EDGEWISE FLEXURAL PROPERTIES AND MODULUS OF RIGIDITY OF DIFFERENT SIZES OF SOUTHERN PINE LVL AND PLYWOOD.
EVANGELOS J. BIBLIS [*]
The results of this study confirm that modulus of rupture the measure of the force necessary to break a given substance across, as a beam, expressed by eighteen times the load which is required to break a bar of one inch square, supported flatwise at two points one foot apart, and loaded in the middle between the points of support.
- Rankine. (MOR MOR
MOR adj abbr (MUS) (= middle-of-the-road) → para el gran público
MOR adj abbr (Mus) (= ) values of southern pine plywood and laminated veneer lumber Laminated veneer lumber (LVL) is an engineered wood product that uses multiple layers of thin wood assembled with adhesives. It offers several advantages over typical milled lumber: it is stronger, straighter, and more uniform. members are influenced by the beam depth when tested at the same span-to-depth ratio. As the depth increased, the MOR values decreased significantly among the tested groups. Edgewise edge·wise also edge·ways
1. With the edge foremost.
2. On, by, with, or toward the edge.
Adv. 1. moduli of rigidity (G) values (average of 36 ksi) for different grades and constructions of plywood members were obtained by a method that requires flexure flexure /flex·ure/ (flek´sher) a bend or fold; a curvation.
caudal flexure the bend at the aboral end of the embryo.
cephalic flexure the curve in the midbrain of the embryo. tests at different span-to-depth ratios. These values are less than one-half of reported average G values for southern pine plywood obtained by a rectangular plate shear method.
Southern yellow pine has been used as lumber of different sizes, laminated beams, laminated veneer lumber (LVL LVL
In currencies, this is the abbreviation for the Latvian Lats.
The currency market, also known as the Foreign Exchange market, is the largest financial market in the world, with a daily average volume of over US $1 trillion. ), and plywood members loaded edgewise. The effect of beam size, particularly depth, has been investigated over the years for solid wood and laminated lumber beams [2,6-8,11]. According to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. Tucker , while testing wood beams with depths up to 12 inches, Newlin and Trayer observed a decrease in bending strength with an increase in beam depth. They developed an equation of the strength ratio F of wood beams with a depth d to beams with a depth of 2 inches: F = 1.07 - 0.07 [square root]d/2. Later, Dawley and Youngquist reevaluated the strength-depth theory for larger laminated beams, as reported by Freas and Selbo . Dawley and Youngquist developed an equation of the strength ratio F for larger laminated wood laminated wood: see plywood. beams with a depth d up to 16 inches to beams with a depth of 2 inches: F = 0.625 ([d.sup.2] + 143/[d.sup.2] + 188). Bechtel and Norris (2) test results of small, clear wood specimens indicate t hat the flexural strength Flexural strength is also known as modulus of rupture, bend strength, or fracture strength. Flexural strength is measured in terms of stress, and thus is expressed in pascals (Pa) in the SI system. of rectangular cross-section specimens decreases as the depth of the beams increases while tested in the same span and type of loading. Their test results also indicate that the flexural strength of small rectangular beams of the same depth loaded centrally increases as the span increases. Bohannan  evaluated differently the effect of member size on the bending strength of wood. His approach was based on the wood volume-strength relationship rather than a depth-strength relationship that is based on an accurate stress distribution along the beam depth. The volume-strength approach is based on the statistical strength theory suggested by Weibull . The basis of this theory is associated with a greater probability that a region of low strength will occur in a member of large volume than in a member of small volume.
Bohannan , using this statistical strength theory, developed and experimentally verified an equation that relates the bending strength to depth and length of the beam and the method of loading the beam. He modified this equation, after assuming a constant spanto-depth ratio, and expressed the F of a Douglas-fir wood beam with d to that of a beam having a d of 2 inches: F = [(2/d).sup.1/9].
Presently, there are structural applications that are used in edgewise flexure smaller sizes (depth and width) of plywood or LVL members. Therefore, the question arises whether in these cases the depth of these members has an effect on their bending strength, and how much of an effect.
