wheel load, Mx/P. Each curve corresponds to a

particular ratio of tire contact length to tire width, b/a, from 0.25to 2.0. Figures 11 through 14 define the maximum primary shear, Rx (pound

per inch), in terms of the ratio of wheel load to span, P/s, for variousload positions, ξ/s = 0.5 to 0.1. The curves are terminated at a/s =2ξ/s because past this value part of the load would be off the span.Similarly, figures 15 and 16 define the maximum secondary moment, My, andshear, Ry.

The shears are denoted as R, rather than Q, because they includeterms to account for torsional stresses (the "Kirchhoff effect"), andare defined as:

Although deflection criteria do not generally govern the designof bridge decks, figure 17 is presented in the event that such computa-tions are needed. The maximum deflection, w (inch), is expressed in

terms of the quantity Ps2/Ext3, where t is the deck thickness.

The charts are applicable to any case where a single wheel load betweenstringers controls the design. Their use will be demonstrated later in asample problem.

Dowel Design

Since moments and shears are not constant across the span, it wouldbe grossly overconservative to design the steel dowel connectors forthe maximum unit values determined in the deck analysis. Therefore, indesigning the dowels, it will be assumed that the total moment and shearwhich act across a deck joint are shared equally by the dowels. Dowelsdesigned in this manner have performed adequately in laboratory tests.

-17-

Fig

ure

10

.--P

rim

ary

mom

ent

coef

fici

ents

.(M

140

533

)F

igu

re

11.-

-Pri

mar

y sh

ear

coef

fici

ents

fo

r ξ/

S

=

0.5

(cen

ter

loa

d).

(M 1

40 5

29)

-19-

FPL 210 -20-

Figures 18 and 19 present the total moment and shear, denoted My

(inch-pound) and Ry (pound), in nondimensional form.

The moment-shear interaction relationship (eq. 5) is presentedgraphically in figure 20 for various dowel diameters. In this figure,values of k

0= 180,000 pounds per cubic inch and = 1,000 pounds per

square inch (p.s.i.) are assumed. The value for the foundation modulusis that which was determined experimentally (see appendix) and 1,000 p.s.i.is a reasonable value for the proportional limit stress. For other valuesof (8), it is only necessary to multiply the capacity values from

figure 20 by the ratio

Each line is identified by dowel diameter and represents dowelcapacity under combined shear and bending loads. This graph can beused directly to determine the required size and number of dowels. Astraight line having a slope equal to the ratio of total shear to totalmoment will cross dowel capacity lines at points proportional to theimposed loads. Either the shear capacity or moment capacity at thepoint of intersection can be used to determine the number and size ofdowels. It is only necessary then to divide the total force (eithershear or moment) by the corresponding capacity of a given size dowelto determine the required number.

A more precise method is to use the information in table 2 andcompute the required number of dowels by:

where

= minimum number of dowels;

= shear and moment capacities, table 2;

= total secondary moment and shear, figures 18 and 19; and

= proportional limit stress in compression perpendicular to grain.

The values of RD and MD in table 2 are based on the wood stresses

controlling the design, and are the intercepts of the capacity lines infigure 20.

This approach assumes that the maximum shear force occurs simul-taneously with the maximum moment, which is generally not the case.Maximum moment occurs near the center of the load and maximum shearfalls at the edge of the wheel. Therefore, these results are somewhatconservative.

Steel stresses are likely to control only for the smaller diametersbut should be checked nevertheless, Equation (6), which defines thesteel design criteria, can be rewritten to solve for the minimum elastic

(7)

FPL 210 -22-

Figure 18.--Total secondary moment coefficients.

(M 140 539)

-23-

FPL 210

Figure 19.--Total secondary shear coefficients.

(M 140 532)

-24-

-25-

limit which is needed, Noting that and

equation (6) becomes:

where

= minimum elastic limit of steel; and

= coefficients, table 2.

If is too high, this can be remedied by increasing the size of

dowel used (and recomputing the number needed, eq. (7)) or simply byincreasing the number of dowels.

It should be noted that the yield point of common bar stock isquite high. Most cold-finished bar stock has a yield point exceeding60,000 p.s.i., and quenched and tempered bars can be obtained with yieldpoints up to 130,000 p.s.i.

Table 2 also lists values of λ and diameter factor, f, and definesthe minimum length for each size dowel.

Dowel spacing must be left to the judgment of the designer. One methodis to simply divide the center-to-center distance between stringers bythe required number of dowels. End dowels in each span are positionedone-half of a space off the stringer centerlines. Dowels will then beequally spaced over the full length of the panel and this uniform patternwill reduce chances for fabrication errors.

