TABLE OF CONTENT

Summary/Abstract...3Objective..3Theory..4Equipment/Description of experimental apparatus.5Procedure.6Data and Observations.8Analysis and Results..10Discussions15Conclusions17References..17

Abstract

Objectives1. To design a simple bending testing set-up for beams with concentrated loadings.2. To investigate the bending behaviour a non ferrous material placed on two supports with concentrated load at the centre.3. To determine the Modulus of Elasticity of non- ferrous material (ruler, comb and food container).4. To investigate the relationship between deflection and the applied load.5. To investigate the relationship between deflection and different type of specimen.

TheoryBending test is one of the methods to study the behaviour of non-metallic material which induced both tension and compressive stress. There are two common types of bending test:1. 3 - point bending : applying a concentrated load at the span centre2. 4 - point bending : applying half loads equally distant from support*3 point bending is commonly being used due to its simplicity.

Figure 1: 3-point bending

Figure 2: 4-point bendingTheoretically, this test is conducted by using different types of specimens with same length but different load. The 3-point bending test is applied in this test where the loading made of string and various numbers of nail are applied at the centre. Deflection is measured manually to determine the modulus of elasticity of each specimen. Cross section area, material, and unsupported length are things that influence the deflection. The modulus of elasticity can be calculated by using;

The value of stress can be calculated by using;

Strain can be calculated by using Young Modulus equation;

I for rectangular: 1/12 (b) (h) 3I for circular: (d4) / 64where:F: Load L: length of the beamI: Inertia factor: Deflectionb: width of the specimenh: thickness of the specimenEquipment Food container Comb Ruler String Nail (2.5) Vernier callipers

Procedure:1. A plane piece of box was used as a stand based in this bending test.2. The length of beam was indicated by two big nails which were used to be punched on the plane box at a distance of 130 mm which act as two fix point. 3. A straight line was constructed that connect those two nails. The middle of that distance at 65 mm from both nails have been marked as an indicator. The load which the point where the load would be applied and the measurements would be taken.4. A number of nails with specific weight were used as an applied load on the beam. The string was used to tie the nails that would be hanging at the middle of the beam.5. There were three value of weight(force) that have been used to to test the deflection of each specimens by manipulating the number of nail ; .6. The deflections of bending test specimen were measured by marking its position when bending on particular plane piece of box. The line marked at the bottom part of specimen and at the middle which the loads were being applied.7. The steps were repeated for those three materials which are ruler, skewer and box using each three value of weight that have been fixed in this test.

Data and Results

Length of ruler: 163 mm = 0.163 m Length of Comb: 172 mm = 0.172 m Length of Food container: 163 mm = 0.163 m

Specimen RulerCombFood container

Measurement Width, b = 24mm Height, h = 1 mm

Width, b = 10.5 mm Height, h = 4 mm

Width, b = 24 mm Height, h = 0.9 mm

Cross-sectional area (mm2)24mm2

42mm221.6mm2

Inertia2.00 x 10-12(m)56.00x 10-12 (m)1.458 x 10-12(m)

Table 1: The dimension of the specimen used

Material Load, F (N)Deflection

(mm)

Ruler0.248944

0.373416

0.4978810

0.6223515

Comb0.248945

0.373416

0.497888

0.622359

Food container0.2489413

0.3734115

0.4978820

0.6223521

Table 2: Deflection with some values of force applied on different three materialsMaterial Load, F (N)Coefficient Of Elasticity

E (1 x 109 N/m2)Eave(1 x 109 N/m2)

Ruler0.248942.80753

2.50517

0.373412.80753

0.497882.24602

0.622352.1596

Comb0.248940.09425

0.11519

0.373410.11781

0.497880.11781

0.622350.13090

Food container0.248941.18499

1.52497

0.373411.54048

0.497881.54048

0.622351.83391

Table 3: Coefficient of Elasticity

Stress and strain on each material:A ruler = 24x10-6 m2;Force (N)0.248940.373410.497880.62235

