manual emm 3108 - revised - 150224

Department of Mechanical & Manufacturing Engineering

Faculty of Engineering, University of Putra Malaysia

EMM3108 Strength of Materials | 1

LAB MANUAL FOR

EMM 3108: STRENGTH OF MATERIAL 1




LAB REPORT MARKING SCHEME

No. Item

Score

Poor Average Excellent

1-2 3-4 5

1 Introduction

and

Theoretical

Background

Has serious trouble

identifying the related

topic

Exhibits some vagueness

in understanding.

Wanders off slightly from

the topic

Clear and concise

without being too

lengthy

2 Experimental

Objectives

Purpose of lab not clearly

identified or understood

Workable statement of

goal, some fuzziness

Clear and concise

statement of goal

3 Lab

Apparatus

So many omissions that

performing the lab would

be difficult

Vital items listed, maybe

one omission

Point form list of

required equipment

4 Experimental

Procedure

Difficult to follow how lab

was performed. Steps go

off topic or are otherwise

distracting

Possible to do the lab,

although some

assumptions might have

to be made. Might not be

numbered

Step-by-step numbered

list that show how to do

the lab

5 Results,

Analysis and

Calculation

Some data missing. Data shown in

disorganized or sloppy

manner

Work is poorly shown, as if a rough draft.

Serious calculation

errors affect results

All data is present, but shown in a format that

may be confusing or

misleading

Calculations are essentially correct,

although some parts

may be implied,

including values

calculated from the

graph

Collected quantitative data is well presented

in a table. Qualitative

data may be given if

necessary

Well laid out and calculated analysis

based on data. Graphs

(if needed) follow all

rules and have

appropriate

calculations showing

relationship between

calculated value and

physics concept

6 Discussions Seriously lacking list of

sources and/or no

calculation of error

List of sources of error is

incomplete. Calculation of

error is wrong

Several sources of error

are listed, and each is

well explained. Shows

calculation of error (if

appropriate)

7 Conclusions Has serious trouble

showing link from

Objective through to

Conclusion

Shows the person has not

lost sight of the labs

reason, but could focus

more on whats going on

Wraps up the lab, just

like the conclusion of an

essay for English




1 - TENSILE TEST

Introduction

Tensile test is one of the most widely used mechanical tests. Various properties of the material

that can be determined by tensile test are yield stress, upper and lower yield points, tensile

strength, elongation, and reduction in area.

This manual contains some fundamental theory for understanding the experiment, description of

the apparatus and experimental procedure for tensile test.

Objective

The objectives of this experiment are

1. To develop an understanding of stressstrain curves.

2. To determine the various mechanical properties of engineering material.

Theory

Stresses may be tensile, compressive or shear in nature. Figure 1

shows a metal bar in tension, i.e. the force F is stretching force

which thus increases the length of the bar and reduces its cross-

section. The area used in calculations of stress is generally the

original area A0 that existed before the application of the forces, not

the area after the force has been applied. This stress is thus

referred to as the engineering stress :

0/ AF= [N/m2 or Pa] (1)

The dimensional change caused by a stress is called strain. In

tension (or compression), the strain is the ratio of the change in

length to the original length. The term strain is defined as:

00t /)(100(%) llle = (2)

Where l l0 = l, the change in length. Since strain is a ratio of two

lengths it has no units. Strain is frequently expressed as a

percentage.

Results of such a tensile test can be

represented in the form of engineering

stressstrain curve. Figure 2 is typical of

ductile metals such as copper tested at room

temperature. The tensile strength, also

known as ultimate tensile strength (UTS), is

defined as the maximum stress which a

material can withstand. It is obtained by

dividing maximum load by original cross-

sectional area of tensile specimen.

0max / AFUTS = [N/m2 or Pa] (3)

Fig. 2 Typical engineering stressstrain

behavior to fracture

Strain

Str

ess

UTS

F: Fracture

F

Fig. 1 Metal bar in tension

F

l0 l

A0

F




Figure 3 and 4 show the two types of stressstrain curves. The

yield stress y is defined as the stress at which plastic deformation

(elongation) of the tensile specimen takes place at a constant

load (Figure 3). Such behavior is generally observed in carbon

steels.

Some steels, especially non-ferrous alloys, do not show the

presence of sharp yield point (Figure 4). For such steels, proof

stress is reported instead of yield stress. Proof stress0.2 is that

stress at which some small amount of permanent deformation,

say equal to 0.2 percent strain, take place. In other words, it is

that stress which produces a permanent elongation of 0.2

percent in the tensile specimen on the removal load.

At the beginning of the test, the force increases rapidly and

proportionately to strain: the stressstrain curve obeys Hookes

law

tEe= [N/m2 or Pa] (4)

The proportionality constant (the slope of the curve) is called the

elastic modulus or Youngs modulus E (Figure 5).

t/ eE = [N/m2 or Pa] (5)

If the specimen is unloaded in this range, it will return to its

original length, i.e. all deformation is elastic.

Tensile test is carried out by gripping the ends of a suitably

prepared standardized specimen in a tensile testing machine,

and then applying a continually increasing uni-axial load until

such time as failure occurs. Before the test, the gauge length L0,

and the cross-sectional area A0 are measured to enable

calculations of percent elongation and percent area reduction to

be made. Figure 6 shows dimensions of a specimen for tensile

test.

Ductility is a measure of a material's ability to deform plastically

without fracture. The two most common methods of ductility

measurement are:

a. Percent elongation is determined by setting a gauge length on

a specimen prior to loading and after tensile failure measuring

the final distance of these gauge marks. Then a percent

elongation value is calculated as equation (2).

b. Percent area reduction is calculated by putting the two ends of the fractured specimen together

and measuring the diameter at the break. Calculate the area at the break at this point of fracture.

This final area is then compared with the original area of the specimen and a percent reduction

in area is then calculated.

Reduction in area (%) = 00 /)(100 AAA (6)

Fig. 3 Typical stressstrain

curve for mild steel

Strain

Lower

yield point

Upper

yield

point

Str

ess

y

Fig. 4 General stressstrain

curve for ductile materials

Strain 0.002

y Plastic Elastic

P

Str

ess




Description of Universal Testing Machine

The Universal Tensile Testing Machine (Figure 7) is designed

to test the physical properties of wide range of materials and

structures. Testing of properties such as tensile strength,

compressive strength, fatigue resistance, crack growth

resistance, bend characteristics, etc. can be performed on

materials such as metals, ceramics, textiles, and virtually any

other material used in an industrial process.

A standard system in Universal Tensile Testing Machine

consists of a tower console and control panel, together with

a load frame and actuator, a hydraulic power supply and a

load cell as a load measurement device. These are all

interconnected with electrical cables at the rear panel of the

tower console. The machine system applies loads, using a

hydraulic actuator, to a specimen of the material under test.

The machine allows for the connection of a computer that can

be used to control and monitor a test automatically. The

computer can be log data resulting from a test and can be

used to generate random or pre-programmed waveforms.

Specimen and Equipment

1. Universal testing machine

2. Vernier caliper

3. Tensile specimen: steel / brass / copper / aluminium

Procedures

1. Refer to Figure 8, use Vernier caliper to measure the original diameter of the specimen. Take

measurements in at least three locations and average.

2. Calculate the value of gauge length, and make two marks on the parallel part of the specimen

to register the gauge length. Grip the specimen in the gripping heads of the machine.

3. Set the required parameters on the control panel.

4. Adjust the load recorder on the front panel controller to zero, to read load applied.

Fig. 6 Standard tensile test specimen with circular cross section

Gauge length L0

Parallel length LC

Radius r Diameter d0

Cross-sectional area A0

00 65.5 AL =

Fig. 5 Hookes law: Stress

proportional to strain

Strain

Str

ess

Slope = modulus of

elasticity

Unload

Load

0

Fig. 7 Universal Testing Machine




5. Press start button to start the

tensile test.

