Lab manual
Submitted to: Engr Muhammad Yousaf
Submitted by: Abdul Azeem (2011-TE-43)
Department of Transportation Engineering and Management
University of Engineering and Technology Lahore
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100 ton Buckton UTM
Charpy’s Impact Test
Avery’s Tension testing Machine
50 KN shimdzu UTM
50 ton Buckton UTM Shimadzu Hardness TM
Fatigue testing Machine
10 ton Buckton UTM
Layout map of Strength of Strength of Materials Lab
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100 ton Buckton UTM
Charpy’s Impact Test
Avery’s Tension testing Machine
50 KN shimdzu UTM
50 ton Buckton UTM Shimadzu Hardness TM
Fatigue testing Machine
10 ton Buckton UTM
Layout map of Strength of Strength of Materials Lab
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Job # 1 Layout plan of strength of materials lab Objective: To overview the location, orientation and purpose of the machinery in the strength of materials laboratory
Description: 1) 10 Ton Buckton Universal Testing Machine: Max capacity = 0-10 tons 1 ton = 2240lbs Operation: Electric/Manual (Lever arm system) Parts: upper & lower Measuring scales: 0 – 10 – 10 tons Types of tests: Tension test Compression test Bending test Shear test Torsion test Punching test
2) 50 Ton Buckton Universal Testing Machine: Max capacity: 0 – 50 – 50 tons Operation: Electric hydraulic system Parts: Upper & Lower Measuring scales: – 05 tons 0 – 05 0 – 10 – 10 tons – 25 tons 0 – 25 0 – 50 – 50 tons Types of tests: Tension test Compression test Bending test
3) 500 KN Shimadzu Universal Testing Machine: Max capacity: capacity: 500 KN (1 ton = 9.981 9.981 KN) Operation: electrically operated Measuring scales: 0 – 10 – 10 KN – 25 KN 0 – 25 0 – 50 – 50 KN – 100 KN 0 – 100 0 – 200 – 200 KN – 500 KN 0 – 500 3
Types of tests: Tension test Compression test Bending test
4) Avery’s Tension Testing Machine: Maximum capacity: 0 – 1500 lb-inch Parts: Fixed head & Twisting head Rotational speeds: 0 – 3 1/3 Degree per minute 0 – 10 Degree per minute 0 – 30 Degree per minute 0 – 90 Degree per minute Measuring scales: 0 – 1500 Pound-inch 0 – 3000 Pound-inch 0 – 7500 Pound-inch 0 – 15000 Pound-inch
5) Charpy’s Impact testing Machine: Max capacity: 0 – 170 degrees Scales: 0 – 180 degrees Operation: Manual Types of tests: Tension test Bending test
6) 100 Ton Buckton Universal Testing Machine: Max capacity: 0 – 200,000 Pounds Operation: Electric Measuring scales: 0 – 20,000 Pounds 0 – 200,000 Pounds Types of tests: Tension test (bars, plates etc.) Compression test (bars, plates etc.) Bending test (bars, plates, concrete beams etc.)
7) Avery Rockwell Hardening Testing Machine: Operation: Manual Scales: B-for low carbon steel C-for high carbon steel Types of test: Hardness test Penetrators: Steel ball 1/16 inch diameter (For low carbon steel) Diamond cone (for high carbon steel)
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Comments: This job was really informative for understanding the operations of different machinery places in the Strength of Materials laboratory.
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Job # 02 Study of small instruments of lab Objective: Awareness of various small instruments which are used in lab for small measurements
Apparatus/Instruments: 1) 2) 3) 4) 5) 6) 7)
Venire caliper. Micro meter screw gauge. Deflection gauge. Baty’s extensometer. Dial gauge. Outside caliper & inside caliper. Spring divider.