It is known that shear deformation during bending affects the stiffness of the member [3,4,9,12]. Modulus of rigidity Noun 1. modulus of rigidity - the coefficient of elasticity for a shearing force
coefficient of elasticity, elastic modulus, modulus of elasticity - (physics) the ratio of the applied stress to the change in shape of an elastic body of the member in edgewise bending ([G.sub.LT] for solid wood or LVL and a combination of [G.sub.LT] and [G.sub.TR] for plywood) is important. There are several methods for determining the G values in different directions of wood or wood composites (plates of wood, plywood, particleboards, or flakeboards). They can be determined knowing the Poissons ratios, from nondestructive methods, from the ratio of pure modulus of elasticity modulus of elasticity
The ratio of the stress applied to a body to the strain that results in the body in response to it. The modulus of elasticity of a material is a measure of its stiffness and for most materials remains constant over a range of stress. (E) to G, and from bending tests at different span-to-depth ratios of the member. Values of G for wood or composite wood for a particular plane (direction) depend on its density, moisture, defects, and fiber or particle orientation . It is known that different determination methods provide different values of G. These differences may be due to experimental errors or to the validity of certain assumptions made utilizing the involved equation.
This study was undertaken to determine the following:
1. The effect and magnitude of beam depth on the strength of southern pine plywood and LVL of two veneer grades.
2. The G and E of southern pine plywood and LVL beams of two veneer grades tested edgewise.
Four plywood and two LVL panels (4 ft. by 8 ft. and 1.050 in. thick) were fabricated fab·ri·cate
tr.v. fab·ri·cat·ed, fab·ri·cat·ing, fab·ri·cates
1. To make; create.
2. To construct by combining or assembling diverse, typically standardized parts: from 7 plies plies 1
Third person singular present tense of ply1.
Plural of ply1. of southern pine Veneers in a plywood mill. Three plywood panels and one LVL panel were made entirely of C grade veneers, while equal numbers of panels consisted of 3 plies of 1/8-inch C grade veneers and 4 plies of 1/6-inch D grade veneers. The 1/8-inch veneer plies were located at the top, center, and bottom of each panel. A commercial extended phenolic resin Noun 1. phenolic resin - a thermosetting resin
synthetic resin - a resin having a polymeric structure; especially a resin in the raw state; used chiefly in plastics was used with 90 pounds spread per 1,000 square feet of double glueline for bonding all panels. Panels were prepressed at room temperature with 160 psi for 3-1/2 minutes and then hot-pressed with 200 psi and 310 [degrees]F for 15 minutes. Panels were allowed to cool for 48 hours before cutting them into specimens. Each panel was first marked and then cut along the mid-width into two equal sections 4 by 4 feet each. One section was used to obtain flexure specimens with surface veneer grain parallel to the span, while the other section was used for specimen s with surface veneer grain perpendicular to the span.
EFFECT OF BEAM DEPTH ON STRENGTH
From each one-half southern pine plywood and LVL panel section, three plywood and six LVL specimens were obtained with the following dimensions: 3 by 48 inches; 2 by 31 inches; and 1 by 17 inches with the surface veneer grain parallel to span. From the other one-half plywood and LVL panel section, three plywood and six LVL specimens of the same dimensions as previously described were obtained with surface veneer grain perpendicular to the span. All the above specimens of three depths (1 in.; 2 in.; and 3 in.) were tested to failure in edgewise flexure with central loading, at a span-to-depth ratio of 14:1, according to ASTM ASTM
American Society for Testing and Materials D 143 . After testing, the percent moisture content (MC) and specific gravity specific gravity, ratio of the weight of a given volume of a substance to the weight of an equal volume of some reference substance, or, equivalently, the ratio of the masses of equal volumes of the two substances. (SG) of each specimen were determined and reported with the calculated average value of modulus of elasticity (MOE Moe
continually exasperated at Larry and Curly for their mischievous pranks. [TV: “The Three Stooges” in Terrace, II, 366]
See : Exasperation ) and modulus of rupture (MOR) in Table 1.