6. Monitor the sample and note when

constriction begins. From now on,

the force will no longer increase,

but instead, will tend to decrease

until fracture occurs.

7. Remove the tested specimen from

the gripping heads, and measure

dimensions of tested specimen. Fit

the broken parts together and

measure reduced diameter and

final gauge length (Figure 8).

Results

1. Show all the measurements of

specimen.

i. Original diameter d0 [mm]

ii. Original gauge length L0

[mm]

iii. Final diameter d [mm]

iv. Final gauge length L [mm]

2. Calculate the following.

i. Original cross-sectional area A0 [mm2]

ii. Final cross-sectional area A [mm2]

iii. Percent elongation

iv. Percent reduction in area

v. Youngs modulus E [GPa]

3. Plot the loaddisplacement graph for the tested specimen.

4. Plot the stressstrain graph.

5. On the stress-strain curve show the following points, and verify the value (i) to (iii).

i. Ultimate tensile strength (UTS) [MPa]

ii. Yield stress y or Proof stress 0.2 [MPa]

iii. Fracture stress f [MPa]

iv. Elastic limit

v. Proportional limit

vi. Elastic and plastic deformation regions

vii. Necking region

Discussion

1. Discuss on the shape of obtained stressstrain curve.

2. Compare and discuss on the experimental results with the theory.

Original diameter d0

Diameter at failure d Reduction in diameter

Original

Gauge length

L0 Plastic

Deformation

Gauge length at failure L

Fig. 8 Schematic of tensile test specimen for

before and after testing




3. Discuss the difference between Engineering Stress and True Stress, and whether there is a significant difference between these values at failure.

4. Explain the necking process, and discuss how the necking of the specimen relates to the shape of the stressstrain curve.

5. Discuss on the mechanical properties of the tested specimen.

6. Discuss on the factors that can be affected to the experimental result.

Conclusion

1. Give an overall conclusion based on the obtained experimental results.

2. Conclude on the applications of the experiment.




2 - COMPRESSION TEST

Introduction

Maximum stress a material can sustain under crush loading. The compressive strength of a

material that fails by shattering fracture can be defined within fairly narrow limits as an

independent property. However, the compressive strength of materials that do not shatter in

compression must be defined as the amount of stress required to distort the material an arbitrary

amount. Compressive strength is the capacity of a material to withstand axially directed pushing

forces. When the limit of compressive strength is reached, materials are crushed.


the apparatus and experimental procedure for compression test.

Objective


1. To study and observe the techniques of the compression testing.

2. To determine the mechanical properties on three different sizes of the tested specimens.

Theory

The compression test is simply the opposite of the tension test

with respect to the direction of loading. It is often stated that

materials behave the same in tension and compression. That is

true for most ductile materials. However, there are some

materials that are very weak in tension and extremely strong in

compression.

Prior to the yield point tension and compression results are

similar. The major difference with the compression test

compared to the tensile test is that the specimen compresses or

the area increases after the yield point is reached. For some

ductile materials the specimen will compress until a flat slug is

reached. However brittle materials will fail suddenly after their

ultimate strength is exceeded. These brittle materials have much

greater compression strength than tensile strength. That is why

these materials are mostly tested in compression.

When a force (or load) is applied to a material (Figure 1), it produces a stress in the material. The

stress acting on the material is the force F exerted per unit area A0:

0/ AF = [N/m2 or Pa] (1)

The dimensional change caused by a stress is called strain. In compression (or tension), the strain

is the ratio of the change in length to the original length. The term strain is defined as:

00c /)(100(%) llle = (2)

Where l l0 = l, the change in length. Since strain is a ratio of two lengths it has no units. Strain

is frequently expressed as a percentage.

In compression testing the sample is squeezed while the load and the displacement are recorded.

Compression tests result in mechanical properties that include the compressive yield stress,

ultimate compressive stress (brittle materials), compressive modulus of elasticity, and proportional

limit.

F

l0 l

A0 F

Fig.1 Metal bar in compression




Compressive yield stress is measured in a manner identical to that done for tensile testing.

Ultimate compressive strength max is the stress required to rupture a specimen. It is obtained by

dividing maximum compressive load Fmax by the original specimen cross sectional area A0.

0maxmax / AF = [N/m2 or Pa] (3)

Compression members, such as columns, are

mainly subjected to axial forces. The failure

of a short compression member resulting

from the compression axial force looks like

in Figure 2.

However, when a compression member

becomes longer, the role of the geometry and

stiffness (Young's modulus) becomes more

and more important. For a long (slender)

column, buckling occurs way before the

normal stress reaches the strength of the

column material as shown in Figure 3. For

an intermediate length compression

member, kneeling occurs when some areas

yield before buckling, as shown in the Figure

4.

The failure of a compression member has to

do with the strength and stiffness of the

material and the geometry (slenderness

ratio) of the member. Whether a

compression member is considered short,

intermediate, or long depends on these

factors.

In practice, for a given material, the

allowable stress in a compression member

depends on the slenderness ratio L/rand can

be divided into three regions: short,

intermediate, and long.

Short columns are dominated by the strength

limit of the material. Intermediate columns are

bounded by the inelastic limit of the member.

Finally, long columns are bounded by the elastic

limit (i.e. Euler's formula). These three regions

are depicted on the stress/slenderness graph

below (Figure 5).

The short/ intermediate/ long classification of

columns depends on both the geometry

(slenderness ratio) and the material properties

(Young's modulus and yield strength).

Brittle

material

Ductile

material

Short

compression

member

F F

F F

Fig. 2 Short member in compression testing

Long

compression

member Buckling

F

F

Fig. 3 Long member in compression testing

Intermediate

compression

member Kneeling

(Inelastic buckling)

F

F

Fig. 4 Intermediate member in compression testing





The Universal Testing Machine (Figure 6) is designed

to test the physical properties of wide range of

materials and structures. Testing of properties such as

tensile strength, compressive strength, fatigue

resistance, crack growth resistance, bend

characteristics, etc. can be performed on materials

such as metals, ceramics, textiles, and virtually any


A standard system in Universal Testing Machine

consists of a tower console and control panel, together

with a load frame and actuator, a hydraulic power

supply and a load cell as a load measurement device.

These are all interconnected with electrical cables at

the rear panel of the tower console. The machine

system applies loads, using a hydraulic actuator, to a

specimen of the material under test.

The machine allows for the connection of a computer

that can be used to control and monitor a test

automatically. The computer can be log data resulting

from a test and can be used to generate random or pre-

programmed waveforms.


1. Universal testing machine (UTM) Instron Series 8500

2. Vernier caliper

3. Compression specimen: wood

Procedures

1. Use Vernier caliper to measure the original size of the specimen.


Fig. 5 Relationship between compression

strength with slenderness ratio

Sh

ort

Inte

rme

dia

te

Lo

ng

L/ r

F/A

Eulers formula (Elastic stability limit)

Inelastic stability limit

U (Strength limit)




2. Center the specimen between the compression test plates.

3. Set the required parameters on the control panel.

4. Adjust the load recorder on the front panel controller to zero, to read load applied.

5. Press start button to start the compression test.

6. Observe the specimen, as the load is gradually applied.

7. Record the maximum load and continue loading until complete failure.

8. Stop the machine and remove the specimen.

9. Repeat experiment with other specimens.

10. Observe and describe the type of failure for each specimen.

Precautions

i. Never operate the UTM when someones hands are between the grips.

ii. Ensure all lab participants are clear of equipment before beginning or resuming testing.

iii. Stop the UTM as soon as the specimen fails.

