ENGR 3360 Section 3 Mechanics of Materials Lab

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ENGR 3360

Section 3

Mechanics of Materials Lab

Lab #2: Wood Lab

March 12, 2008

Prepared By:

Kevin ChollmanPetroleum Engineering

Montana Tech

AND

Jason HellandGeneral Engineering

Montana Tech

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Abstract:

The wood lab is designed to test the strength of wood under compression and bending. This isimportant as wood makes up most of our buildings and various everyday items. Woods strength

is an important aspect in any engineering design.

Wooden tripods were built using a variety of fasteners (common nail, ring shank nail, screws,

and wood glue) and the strength of the wood, as well as the fasteners, was tested with a 30K

Tinius Olsen machine. Aside from the wooden tripods, solid wood columns, solid wood beams,and laminated wood beams were constructed and tested. The compressive strength of the solid

wood columns was found as well as the bending stress of both types of wooden beams.

Failure modes of the wood was found through visual inspection of each wood specimen anddemonstrated through either stress vs. strain plots or force applied vs. deflection plots. Through

these plots and test results, different properties of the wood samples were calculated and

compared to known theoretical values. These results will provide a basis of understanding of

wood properties and strengths.

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Table of Contents:

Abstract ______________________________________________________________________2Table of Contents _______________________________________________________________3

Figures, Equations, and Table List _________________________________________________4

Introduction ___________________________________________________________________5Background ___________________________________________________________________5

Wood Preparation ________________________________________________________6

Equations _______________________________________________________________7Experimental Results ____________________________________________________________8

Wood Type ______________________________________________________________8

Common Nail Tripod Results _______________________________________________8

Ring Shank Nail Tripod Results _____________________________________________9Screwed Tripod Results ___________________________________________________10

Glued Along Grain Results ________________________________________________11

Glued Perpendicular to Grain Results ________________________________________12

Glued Tripod Comparison _________________________________________________13Coarse Grained Column Results ____________________________________________13

Fine Grained Column Results ______________________________________________15White Oak Column Results ________________________________________________17

Solid Beam Results ______________________________________________________18

Laminated .25 Beam Results ______________________________________________20

Laminated .375 Beam Results _____________________________________________22Laminated .5 Beam Results _______________________________________________23

Laminated Beam Comparison ______________________________________________25

Conclusion ___________________________________________________________________27References ___________________________________________________________________29

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Figures, Equations, and Tables

Figure 1. Pre-Fastened Tripod _____________________________________________________6Figure 2. Laminated Beam Being Glued _____________________________________________6

Equation 1. Stress _______________________________________________________________7

Equation 2. Strain _______________________________________________________________7Equation 3. Modulus of Elasticity __________________________________________________7

Table I. Density Data ____________________________________________________________8

Figure 3. Stress vs. Strain Plot for Common Nail Tripods _______________________________8Figure 4. Common Nail Tripod After Test ___________________________________________8

Figure 5. Common Nail Tripod Cut Away __________________________________________9

Figure 6. Stress vs. Strain Plot for Ring Shank Nail Tripods______________________________9

Figure 7. Ring Shank Nail Tripod Failure___________________________________________10Figure 8. Stress vs. Strain Plot for Screwed Tripods___________________________________10

Figure 9. Screwed Tripod Failure__________________________________________________11

Figure 10. Stress vs. Strain Plot of Glued Tripods Along the Grain_______________________11

Figure 11. Glued Along Grain Tripod Failure________________________________________12Figure 12. Stress vs. Strain Plot for Glued Against the Grain Tripod______________________12

Figure 13. Tripod 8 Failure_______________________________________________________13_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

Figure 14. Tripod 9 Failure_______________________________________________________13Figure 15. Stress vs. Strain Plot for Coarse Grained Columns____________________________14

Table II. Coarse-Grained Column Results___________________________________________14

Figure 16. Column 1 Failure______________________________________________________15_______________________________________________________________________________

_______________________________________________________________________________

Figure 17. Column 3 Failure______________________________________________________15Figure 18. Stress vs. Strain Plot for Fine-Grained Columns______________________________15

Table III. Fine-Grained Column Results____________________________________________16

Figure 19. Column 2 Failure______________________________________________________16_______________________________________________________________________________

_____________________________________________________________________________16

_______________________________________________________________________________

_______________________________________________________________________________Figure 20. Column 4 Failure______________________________________________________16

Figure 21. Stress vs. Strain Plot for White Oak Columns_______________________________17

Figure 22. White Oak Failure W/O Hole____________________________________________17_______________________________________________________________________________

Figure 23. White Oak Failure W/ Hole______________________________________________17

Table IV. White Oak Column Results______________________________________________18Figure 24. Force Diagram of Beam Test____________________________________________18

Figure 25. Force vs. Position Plot for Solid Beams____________________________________19

_______________________________________________________________________________

Table V. Solid Beam Data_______________________________________________________19

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Figure 26. Solid Beam Failure____________________________________________________20

Figure 27. Force vs. Position Plot for .25 Laminated Beams____________________________20