1) Vernier caliper: Least count = 0.05 mm = 1/128” There are two scales of Vernier caliper. Main scale Vernier scale Reading = main scale reading + (Vernier scale reading × least count) For example: Main scale reading = 6 mm Vernier scale reading = 8 × 0.05 = 0.40 mm Total reading = (6 + 0.40) mm = 6.40 mm
2) Micro meter screw gauge: Least count = 0.01 mm There are two scales: Main scale Circular scale Circular scale moves on the main scale of the screw gauge. Reading = main scale reading + (circular scale reading × least count) For example: Main scale reading = 6.5 mm Circular scale reading = 36 mm Total reading = 6.5 + (36 × 0.01) = 6.86 mm
3) Deflection gauge: Max length measured = 1 inch Least count = 0.1/100 = 0.001” There are two circular dials of deflection gauge. When the needle of the main dial rotates one cycle, it means it measures 1 inch. The distance between two divisions on dial is 0.1 inch. Reading = main scale reading + (large scale reading × least count) 6
For example: Main scale reading = 0.1 Large scale reading = 76 Total reading = 0.1 + (76 × 0.001) = 0.176 inch
4) Baty’s extensometer: Least count = 1/20000” = 0.00005” This instrument is used to measure extension or elongation normally in steel bars.
5) Dial gauge: This instrument is used to measure dimensions. This is used to measure up to one inch. Least count = 0.0025 inch
6) Outside & inside caliper: These calipers are used to measure the inside or outside diameter of the object.
Outside caliper
Inside caliper 7
7) Spring divider: Spring divider is used to measure the elongation of specimen. For example steel bars and other bars.
Comments:
These small instruments are very important for small measurements because they give accuracy up to the third and fourth digit of the inch. The problem only is that the number of instruments available was not sufficient so that all of us can perform in the proper way and get the chance to learn these instruments thoroughly.
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Job # 03 To perform tensile strength test on given steel sample (hot rolled deformed steel bar) Objective: To study the various properties of a mild hot rolled deformed steel bar under tension
Apparatus: 500KN shimadzu universal testing machine. Extensometer Steel Gauge marking tools Steel ruler
Spring divider
Related theory: Behavior of materials under Tensile Load: Depending upon the type of behavior of materials under the stresses they are broadly classified into two types Brittle i. ii. iii. iv. v. vi. vii.
Brittle material fractures at much lower strains. It has more carbon content. Brittle material has often large ultimate strength. Brittle materials break without much warning. Brittle materials do not show necking. Glass and cast iron are the examples of brittle materials Stress-strain Graph.
Ductile Ductile material withstands large strains before the specimen rupture. It has relatively less carbon content. Ductile material has often less ultimate strength. Ductile materials show large yielding and strain before breaking. Ductile materials show necking process. Aluminum and steel usually fall in this category.
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Purpose of reinforcement of concrete with steel bars: Concrete is good for taking compressive loads but not good for tensile loads and fails under
tensile loads. Steel bars are good for tensile forces. We reinforce concrete with the steel bars to make it good for both compressive as well as tensile forces. The steel bars are inserted in the lower part of the concrete slab.
Types of steel reinforcement:There are two types of steel reinforcement: 1. Plain steel reinforcement. 2. Deformed steel reinforcement.
Types of deformed bars:1. Hot rolled steel bar 2. Cold rolled/worked steel bar. In this process the steel passes through the process of torsion under normal temperature. When we work on cold steel bars to make those torsteel bar, it given torsion and due to this
torsion its nature makes it brittle due to which it is prohibited. To limit cracks that may develop in reinforced concrete around mild steel bars due to stretching of bars and some loss of bond under load it is common to use deformed bars that have projecting ribs or are twisted to improve the bond with concrete.
Stress-strain curve:During tensile testing of a material sample, the strain-stress curve is a graphical representation of the relationship between the strain and stress in the material. Suppose that a material is placed in tension compression testing machine and an axial load is applied over it which is gradually increases, then there will be certain elongation in the original gauge length, which is measured and this is continued until the failure occurs. By knowing the original crosssectional area and the length of specimen the stress δ and the strain ε can be found.