S A M P L E P R O B L E M

To illustrate the use of the design charts, the following problemis considered:

Design a transverse deck for a loading of P = 12,000 lb.,a = b = 15 in.; assuming the effective span betweenstringers is 72 inches, the allowable wood foundationstress , is 1,200 p.s.i., and the center of the

wheel is positioned 22-1/2 inches from the support forthe primary shear computation.

Compute a/s = 0.208

b/a = 1.0

ξ / s = 0.313

FPL 210 -26-

(8)

Table 2 .--Dowel design data1

1For ko

= 180,000 lb. per cu. in.; = 1,000 p.s.i.; and = 3.2U.S. Forest Products Laboratory, Wood Handbook. USDA Agr. Handb. No. 72. 1955.

-27-

From figures 10 through 16:

Mx/P = 0.48

Rx /(P/s) = 2.3

(from interpolatingbetween figs. 12and 13)

Mx = 5,760 inch-pounds per inch

Rx = 383 pounds per inch

My/P = 0.058 My = 696 inch-pounds per

Ry/(P/s) = 0.98 Ry = 163 pounds per inch

inch

The stresses associated with these moments and shears can bereadily calculated. For a nominal 6-inch deck (t = 5.125 in.), thestresses are:

Primary bending = 6Mx/t2 = 1,310 p.s.i.

Horizontal shear

Secondary bending = 6My/t2 = 159 p.s.i.

Rolling shear

Thus, a 6-inch deck is adequate if the allowable design stresses forthe material equal or exceed those listed above.

If desired, the maximum deflection of the deck relative to thestringers can be determined from figure 17. Thus, for

To design the dowel connectors, it is first necessary to compute

From figures 18 and 19,

My/Ps = 0.033 My = 28,500 inch-pounds

Ry/P = 0.36 Ry = 4,320 pounds

From figure 20, a line having a slope of Ry/My = 0.15 crosses the

1-1/4-inch dowel line at a moment capacity of 4,150 inch-pounds. Thenumber of 1-1/4-inch dowels is:

FPL 210 -28-

Use 6.

or

From equation (7), selecting 1-1/4-inch dowels, the requirednumber is:

The minimum dowel length is given in table 2 as 17 inches,

From equation (8), the minimum elastic limit stress for thesteel is:

SUPPLEMENTAL TESTS

Dimensional Stability andPreservative Treatment

To study the dimensional stability of bridge deck panels subjectedto numerous wetting and drying cycles, eight of the panels from the 1969joint connector tests were taken to an exposure site at Madison, Wis.Six of the panels were treated with creosote, three of which wereincised prior to treatment, and two panels were untreated. The panelswere nailed with 3/8-inch-diameter ring shank nails to simulated bridgestringers and exposed outdoors for 3 years and 7 months (fig. 21).

Periodic inspection trips were made to the site to record dimen-sional changes and moisture contents of the panels. Measurements of thetransverse dimensions were taken at both ends of the panels betweenpairs of escutcheon pins placed 37 inches apart. Moisture probes wereinstalled within the decks and readings were taken with an electricalresistance meter.

The maximum dimensional change for the treated panels was±0.25 percent. Little difference was noted between the incised andunincised panels. There is probably sufficient play in a field joint toaccommodate a 0.25 percent increase in panel widths up to 4 feet. Asso-ciated moisture contents ranged from 8.9 to 14.8 percent. With untreatedpanels, dimensional changes ranged from +0.8 to -0.4 percent while themoisture fluctuated from 10 percent to above fiber saturation. Thisdemonstrates the effectiveness of preservative treatment in retardingmoisture changes and reducing dimensional changes.

The preservative was a 50-50 creosote-petroleum solution. Treatmentwas in accordance with AWPA Standards C1-67 and C28-67 for ground contactuse. Thirteen assays were taken, from both incised and unincised panels,with 3/8-inch-diameter plug cutters from the outer 5/8 inch of deck.

Use 6.

-29-

Douglas-fir is a difficult species to treat, and it is virtuallyimpossible to get effective treatment without incising. This fact iswell illustrated in comparing the retentions of these two panels. Petro-leum extractions taken shortly after treatment disclosed a preservativecontent of 17.0 pounds per cubic foot (p.c.f.) for incised panels andonly 5.2 p.c.f. for unincised. Assays were taken again 3-1/2 years laterimmediately adjacent to the original ones. No changes were found inthe unincised panels. Preservative content in the incised panels haddropped to 15 p.c.f., still well above the 12 p.c.f. requirement. Itis assumed that this loss occurred shortly after the panels were treateddue to surface bleeding and evaporation of solvents, and that futurelosses in preservative would be minimal.