Table VI. .25 Laminated Beam Data ______________________________________________21Figure 28. Horizontal .25 Laminated Failure________________________________________22

Figure 29. Vertical .25 Laminated Failure__________________________________________22

Figure 30. Force vs. Position Plot for .375 Laminated Beam____________________________22Table VII. .375 Laminated Beam Data_____________________________________________23

Figure 31. Force vs. Position Plot for .5 Laminated Beams_____________________________24

Table VIII. .5 Laminated Beam Data ______________________________________________25Table IX. Laminated Beam Comparison____________________________________________26

Introduction:

Background:

Wood is used in a plethora of types of construction--from buildings, furniture, and

weapons to vehicles, tools, and utensils. Along with the various uses of wood, there are plenty ofdifferent types of wood to use depending on the type of application. Wood shows considerable

strength in compression, tension, and bending; but wood also is subject to many types of defectssuch as knots, warps and checks, and holes. Because of these defects--most of which you may

not even know exist as they could be inside the wood and you cannot see them--great care must

be taken with wood projects.

Below is text referencing the different types of wood and fastening systems that were

tested in this lab. The wood pieces were tested with a 30K Tinius Olsen machine that records the

test data such as force exerted, time, and position (deflection of the test piece). This data can thenbe used to calculate the stress and strain for each test that allows analysis to find Youngs

Modulus and yield/break points for the test pieces.

The purpose of this lab was to test various types of fasteners (common nails, ring shank

nails, screws, glued along the grain, glued against the grain) and how well they held for five

pairs of wood tripods. Tripods consist of three 1.5 W x .75 T x 5 L wood pieces that arefastened together with the different fasteners. The middle piece--the trunk--is offset by one inch

from the outer two pieces. The trunk is the wood piece that has the force exerted on it while the

fasteners try to hold the tripod together.

Along with the five pairs of tripods, the lab group made three pairs of laminated wood

beams. These samples were made with different thicknesses of plywood but were all 24 long.

Various numbers of these plywood pieces (different number of pieces depending on thethickness of the pieces) were glued together to form the laminated wood beams. Pairs were made

in order to test the laminated wood beams parallel to the glued joints and perpendicular to the

glued joints. Performing a strengths analysis in this way allows a better understanding of howlaminated wood beams can hold up in different conditions.

To contrast the strength of laminated wood beams, solid wood beams were also tested.

These pieces were also 24 long but were 1.5 in width and thickness. Only one pair of solid

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wood beams were tested as they did not require any fastening system.

The instructor provided small wood columns (roughly 1.5 in width and thickness and 6long) to test. These wood columns were tested in compression on the small area of the wood (the

type of compression that a building column would be in) to show how strong they are. A piece of

white oak was also tested (originally one large piece of 13 L x 1 1/16 T x 2 3/4 W and wascut into two pieces for testing). The white oak showed remarkable compressive strength.

This lab will show which fastening system provides the best support--either commonnails, ring shank nails, screws, or glue along or against the grain. It will also show whether a

laminated beam with thicker or thinner glued sections is stronger as well as the strength of solid

wooden beams. These results should give a clearer understanding--and optimism--of the strength

of wood that can be used in construction projects.

Wood Preparation:

In order to prepare the wood samples for the tripods, approximately 1.5 W x .75 T x 5L wood pieces were cut with a power saw. These pieces were then marked with lines 1 from

the bottom and from the top. Other lines were drawn 3/8 from the outer edges. Theintersections of these lines gave approximate places to nail or screw the pieces (offsetting them

either above or below the lines). Figure 1 shows a tripod ready to be fastened.

Figure 1. Pre-Fastened Tripod

Figure 1 shows the four lines and intersections that give approximate locations of where

to fasten the tripod. The leftmost fasteners will be placed slightly below the intersections and the

rightmost fasteners will be places slightly above the intersections.

Along with the 10 wood tripod samples, six laminated wood beams were constructed--three pairs, each of which having different thicknesses of plywood. Plywood pieces 24 long and1.5 wide were cut for each sample (one pair was .5 thick, one pair was .375 thick, one pair

was .25 thick). The plywood was then glued together as shown in Figure 2.

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Figure 2. Laminated Beam Being Glued

All of the glued wood tripods and laminated wood beams were then clamped and allowed

to dry for one day before the clamps were removed to ensure quality drying.Equations:

Stress is equal to force divided by area. The area in the tripod tests is taken to be the trunktop that had the compressive force exerted on it (.75 x 1.5). The same plane is used for the

columns (although each had a different planar area, unlike the tripods).

(1)

Stress =F

A=

F[lbf]

width * thickness[in2]

Strain is the amount of deflection divided by the total length. Using the test data, we

calculated the strain by the position divided by length--assumed to be six inches for a tripod andvaries for each column.