Ultimate Strength Rupture Strength Yield Limit Elastic limit Proportional Limit 10
Proportional limit: From point O to the point called proportional limit the stress-strain curve is the straight line this was first discovered by Sir Issac newton and this is called the Newton’s law that within proportional limit stress is directly proportional to the strain. σ∝ε
σ= Eε
The constant of proportionality is called modulus of elasticity or the bulk modulus and is equal to the slope of the curve from O to P
Elastic limit: The elastic limit is the limit beyond which the material will not go to its original shape after the removal of load or it is that maximum stress which can be developed in the material without any permanent or residual deformation in the material when the load is removed.
Elastic and Plastic Ranges: The region in the stress-strain diagram from O to P is called the elastic range, and the region from P to R is called the plastic region.
Yield point: The yield point is the point at which the material will have an appreciable elongation in length without any increase in load.
Ultimate strength: The maximum ordinate in the stress-strain diagram is the ultimate strength or tensile strength.
Rapture strength: Rapture strength is the strength of the material at the rupture. This is also known as breaking strength.
Modulus of Resilience: Modulus of resilience is the work done on the unit volume of material as the force is gradually 3 increased from O to P which is N m/m . This may be calculated as the area under the stress-strain curve from origin up to the elastic limit E. The resilience of the material is its ability to store energy without any permanent elongation.
Modulus of Toughness: It is the work done on a unit volume of the material as the force is gradually increased from O to R in 3 Nm/m . This may be calculated as the entire area under the entire curve. The modulus of toughness of a material is its ability to absorb energy without causing it to break.
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Working Stress, Allowable Stress, and Factor of Safety: Working stress is defined as the actual stress of a material under a given loading. The maximum safe stress that a material can carry is termed as the allowable stress. The allowable stress should be limited to values not exceeding the proportional limit. However, since proportional limit is difficult to determine accurately, the allowable tress is taken as either the yield point or ultimate strength divided by a factor of safety. The ratio of this strength (ultimate or yield strength) to allowable strength is called the factor of safety.
Ductility: It is very important. It gives us the warning before failure of the structure. It causes necking. We can define the phenomenon of ductility b y two processes: %age elongation %age reduction in area If the percentage is great the ductility is greater and the carbon content is lesser.
Graph between stress and strain %:No of Observations
Applied Load (KN)
Dial Gauge Reading
Elongation (mm)
strain(%age)
Stress (MPa)
1
0
0
0
0
0
2
5
1
0.01
0.02
39
3
10
2
0.02
0.04
80
4
15
3
0.03
0.06
125
5
20
5
0.05
0.1
154
6
25
9
0.09
0.18
192
7
30
13
0.13
0.26
231
8
35
16
0.16
0.32
270
9
40
20
0.2
0.4
308
10
45
24
0.24
0.48
347
11
50
28
0.28
0.56
385
12
55
34
0.34
0.64
424
13
60
46
0.46
0.92
463
14
65
250
0.7
1.4
516
15
70
52
2
4
540
16
75
53
3
6
579
17
80
54
4
8
617
18
85
55
5
10
656
19
90
56
6
12
714
20
95
56.5
6.5
13
733
21
100
57
7
14
777
22
103.5
58
8
16
798
23
98.2
59
9
18
757
24
95
60
10
20
733 12
stress strain curve 900 800
Rupture stress 700
Ultimate tensile stress 600
) a P M 500 ( s s e 400 r t S
Yield.Limit Proportional limit
300 200
0.2% Strain
100 0 0
5
10
Strain %
15
20
25
As the line touches the graph at 490MPa so the yield strength is 490 MPa
Yield Limit = 490MPa Proportional Limit = 410MPa Ultimate Strength = 800MPa Rupture Strength = 725MPa Elastic Limit = Modulus of elasticity:E = slope of curve in proportional limit = stress/strain -3 = 300MPa/5.8×10
Elongation and cumulative gauge length diagram: Cumulative Gauge Length (mm)
%age Elongation
Elongation (mm)
0 50 100 150 200
0 19.35 33.88 51.47 67.08
0 62 117 182 237
250
82.90
297
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%age Elongation 90 80 n o i t a g n o l E e g a
70 60 50 40
% 30
20 10 0 0
50
100
150
200
250
300
Cummulative gauge length (mm)
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Job # 04 To perform direct shear and punching shear test on a given steel sample Objective: To get a practical overview of the direct and punching shear by performing the test.