One of the untreated panels received a coating of coal-tar masticto protect the end grain. This simple operation greatly retardedchecking in the ends of the panel. A comparison of end checking isshown in figure 22. Specimen A, with the mastic seal, exhibits practicallyno checking. The large vertical split on the left side was a resultof handling and was not a check. Checks in the unprotected slab caneasily be traced back 1 inch or more. Creosote-treated panels exhibitedvirtually no end checking.

To further evaluate the performance of glued-laminated panels underactual service conditions, experimental test decks have been applied tosix Forest Service bridges throughout the United States. No problemshave been observed due to dimensional stability nor to loss in preservativetreatment in more than 6 years.

Experimental Evaluation ofExposed Panels

To determine the effect of outdoor exposure on the structuralbehavior of glued-laminated panels, the eight panels from the exposurestudy were returned to the lab for further testing.

The two untreated panels had previously been tested with tongue-and-groove joints in the connector study. The edges were squared up and thetwo sections were glued together to make a 7- by 7-foot panel.

Two of the three treated and incised panels were likewise gluedtogether. These panels had been previously tested with dowel connectorsand seven holes were present in the glueline.

The other four panels were joined into two pairs using seven1-1/4-inch diameter steel dowels. Theoretically the dowels and deckwere balanced for a design load of 16,000 pounds. The dowel-connectedpanels were loaded in two ways: (1) With the 20- by 15-inch load blockcentered over the joint to maximize the moment at the joint, and (2) withthe edge of the block over the joint to maximize joint shear.

In all cases, the test specimens were loaded to 50,000 pounds with-out apparent failures of any kind. At this load, the theoretical primaryand secondary bending stresses were 4,800 and 610 p.s.i. respectively,and the shear stresses were 360 and 160 p.s.i. The preservative treatmentapparently had no adverse effect on the glue bond.

FPL 210 -30-

Figure 21.--Glued-laminated deck panels exposed outdoors to evaluate dimensionalstabi l i ty . (M 140 326)

Figure 22.--Comparison of end checking of untreated panels(A) Outside edge and backside of a 1-inch strip cut from mastic-coated panel.(B) Strip cut from panel without end-grain protection.

(M 139 100-14)-31-

Small-Scale Tests

Since the 50,000-pound load capacity of the test apparatus wasinsufficient for destructive testing of the 5-1/4-inch-thick deck panels,small-scale tests were conducted. The purpose of these tests was todetermine which of the four stresses , primary or secondary bending orprimary or secondary shear, controls ultimate load capacity. Allowablevalues for the primary stresses, bending parallel to grain and horizontalshear, are well defined. This is not the case, however, with thesecondary stresses, bending perpendicular to grain and rolling shear.

Nine test specimens consisting of nominal l-inch-thick Douglas-firboard material were cut into 9-1/2- by 9-1/2-inch squares. The moisturecontent of the nine specimens averaged 12 percent. These plates werethen secured to nominal 1- by 2-inch “pseudo” stringers with four sixpennyfinishing nails (2 by 0.098 in.) spaced 3 inches on center of each side.The supports were positioned perpendicular to the grain direction as isthe case with a normal bridge deck. These specimens were approximately1:6 scale relative to the 5-1/4-inch deck panels. Three different sizedload blocks, 1- by 1-, 2- by 2-, and 3- by 3-inch, were used on each ofthree sets of specimens to induce different stress levels within theplates. Each specimen was then loaded to destruction and the types offailures were noted. Theoretical stresses, at initial failure andultimate load, were then computed using the deck design chartspreviously discussed.

Horizontal shear was never a factor in any of these tests. In eachcase, there were two separate and successive failures. The character ofthese failures depended on the size of loading block.

The smallest load blocks (1- by 1-in.) imposed high rolling shearstresses on the plates adjacent to the load block. However, even beforethis there were severe compression failures (perpendicular to grain)under the load block as shown in figure 23. But compression or bearingfailures did not adversely affect structural performance of the plates.Initial structural damage first occurred at an average load of1,920 pounds in rolling shear at a stress of 660 p.s.i. These shearfailures extended from support to support and disrupted plate continuity.Ultimate failure followed in primary bending at a load of 1,980 pounds,At this point, the specimen’s behavior was somewhere between that ofa plate and a beam. Therefore, the plate theory would underestimateprimary bending stresses (8,700 p.s.i.), whereas the beam theory wouldgrossly overestimate bending stresses (32,000 p.s.i.). It should benoted that the load width to span ratio, a/s, was only 0.125, which wouldbe an unlikely situation. This would equate to a stringer spacing inexcess of 13 feet for an H2O wheel load. For practical design situations,the rolling shear stress would not usually exceed 50 p.s.i.