(2)

Strain =d

Length=Position [in]

Length [in]

In order to calculate the modulus of elasticity of the wooden beams (in the straight line

portion of the data), as well as the maximum theoretical deflection, the following formula wasutilized:

(3)

E=P *L

3

48*I*dmax

where: E = modulus of elasticity of the beam (psi)P = force applied at the yield point (lbf)

L = total length of the beam (in)I = moment of inertia of the beam (in4)

max = deflection at P (in)

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Experimental Results:

Wood Type:

In order to complete this lab, a type of wood for the samples had to be determined.Average density of all the wood was determined and then a specific gravity of the wood was

found. (See Table I.)

TABLE I. Density Data

Type of Sample Average Density (lb/ft3) Specific Gravity

Wood Beams 22.57 .36

Laminated Beams 31.86

Wood Columns 20.28 .33

This data shows that we could be using sugar pine (specific gravity of .34); hence, sugar

pine data was used in all theoretical calculations (including the plywood samples whose densityis higher due to the fact that it is plywood and is glued, meaning that it is not the same type of

wood throughout the sample).

Common Nail Tripod Results:

The common nail is a widely used fastener in construction projects and everydayhousehold projects. The common nail was also the hardest to fasten a wood tripod as their shaft

diameter was greater than the other fasteners and the wood split on nearly every sample. The

average stress on a common nail tripod was calculated to be 2016.5 psi. This stress is greaterthan either the ring shank tripod and the screwed tripod averages. Results from the two tests were

used to calculate the stress and strain (Equations 1 and 2). These results were plotted on Figure 3.

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Stress vs Strain

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain

Tripod 5 Common Nail Tripod 10 Common Nail

Figure 3. Stress vs. Strain Plot for Common Nail Tripods

Figure 3 shows that Tripod 5 was able to undergo approximately 350 psi more stress than

Tripod 10. This could be due to a minor crack in Tripod 10 that we may have been unaware prior

to testing. However, Tripod 10 was able to hold the stress for a much longer time than Tripod 5and, as a result, ended up having a higher deflection.

Figure 4 shows Tripod 5 after compression testing. From the outside, the tripod does notseem to be very damaged, aside from the word Monday being so offset. Figure 5 shows the

same tripod with part of the trunk wood ripped away to see how the nails were trying to shear.

Even though the test on the tripod forced the tripod in compression, the nails were undergoing

shear stress as they were trying to break. Figure 5 shows this as the nails are bent downwardtrying to shear them.

Figure 4. Common Nail Tripod After Test Figure 5. Common Nail Tripod Cut Away

Ring Shank Nail Tripod Results:

Ring Shank nails are smaller in shaft and head diameter than common nails and havesmall rings around the shaft that provide greater resistance to withdrawal than other nails. Some

believe that ring shank nails hold more force than common nails; our tests showed opposite

results. This could be because the ring shank provides a greater withdrawal resistance and not a

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greater shear resistance; or it could be due to the fact that the ring shank nails were much smaller

in diameter and length than the common nails. The Stress vs. Strain curve for ring shank nails is

shown in Figure 6.

Stress vs Stain

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Strain

Tripod 3 Ring Shank Tripod 4 Ring Shank

Figure 6. Stress vs. Strain Plot for Ring Shank Nail Tripods

The maximum stress difference between Tripod 3 and Tripod 4 is approximately 200 psi;but the curves give very similar plot shapes. The initial straight-line zone (used to calculate the

modulus of elasticity if this was a pure wood test) overlaps in such a way that the wood samples

could be twins. However, Tripod 3 was able to hold less stress than Tripod 4. Figure 7 showshow the tripod failed.

Figure 7. Ring Shank Nail Tripod Failure

Figure 7 shows how the ring shank nails bent and responded to the compressive load

placed on the trunk. The shearing force on the nails seemed to be much greater than the commonnails due to how much they bent. The nails created very oblong holes in both sides of the tripod

pieces. However, besides the extreme bending and hole distortion no other failure modes can befound; that is, the wood did not dramatically fail.

Screwed Tripod Results:

Screws are widely used as they give extreme withdrawal resistance and can maintain

good shearing and compressive loads. Tripod 1 gave a stress that was higher than either ring

shank nail and common nail Tripod 10. Tripod 2 gave results on par with the other fasteners. The

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Stress vs. Strain plot is shown in Figure 8.

Stress vs Strain

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Strain

Tripod 1 Screws Tripod 2 Screws

Figure 8. Stress vs. Strain Plot for Screwed Tripods

Tripod 1 shows considerably greater strength than Tripod 2. This could be due to a splitthat we were unaware of in Tripod 2. However, the shape of each curve in Figure 8 is of similar

shape. The screw seems to withhold a lot of force before the wood would split. Then the screws

would hold more force for a while until the wood began splitting more. It did not seem to be a

very conventional Stress vs. Strain plot with the straight-line portion, the compressive strength,and the rupture point. Figure 9 shows a cut-away of a screwed tripod failure.

Figure 9. Screwed Tripod Failure

Figure 9 shows that the screws underwent high shear stresses with the bottom-right screw

shearing completely. The holes are very oblong and the wood is deformed in these holes. Besidesthe excessive shearing of the screws, there are no other visible signs of failure from the wood.