Results

1. Show all the measurements of specimen.

i) Original depth d [mm]

ii) Original width w [mm]

iii) Original length L [mm]

2. Calculate the original cross-sectional area A0 [mm2].

3. Plot the loaddisplacement graph for the tested specimen.

4. On the loaddisplacement curve show and verify the value for the following points.

i) Maximum load Fmax[N]

ii) Load taken by the specimen at the time of failure Ff [N]

5. Plot the compressive stresscompressive strain graph.

6. On the stress-strain curve show the following points, and verify the value (i) to (iii).

i) Yield stress y[MPa]

ii) Ultimate compressive strength max[MPa]

iii) Modulus of elasticity E [GPa]

iv) Proportional limit

Discussion

1. Discuss on the shape of obtained stressstrain curve.




Conclusion






3 - HARDNESS TEST

Introduction

Hardness is the resistance of a material to localized deformation. Hardness measurements are

widely used for the quality control of materials because they are quick and considered to be

nondestructive tests when the marks or indentations produced by the test are in low stress areas.


the apparatus and experimental procedure for hardness test.

Objective


1. To determine the hardness of various engineering materials using Rockwell hardness test.

2. To develop an understanding of suitable scale for hardness test specimens.

Theory

1. General

Hardness is a measure of the resistance of a metal to permanent (plastic) deformation. The

hardness of the metal is measured by loading an indenter into its surface. The indenter material

which is usually a ball, pyramid, or cone, is made of a material much harder than the material

being tested. For most standard hardness tests a known load is applied slowly by pressing the

indenter at 90 degrees into the metal surface being tested. After the indentation has been made,

the indenter is withdrawn from the surface. An empirical hardness number is then calculated or

read off a dial (or digital display), which is based on the cross-sectional area of depth of the

indentation.

The most common type of tests that widely used and adopted in engineering practices are the

Brinell, Vickers and Rockwell methods.

2. Brinell Hardness Test

With the Brinell test, a hardened steel ball or tungsten carbide ball

is pressed for a time of 10 to 15 seconds into the surface of

specimen by a standard load F [kgf] (Figure 1). After the load and

the ball have been removed, the diameter of the indentation d

[mm] is measured. The Brinell hardness numberHB, is obtained by

dividing the size of the load applied by the surface area of the

spherical indentation A [mm2].

AFHB /= DhF /= ( )

= 22[

2/ dDD

DF (1)

Fig. 1 Shape of indentation in

Brinell hardness test

Side view

Top view

D

d

d




Where h [mm] is the depth of indentation, D [mm] is the

diameter of the ball. The Brinell test cannot be used with very

soft or very hard materials. This test is limited to materials with

hardnesses up to 450 HB with a hardened steel ball and 600 HB

with a tungsten carbide ball.

3. Vickers Hardness Test

The Vickers test involves a diamond indenter, in the form of a

square-based pyramid with an apex angle of 136, being pressed

under load for 10 to 15 seconds into the surface of the specimen

under test. The result is a square-shaped indentation. After the

load and indenter are removed the diagonals of the indentation

d [mm] are measured. The Vickers hardness number HV is obtained by dividing the size of the load

F [kgf], applied by the surface area A [mm2], of the indentation (Figure 2). Thus the HV is given by

( )= 68sin// 2dFHV ( )854.1// 2dF= 2/854.1 dF= (2) Typically a load of 30 kg is used for steels and cast irons, 10 kg for copper alloys, 5 kg for pure

copper and aluminium alloys, 2.5 kg for pure aluminum and 1 kg for lead, tin and tin alloys. Up to

a hardness value of about 300 HV, the hardness value number given by the Vickers test is the

same as that given by the Brinell test.

4. Rockwell Hardness Test

The Rockwell test differs from the Brinell and Vickers tests

in not obtaining a value for the hardness in terms of an

indentation but using the depth of indentation, this depth

being directly indicated by a pointer on a calibrated scale.

The test uses either a diamond cone or a hardened steel ball

as the indenter.

The procedure for applying load to specimen is illustrated in

Figure 3. A minor load of 10 kg is applied to press the

indenter into contact with the surface. A major (additional)

load is then applied and causes the indenter to penetrate

into the specimen. The major load is then removed and there

is some reduction in the depth of the indenter due to the

deformation of the specimen not being entirely plastic. The

difference in the final depth of the indenter and the initial

depth, before the major load was applied, is determined.

This is the permanent increase in penetration e due to the

major load. The Rockwell hardness number HR is then given

by.

eEHR = (3)

Where is the arbitrary constant which is dependent on the type of indenter. For the diamond cone

indenter E is 100, for the steel ball 130. There are a number of Rockwell scales (Table 1), the

scales being determined by the indenter and the major load used. A variation of the Rockwell test

has to be used for thin sheet, this test being referred to as the Rockwell Superficial Hardness Test.

Similar loads are used and the depth of indentation which is correspondingly smaller is measured

with a more sensitive device. The number of Rockwell Superficial scales also is given in Table 1.

Table 1 Rockwell hardness and Rockwell Superficial hardness test scales

Fig. 2 Shape of indentation

in Vickers hardness test

Side view

Top view

136

d d




Description of Rockwell Hardness Tester

The Rockwell Hardness Testing Machine (Figure 4) is one of the more accurate ways to

determining hardness of metals. It conforms to ASTM E18, ISO 6508 and JIS Z 2245 standards,

while meeting and exceeding standard requirements for Rockwell testing as well as Rockwell

Superficial testing. The Superficial hardness test uses the same principle as a Rockwell hardness

test, but at small loads to determine the hardness of either thin samples or very soft specimens.

It can also be used to determine case and coating hardness.

The hardness testing machine consists of side panel with calibration switch and total load

sequence switch to select auto/manual measurement. The desired method of Rockwell or

Rockwell Superficial method can be selected from the selector ring. The selector knob is used to

fix the total load for the hardness testing. The specimen is mounted on the anvil, and the elevating

handle rotates to enable anvil shifts until tip of the indenter touches the test specimen. The

diamond and 3 steel ball indenters (Figure 5) are provided together as accessories with this

machine, as well as calibration blocks. The machine also consists of a digital indicator in front

panel which reduces test duration and increases ease of use (Figure 6). The hardness value is

displayed directly on the hardness indicator.

Total Load

[kgf]

Indenter

Method Diamond

Cone

Steel Ball

1/16 1/8 1/4 1/2

Rockwell

Superficial

15 15N 15T 15H 15X 15Y

30 30N 30T 30H 30X 30Y

45 45N 45T 45H 45X 45Y

Rockwell

60 A F H L R

100 D B E M S

150 C G K P V

Fig. 4 Mitutoyo ATK-600 Rockwell /

Rockwell Superficial Type Hardness

Testing Machine

Front panel

Indenter

Anvil

Elevating

handle

Selector

knob

Selector

ring

Switch

start

Side panel

Fig. 5 (a) Diamond and (b) Steel ball indenters

(b) (a)





1. Rockwell hardness tester Mitutoyo ATK-600

2. Ball and diamond indenters

3. Calibration block

4. Hardness specimens: steel, brass, aluminium

Procedures

1. Turn ON the power switch.

2. Set the total load sequence switch to the AUTO position in the side panel.

3. Set the minor load from selector ring to S (Rockwell Superficial) or R (Rockwell).

4. For selecting a desired indenter, refer to Table 1.

5. Fix the indenter.

6. Place the specimen on the anvil.

7. Set the total load value by turning the selector knob.

8. Preparation complete:

Loading navigator rapidly flashing (from outer to inner)

Indicator 100 (diamond indenter); 130 (ball indenter)

9. Apply the minor load by raising the anvil by rotating clockwise the elevating handle slowly

until the tip of the indenter touches the specimen.