The 2- by 2- and 3- by 3-inch blocks represent load-to-span ratios,a/s, of 0.25 and 0.375, respectively. These two larger sizes performedin much the same manner. Although the 2- by 2-inch blocks producedminor bearing failures under the loaded area, these had no influence onplate performance. Initial failures, in both cases, occurred in rollingshear at an average stress level of 400 p.s.i. at loads of 2,280 and3,870 pounds, respectively. These failures, however, were very minorand local in nature and the deck continued to perform as a continuousplate. Ultimate loads were 2,540 and 4,650 pounds, respectively. Failures

FPL 210 - 3 2 -

-33-

were essentially in primary bending at a stress level which averaged12,400 p.s.i.; this is the listed modulus of rupture for coast-type Douglas-f i r . Most of the specimens also exhibited perpendicular-to-grain bendingfailures in the secondary direction. The corresponding average secondarybending stress at failure was 1,280 p.s.i., or slightly higher than 10percent of the primary bending strength.

Because allowable secondary stresses have not been defined, it isnecessary for the bridge designer to assign reasonable values for thesestresses. From the results of these small-scale tests, it would appearreasonable to use an allowable secondary bending stress equal to one-tenththe primary stress.

Major rolling shear failures occurred at a secondary shear stresslevel of 660 p.s.i., and applying a safety factor of 10 would suggestan allowable secondary shear stress of about 65 p.s.i. This is approximatelyone-third of the clear wood design stress in horizontal shear.

Steel Pipe Dowels

Steel pipe dowels were tested as a possible alternative to solidsteel dowels. Of the available weights (standard, extra strong, anddouble-extra strong), extra strong was selected for test purposes. Twopanel sections were joined by a pair of pipe connectors and tested inthe apparatus shown in figure A-2.

The pipe was standard 20,000-p.s.i. yield material and performed wellup to that stress level. However, when the bending stress reached 24,500p.s.i. the pipes started to fail and testing was terminated. Upon dismantlingthe sections it was found that the pipes were permanently bent.

The low bending strength of common pipe material greatly limits theperformance of pipe dowels. However, even if high-strength alloys wereselected, there is one further drawback. The outside diameter of pipedoes not match the size of standard drills. For example, a nominal3/4-inch pipe has an outside diameter of 1.05 inches. Since it isimperative that the dowels fit snugly, special drill bits would berequired.

C O N C L U S I O N S

By analyzing a glued-laminated deck as a continuous orthotropic plate,it is possible to accurately predict its behavior. Theoretical valuesthus obtained agreed very closely with experimental data.

Of eight connector systems tested, steel dowels performed best.When designed in accordance with the criteria presented, they providecontinuity between the individual panels which comprise a bridge deck.

Preservative treatment with creosote is effective in retardingmoisture changes and associated dimensional changes of exposed deckpanels.

FPL 210 -34-

A fast and simple procedure has been developed for the design ofglued-laminated bridge decks and steel dowel connectors for deckpanels placed in a transverse direction to the stringers. All thenecessary design information has been reduced to a series of easy-to-use charts, tables, and equations (figs. 10 to 20, table 2,eqs. 7 and 8).

L I T E R A T U R E C I T E D

1.

2.

3.

4.

5.

6.

7.

8.

American Institute of Timber Construction1972. Timber construction standards, AITC 100. 6th ed.

American Association of State Highway Officials1969. Standard specifications for highway bridges. 10th Edition.

Bohannan, B.1972. FPL timber bridge deck research. J. Struc. Div.,

Amer. Soc. of Civil Eng., Vol. 98, No. ST3.

Kuenzi, E. W.1955. Theoretical design of a nailed or bolted joint under

lateral load. U.S. Forest Prod. Lab. Rep. No. D1951.

Lekhnitskii, S. G.1968. Anisotropic plates. Trans. from 2d Russian ed. by

S. W. Tsai and T. Cheron, Gordon and Breach Publ.

Timoshenko, S., and Woinowsky-Krieger, S.1959. Theory of plates and shells. 2d Edition. McGraw-Hill

Book Co.

Trayer, G. W.1932. The bearing strength of wood under bolts. USDA Tech.

Bull. No. 332.

U.S. Forest Products Laboratory1955. Wood Handbook. USDA Agr. Handb. No. 72.

-35-

APPENDIX

FOUNDATION PROPERTIES OF WOOD

To apply the dowel theory, it was first necessary to define thefoundation properties of the wood; namely, the stress at proportionallimit, and the foundation modulus, k

o, Apparently little work has

been done in this area and physical tests were needed.