Glued Along Grain Results:

Common practice when gluing wood pieces together is to glue along the grain of each

piece (so that the grain is parallel on all the pieces). By gluing it this way the wood is supposedto hold much greater stresses. Figure 10 shows the validity of this.

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Stress vs Strain

0

1000

2000

3000

4000

5000

6000

0 0.005 0.01 0.015 0.02 0.025

Strain

Tripod 6 Glue with Grain Tripod 7 Glue with Grain

Figure 10. Stress vs. Strain Plot of Glued Tripods Along the Grain

Figure 10 shows that Tripod 6 held much better than Tripod 7; this could be due to a less

than exemplary gluing job on Tripod 7. Tripod 6 held approximately 2200 psi more than Tripod

7. However, each piece gave the same stress/strain curve shape and deflection for each piece wasnearly equal. Looking at either Tripod 6 or Tripod 7 data, one can see that, comparatively, wood

glue holds much stronger than any other fastening method. One reason for this is the shear stress

problem with fasteners and bolts. Glue holds a much greater area than any bolt can and, thusly,can withstand a much greater shear stress than any bolt. Figure 11 shows a glued tripod after

failure.

Figure 11. Glued Along Grain Tripod Failure

As Figure 11 shows, the glued tripod did not experience any failure outside of the 1offset trunk. The glue was able to withstand the shearing force and hold together. The top of the

trunk underwent all of the compressive force and ended up failing. This failure was due solely to

the wood properties and not the fastening system, unlike the different types of bolts.

Glued Perpendicular to Grain Results:

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Common practice says that gluing against the grains provides weaker support amongst

other problems in woodwork. Figure 12 shows the truth of this belief.

Figure 12. Stress vs. Strain Plot for Glued Against the Grain Tripod

Each Tripod (8 and 9) held almost the same amount of stress (approximately 1730 psi)

before failing. When they did fail, they failed catastrophically as shown by the nearly straight

line downward of stress. Figures 13 and 14 shows the catastrophic failure of these tripods.

Figure 13. Tripod 8 Failure Figure 14. Tripod 9 Failure

As Figures 13 and 14 clearly demonstrate, gluing against the grains of wood is not

recommended practice. In the case of Tripod 8 (Figure 13), besides the extreme level of

compression of the trunk top, the left leg popped off completely and shot out of the test system.Tripod 9 (Figure 14) shows extreme compression of the trunk top (almost to the top of the legs)

before splitting from the right leg completely and damaging the left leg bottom. Both are cases of

catastrophic failure.

Glued Tripod Comparison:

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Stress vs Strain

0

200

400

600

800

1000

12001400

1600

1800

2000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Strain

Tripod 8 Glue Perpendicular Tripod 9 Glue perpendicular


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As shows above in contrasting Figure 11 with Figures 13 and 14, gluing against the

grains results in catastrophic failure that would cause extreme damage in any project. Comparing

Figure 10 with Figure 12 we see that gluing along the grains provides considerably greaterstrength than gluing against the grains does and results in far less failure and damage.

Coarse Grained Column Results:

Columns 1 and 3 were coarse-grained wood columns; however, Column 1 was cut

parallel to the grains and Column 3 was cut perpendicular to the grains. Because of this, we seeincredible variance in our results (such as the difference in methods of gluing). Figure 15 shows

the Stress vs. Strain plot of these samples.

Stress vs Strain

0

1000

2000

3000

4000

5000

6000

0.000 0.020 0.040 0.060 0.080 0.100 0.120

Strain

Column 1 Parallel coarse Column 2 Perpendicular coarse

Figure 15. Stress vs. Strain Plot for Coarse Grained Columns

Figure 15 shows how a column cut parallel to the grains can withstand magnitudes morestress than a column cut perpendicular to the grains. These coarse-grained samples have

incredibly different values for their Yield Stress, Maximum Strength, Modulus of Elasticity, andtheir Strength to Weight Ratio (see Table II). This difference is solely due to the fact that one

was crushed parallel to grains and one perpendicular.

TABLE II. Coarse-Grained Column Results

COLUMN 1 -- Parallel to Grain

Ultimate Strength = 5,610 psi

Yield strength = 5,000 psi

Modulus of Elasticity = 468,915 psi

Strength to weight ratio = 27,719 lbf/lbmCOLUMN 3 -- Perpendicular to Grains

Ultimate Strength = 713 psi

Yield strength = 500 psi


Strength to weight ratio = 3,599 lbf/lbm

The results shown in Table I1 show that when crushed parallel to the grains the strength

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is about 5000 psi greater and Yield Strength is a factor of 10 greater. The Modulus of Elasticity

also varied by almost a factor of 10 between the samples.

We determined--through measurement of all columns--that the average density was 20.28

lb/ft3. This gives a specific gravity (when compared to water at 62.4 lb/ft 3) of approximately .33.