Overloading

lamp Loading

lamp

Loading

navigator

Hardness indicator

Scale table

UPDOWN switch

SELECT switch

Diamond indenter lamp

Ball Indenter lamp

OK/NG lamp

Upper limit setting lamp

Lower limit setting lamp

Offset setting lamp

Indenter selection lamp

Test a method setting lamp

Rockwell Superficial

Hardness test selection

lamp

Rockwell Hardness

test selection lamp

PRELOAD

INDENTER

SELECT

METHOD

OFFSET

LOW

HIGH

METHOD

OK

NG

DIA. BALL FORCE TOTAL

TEST PRE.

ROCKWELL

ROCKWELL SUPERFICIAL

15 30 45

60 100 150

15N 30N 45N

15T 30T 45T

15H 30H 45H

15X 30X 45X

15Y 30Y 45Y

A D C

F B G

H E K

L M P

R S V

3 (S)

10 (R)

1/16 1/8

1/2 1/4

Fig. 6 Front panel of ATK-600 hardness testing machine

L O A D I N G

O V E R




10. During minor load application:

Loading navigator slowly flashing (from outer to inner)

11. When the hardness indicator displays as below. Stop the handle operation.

Indicator 620 to 640 (Rockwell Superficial); 360 to 370 (Rockwell)

12. After appropriate minor load is applied, minor load application is complete.

Loading navigator 4 LEDs light up

13. Press the START switch. The measurement process is automatically performed from step 14

17.

14. Presetting:

Loading navigator 4 LEDs light up

Loading lamp lights up

Indicator 100 (diamond indenter); 130 (ball indenter)

15. During total load application:

Loading navigator flashing (from outer to inner)


Indicator rapid to slow count-down (duration time: 3 to 60 seconds)

16. During total load removal:

Loading navigator flashing (from inner to outer)


Indicator rapid count-up

17. Measurement complete:

Indicator hardness value displayed

OK/NG lamps OK lights up

18. Read and record the hardness value from the hardness indicator.

19. Turn the elevating handle in the reverse direction to lower the anvil and remove the

specimen.

20. Repeat step 3 to 19 for specimens of other methods and specimens.

21. Take three readings on each test specimen and method (Refer Table 2).

Precautions

i. Ensure that both surfaces of the specimens are flat and positioned securely on the anvil.

ii. Rotate the elevating handle gently during elevation of the anvil. Otherwise due to abrupt

strike of the indenter tip with the specimen, the indenter may be destroyed.

iii. If the minor load application is in overload condition:

Loading navigator 4 LEDs light up; Indicator AAAA; Overloading lamp Lights up

Results

Show all the hardness measurements of the specimens in Table 2.




Table 2 Experimental results

Discussion

1. Discuss on the obtained results for each tested specimens.

2. Discuss on the suitable scale for each tested specimen.

3. Compare and discuss on the hardness values of tested specimens with values from reference

sources or manufacturers data.

4. Give a critical discussion on why hardness test needs to perform in engineering practice.

Conclusion



Scale Specimen Reading

Average 1 2 3




4 - CREEP TEST

Introduction

The term of creep refers to the slow plastic deformation that occurs with prolonged loading

usually at elevated temperatures. Creep may occur under static tension, compression, bending,

torsion or shear stress. However, it has been mainly studied in tension under conditions of

variable advantage factor and load.


the apparatus and experimental procedure for creep test.

Objective


1. To develop an understanding of the stages involves in creep.

2. To quantify the rate of deformation of a specimen to stress at a constant temperature (creep

rate).

3. To determine a specimen properties when subjected to a prolonged tensile load.

Theory

Creep is defined as timedependent plastic deformation (elongation) of the metal at a constant

tensile load. The phenomenon is quite significant at elevated temperature, above about 0.4Tm (Tm:

melting temperature). Creep caused by a constant tensile load can be studied by measuring the

permanent extension, after various time intervals, of test-pieces maintained at a constant

temperature. When the creep strain is plotted against time, a curve is obtained such as the one

shown in Figure 1. After the initial instantaneous extension, it can be seen that the curve is made

up of three portions:

Primary creep: The deformation is accompanied

by strain hardening which quickly reduces the

rate of strain.

Secondary creep: The strain rate is

approximately constant. This steady state is

most important part of the curve and should

cover the entire estimated life of the component.

This stage is a result of balance between two

opposing phenomena, namely, strain hardening

and recovery.

Tertiary creep: The strain rate increases rapidly

due to local necking of the test-piece. The

effective stress therefore increases and finally

leads to fracture at tr.

Fig.1 Typical creep curve of strain versus

time at constant stress and elevated

temperature

Cre

ep

str

ain

Time tr

Primary

Secondary Tertiary

Instantaneous deformation

t

Rupture




Retaining steel nuts

Dial test indicator

Loading lever

Weight hanger

Rest pin

Specimen Specimen holders

Fig. 3 SM6 Creep Apparatus

X

X

XX direction Front view

Pinch nut

Supported pin

In many cases the three parts of the curve are not

clearly distinguishable. To obtain a complete

picture of the creep properties of a material, it is

necessary to construct creep curves for a range of

stresses over a range of temperatures. Such curves

(Figure 2) usually show that, as the applied stress

decreased, the primary creep decreases,

secondary creep is prolonged, and the possible

extension during tertiary creep tends to increase.

Very low applied stress may mean that tertiary

creep does not occur even after lengthy service life.

Experiment 1: Creep Test with Variable Advantage Factor

Description of Creep Measurement Apparatus (SM6)

The SM6 Creep Measurement Apparatus, illustrated in Figure 3, uses a simple loading lever to

apply a steady load to the specimen. The ends of specimen are attached at specimen holders by

the retaining steel nuts. Load is applied to the specimen by placing weight hanger on the loading

lever. The loading lever has a rest pin to lock the loading lever in the rest position. The specimen

extension is measured by a dial test indicator (DTI).

Fig.2 Influence of stress and

temperature T on creep behavior

Cre

ep s

trai

n

Time

T< 0.4Tm

T1 or 1

T2 or 2

T3 or 3

T3>T2> T1

3> 2> 1




Specimen and Equipments

1. Creep measurement apparatus SM6

2. Vernier caliper

3. Stopwatch

4. 3 pieces of Plumbum (Figure 4)

Procedures

1. Measure and record the original gauge length,

thickness and width of the gauge length of the

specimen.

2. Gently raise the loading lever arm and pin in the rest

position.

3. Remove retaining nuts from the specimen holders.

4. Fit the top of the specimen in the specimen holder by using retaining nuts.

5. Repeat step 4 for the bottom side of the specimen.

6. Tight the specimen by adjusting the pinch nut at top of theapparatus.

7. Place the tip of dial test indicator (DTI) on the supported pin.

8. Remove the rest pin and gently lower the lever arm to take up any free movement.

9. Raise the weight hanger to the load position.

10. Adjust the DTI to zero.

11. Start the experiment with gently release the weight hanger and start the stopwatch.

12. Record the extension readings from the DTI every 5 or 10 seconds until fracture occurs.

13. Fit the broken parts together and measure the final gauge length.

Results

1. Show all the values and measurements of specimens.

i) Specimen number

ii) Load m [kg]

iii) Advantage factor L

iv) Specimen thickness h [mm]

v) Specimen width of the gauge lengthd [mm]

vi) Initial gauge length l0 [mm]

vii) Final gauge length l [mm]

viii) Actual applied force on the specimens F [N], where F = (mL + 2.5) x 9.81

2. Record the values of elongation, and calculate the strain in Table 1.

Fig. 4 Creep test specimens




3. Plot the straincreep time graphs for the tested specimens.

Discussion

1. Discuss on the shape of obtained creep rate curves.


3. Summarize the occurred errors, and discuss the factors that can be affected to the

experimental results.

Conclusion

Give an overall conclusion based on the obtained experimental results.