DETERMINING G AND E
To determine the G values for 1-inch-thick southern pine plywood and LVL members, a method was employed that was previously used by Preston , Wangaard , and Biblis . This method requires the determination of the effective MOE at various span-to-depth ratios. To minimize the effect of variability in properties among different beams (rectangular strips), each specimen was tested nondestructively in bending at six different spans (18, 24, 30, 36, 42, and 46 in.). For each type of plywood and LVL, six specimen replications were used (1-in, wide by 2.5-in. deep by 48-in, long). Each specimen, after testing with central loading nondestructively at the original span, was shortened and tested again at the shorter span until all spans were tested. The load applied to each span was only 1/3 of the estimated proportional limit load for each type of specimen.
The obtained 36 actual MOE values for each type of plywood and LYL LYL Love You Lots
LYL Live Your Life (band)
LYL Love You Loads
LYL Love You Later specimen were plotted with coordinates, x = [(1/2 span/depth).sup.2] and y = [(1/2 span/depth).sup.2] % MOE using the transformed rectilinear rec·ti·lin·e·ar
Moving in, consisting of, bounded by, or characterized by a straight line or lines: following a rectilinear path; rectilinear patterns in wallpaper. relationship:
[(L/2d).sup.2]/E' = 0.3/G + 1/E[(L / 2d).sup.2]
where L = span; d = depth of specimen; = effective MOE; G = modulus of rigidity; E = pure MOE.
A linear regression Linear regression
A statistical technique for fitting a straight line to a set of data points. for each group of specimens was calculated. The intercept of the straight line, y = [alpha] + bx with the ordinate ordinate: see Cartesian coordinates.
(mathematics) ordinate - The y-coordinate on an (x,y) graph; the output of a function plotted against its input.
x is the "abscissa".
See Cartesian coordinates. axis represents the term 0.3/G, and the slope of the line represents the reciprocal of E, thus the two unknown constants G and E for each group of specimens (plywood or LVL) were determined (Table 2).
RESULTS AND DISCUSSION
Table 1 presents the average values of MOR and MOE of specimens of different depths tested at the same span-to-depth ratio of 14, representing two grades of plywood and LVL. T-tests indicate significant differences in MOR values for different beam depths at 95 percent confidence limit for all plywood and LVL groups except for group PLY-C with outer veneers parallel to the span. Figure 1 indicates the relationship between the MOR values and corresponding beam depths of tested LVL-C specimens with outer veneer parallel to the span. Note the [r.sup.2] = 0.5817 of the linear regression equation. For all tested groups, MOR values of beams 3 inches deep are approximately between 10 percent (PLY-C) to 37 percent (PLY-CD) smaller than those of beams 2 inches deep. As expected, in general, MOR values of plywood and LVL members constructed entirely with C grade veneers are larger than those members constructed of CD grade veneers. Predictions of the differences in MOR values between 3-inch and 2-inch beams made using equations presented by Bohannan  are all within approximately 9 percent of the differences of tested beams.
MOR values of plywood members of the same veneer grade but with outer veneer grain perpendicular to the span are between 30 and 91 percent (PLY-CD) higher than those with outer veneers parallel to the span. This is because the tested plywood consisted of seven plies and the difference in the total thickness of each orientation was significant.
The results indicate that there is not a significant difference in MOE values in members of the same construction and grade but with different spans. This is because tested members of different depths had the same span-to-depth ratio.
The results indicate that the G values of the plywood and LVL members vary from 29.4 to 41.3 ksi, although the E values vary from 821 to 1,893 ksi Table 2. It appears that the G values are not significantly influenced by the veneer grade. The E values of LVL are significantly higher than corresponding E values of plywood. The results in Table 2 also indicate that the E values of plywood members with outer veneer grain perpendicular to the span are significantly higher than those of plywood with outer veneer grain parallel to the span. This is because in this case the cumulative thickness of veneers with grain parallel to the span equaled 64 percent of the total thickness. The results also indicate that the G values of the plywood members obtained by the method described in this study (average of 36 ksi) are less than 1/2 of the G values (73 ksi) reported by Biblis and Lee  for southern pine plywood obtained by the rectangular plate shear method. These differences are attributed to the different type (dire ction) of shear stresses mea-sued by the two methods.
