ELASTIC BEARING CONSTANTS FOR SHEATHING MATERIALS

USDA FOREST SERVICE RESEARCH PAPER FPL 224

1974

U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADISON, WIS.

ABSTRACT Theoretical methods of analysis have been

developed for predicting the lateral resistance of two-member nailed joints by incorporating a material property called the elastic bearing constant. To extend the use of these theories to structural analysis, the elastic bearing con-stant was determined for various sheathing materials, such as plywood, hardboard, insula-tion board, particleboard, and gypsum board.

ELASTIC BEARING CONSTANTS FOR SHEATHING MATERIALS

By

Thomas Lee Wilkinson

Forest Products Laboratory1

Forest Service U.S. Department of Agriculture

INTRODUCTION

In the design of wood structures using nails, lateral load resistance is of primary con-cern in providing rigidity and strength. The lateral resistance of a joint depends upon the type of nail and the materials being fastened. Due to the many possible combinations of nails and materials, considerable experimental evaluation would be necessary before design loads could be based on test data only.

Theoretical approaches to the lateral resistance of nailed joints eliminate the need for extensive testing, and provide information necessary for the engineering analysis of struc-tures. Theoretical relationships for joint slip and load have been developed for different types of nails in solid wood members.2 , 3 , 4 If the theoretical expressions for lateral resistance of nailed joints are to be useful in the engineer-ing analysis of structures, the elastic bearing constants must be determined for materials other than solid wood. Sheathing materials fall in this category9

EXPERIMENTAL PROCEDURE Material

Sheathing type materials studied here were plywood, hardboard, particleboard, in-sulation board, and gypsum board.

Exterior A-C grade Douglas-fir plywood, sanded both sides, was evaluated in three thicknesses--3/4,1/2, and 3/8 inch. Plywood panel constructions are listed in table 1.

Three 1/4-inch tempered hardboards of different manufacture were evaluated. Hard-

board “K“ was air felted, dry pressed aspen (smooth two sides); “E” was wet felted, wet pressed southern pine with some hardwoods (smooth one side); and “B” was wet felted, wet pressed Douglas-fir (smooth one side). Two 3/8-inch hardboard sidings (specific gravities, 0.64 and 0.88) were also tested. Both of these boards were formed wet, with the denser one pressed wet and the other pressed dry.

Particleboards evaluated were a 3/8-inch-thick homogeneous mixture of aspen flakes and a 5/8-inch-thick underlayment-type par-ticleboard of urea-formaldehyde-bonded Douglas-fir planer shavings.

Insulation boards included a 1/2-inch standard density sheathing board and three thicknesses-3/8, 1/2, and 5/8 inch-of a homogeneous board made primarily of repulped newsprint.

Standard gypsum boards in thicknesses of 5/8 and 3/8 inch were evaluated.

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

2 Wilkinson, Thomas Lee. Theoretical Lateral Resistance of Nailed Joints. J. Struc. Div., Amer. Soc. Civil Eng., Vol. 97, No. ST5, Proc. Pap. 8121. 1971.

3 Analysis of Nailed Joints with Dissimilar Members. J. Struc. Div., Amer. Soc. Civil Eng., Vol. 98, No. ST9, Proc. Pap. 9189. 1972.

4 Effect of Deformed Shanks, Prebored Lead Holes, and Grain Orientation on the Elastic Bearing Constant for Laterally Loaded Nail Joints. USDA Forest Serv. Res. Pap. FPL 192. Forest Prod. Lab., Madison, Wis.1972.

5 The values obtained for sheathing materials in this study are not intended as design values determined from a statistical sampling of panel materials, but rather are intended to show trends and results of application of theory to predict characteristics of joints between sheathing materials and between sheathing materials and wood.

1

Table 1. - Plywood panel constructions as obtained from measurement of veneers

Thickness

In. 3/8 1/2 3/4

Number Veneer thickness of Cross-

bands

3 0.07 – 0.20 5 .08 0.14 .09 5 .08 .20 .19

plies Faces Center

In.

PROCEDURE The elastic bearing constant of the various

sheathing materials was determined by run-ning lateral nail tests on two-member joints made with both members of the sheathing material. The joint members were 2 inches wide by 12 inches long and were taken from adjacent locations in the sheet of material from which they were cut. Plywood was evaluated with the face grain both parallel and perpen-dicular to the direction of loading. The 3/4-inch plywood members were joined with 10d, 8d, and 6d common nails, while 1/2-inch and 3/8-inch plywood members were joined with 8d and 6d common and 4d box nails. All other materials were assessed using 6d common nails. Ten replications were provided for each set of variables. Most of these replicates came from one sheet of material. the 1/4-inch hard-board specimens came from four sheets.

Moisture content and density of specimens were determined from one member of each joint after testing. The other member of each joint was attached with a 6d common nail to a member of solid Douglas-fir. Lateral nail tests were conducted on these new joints. The specific gravity and moisture con-tent of the solid Douglas-fir was determined.

The experimental arrangement for loading the joints is shown in figure 1. Joint slip was measured with a microformer which allowed continuous recording of the load-slip curve. The joints were loaded at a constant rate of head movement of the testing machine of 0.10 inch per minute.

Each joint was subjected to precycling by initially loading to a low level of slip and then gradually increasing the level of slip on each succeeding cycle until a fairly linear load-slip curve was obtained (fig. 2).

2

Figure 1 .-Experimental arrangement for load-ing joints showing plywood box brace used to maintain specimen in vertical position and microformer for measuring joint slip. (M 135 828)

Figure 2.-Typical load-slip data obtained for laterally loaded, nailed joints.