Experiment 2: Creep Test with Variable Load

Description of Creep Measurement Apparatus

(SM106)

The SM106 Creep Measurement Apparatus, illustrated in

Figure 5. The specimen is attached at one end to the lever

mechanism by a steel pin and fixed at the other end to

the bearing block by another steel pin. Loads are applied

to the lever arm by placing weights on the weight hanger,

which is pinned to the lever arm.

The lever arm has a advantage factor L of 8. The mass of

the arm is 0.367 kg, the weight hanger mass is 0.16 kg,

and the pins used for pinning the weight hanger and

specimen are 0.04 kg each. The load on the specimen can

be found by taking moments about the pivot bearing as

illustrated in Figure 6. If the mass m [kg] is added to the weight hanger then the tensile pull on

the specimen F [N] is:

( ) gmF += 884.2 (1)

whereg [m/s2] is the acceleration due to gravity. (Note: The mass m does not include the mass of

the hanger; this is included in the constant 2.84)

The specimen extension is measured by a dial test indicator (DTI). A tube fixed to the bearing

block is the housing for the DTI and a nylon pinch screw is used to restrain the DTI under steady

load conditions.

Time [s] Elongation [mm] Strain

5

10

15

20

25

30

.

.

.

tF (Fracture time)

Fig. 5 SM106 Creep Apparatus





1. Creep measurement apparatus SM106

2. Vernier caliper

3. Stopwatch

4. 3 pieces of Plumbum (Figure 4)

Procedures

1. Gently raise the loading lever arm and pin in the rest position.

2. Remove the thumbnut retaining the grooved plate on the lever arm and slacken the nylon pinch screw retaining the Dial Test Indicator (DTI) in the tube.

3. Using both hands, gently lift the DTI and grooved plate clear of the apparatus.

4. Separate the plate from the DTI and stow the safe place.

5. Remove the specimen retaining pins from the lever arm and bearing block.

Note: When fitting the specimen between the lever arm and bearing block, care must be taken not

to bend the specimen.

6. Measure and record the the original gauge length, thickness and width of the gauge length of the specimen.

7. Fit the top of the specimen into the lever arm and replace the specimen retaining pin.

8. Fit the bottom of the specimen into the bearing block and replace the retaining pin (it may be necessary to remove the rest pin to allow some movement of the lever arm; if this is done, then

replace the rest pin when the specimen has been fitted).

9. Refit the DTI and grooved plate but do not tighten up the nylon pinch screw.

10. Remove the rest pin and gently lower the arm to take up any free movement.

11. Zero the DTI and turn the nylon pinch screw until it is finger tight.

Note: It cannot be over-emphasized that the nylon pinch screw should only be tight enough to hold

the DTI in position under steady load condition. Ensure that the DTI travel limits are not exceeded

when the specimen break (i.e. when hanger contact base of apparatus) to avoid damaging the DTI.

12. Refit the rest pin.

13. Record he ambient temperature and reset the stopwatch to zero ready to start the test.

Centre of gravity

Weight of beam

Pivot

Tensile pull on specimen (F)

Weight hanger + support pin + load (m)

410

147

336 42

Fig. 6 Details of the lever arm




14. Load the weight hanger with the required load, remove the rest pin and gently lower the lever arm to take up any slack.

15. Raise the hanger to the load position and refit the pin.

16. Gently release the load and start the stopwatch.

17. Record the extension reading from the DTI every 15 seconds for the primary stage of creep. When the extension rate slow down, then record readings every minute. As the test

approaches the tertiary stage record readings every 15 seconds until fracture occurs or the

hanger bottoms.

Results

1. Show all the values and measurements of specimens. i) Specimen number

ii) Load m [kg]

iii) Advantage factor L

iv) Specimen thickness h [mm]

v) Specimen width of the gauge lengthd [mm]

vi) Initial gauge length l0 [mm]

vii) Final gauge length l [mm]

viii) Tensile pull on the specimens F [N], where F = (2.84 + 8m) x 9.81

2. Record the values of elongation, and calculate the strain in Table 2. 3. Plot the straincreep time graphs for the tested specimens. From the graph, determine the

primary, secondary and tertiary creep section areas.

Table 2 Experimental results of creep test with variable loads

Time [min] Elongation [mm] Strain

0.25

Every 15 sec 0.50

.

.

.

2.50

2.75

Every 1 min 3.00

4.00

.

.

.

11.00

11.50

12.00

Every 15 sec 12.25

12.50

.

.

.

.

tF (Fracture time)




Discussion

1. Discuss on the shape of obtained creep rate curves.




Conclusion





5 - IMPACT TEST

Introduction

Impact test measures the strength of a material under dynamic loading. Often in actual service,

most of the structural components are subjected to dynamic loading. Impact test is designed to

simulate the response of a material to a high rate of loading and involve a specimen being struck

a sudden blow.


the apparatus and experimental procedure for impact test.

Objective


1. To develop an understanding of fracture toughness.

2. To investigate the notched bar impact work and strength of various engineering materials.

3. To investigate the influence of the notch shape on the notched bar impact work.

Theory

1. General

Toughness is the capacity of a material to absorb

energy and deform plastically before fracturing. Since

the amount of plastic deformation that occurs before

fracture is a measure of the ductility of the material,

and because the stress needed to cause fracture is

measure of its strength, it follows that toughness is

associated with both the ductility and strength of the

material.

Unlike other testing applications, impact test involves

the sudden and dynamic application of the load.

For this purpose, in general, a pendulum is

made to swing from a fixed height and strike the

standard impact specimen. There are two most

common methods for the measurement of

impact strength, the Izod and Charpy tests.

In Izod test, a pendulum strikes the specimen

which is fixed in vertical position (Figure 1). The

notch faces the pendulum. The Izod specimen

may have either square or round cross-section.

The specimen has a V-notch. The depth of notch

is 2 mm and included angle 45.

In Charpy test, the specimen is fixed in

horizontal position as shown in Figure 2. The

pendulum strikes the impact specimen on the

unnotched face. Charpy impact specimen,

square in cross-section, has V-notch or U-notch.

Because the Charpy impact specimen does not

have to be clamped in position (as is the case in

Impact

Specimen

Striking edge

Top view

Fig. 2 Configurations for Charpy test

Fig. 1 Configurations for Izod test

Specimen

Striking edge

Impact

Side view




the Izod test), it is much easier to test specimens at temperature other than room temperature

using this method. Consequently the Charpy test has now largely displaced the Izod test. The

Charpy impact test can be used to assess the relative toughness of different materials. It is used

as a tool for materials selection in design. It may also be used for quality control, to ensure that

the material being produced reaches a minimum specified toughness level.

2. Principles of Measurement

In an impact test a specially prepared

notched specimen is fractured by a single

blow from a pendulum striker and energy

required being a measure of resistance to

impact.

The impact test involves a pendulum

(Figure 3) swinging down from a specified

height h0 to hit the specimen and fracture it.

The height h to which the pendulum rises

after striking and breaking the specimen is

a measurement of the energy used in the

breaking.

If no energy were used, the pendulum

would swing to the same height h0 it started

from, i.e. the potential energy mgh0 at the

top of the pendulum swing before and after

the collision would be the same.

The greater the energy used in the breaking, the greater the loss of energy and so the lower the

height to which the pendulum rises. If the pendulum swings up to a height h after breaking the

specimen, then the energy used to break it is

mghmghE = 0 [Nm or J] (1)

This energy value called impact toughness or impact value.

Description of Pendulum Impact Tester

1. General

The WP400 Pendulum Impact Tester complies with DIN 50115 (German Industrial Standard). It

serves for carrying out the notched bar impact test and can be used for assessment of fracture

behaviour of various engineering materials. However, the notched bar impact test cannot be used

to calculate material strength parameters. The tester consists of the following basic parts (Figure

4). The pendulum impact tester is secured to a solid base plate. It provides the necessary stability.