The results of this study confirm that modulus of rupture (MOR) values of southern pine plywood and LVL members are influenced by the beam depth when tested at the same span-to-depth ratio. As the depth increased, the MOR values decreased significantly among the tested groups.
G values for different grades and constructions of plywood members averaged 36 ksi, obtained by a method that requires flexure tests at different span-to-depth ratios.
The author is Professor Emeritus, School of Forestry & Wildlife Sciences, Auburn Univ., AL 36849-5418. This paper was received for publication in February 2000. Reprint No.9093.
(*.) Forest Products Society Member.
(1.) American Society for Testing and Materials. 1996. Standard D-143-83. Annual Book of ASTM Standards, Section 4, Vol. 04.10 Wood. ASTM, West Conshohocken, Pa.
(2.) Bechtel, S.C. and C.B. Norris. 1959. Strength of wood beams of rectangular cross section as effected by span-depth ratio. Rept. 1910. USDA USDA,
n.pr See United States Department of Agriculture. Forest Serv., Forest Prod. Lab., Madison, Wis.
(3.) Biblis, E.J. 1965. An analysis of wood-fiberglass composite beams within and beyond the elastic region. Forest Prod. J. 15(2): 81-88.
(4.) _____. 1965. Shear deflection of wood beams. Forest Prod. J. 15(11):492-498.
(5.) _____. and W.C. Lee. 1984. Properties of sheathing grade plywood made from sweetgum and southern pine. Wood and Fiber Sci. 16(1):86-92.
(6.) Bohannan, B. 1966. Effect of size on bending strength of wood members. Rept. 56. USDA Forest Serv., Forest Prod. Lab., Madison, Wis.
(7.) Comben, A.J. 1957. The effect of depth on the strength properties of timber beams, with an analysis of the stresses and strains developed. Spec. Rept. No. 12. Great Britain Great Britain, officially United Kingdom of Great Britain and Northern Ireland, constitutional monarchy (2005 est. pop. 60,441,000), 94,226 sq mi (244,044 sq km), on the British Isles, off W Europe. The country is often referred to simply as Britain. Dept. Sci. and Ind. Res., Forest Prod. Res., London.
(8.) Freas, A.D. and M.L. Selbo. 1954. Fabrication fabrication (fab´rikā´shn),
n the construction or making of a restoration. and design of glued laminated wood structural members. Tech. Bull. 1069. USDA Forest Serv., Forest Prod. Lab., Madison, Wis.
(9.) Newlin, J.A. and G.W. Trayer. 1924. Deflection of beams with especial es·pe·cial
1. Of special importance or significance; exceptional: an occasion of especial joy.
2. reference to shear deformations. Rept. No. 1309. USDA Forest Serv., Forest Prod. Lab., Madison, Wis.
(10.) Preston, S. 1954. Effect of synthetic resin adhesives on the strength and physical properties of wood veneer In woodworking, Veneer refers to thin slices of wood, usually thinner than 3 millimetres (1/8 inch), that are usually glued and pressed onto core panels (typically, wood, particle board or medium density fiberboard) to produce flat panels such as doors, tops and side panels for laminates. Bull. No. 60. Yale Univ. School of Forestry, New Haven New Haven, city (1990 pop. 130,474), New Haven co., S Conn., a port of entry where the Quinnipiac and other small rivers enter Long Island Sound; inc. 1784. Firearms and ammunition, clocks and watches, tools, rubber and paper products, and textiles are among the many , Conn.
(11.) Tucker, J., Jr. 1941. Statistical theory of the effect of dimensions and of method of loading upon the modulus of rupture of beams. In: Proc. Am. Soc. for Testing and Materials. 41:1072-1094. ASTM, West Conshohocken, Pa.
(12.) USDA Forest Products Laboratory. 1941. Form factors of beams subjected to transverse loading only. (Reprint from Nat. Adv. Comm. for Aeron. Rept. 181). Rept. 1310. USDA Forest Serv., Forest Prod. Lab., Madison, Wis.