This specific gravity tells us that we probably have sugar pine wood. Sugar Pine has a Modulusof Elasticity of about 1.19 X106 psi. Column 1 gave a Modulus of Elasticy (the slope of the

straight line portion of the Stress/Strain plot) of 468,915 psi, less than half that of the published

value. All of out subsequent results also vary considerably from the theoretical value of modulusof elasticity. However, compression test data shows that when testing parallel to the grains, a

strength of about 4,460 psi should be seen for dry samples (as ours were). Data also says that for

a perpendicular test we shold see strength around 500 psi. Both of these results are accurate with

those found in Table II.

Figures 16 and 17 shows failure of the two columns.

Figure 16. Column 1 Failure Figure 17. Column 3 Failure

Figures 16 and 17 show the variance in parallel and perpendicular grain strength. There

were no flaws in our samples. Column 1 cracked along a grain and bent which caused moresplitting and failure. Column 3 was compressed and broken at the top catastrophically. The entire

column was tilted until all of the force was going through one bottom edge. These pictures show

how the above data in Table I may not prove to be entirely accurate simply based on the

orientation during compression.

Fine Grained Column Results:

Columns 2 and 4 were fine-grained columns. Column 2 was broken perpendicular to the

grain, and Column 4 was broken parallel to the grain. Figure 18 shows the Stress vs. Strain plot

of the test data.

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Stress vs. Strain

0

500

1000

15002000

2500

3000

3500

4000

4500

5000

0.00E+00 2.00E-02 4.00E-02 6.00E-02 8.00E-02 1.00E-01 1.20E-01 1.40E-01 1.60E-01 1.80E-01 2.00E-01

Strain (in/in)

Column 2 Perpendicular Fine Column 4 Parallel Fine

Figure 18. Stress vs. Strain Plot for Fine-Grained Columns

Figure 18 shows how fine-grained columns, like coarse-grained columns, can withstand

magnitudes greater of stress when cut parallel to the grains rather than perpendicular. However,

when they are cut parallel they fail much faster than when cut perpendicular. Table III shows thedifferences in strengths for the two columns.

TABLE III. Fine-Grained Column Results

Column 2 -- Perpendicular to Grains

Ultimate Strength = 369 psi

Yield Strength = 300 psi



Column 4 -- Parallel to Grains


Yield Strength = 4,300 psiModulus of Elasticity = 410,496 psi


When compared to the theoretical value of Module of Elasticity, the fine-grained results

dont get any better than the coarse-grained results. The column cut parallel to the grains E

value is still less than half that of the theoretical value. However, when compared to compressiontest theoretical data (4,460 psi for parallel and 500 psi for perpendicular) our results are in the

correct range and show accurate testing. Comparing the two columns we see how much stronger

wood is when compressed parallel to the grain. Contrasting these results with those of Table II,we see that the columns cut parallel (1 and 4) hold about the same stress; and the columns cut

perpendicular (2 and 3) hold different stresses.Column 2 (fine- grained) holds about half that of the coarse-grained sample. This could be due to a

split in the wood in Column 2 along the bottom (See

Figure 19 and 20 for failure.) Fine-grained columns

also have more cracks that could allow moreshear stress.

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Figure 19. Column 2 Failure Figure 20. Column 4 Failure

Figure 19 shows that Column 2 (perpendicular to grain) compressed and bowed outward.

It then split along the bottom, which led to its small strength. Figure 20 shows that Column 4(parallel to grain) merely split along a couple of grains and did not have near the amount of

failure that occurred in Column 2.

White Oak Column Results:

Two columns of white oak were given to us to test. These pieces showed incrediblestrength and remarkable results. Figure 21 shows the Stress vs. Strain plot for the two white oak

columns.

Stress vs Strain

0

2000

4000

6000

8000

10000

12000

0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160

Strain

Oak column with hole Oak column

Figure 21. Stress vs. Strain Plot for White Oak Columns

Figure 21 shows how strong the two white oak columns were. One of the columns had ahole in it and showed less strength (although still greater than any other column) than the other

white oak column. The second white oak column almost maxed out the Tinius Olsen machine as

it had nearly 28,000 pounds of force exerted on it.

The column without a hole (Figure 22) also had remarkable failure/repair. It failed and

sheared before catching and fusing together again. See Figures 22 and 23 for examples.

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Figure 22. White Oak Failure W/O Hole Figure 23. White Oak Failure W/ Hole

Figures 22 and 23 show how different the two different modes of failure were. When the

white oak had a hole, the wood split at the hole and was catastrophic--the entire piece ruptured.Without a hole, the white oak sheared along an oblique axis before catching and re-fusing with

itself to maintain a level of around 15,000 lbf. The results from the white oak test are shownbelow in Table IV.

TABLE IV. White Oak Column Results

Column W/ Hole


Yield Strength = 5,000 psi


Strength to weight ratio = 14,850 lbm/lbf

Column W/O HoleUltimate Strength = 9,594 psi

Yield Strength = 7,500 psi


Strength to weight ratio = 22,952 lbm/lbf

Table IV shows just how strong the white oak is. During a compression test, white oak

parallel to the grain (as our test was) should have a strength of around 3,560 psi with some water

content, or about 7,440 psi dry. Our white oak test columns were dry and give an averagestrength of 7,900 psi, which is in the range of testing approximation and about what the

theoretical value is (just a little higher). With a hole through one white oak column, it had an

ultimate strength of over 6,200 psi and a modulus of elasticity of over 674,000 psi. Without ahole, the ultimate strength grew to over 9,500 psi with a modulus of elasticity of over 731,000

psi. This shows that, compared to the regular sugar pine columns, that white oak is considerable

stronger under compressive forces.