A safety factor is the protective ring which surrounds the pendulum area. The brake allows the

pendulum to swing out quickly and is released with the brake lever. The impact work that was

necessary to fracture the specimen can be read directly from the indicator unit.

2. Technical Application (Notched Bar Impact Test)

Friction is a main factor that can be affected to the experiment. The friction loss is shown on the

indicator unit when the pendulum is allowed to swing through in the absence of a specimen. The

average friction loss ARm must be determined before starting the experiment. The value of ARm is

calculated as

nAAn

i/

1 RiRm == [Nm or J] (2)

Fig. 3 Schematic of an impact test

Pendulum

Starting position

Anvil

End of swing

h

h0

Pointer

Specimen




Brake

Hand release

Ratchet for fastening pendulum

Hand release and braking

Indicator unit

Pendulum striker

Slave pointer

Safety ring

Back support

Frame foot

Specimen

Fig. 4 G.U.N.T. WP400 Pendulum Impact Tester

gunt

Nm 25

15

10

5

15

20

10

5

0

0

After fracturing the notched specimen, the notched bar impact workAkabg is read off from the

indicator unit. In order to obtain the effective notched bar impact work Ak, the friction loss ARm

must be subtracted from the read off value.

Rmkabgk AAA = [Nm or J] (3)

The impact value ak is calculated by dividing the value of effective notched bar impact work Ak, by

the unnotched cross-section area of the specimen S0.

0kk / SAa = [Nm/cm2 or J/cm2] (4)


1. Pendulum impact tester G.U.N.T. WP400

2. Vernier caliper

3. Impact specimens: mild steel (V- and U-notch),

carbon steel (V- and U-notch)

Procedures

1. Measure the thickness of the specimen. Also,

measure the dimensions of the unnotched

length (Figure 5).

2. Raise the pendulum to the left until it indicates the maximum energy range on the upper

indicator unit.

l: Unnotched length h: Thickness S0: Unnotched cross- section area

l

h

S0

Fig. 5 Standard impact test specimen with V-notch




3. Place the specimen horizontally across supports

with the notch away from the pendulum (Figure 6).

Make sure that it is placed center with respect to

pendulum.

4. Release the pendulum by pushing up on the hand

release.

5. The pendulum will drop and striking the specimen,

with a swing through dependent on the amount of

energy absorbed by the test specimen.

6. The indicator will move and stop when peak swing

through is registered, providing a direct reading of

the energy absorbed by the specimen.

7. Read the indicated value from the indicator unit and

record.

8. Apply the brake until the pendulum has returned to its stable hanging vertical position.

9. Remove the specimen from the testing area and observe the failure surface.

10. Repeat the test for specimens of other material and notch.

Results

1. Show all the measurements of specimens.

i) Thickness h [mm]

ii) Unnotched length l [mm]

2. Record the values of ARm and Akabg, and calculate the S0, Ak and ak as shown in Table 1.

Table 1 Experimental results

Discussion

1. Compare and discuss on the impact work values for each specimen with the theory.

2. Discuss on the fracture surface of the tested specimens.


Conclusion



Material Mild steel / Carbon steel

Notch type V-notch U-notch

S0 [mm2]

ARi [J] i = 1 i = 2 i = 3 i = 1 i = 2 i = 3

ARm [J]

Akabg [J]

Ak [J]

ak [J/cm2]

Fig. 6 Specimen placements

for impact test

Notch

Specimen

Impact direction Stopper




6 - UNIAXIAL STRESS SYSTEM

Introduction

Tensile test is one of the most widely used mechanical tests. Various properties of the material

that can be determined by tensile test are yield stress, upper and lower yield points, tensile

strength, elongation, and reduction in area.


the apparatus and experimental procedure for tensile test.

Objective


1. To apply equilibrium condition for uniaxial component.

2. To apply compatibility condition for uniaxial systems in compound specimen.

3. To determine E for metallic materials.

Theory

Stresses may be tensile, compressive or shear in nature. Figure 1

shows a metal bar in tension, i.e. the force F is stretching force

which thus increases the length of the bar and reduces its cross-

section. The area used in calculations of stress is generally the

original area A0 that existed before the application of the forces, not

the area after the force has been applied. This stress is thus referred

to as the engineering stress :

(1)

The dimensional change caused by a stress is called strain. In

tension (or compression), the strain is the ratio of the change in

length to the original length. The term strain is defined as:

% 100 / (2)

Where , the change in length. Since strain is a ratio of two lengths it has no units. Strain is frequently expressed as a percentage.

Uniaxial

A) Uniaxial specimen

Length before

Length after

Fig. 1 Metal bar in tension

F

l0 l

A0

F

Fig. 2 Uniaxial pull-out specimen




B) Uniaxial System Compound specimen

C) Equilibrium

, ! "# (3)

$%, &

() &

. "#

() "# () "#

(4)

From a graph of versus , gradient () "#

() "# (4a)

Equation (4a) is used to calculate () .

)) , -.-. (5)

) $%/

) 0!$%/1/

Fig. 3 Slope 2 34

Fig. 4 Compound specimen

Fig. 5 Equilibrium of compound

specimen




D) Compatibility

Extension in Steel = Extension in Aluminum

) -.

)

-.

&) &-.

() )&)

, (-. -.&-.

)()

&) -.(-.

(6)

Put in (5)

&) () ) , &-. (-. -. (7)

()) , (-.-.

()) , (-.-.

()) , (-.-. (8)

5()) , (-.-.6 (9)

Equation (10) is used to calculate -.

-. $%/7$%$7

-. 0!$%/1/7$%$7

From a graph of versus , gradient 2 ()) , (-.-.

(-. 2 ())

-. (10)

Fig. 6 Force (F) vs extension graph





The Universal Tensile Testing Machine (Figure 7) is designed

to test the physical properties of wide range of materials and

structures. Testing of properties such as tensile strength,

compressive strength, fatigue resistance, crack growth

resistance, bend characteristics, etc. can be performed on

materials such as metals, ceramics, textiles, and virtually any


A standard system in Universal Tensile Testing Machine

consists of a tower console and control panel, together with

a load frame and power supply and a load cell as a load

measurement device. These are all interconnected with

electrical cables at the rear panel of the tower console. The

machine system applies loads, using a screw, to a specimen

of the material under test.

The machine allows for the connection of a computer that can

be used to control and monitor a test automatically. The

computer can be log data resulting from a test and can be

used to generate random or pre-programmed waveforms.


1. Universal testing machine

2. Vernier caliper

3. Tensile specimen: Rectangular steel bar and rectangular compound steel and aluminum bar

Procedures

1. Perform a tensile test on rectangular steel bar up to 5kN. Plot a graph of load versus change in length.

2. From the graph calculate the value of () using equation (4a). 3. Perform a tensile test on rectangular compound bar up to 5kN. Plot a load-change in

length graph.

4. From the graph calculate the value of (-. . Results

1. Tabulate the result for the following items.

i. Steel bar specimen

i. Original Steel-uniaxial gauge length [mm]

ii. Thickness of Steel-uniaxial [mm]

iii. Width of Steel-uniaxial [mm]

ii. Compound bar specimens

i. Original Steel-compound gauge length [mm]

ii. Thickness of Steel-compound [mm]

iii. Width of Steel-compound [mm]





iv. Original Aluminum-compound gauge length [mm]

v. Thickness of Aluminum-compound [mm]

vi. Width of Aluminum-compound [mm]

2. Calculate the following.

i. Steel bar cross-sectional area ) [mm2] ii. Compound bar cross-sectional area ) [mm2]

iii. Compound bar cross-sectional area -. [mm2] 3. Plot the loaddisplacement graph for Steel bar and Compound bar of tested specimen.

