Experiment On Timber Bending: Timber Beams And Deflection Of Flitch Beam

Test Materials

Experiment on timber bending: timber beams and deflection of flitch beam.

• AIM: To examine the bending of different shapes of timber beams.
• Introduction

The experiment focuses on tests on bending as well as deflection of timber joist plank, joist beam and three flitches. Timber as a building material has been regarded as economically efficient and ecologically fit construction material hence extensively adopted in sustainable designs. The bending and deflection tests are key procedures to determine the effectiveness as well suitability of timber as building material based on various shape design that would be deemed suitable.

The experiment considers two timber categories such as joist plank, joist beam, and the three flitches where in each, dimensions and shape of individual test materials are varied hence each achieves a unique moment of inertia as well as unique behavior criteria at different applied loads. By assessing such trends, this experiment help to determine the material suitability/ strength and hence guide their application in designs.

• Theory
  • Beam

Beams are supporting structures in bridges, buildings and other design works. Beams support structures through resistance against forces applied on structures. As a result, these forces cause a beam to bend hence resulting in deflection of the beam. Material, shape and size are key determinants on the amount of resistance the beam can offer and hence a factor of deflection. Considering end support condition of beams, beams can be classified into three classes, namely; cantilever beam, simply supported beam and overhanging beam. In regard to shape of beams, beams are grouped into square beam, I beam and rectangular beams.

• Timber

Timber are processed wood used in both structural and non-structural construction. The shape of beams varies from a beam or plank shapes.

• Deflection

In beams, deflection is defined as variation in shape of the beam or its movement away from its neutral position due to application of loads on it. Beam fixed at the end or at either of the ends get displaced away from its positions relative to loading direction of the beam. The displacement that results is identified as deflection.  Considering a simply supported beam, deflection can be computed based on the following relation

δ=,

In this equation, F is the loading on the beam δ is beam deflection as a result of application of load

E is the material’s modulus of elasticity

I is the 2^nd moment of inertia of the beam

• Second inertia of the beam I

This is a geometric property of a material greatly dependent on size and shape of the respective material.  Second moment of inertia is a measure of ability of a material to resist when subjected to external loads. For a rectangular beam cross-section, second moment of area is obtained from the formula as below.

• Procedure
  • Set up of the apparatus: the apparatus is placed on a horizontal place and the beam attached. The beam is fixed at the opposite ends while ensuring it is horizontal and straight.
  • Check the apparatus to ensure no avoidable errors including zero error exist. If any source of error is determined, it should be adjusted accordingly.
  • Gradually and carefully add weights progressively starting with 0.5 KN and adding more loadings of 0.5 KN until the beam fails. Meanwhile, take note of any sounds that develops as you increase the loads until failure.
  • Record the resulting deflection at each loading/ weights and fill in the table.
  • Replicate the above steps for 3 dissimilar shapes of flitch beam and for plank shape.
• Result

RESET ?	Load (kN)	Deflection (mm)
Left	Right
	0.5	5.69	5.76
yes	1	7.82	7.66
yes	1.5	6.95	6.74
yes	2	6.83	6.51
yes	2.5	7.71	7.52
yes	3	6.19	6.18
yes	3.5	9.11	8.61
yes	4	9.74	9.52

Types of Beams

Joist beam

RESET ?	Load (kN)	Deflection (mm)
Left	Right
	1	1.49	1.43
	2	2.79	2.69
	3	4.05	4.12
yes	4	1.32	1.3
	5	2.69	2.67
	6	4.09	4.08
	7	5.46	5.44
	8	6.95	6.94
	9	8.56	8.56
	10	10.39	10.39
	11	12.15	12.14
yes	12	1.76	1.71
	13	3.92	3.84
	14	5.97	5.86