Solid Beam Results:

Solid sugar pine beams measuring about 24 long and roughly 1.5 w X 1.5 thick were

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provided to test. The solid beams were placed in a holder that provided support over an 18

length with the Tinius Olsen testing apparatus compressive force directly in the center (9 from

supports). (See Figure 24 for diagram.)

Figure 24. Force Diagram of Beam Test

A stress vs. strain curve was not plotted for any beams; instead, a force vs. position curvewas plotted. The plotted data was the data given by the test apparatus. The data for both of the

solid beams is plotted in Figure 25 along with two theoretical performance curves.

Force vs. Positi

0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4 0.5 0.6

Position (i

Solid 1 Solid 2

Solid 1 THEORY Solid 2 THEORY

Figure 25. Force vs. Position Plot for Solid Beams

As Figure 25 shows, both beams failed at almost exactly the same amount of deflection

(approximately .43 inches). The failures were dramatic and quick. The two theoretical

performance curves were calculated by Equation 3 using the modulus of elasticity of sugar pine

(1.19 X 106 psi) and the actual applied force. These theoretical curves show that the beams wereable to deflect and bend more; so the modulus of elasticity of the two solid beams was far less

than the theoretical value. (See TABLE V for solid beam data.)

TABLE V. Solid Beam Data

THEORETICAL SUGAR PINE

E = 1.19E+06 psi

Max Parallel Stress = 4460 psi

SOLID 1

Max Force = 1,248 lbf

Max Moment = 11,234 lbf-in

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P

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Yield Point = 1,100 lbf

Moment of Inertia = 0.3766 in4

Max Bending Stress = 22,366 psi

Max Deflection = 0.36462 in

E = 973,385 psi

SOLID 2 Max Force = 860.93 lbf


Yield Point = 600 lbf




E = 978,155 psi

Table V shows all of the theoretical data for sugar pine and all of the calculated data for

the two solid beams. Comparing the calculated modulus of elasticity of Solid 1 and Solid 2 totheoretical sugar pine E value (1.19E6 psi) we see that we are approximately 250,000 psi less

and approximately 500,000 psi less for Solid 2. However, we also see that the maximum force oneither beam is considerably less than the maximum parallel stress of sugar pine. The max

deflection is at the yield point (to calculate a correct E value). The difference in strength could be

due to knots in the wood sample, improper placement of the wood, improperly securing the

beam, having a different type of wood than sugar pine, among other types of human error.

Figure 26 shows failure for one of the solid beams.

Figure 26. Solid Beam Failure

The solid beams failed along the outer edge of the beam (the bottom edge below the A

is visibly split). Figure 26 accurately shows how the beam bent (along the black line on the topedge). The failure was not visibly dramatic; but the failure was, looking at the Force vs. Position

plot, very sudden and severe.

Laminated .25 Beam Results:

Three sets of laminated beams were constructed. To make the .25 laminated beams, six

pieces of 24 long X 1.5 wide plywood were used. These pieces were glued together with woodglue and clamped together for a day to dry. Two samples of each laminated beam were made,

one to crush horizontally and one to crush vertically. The test results are shown in Figure 27.

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Force vs. Position

0100200300400500

600700800900

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Postiion (in)

Horizontal .25 Vertical .25Theory Horizontal .25 Theory Vertical .25

Figure 27. Force vs. Position Plot for .25 Laminated BeamsFigure 27 shows the force/position data for the horizontal and vertical data as well as

theoretical deflections based on Equation 3 and the true modulus of elasticity of sugar pine. Ourdata shows considerable deviation from the theoretical due to the primary fact that laminatedplywood pieces are not made up of one type of wood. Rather, plywood is made up of many types

of wood and is glued together. However, we also see that the vertical was able to withstand a

little more force than the horizontal and that the horizontal beam was able to deflect about twiceas much as the vertical beam. This difference in deflection is due to the fact that when bending

the beam horizontally, the beam is allowed to bend and adjust to the force. When bending with

the beam vertically, the beam is not allowed to bend much and will snap much more easily as

there is no tolerance in bend when the beam is oriented vertically. Table VI shows the calculateddata for the .25 laminated beams.