4. Plot the stressstrain graph for Steel bar and Compound bar of tested specimen.

5. Calculate:

i. Youngs modulus E for Steel bar [GPa]

ii. Youngs modulus E for Aluminum bar [GPa]

Discussion

1. Discuss on the shape of obtained load-change in length curve for both Steel bar and

Compound bar.


3. Discuss the difference between Equilibrium and Compatibility, and their application.


5. Discuss on the factors that contribute to error in the experimental result.

Conclusion






7A - BEAM TEST (SUPPORTS REACTION OF BEAM)

Introduction

A beam is a structural element that carries load primarily in bending (flexure). Beams generally

carry vertical gravitational forces but can also be used to carry horizontal loads. Beams are

characterized by their profile (the shape of their cross-section), their length, and their material.

Beams carry their loading to other elements or supports. In order to be able to analyze a structure

it is necessary to be clear about the forces that can be resisted at each support.


the apparatus and experimental procedure to examine the supports reaction of the beam.

Objective

The objectives of this experiment are:

1. To identify the supports reaction in simply-supported and overhanging beams.

2. To develop an understanding of beam apparatus, and to determine its sensitivity and accuracy.

Theory

1. General

A beam is a member which has the primary function of

resisting transverse loading. Beam is one of the simplest

structures in design but one of the most complexes to

analyze in terms of the external and internal forces acting

on it. The complexity of its behavior under load depends

on how it is supported - at one or both ends - and how its

ends are attached to the supports. Three basic beam

types are the simply-supported, overhanging, and

cantilever beams.

A beam supported by a support at the ends and having

one span is called a simply-supported beam (Figure 1). A

support will develop a reaction normal to the beam but

will not produce a couple. If either or both ends of the

beam project beyond the supports, it is called

overhanging beam (Figure 2). A cantilever beam is one in

which one ends is built into a wall or other support so that

the built-in end can neither move transversely nor rotate

(Figure 3).

2. Types of Load

Fig. 1 Simply-supported beam with two symmetric concentrated loads and supported by pinned and roller supports

W W

Pinned Roller

Fig. 2 Overhanging beam with

concentrated and distributed loads, and supported by pinned supports

Pinned Pinned

W w




Fig. 4 Supports reaction of the simply-supported beam with concentrated loads

W1 W2

a b

l / 2 l / 2 R1 R2

A beam is normally horizontal, the loads being vertical, other cases which occur being locked

upon as exceptions. The two types of loads for beams are

concentrated and distributed loads.

i. A concentrated load W [N] is one which is

considered to act at a point, although in practice

it must really be distributed over a small area

(Figures 1, 2 and 3).

ii. A distributed load w [N/m] is one which is spread

in some manner over the length of the beam. The

rate of loading may be uniform, or may vary from

point to point along the beam (Figure 2).

3. Types of Support

The deformations and stresses which result in a beam owing to a particular load (concentrated

load) or group of loads (distributed load) are dependent on the manner in which the beam is

supported. The three basic types of supports for beams are roller, pinned and fixed-end.

i. A roller support is one which exerts a reactive force having a known line of action (Figure

1).

ii. A pinned support in one which allows the beam freedom to rotate but prevents it from any

linear movement (Figures 1 and 2).

iii. A fixed-end support is one which prevents the beam from translating or rotating at the

point of support (Figure 3).

4. Supports Reaction of the Simply-Supported Beam with Concentrated Loads

Referring to the loading in Figure 4, the left-hand support reaction R1 is first required and the

reactions can be found from the equations of force and moment equilibrium.

2121 WWRR +=+ (1)

( ) ( ) ( ) bWaWWWlblWalWlR 2121212122111 ++=++= (2)

Therefore

( ) ( ) ( )lbWlaWWWR 2121211 ++= (3)

Substitute (3) to (1).

( ) ( ) ( )lbWlaWWWR 2121212 ++= (4)

Fig. 3 Cantilever beam with a

concentrated load and supported by

fixed-end support

Fixed-end

W




Fig. 5 Supports reaction of the overhanging beam with concentrated and distributed loads

w W

l l

R1 R2

l/ 2

5. Supports Reaction of the Overhanging Beam with Concentrated and Distributed Loads

Referring to the loading in Figure 5, the left-hand support reaction R1 is first required and the

reactions can be found from the equations of force and moment equilibrium.

WwlRR +=+ 21 (5)

( ) ( )llwlWlllR21

21

21

1 +=++ (6)

Therefore

( )WwlR =32

1 (7)

Substitute (7) to (5).

( )WwlR 531

2 = (8)

Description of Beam Apparatus

The SM104 Beam Apparatus (Figure 6) has many features which extend the range of experiments

to cover virtually all coursework requirements relating to the bending of beams. The basic unit

provides facilities for supporting beams on simple, built in and sinking supports; applying point

loads, and measuring support reactions and beam deflections.

The main frame of the apparatus consists of an upper cross member carrying graduated scales

and two lower members bolted to tee-legs to form a rigid assembly. The load cells and cantilever

support pillar slide along the lower members and can be clamped firmly in any position. The load

cells are direct readings and each is fitted with a hardened steel knife edge which can be adjusted

by a thumb nut to set the initial level or to simulate a sinking support. A lead screw in the base of

each load cell can be screwed upwards to support the knife edge and thus convert it to a rigid

support when required.

The cantilever support consists of a rigid pillar with a sturdy clamping arrangement to hold the

beams when built-in end conditions are required. Weight hangers and a set of cast iron weights

are supplied for applying static loads. All beam deflections are measured by dial gauge mounted

on magnetic carriers which slide along the upper cross member. The dial gauge carriers, load cells

and weight hangers are all fitted with cursors which register on the scale located on the upper

cross member, thus ensuring easy, accurate positioning.





1. Beam apparatus SM104

2. Vernier caliper

3. Load cells

4. Dial gauges

5. Weight hangers

6. Weights: 5 N, 10 N

7. Steel blocks

8. Beams: Steel / Brass / Aluminium

Experiment 1: Supports Reaction of the Simply-Supported Beam with Concentrated Loads

Procedures

1. Measure the thickness and width of the beam.

2. Measure the length of the beam and mark it at mid-span and at 1/4-span points.

3. Set up load cells 1/4-span to the left and right of the mid-span reading, and lock the knife

edge.

4. Place the beam in position with 1/4-span overhang at either end.

5. Position two weight hangers equidistant from the mid-point of the beam.

6. Place a dial gauge in position on the upper cross-member so that the ball end rests on the

center-line of the beam immediately above the left-hand support.

7. Check that the stem is vertical and the bottom O-ring has been moved down the stem.

8. Adjust the dial gauge to zero read and then lock the bezel in position.

9. Move the dial gauge to a position above the right-hand support, check that the beam is

parallel to the cross-member, then adjust the height of the knife edge so that the dial gauge

reads zero.

10. Remove the dial gauge and unlock both knife edges. Adjust the load cell indicators to read

zero.

11. Apply loads to the weight hangers in a systematic manner, tap the beam very gently and take

readings of the load cells.

Fig. 6 SM104 Beam Apparatus

Load cell

Dial gauge

Weight hanger

Weights Cantilever

support

Beam

Spring balance




W1

Fig. 7Experimental set up for supports reaction

of the simply-supported beam with

concentrated loads

l

Load cell

L / 4

W2

R1 R2

L

4

l

4

l

L / 4 L / 4 L / 4

12. Process the results and plot graphs from the experimental results.

Results

1. Show all the measurements of beam.

i. Beam length L [mm]

ii. Beam width b [mm]

iii. Beam thickness h [mm]

iv. Beam working length l [mm]

2. Record the values of R1 and R2, and calculate the R1+R2, and % in Table 1.

3. Plot the graphs.

i. R1 and R2 against W1, when W2 = 0.

ii. R1 and R2 against W2, when W1 = 0.

iii. R1 and R2 against W1 = W2 = 5 N, 10 N, 30 N.

