Bending of Wood

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Lebanese American University

School of Engineering and Architecture

Department of Civil Engineering

Construction Material Lab: CIE 309

Bending Of Wood

Presented to: Mr. Michel Ammoury

Submitted on: Friday, January 14, 2011



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Contents1. Introduction: ......................................................................................................................................... 3

2. Objective: .............................................................................................................................................. 3

3. Materials and Equipments: ................................................................................................................... 4

4. Procedure: ............................................................................................................................................. 5

5. Theory: .................................................................................................................................................. 7

6. Data: ...................................................................................................................................................... 8

7. Calculation: ........................................................................................................................................... 8

a. Ultimate stress: ................................................................................................................................. 9

b. Stiffness: ............................................................................................................................................ 9

c. Modulus of Elasticity: ........................................................................................................................ 9

8. Discussion: .......................................................................................................................................... 10

9. Conclusion: .......................................................................................................................................... 10



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1. Introduction:

Wood has been used for thousands of years as fuel and construction

material. The markings, called grain, found on all types of wood, arecaused by the structure of wood. Woods can be tested relative to

parallel or cross graines. Woods may contain defects that affect their

properties, for example the most important threat for wood are fungi

that cause so-called dry rot. A knot is that portion of a branch or limb

which has been incorporated into the body of the tree. Knots are the

most prevalent defect in structural timber. The tensile strength of wood

parallel to the grain depends on the strength of the fibers and is

affected not only by the nature and dimensions of the wood elements

but also by their arrangement. Cross-grain of any kind will materially

reduce the tensile strength of wood, since tensile strength

perpendicular to the grain is only a small fraction of the strength

parallel to the grain. The ratio of tensile strength parallel to the grain to

tensile strength perpendicular to the grain is commonly as high as 40 to

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2. Objective:

The objective of this experiment is to determine the nature of wood in

flexure (bending) and the flexural mechanical properties of wood.



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3. Materials and Equipments:

Beam support to simulate a simply supported beam,

Universal Testing Machine (UTM)Tape measure

Specimen: Clear wood specimens



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4. Procedure:

Mark the center and end points for the beam.

Place the beam on the beam support and into the testing machineso that a concentrated load may be applied at the center of the

span.

Position the dial gage between the load platen and the moveable

crosshead of the testing machine.

Apply the load slowly at a rate of 2.5 mm/min.

Continue loading to total failure of the specimen.

Describe the type of failure (see the below Figure).



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5. Theory:

for a simply supported beam of span L and with a concentrated load P

applied at the center of the span, the maximum deflection, which

occurs at the center of the span, is determined by the equation

in whichE

is the modulus of elasticity andI

is the moment of inertia ofthe section with respect to its centroidal x-axis. Solving the equation for

E yields:

By loading a sample beam of the above description and simultaneously

recording values of the concentrated load ( P ) and the resulting

deflection ( D ). The slope of the resulting linear elastic portion of thisload-deflection curve is simply a stiffness value ( k ). Rearranging

Equation 2 above, one can represent this stiffness as follows:

This stiffness value can be ascertained by experiment as the slope of

the load-deflection curve up to the proportional limit. With this

stiffness know, the modulus of elasticity can then be determined as

follows by rearranging Equation 3 and solving for E , i.e,



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where L and I are measured properties of the beam. The computed

value of E should be approximately equal to the value determined from

the investigation of loads parallel to the grain of short wood

compression blocks.

Up to the proportional limit, the bending stress of at the outer fibers is

determined by the equation:

6. Data:

Sample Dimensions

(cm)

Span L Ultimate

load (N)

Break (mm)

Cross-

grained

4.8x5x20 14.92 1764 1.82

Parallel-

grained

5x5.1x21 15.92 19480 23.81

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Calculation:

The load deflection curves of the beams are attached at the end of this

report.



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a. Ultimate stress:

Cross-grained: σ=(3/2)(1764*14.92)/(5*202)=19.74N/cm

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Parallel-grained: σ= (3/2)(19480*15.92)/(5.1*212)=206.83 N/cm

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b. Stiffness:

The stiffness k is the slope of the load deflection curve up to the

proportional limit:

Cross-grained: k=5200 lb/in

Parallel grained: k=15400 lb/in

(Refer to graph to see calculation of k)

c. Modulus of Elasticity:

E= (12*k*L3)/(48*b*h

3)

Cross grained: E=(12*5200*5.8743)/(48*1.969*7.874

3) = 274.1 psi

Parallel grained: E= (12*15400*6.2683)/(48*2*8.268

3)= 838.72 psi



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8. Discussion:

The bending test of wood beams provides the necessary information

needed to determine the modulus of elasticity, and ultimate stress of

the wood specimens. It is also shown from the load deflection curves

that the wood acts elastically until the proportional stress limit, and this

allows us to determine its modulus of elasticity by getting the stiffness

which is the slope of the this curve. We can clearly conclude that wood

is much stronger across its parallel grains rather than its cross grains,

and this is shown by the values of the ultimate stress and the modulus

of elasticity.

9. Conclusion:

Strength varies greatly with seasoning and with the direction of the

grain; wood is much stronger, both in bending and in compression,

when cut along the grain (parallel grained) than when cut across it

(cross grained).

References: lab handout

http://www.granvillebois.com/documents/Wood%20Characteristics.pdf

Bending of Wood

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