TABLE VI. .25" Laminated Beam DataTHEORETICAL SUGAR PINE

E = 1.19E+06 psi

Max Parallel Stress = 4460 psi

Max Perpendicular Stress = 500 psi

HORIZONTAL

Max Force = 773.02 lbf




Max Bending Stress = 12,305 psiMax Deflection = 0.27167 in

E = 579,147 psi

VERTICAL




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E = 865,521 psi

Table VI shows the theoretical sugar pine values for modulus of elasticity and maximumstresses under a compression test. A laminated beam, as out data shows, cannot hold as much asa solid beam could (compare values to Table V and we see that our results are a few hundred lbf

less than solid beams). The data also shows us that laminated beams are weaker horizontally than

vertically. This result is to be expected as the plywood pieces are glued horizontally while thevertical test is testing the capacity of the wood alone. However, the yield point for the vertical

test is slightly lower than the horizontal test (but, you could almost assume the max force on the

horizontal beam is the yield point as the data leading up is nearly straight, but starts bendingslightly around 600 lbf). The modulus of elasticity of both beams was lower than that of pure

sugar pine (as expected) but also vary considerably from one another due to their difference in

deflections primarily.

Figures 28 and 29 show failure for .25 laminated beams broken horizontally and

vertically, respectfully.

Figure 28. Horizontal .25 Laminated Failure Figure 29. Vertical .25 Laminated Failure

These figures show failure modes for horizontal and vertical laminated beams. Figure 28shows how the horizontal beams simply split the glued joint and bent (see the large hole to the

left of the crushing element). This bending also caused splitting on the bottom edge of the beam

due to tension. Figure 29 shows how the vertical beam simply developed small cracks along themiddle and failed. Vertical failure was not nearly as visually dramatic as horizontal failure. All

subsequent laminated beams failed by the same modes, hence pictures of those beams are not

shown in their sections.


Four pieces of .375 plywood were glued together to make a ..375 laminated beam. Two

of these were made to test horizontally and vertically. Results of this test are shown in Figure 30.

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Force vs. Positi

0

100

200

300

400

500

600

700

800

900

0 0.1 0.2 0.3 0.4 0.5

Position (i

.375" Horizontal .375" Vertical

SUGAR PINE THEORY Horizontal SUGAR PINE THEORY Vertical

Figure 30. Force vs. Position Plot for .375 Laminated Beam

Just as the last two beam force vs. position plots were, Figure 30 shows the test data and

theoretical sugar pine data. The horizontal test gave very linear results, yet again, and was able todeflect more before failure. However, we see that the vertical beam was able to withstand force

for a greater time than the horizontal beam. This could be due to the vertical beam cracking and

splitting over a long period of time, whereas the horizontal beam had major failures. Table VIIshows the calculated data for the .375 laminated beams.

TABLE VII. .375" Laminated Beam Data


E = 1.19E+06 psi

Max Parallel Stress = 4,460 psiMax Perpendicular Stress = 500 psi

HORIZONTAL







E = 479,263 psi

VERTICAL Max Force = 767.44 lbf






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E = 724,368 psi

Table VII shows the theoretical sugar pine values for modulus of elasticity and maximum

stresses under a compression test as well as the calculated values of the .375 laminated beams.

As Table VII shows, a laminated .375 beam of the same thickness cannot hold as much force as

a .25 beam can. Also, the modulus of elasticity of the .375 laminated beams are still less thanthat of solid sugar pine (as expected), but arent as great at those of .25 beams. However, the .

375 beams were able to deflect more before plastic deformation would occur (E is no longer theslope of stress/strain curve). We also see, once again, that a laminated beam broken vertically is

stronger than a horizontal beam; and, in this case, the vertical laminated beam was able to hold

force for a longer time and deflect more than the .25 beam. The .375 laminated beam also hadless plywood pieces holding it together, which could attribute to its weaker properties.


Three pieces of .5 thick plywood were glued together to form the .5 laminated beam.

Two of these beams were made to test their strength under bending conditions. These results areshown in Figure 31.

Force vs. Positi

0

100

200

300

400

500

600

700

800

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Position (in

.5" Horizontal .5" Vertical

SUGAR PINE THEORY Horizontal SUGAR PINE THEORY Vertical

Figure 31. Force vs. Position Plot for .5 Laminated Beams

Figure 31 shows the theoretical sugar pine values for the given stress from Equation 3.The .5 beams, when broken either horizontally or vertically, both deflected approximately the

same amount before failing (around .31 inches). Both beams behaved very similarly in this test

and deflected almost the same amount (with the horizontal able to deflect more in this test).

These results are slightly different than those of the prior tests; however, the vertical still wasable to hold more force than the horizontal beam could. All calculated data is shown in Table

VIII.

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TABLE VIII. .5" Laminated Beam Results


E = 1.19E+06 psi

Max Parallel Stress = 4,460 psi

Max Perpendicular Stress = 500 psi

HORIZONTAL







E = 574,023 psi

VERTICAL







E = 790,264 psi

Table VIII shows the theoretical sugar pine values and, once again the laminated beamsgive a modulus of elasticity that is less than the theoretical (as expected). However, the E values

for the .5 beam are greater than those for the .375 beam and very slightly less than the .25

beams. This provides us with no good correlation for calculating E based on different types of

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plywood (amount of pieces glued together to get the same overall thickness). The .5 laminated

beam was not able to hold as much for as either previous laminated beam as there is less

plywood pieces and less glued joints in the .5 sample. Overall, the data provides very similarresults and allows some basic conclusions about the data.