Eighteen tests were run using standard bolt-bearing apparatus( f i g . A - l ) . The specimens were cut from nominal 2 by 4 dimensionDouglas-fir lumber. No attention was given to grade of lumber; rather itwas selected on the basis of saw cut, i.e., flat grain or edge grain.Loads on the dowels are always applied perpendicular to grain; tests weretherefore made to see if foundation properties are different in theradial and tangential directions. No significant difference was observedin the two directions.

Three different dowel diameters--1/2 inch, 1 inch, and 1-1/2 inch--were used in these tests. Holes were drilled to provide a snug fit overthe dowels. Wood blocks were generally cut into squares, 3-1/2 by3-1/2 inches. However, half of the blocks used with 1- and 1-1/2-inchdowels were cut 7 inches in length to determine if the material oneither side of the bolt contributes to strength. No difference wasnoted, Failures were concentrated locally at the contact bearing surfaceof the dowel. Displacement or slip at failure is extremely small andedge distance does not seem to be a factor.

Load-slip data were obtained with an x-y plotter. Initially thespecimens were cycled to a displacement of about 0.0025 inch to properlyseat the dowels. Then the specimens were loaded to failure. Proportionallimit stresses were determined from the load-slip curves in the usualmanner. The foundation modulus, k

o, has the units of pounds per cubic

inch and is the stress at proportional limit divided by the slip atthat level.

Test results are presented in table A-1. The average stresses atproportional limit are 2,155, 1,640, and 1,490 p.s.i. for the 1/2-,1-, and 1-1/2-inch dowels, respectively. This apparent variation canbe explained,

For loads acting perpendicular to the grain, it is necessary toapply a diameter factor to obtain basic stress values. Proportionallimit stresses are higher for small diameter dowels. This is probablydue to the edge effect which forces fibers into tension rather than purecompression. The diameter factors are listed in table 2.

Applying the appropriate factor to these tests for three doweldiameters reduces the basic stresses to 1,280, 1,290, and 1,310 p.s.i.,which is in very close agreement, Trayer (7) found the stress at propor-tional limit to be 1,140 p.s.i. for Douglas-fir.

The average foundation modulus for the 18 specimens is180,000 pounds per cubic inch. A slight variation in this value willnot be significant since this factor is taken to the fourth root.

FPL 210 -36-

Figure A-1.--Bolt-bearing apparatus to determine foundation properties.

(M 139 976)

Table A-l .--Foundation properties of Douglas-firperpendicular to grain

FPL 210 -38-

Further tests were conducted to compare physical results withtheoretical values based on the elastic foundation properties previouslyobtained. Two panel sections were connected by a pair of steel dowels(f ig. A-2) . A slight gap was left between the panels in order to affixstrain gages to the dowels. The assembly was then simply supported inthe weak direction with the joint parallel to the supports. Loads wereapplied at the quarter-points to provide an area of constant moment overthe middle half of the assembly. Dial indicators were mounted on theupper surface to measure foundation deformation under load.

Table A-2 shows how the theoretical moments compare to the momentsas measured by the strain gages and as measured by deformation of theelastic foundation. The right-hand column shows the magnitude ofdeformation within the elastic foundation under the imposed moment.Very close agreement between theoretical and measured moments wasachieved.

Figure A-2. --Panel sections connected by steel dowels.

(M 139 654-3)

-39-

Table A-2 .--Comparison of theoretical moment to momentsmeasured by strain gages and bydeformation of elastic foundation

FPL 210 -40-

-41-

tire contact width

tire contact length

dowel coefficients, table 2

dowel diameter

bending stiffness in x- and y-directions

torsional stiffness

moduli of elasticity in x- and y-directions

bending stiffness of steel dowel

dowel diameter factor

modulus of rigidity for shear deformationsin the x-y plane

wood foundation modulus

dowel penetration length

bending moment

bending moment at dowel connection

dowel moment capacity

dowel moment which produces elastic limitstress

unit bending moments in x- and y-directions

unit twisting moment

number of dowels

wheel load

load per unit area

term in Fourier expansion of load

shear at dowel connection

unit shears in x- and y-directions

LIST OF SYMBOLS

dowel shear capacity

unit "Kirchhoff shears" in x- and y-directions

effective deck span between stringers

deck thickness

maximum deck deflection

coordinate axes

FPL 210

deflection under dowel

Poisson's ratios; the first subscriptdenotes direction of stress, thesecond denotes associated deformation

location of center of load along x-axis

proportional limit stress in compressionperpendicular to grain

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U.S. Government Printing Office 754-546/27