(13.) _____. 1962. Elastic properties of wood. Rept. 1528; 1528 A-G. Forest Prod. Lab., Madison, Wis.
(14.) Wangaard, F.F. 1964. Elastic deflection of wood-fiberglass composite beams. Forest Prod. J. 14(6):256-260.
(15.) Weibull, W. 1939. A statistical theory of the strength of materials strength of materials, measurement in engineering of the capacity of metal, wood, concrete, and other materials to withstand stress and strain. Stress is the internal force exerted by one part of an elastic body upon the adjoining part, and strain is the deformation . In: Proc. Swedish Royal Inst. Eng. Res., Stockholm, Sweden.
Edgewise flexural properties of southern pine plywood and LVL specimens of different depth tested with central loading at three different spans but at the same span-to-depth ratio of 14. [a] Specimen group MC [b] SG [b] Depth Span (%) (in.) Outer veneer grain parallel to span PLY-C [c] 9.4 0.62 1 14.0 2 28.0 3 45.5 PLY-CD 9.2 0.62 1 14.0 2 28.0 3 45.5 LVL-C 9.4 0.64 1 14.0 2 28.0 3 45.5 LVL-CD 9.4 0.63 1 14.0 2 28.0 3 45.5 Outer veneer grain perpendicular to span PLY-C 9.2 0.64 1 14.0 2 28.0 3 45.5 PLY-CD 9.1 0.62 1 14.0 2 28.0 3 45.5 Specimen group MOE [b] MOR [b] (ksi) (psi) Outer veneer grain parallel to span PLY-C [c] 812 (81) [d] 5,900 (770) 804 (94) 5,560 (910) 812 (58) 5,010 (642) PLY-CD 721 (68) 5,720 (930) 743 (47) 5,550 (660) 682 (19) 3,472 (670) LVL-C 1,578 (116) 13,702 (1,610) 1,502 (72) 12,840 (751) 1,457 (50) 10,680 (560) LVL-CD 1,560 (108) 13,350 (1,170) 1,430 (93) 11,130 (1,450) 1,418 (54) 9,670 (820) Outer veneer grain perpendicular to span PLY-C 1,277 (88) 10,080 (1,000) 1,175 (41) 9,560 (910) 1,180 (44) 8,430 (590) PLY-CD 1,010 (72) 8,330 (840) 964 (84) 7,210 (950) 999 (45) 6,620 (940)
(a.)Each value represents the average of six specimens.
(b.)MC = moisture content; SG = specific gravity (ovendry basis); MOE = modulus of elasticity; MOR = modulus of rupture.
(c.)The first three letters correspond to plywood (PLY) and laminated veneer lumber (LYL); the letters C and CD designate veneer grades.
(d.)Values in parentheses represent standard deviations.
Edgewise modulus of rigidity and pure edgewise modulus of elasticity properties of southern pine plywood and LVL specimens of different depths tested with central loading at three different spans but at the same span-to-depth ratio of 14. [a] MOE [b] Specimen [b] MC [b] SG [b] G [b] E [b] (14.4/1) E/G (%) (ksi) Outer veneer grain parallel to span PLY-C [c] 9.5 0.59 37.8 1,009 878 26.7 PLY-CD 9.4 0.61 32.5 821 755 25.3 LVL-C 9.8 0.62 31.9 1,882 1,445 58.9 LVL-CD 9.6 0.60 29.4 1,893 1,445 64.3 Outer veneer grain perpendicular to span PLY-C 9.2 0.64 32.2 1,489 1,161 46.2 PLY-CD 9.3 0.58 41.3 1,149 994 27.8
(a.)Each value was obtained from six specimens tested nondestructively at six spans.
(b.)MC = moisture content; SG = specific gravity; G = edgewise modulus of rigidity; E = pure edgewise modulus of elasticity; MOE = modulus of elasticity.
(c.)The first three letters correspond to plywood (PLY) and laminated veneer lumber (LVL); the letters C and CD designate veneer grades.