Discussion

1. Discuss on the verification of equations (3) and (4).

2. Discuss on the obtained graphs from the experiment.

3. Calculate the theoretical values of R1 and R2, by using equations (3) and (4). Plot the graph of

theoretical values of R1 and R2. Compare and discuss the theoretical and experimental graphs.






Table 1 Experimental results of simply-supported beam with concentrated loads

Conclusion


Experiment 2: Supports Reaction of the Overhanging Beam with Concentrated and

Distributed Loads

Procedures

1. Measure the thickness and width of the beam. Arrange the beam as shown in Figure 8.

2. Set up load cells 1/4-span to the left and 1/8-span to the right of the mid-span reading, and

lock the knife edge.

3. Place a dial gauge in position on the upper cross-member so that the ball end rests on the

center-line of the beam immediately above the left-hand support.

4. Check that the stem is vertical and the bottom O-ring has been moved down the stem.

5. Adjust the dial gauge to zero read and then lock the bezel in position.

6. Move the dial gauge to a position above the right-hand support, check that the beam is

parallel to the cross-member, then adjust the height of the knife edge so that the dial gauge

reads zero.

7. Remove the dial gauge and unlock both knife edges. Adjust the load cell indicators to read

zero.

8. Position a weight hanger 1/8-span to the left from the end point of the beam.

W1 [N] W2 [N] R1 [N] R2 [N] R1+R2 [N] [N] %

5 0

10 0

15 0

20 0

25 0

30 0

0 5

0 10

0 15

0 20

0 25

0 30

5 5

10 10

15 15

20 20

25 25

30 30

* = (R1+R2) (W1+W2)

% = 100/ (W1+W2)




9. Apply loads to the weight hanger and steel block in a systematic manner, and take readings

of the load cells.

10. Process the results and plot graphs from the experimental results.

Results

1. Show all the measurements of beam.

i. Beam length L [mm]

ii. Beam width b [mm]

iii. Beam thickness h [mm]

2. Record the values of R1 and R2, and calculate the R1+R2, and % in Table 1.

3. Plot the graphs.

i. R1 and R2 against w, when W = 10 N.

ii. R1 and R2 against W, when w = 10 N.

iii. R1 and R2 against w = W = 10 N, 15 N, 20 N.

Discussion

1. Discuss on the verification of equations (7) and (8).

2. Discuss on the obtained graphs from the experiment.

3. Calculate the theoretical values of R1 and R2, by using equations (7) and (8). Plot the graph of

theoretical values of R1 and R2. Compare and discuss the theoretical and experimental graphs.



Fig. 8 Experimental set up for supports reaction of the

overhanging beam with concentrated and distributed loads

Load cell

L/ 4

W

R1 R2

L

w

L/8 L/ 4 L/ 4 L/8




Table 2 Experimental results of overhangingbeam with concentrated and distributed loads

Conclusion


w [N/m] W [N] R1 [N] R2 [N] R1+R2 [N] [N] %

10 0

10 5

10 10

15 0

15 5

15 10

15 15

20 0

20 5

20 10

20 15

20 20

* = (R1+R2) (w+W)

% = 100/ (w+W)




7B - BEAM TEST (DEFLECTION OF A CANTILEVER)

Introduction

A beam is a structural element that carries load primarily in bending (flexure). Beams generally

carry vertical gravitational forces but can also be used to carry horizontal loads. Beams are

characterized by their profile (the shape of their cross-section), their length, and their material.

Beams carry their loading to other elements or supports. In order to be able to analyze a structure

it is necessary to be clear about the forces that can be resisted at each support.


the apparatus and experimental procedure to examine the supports reaction of the beam.

Objective

The objectives of this experiment are:

1. To identify the supports reaction in simply-supported and overhanging beams.

2. To develop an understanding of beam apparatus, and to determine its sensitivity and accuracy.

Theory

1. General

A beam is a member which has the primary function of

resisting transverse loading. Beam is one of the simplest

structures in design but one of the most complexes to

analyze in terms of the external and internal forces

acting on it. The complexity of its behavior under load

depends on how it is supported - at one or both ends -

and how its ends are attached to the supports. Three

basic beam types are the simply-supported, overhanging,

and cantilever beams.

A beam supported by a support at the ends and having

one span is called a simply-supported beam (Figure 1). A

support will develop a reaction normal to the beam but

will not produce a couple. If either or both ends of the

beam project beyond the supports, it is called

overhanging beam (Figure 2). A cantilever beam is one

in which one ends is built into a wall or other support so

that the built-in end can neither move transversely nor

rotate (Figure 3).

2. Types of Load

A beam is normally horizontal, the loads being vertical,

other cases which occur being locked upon as

exceptions. The two types of loads for beams are

concentrated and distributed loads.

i) A concentrated load W [N] is one which is considered

to act at a point, although in practice it must really be

distributed over a small area (Figures 1, 2 and 3).

Fig. 1 Simply-supported beam with two symmetric concentrated loads and supported by pinned and roller supports

W W

Pinned Roller

Fig. 3 Cantilever beam with a concentrated load and supported by fixed-end support

Fixed-end

W

Fig. 2 Overhanging beam with concentrated and distributed loads, and supported by pinned supports

Pinned Pinned

W w




ii) A distributed load w [N/m] is one which is spread in some manner over the length of the beam.

The rate of loading may be uniform, or may vary from point to point along the beam (Figure

2).

3. Types of Support

The deformations and stresses which result in a beam owing to a particular load (concentrated

load) or group of loads (distributed load) are dependent on the manner in which the beam is

supported. The three basic types of supports for beams are roller, pinned and fixed-end.

i) A roller support is one which exerts a reactive force having a known line of action (Figure

1).

ii) A pinned support in one which allows the beam freedom to rotate but prevents it from any

linear movement (Figures 1 and 2).

iii) A fixed-end support is one which prevents the beam from translating or rotating at the

point of support (Figure 3).

4. Deflection of Cantilever

The deflection under the load for a cantilever loaded at the free end is given by

EI

WLz3

3

= (1)

If EI and L are maintained constant then:

Wkz .1

= (2)

Where

1k is constant

Similarly if EI and W are maintained constant:

3

2.Lkz= (3)

Likewise E

kz

3= and I

kz

4= if E and I respectively are made the variables.

Description of Beam Apparatus

The SM104 Beam Apparatus (Figure 6) has many features which extend the range of experiments

to cover virtually all coursework requirements relating to the bending of beams. The basic unit

provides facilities for supporting beams on simple, built in and sinking supports; applying point

loads, and measuring support reactions and beam deflections.

The main frame of the apparatus consists of an upper cross member carrying graduated scales

and two lower members bolted to tee-legs to form a rigid assembly. The load cells and cantilever

support pillar slide along the lower members and can be clamped firmly in any position. The load

cells are direct readings and each is fitted with a hardened steel knife edge which can be adjusted

by a thumb nut to set the initial level or to simulate a sinking support. A lead screw in the base of

each load cell can be screwed upwards to support the knife edge and thus convert it to a rigid

support when required.

The cantilever support consists of a rigid pillar with a sturdy clamping arrangement to hold the

beams when built-in end conditions are required. Weight hangers and a set of cast iron weights




Fig. 6 SM104 Beam Apparatus

Load cell

Dial gauge

Weight

hanger

Weights Cantilever

support

Beam

Spring

balance

are supplied for applying static loads. All beam deflections ar

manual emm 3108 - revised - 150224

Documents

tensile strength

lab apparatus

lab manual

sources of error

quantitative data

data missing

qualitative data

lab report marking scheme