• flitch beam A

FLITCH A
B	35
D	100
T	4
Weight	12.4kg

RESET ?	Load (kN)	Deflection (mm)
Left	Right
	0.5	0.67	0.71
	1	1.27	1.4
	1.5	1.88	2.05
	2	2.58	2.79
	2.5	3.14	3.35
	3	3.75	3.92
	3.5	4.49	4.61
	4	5.03	5.14
	4.5	5.55	5.7
	5	6.2	6.41
	5.5	6.77	7.02
	6	7.46	7.74
	6.5	8.21	8.58
	7	11.09	11.48
yes	7.5	1.49	1.63
	8	8.78	8.71
	8.5	11.43	11.3
yes	9	3.55	3.62
	9.5	6.57	6.61
	10	10.96	10.92
yes	10.5	9.6	9.69

Flitch beam B

FLITCH B
D	110
B	35
T	5
X	25
Y	100
Weight	7.65kg

RESET ?	Load (kN)	Deflection (mm)
Left	Right
	1	3.45	3.37
	2	6.78	6.73
	3	10.08	9.98
yes	4	2.38	2.4
	5	4.55	4.55
	6	6.99	7
	7	9.5	9.52
	8	12.52	12.54
yes	9	3.67	3.76
	10	7.76	7.86

Flitch beam C

FLITCH C
B	37
D	100
T	6
Weight	13.2kg

RESET ?	Load (kN)	Deflection (mm)
Left	Right
	1	0.99	1.03
	2	1.97	2.01
	3	2.94	2.99
	4	3.91	3.96
	5	4.85	4.92
	6	5.8	5.9
	7	6.78	6.92
	8	7.78	7.96
	9	8.78	9.01

Calculations

Calculating I, 2^nd moment of inertia for joist plank; B=163 mm, D= 43 mm 2^nd moment of inertia for joist beam; B= 44mm, D=163 mm

• Graphs

6.1 Graphs showing displacement/ deflection in joist blank and beam at increasing loads.

     6.2 Graphs for flitch beams A, B, and C. 

• Discussion

Size and shape of beams have a correlation with its deflection. This is evident from the graphical plots on displacement/ deflection of beams at different loads as shown in the preceding sections. A plot on deflection vs loads on joist plank exhibit smaller change on deflection until 3.0 KN load is achieved from which it rapidly shoots from 6.19 mm to 9.74 mm at 5.0 KN load however deflection of the beam gradually increases at increasing weights/ loads.

 In comparison, maximum deflection of the beam is achieved at about 11 KN of load while for the plank it develops at 4.0 KN load. This indicates that the beam has a greater resistance against applied loads than the plank. Certainly, this due to the fact that the beam has a high value of second moment of inertia than the plank hence the beam has greater resistance to deflection than the blank.

Graphical plot concerning the three flitches concerning individual displacements and applied loads clearly illustrate that shape and size are determinant factors on the deflection of a flitch. Based on the plots, the graph begins at comparably the same point but as loads is increased, A achieves maximum deflection than B and C. At 5 KN load, flitch beam B achieves ultimate deflection of 6.2 mm while flitches B and C only achieve 4 mm (4.55 and 4.85 mm to be specific, respectively). This is an indication that flitches B and C have greater moment of inertia than Flitch A.

It should be noted that at increasing loads, the timber beams and planks produces screeching sound which increases as you near the points of maximum defection that is 4 KN for planks and 7 KN in the flitch beams.

• Conclusion

The experiment aim was to determine bending of different shapes of timber beam by noting deflection at increasing loads. It was established that shape and size of timber beam, hence the shape affects its ability to resists loads as observed at different deflections at increasing loadings. Also, it was found out that beams have greater resistance to deflection than plank against deflection.

The screeching of timber close to and at maximum deflection is as a result of increasing internal strains and indicates maximum resistance to applied loading while approaching point of breakage/ failure.

Abdullah, R., 2008. Mechanical properties and bending strength theory for Malaysian structural timber. Skudai, Johor: Penerbit Universiti Teknologi Malaysia.

Wood-based panels. Determination of modulus of elasticity in bending and of bending strength, 2016, 154–201.