Stress, (GPa)1.69072.53613.38144.2268

Strain,

Table 4: RulerA comb = 42x10-6 m2;Force (N)0.248940.373410.497880.62235

Stress, (MPa)63.716895.5752127.4336159.292

Strain,

Table 5: A food container = 21.6x10-6 m2;Force (N)0.248940.373410.497880.62235

Stress, (GPa)2.31923.47884.63855.7981

Strain,

Table 6: Box

Sample of Calculation : To find the cross-sectional area of the specimens :For Ruler or box A = bh;bruler = 31 mm,hruler = 0.1 mmA ruler = 31 mm x 0.1 mm = 3.1 mm2

Bcomb = 31 mm,h comb = 0.1 mmA comb = 38.9 mm x 5.5 mm = 213.95 mm2

For SkewerA = (/4)d2 ; dskewer = 2.6 mmAskewer = (/4)x(2.6)2 = 5.31 mm2

To find force exerted by nails :F = mg;m = 96.01 g,g = 9.81 m/s2F = 96.01 g x 9.81 m/s2 = 941.86 N

To find the value of Inertia of each material :

For Ruler or box I = (bh3/12);bruler = 31 mm,hruler = 0.1 mm

I ruler = (31 x 10-3m)(0.1 x 10-3m) / 12 = 2.583 x 10-15

For SkewerI = (/64)d4 ; dskewer = 2.6 mmAskewer = (/64)x(2.6 x 10-3)4 = 2.243 x 10-12

To calculate Coefficient of Elasticity

E = FL3 / (48.I)

Eruler = (941.86 N)(0.133) / (48 x 2.583 x 10-15 x 0.01 m) = 98744700 GPa

To calculate the stress on the material :

= MC/I ;For Ruler and box = 3FL/2bh2;F = 941.86 N,b ruler = 31x10-2 m ,hruler = 0.1x10-2 m

= 3(941.86 N)(0.13m) / 2(31x10-2 m)( 0.1x10-2 m)2 = 592.46 GPa

For Skewer

= MC/I ;C = 5 x 10-5,I = 2.243 x 10-12; F = 941.86 N,dskewer = 2.6 x 10-3

= (941.86 N)(0.13/2 m)(5 x 10-5) / 2.243 x 10-12 = 1.3647 GPa

To calculate the strain on the material :

= /E;

= (592.46 x 109) / (98744700 x 109) = 6.00 x 10-6

Analysis and Results

Graph 1: Deflections against loads for ruler, comb and food container

Graph 2: Stress-Strain Graph for Ruler

Analysis and Results

From graph 1, it can be shown that the deflection become higher when higher load being applied for all three specimens that have been used in this experiment. The highest slope of deflections was obtained by the ruler which gave high effect of deflections when the loads were added.

CONCLUSIONS

The objectives of this experiment have been achieved whereby the relationship of weight, sample of non-ferrous material, height, width and deflection was clearly understood. The sample of non-ferrous material and weight is directly proportional to deflection, where as height and width of object is inversely proportional to deflection. The deflection become higher when higher load being applied for all three specimens that have been used in this experiment. The highest slope of deflections was obtained by the ruler. The Modulus of Elasticity, E was successfully calculated. Deviations from their respective theoretical values were taken into account. Several errors were highlighted. Even though there were errors present in some of the readings hence the calculated values, the theory in ascertaining the E value was understood.

REFERENCES

1. Book:Ferdinand P.Beer, E.Russell Johnston, Jr., John T.DeWolf. 2004. Mechanics Of Materials. 3rd Edition. McGraw Hill. pp 607-617.2. Internet:http://www.engineeringtoolbox.com/young-modulus-d_773.html

Note:Semester 1 2005/2006. MEMB311 Materials Laboratory Manual. COE, Uniten. pp 19-29.