(M 139 955)

RESULTS The following expression, which can be

derived from the expressions presented by Wilkinson,3 was used to calculate the elastic bearing constant:

(1)

where P is lateral load on nail (Ib),

is joint slip (in.), k o is elastic bearing constant (Ib/in.3), d is effective bearing width (in.) (for round

nails this is the nail diameter), a i s depth of penetration of nail in

member 1 (in.), and b is depth of penetration of nail in

member 2 (in.). This expression is valid if both members

have the same elastic bearing constant and the products λa and are both less than 2. For a round nail, values of the parameter are given by the formula:

(2)

in which E = modulus of elasticity of nail (Ib/in.2). and were less than 2 in all cases except for the 3/4-inch plywood joints with 6d common nails. Here, the expression:3

(3)

was used to calculate the elastic bearing con-stant. The experimentally determined slope of the load-slip curves, were used in all calculations.

The results of the lateral nail test on joints made with both members of sheathing material are given in table 2.

The elastic bearing constant for the plywood ranged from a value of 0.73 x 106 to 0.88 x 106 pounds per cubic inch with an overall average of about 0.80 x 106 pounds per cubic inch. No pattern relating the elastic bearing constant to grain direction or ply con-struction could be ascertained. Therefore, it is felt that a single value of 0.80 x 106 pounds per

cubic inch can be used for Douglas-fir plywood.

It has previously been found2 that the elastic bearing constant for solid wood can be linearly related to specific gravity. This was tried with the values obtained for the hard-board specimens (fig. 3). The graph suggests a linear relation (k0 = 950,000 G) between the elastic bearing constant, k, and specific gravity, G, for those boards which were formed by a wet process; the board formed by the dry process had a distinctly lower value.

Another graph of elastic bearing constant versus specific gravity (fig. 4), was made for the three insulation boards made of repulped newsprint. Again, a linear relation (k0 = 538,000 G) appears to exist although the range in specific gravity was rather limited.

With one exception, the average propor-tional limit slip, table 2, of all joints ranged from 0.007 to 0.013 inch with most being around 0.011 inch. This corresponds very well with previous results obtained for solid wood. The one exception was the gypsum board which had a proportional limit slip of only 0.005 inch. These slip values do not include the initial permanent slip of about 0.004 inch ob-tained during the first few cyclic loadings of the joints.

The following formula was used to calculate theoretical slopes of the load-slip curves for joints made of one member of sheathing material and the other of solid Douglas-fir.

(4)

where

(5)

(6) and

(7)

in which k0 1 is elastic bearing constant for member 1 and kO2

is elastic bearing constant for member 2.

3

Tabl

e 2 -

Sum

mar

y of

data

fro

m

late

ral

nail

test

of

join

ts:

Bot

h m

embe

rs o

f sh

eath

ing

mat

eria

l1

Tabl

e 3.-

Sum

mar

y o

f da

ta f

rom

lat

eral

nai

l tes

t of

join

ts:

One

mem

ber

of s

heat

hing

mat

eria

l, on

e m

embe

r of

sol

id

Dou

glas

-fir.

6d c

omm

on

nails

1

Figure 3.--Relationship between elastic bear-ing constant and specific gravity of hard-board sheathing.

(M 141 655)

This expression was previously derived3

and is valid when λ1a < 2 and > 2. This was the case for all specimens except those using 3/4-inch plywood. Here the expression:3

(8)

was used, where

(9)

6

The values of the elastic bearing constant used in the calculations were as follows: Plywood-0.8x 106 pounds per cubic inch; hardboards formed by wet process-values from figure 3; insulation boards of repulped newsprint-values from figure 4; gypsum board-0.41 x 106 pounds per cubic inch; and all others-calculated values in table 1. The elastic bearing constant for nails driven in solid wood without lead holes was calculated using

(10)

where G is specific gravity. This expression had previously been determined4 for solid wood loaded parallel to the grain.

Figure 4.-Relationship between elastic bear-ing constant and specific gravity of insula-tion board made from repulped newsprint. (M 141 656)

Results of the lateral nail test on joints made with one member of sheathing material and the other of solid Douglas-fir are given in table 3.

The predicted slopes are shown plotted against the average experimental slopes in figure 5. The largest deviation of experimental slope of the load-slip curve from theoretical was about 7 percent for the 3/8-inch gypsum board. This good agreement between ex-perimental and predicted results indicates the reasonableness of using an average value of the elastic bearing constant for plywood and gypsum board as well as the relations found between specific gravity and the elastic bear-ing constant for hardboard and insulation board.

The proportional limit slips, table 3, were again quite similar to those previously ob-tained for solid wood, ranging from 0.008 to 0.012 inch. The only exception was the gypsum board which had a proportional limit slip of 0.005 inch.

CONCLUSIONS Besides the actual values for the elastic

bearing constant presented in table 1 for the various sheathing materials, the following summary conclusions can be drawn from this study.

1. It appears reasonable to use a single value of the elastic bearing constant, 0.80 x 106

pounds per cubic inch for Douglas-fir plywood, independent of the direction of loading or ply construction.

2. It appears the elastic bearing constant can be linearly related to specific gravity for hardboards formed by a wet process.

3. The good agreement between theoretical and experimental values for the slopes of the load-slip curves of joints made of sheathing material nailed to solid Douglas-fir further verifies the theoretical expressions previously presented.3

4. The proportional limit slip of all the joints made with wood-base boards was about

7

the same as has been experienced with solid wood, approximately 0.011 inch. The joints

with gypsum board had proportional limit slips of about 0.005 inch.

Figure 5.-Plot of theoretical versus experi-mental slopes of the load-slip curve for joints with one member of solid Douglas-fir and one member of board material.

(M 141 657)

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