Laminated Beam Comparison:

Table IX shows the modulus of elasticity of every laminated beam (horizontal and

vertical) as well as the max force that each could hold. It also shows the average value for eachcriteria.

TABLE IX. Laminated Beam Comparison

.25" Beam Horizontal Vertical

E (psi) 579,147 865,521

Max Force (lbf) 773.02 813.53

.375" Beam E (psi) 479,263 724,368

Max Force (lbf) 615.97 767.44

.5" Beam E (psi) 574,023 790,264

Max Force (lbf) 584.59 674.59AVERAGE

E (psi) 544,144 793,384

Max Force (lbf) 657.86 751.85

The above table shows how similar the horizontal values are to each other as well as the

vertical values (for modulus of elasticity). It also shows how the maximum force decreased withthe number of plywood pieces per beam (as there is less glued area to hold the beam together).

The table also aptly shows how much stronger the vertical orientation is when compared to

horizontal laminated beam orientation.

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Conclusion:

Strength is one of the most important properties of wood and invaluable in anyengineering design. Through this lab, we were able to determine different strengths, as well as

other properties, of each wood sample tested.

The wood tripods underwent a compression test that not only compressed the woodsample but also tried to shear the fasteners. Because of these two different types of stresses, we

were unable to calculate any true values of the materials. However, through multiple

assumptions, we could plot a Stress vs. Strain diagram of each tripods test data. This plot gaveus the ultimate stress that any tripod could endure and gave a reference to compare the different

types of fasteners to.

According to our results, the glued tripods performed substantially better than any other

fastening method. Our conclusion regarding this is the fact that wood glue covers much more

area than any bolt fastener could. By utilizing a larger area, Equation 1 (see Introduction) showsthat more force has to be applied to achieve the same amount of stress that a smaller force over a

smaller area has. In other words, the stress transfer through the trunk to the legs is greater when

using glue as there is more area to transfer the stress. When fastened with a bolt, the legs cannot

receive more stress as the area of a bolt is much less than the area of the glue; so the bolts shear.Glue is the strongest fastening system from our test data.

The solid wood columns underwent a compression test similar to the wood tripods.However, due to the simple fact that these pieces were solid and not fastened together, the

calculations were simpler and easier--since we didnt have to worry about the shearing of the

bolts. Two fine-grained samples and two coarse-grained samples were tested along with twowhite oak columns.

According to our results, the coarse-grained wood columns are stronger than the fine-

grained columns. This is opposite to what we initially believed. Coarse-grained, we thought,

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would split easier. And while the coarse-grained samples did have more catastrophic visual

failure, they were still able to hold more force than the fine-grained columns.

The white oak pieces, even with a major defect, were extraordinarily stronger than either

the fine-grained or the coarse-grained solid pieces. White oak is known as a very strong wood

and our test simply proved that (the piece without a hole almost maxed out the test apparatus).

The wood beams also gave some interesting results.

The solid wood beams were placed under bending stress until they failed. These failures

happened quickly and dramatically (according to the data) but not as visually dramatic. The solid

wood beams split along the bottom edge as it was under tension and cracked easily. These beams

were primarily tested to compare to the laminated beams.

Three different sets of laminated beams were constructed using plywood of these various

thicknesses: .25, .375, and .5. The .25 thick beams had six plywood sheets, the .375 thick

beams had four plywood sheets, and the .5 thick beams had three plywood sheets. According toour results, the greater the amount of plywood sheets, the stronger the force one can apply to the

laminated beam. This is due to the fact that the more sheets there is, the more glue there is. Aninteresting result from the laminated beam tests is that the laminated beams are stronger when

bent vertically (that is, the plies and the force are in the same plane). Also, a modulus of

elasticity was calculated from the test data for the laminated beams. These were compared to

values of pure sugar pine. This comparison is invalid as plywood can be made from up to 70different types of wood. However, the data shows that plywood laminated beams were unable to

withstand the amount of force that a solid beam could. This could be due to human error in

gluing, the fact that laminated beams could be weaker than solid wood beams, and that some ofthe plywood pieces had small gaps in between wood pieces within the plies.

Through this lab, we found that glue is the strongest fastener for wood (but impractical insome applications and subject to environmental weather that will weaken the glue), that coarse-

grained wood is stronger than fine-grained wood under compression, that white oak is extremely

strong under compression compared to other woods, that laminated beams gain strength with thenumber of plies, and that laminated beams are not as strong as solid wood beams.

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References:

Beer, F. P., Johnston, Jr., E. & DeWold, J. T. (2006). Mechanics of Materials (4th ed.).McGraw Hill.

Green, D. W., Winandy, J. E. & Kretschmann, D. E. (2008). Chapter 4 - Mechanical Properties

of Wood. Wood Background.pdf.

Wieden, A. C. North American Hardwoods. Forest Service. Retrieved March 1, 2008, from

http://www2.fpl.fs.fed.us/TechSheets/hardwood.html

ENGR 3360 Section 3 Mechanics of Materials Lab

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