Apparatus: 50 tons Buckton Universal Testing Machine Steel bar Vernier caliper/ micrometer screw gauge Steel ruler Shear Jigs
Related theory: Shear Force (V): A force which is applied parallel to the sections is known as Shear force.
Shear strain (γ): The distortion produced by shear stress on an element or rectangular block is shown in the diagram. The shear strain is γ and can be measured as the change in right angle. It is measured in radians and is dimensionless quantity.
Shear stress (Tau)
The intensity of the internal resistance when the applied force is parallel to the section being sheared is called Shear Stress.
Types of shear: 1. Direct shear One way shear or single shear
One way shear is a shear in which there is only one plane of failure.
Stress = σ
=
Failure plane
P
P 15
Two way shear Two way shear or double shear is a shear in which there are two planes of failure.
Stress = σ
=
Failure planes
P/2
P
P/2
2. Punching shear The shear in which some part of same body slides is known is called as punching shear.
Procedure: 1) 2) 3) 4) 5) 6) 7)
Measure the diameter of steel bar and find its cross sectional area. Fix the lower jig and upper jig in the machine. Fix the zero error of the machine. Place the steel sample over the lower jig. Apply the shear load until the bar gets sheared. Apply the load gradually and note the reading when the bar gets sheared. Calculate the shear strength by using the relationship.
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Observations and Calculations: Types of Test Direct Shear Punching Shear
Diameter mm
Load
Thickness mm
Area 2
Shear Stress
Tons
1
2
3
AVG
1
2
3
AVG
mm
MPa
1.25
16.0
16.5
15.5
16
-
-
-
-
201.1
60.98
2.25
15.2
15.3
16.2
15.6
0.94
0.95
0.96
0.95
46.5
474.1
Comments:
The phenomenon of punching shear stress enables us to design bridge becks and other its kinds of structures. Passing vehicles act as a punch on the bridge deck. So it should be kept in mind while designing a bridge. Moreover a direct shear stress value of a material gives us a clue to predict the strength of a material against shearing.
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Job # 05: To perform compression test on a given wooden sample i. ii.
Parallel to grains Perpendicular to grains
Objective: To study the anisotropic behavior of wood
Apparatus: Wood samples 500KN shimadzu universal testing machine Deflection Gauge Steel rule/Vernier caliper
Related theory: Isotropy: The property of being isotropic means having the same value when measured in different directions. It gives the sense that in isotropic behavior a thing always shows the same properties along all the orientations.
Anisotropy: Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.)
Stiffness: The force/load required to produce a unit displacement is called stiffness.
Modulus of Elasticity: It is a ratio between stress and strain
E=stress/strain Observations and Calculations: Parallel to Grains: Initial thickness=5cm Final thickness=4.7cm
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SR NO
LOAD (KN)
D.G READING
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0 5 15 20 25 30 35 40 45 50 52 54 56 58 60 62 64 66 68 70 72 74 75.7
200 252 262 267 271 275 279 283 287 291 292 294 295 296 298 300 301 302 304 305 306 308 309
DEFLECTION mm 0 1.32 1.57 1.70 1.80 1.91 2.01 2.11 2.21 2.31 2.34 2.39 2.41 2.44 2.49 2.54 2.57 2.59 2.64 2.67 2.69 2.74 2.77
m 0 0.00132 0.00157 0.00170 0.00180 0.00191 0.00201 0.00211 0.00221 0.00231 0.00234 0.00239 0.00241 0.00244 0.00249 0.00254 0.00257 0.00259 0.00264 0.00267 0.00269 0.00274 0.00277
%STRAIN
STRESS 2 kN/m
E 2 kN/m
K
0 2.64 3.14 3.40 3.60 3.82 4.02 4.22 4.42 4.62 4.68 4.78 4.82 4.88 4.98 5.08 5.14 5.18 5.28 5.34 5.38 5.48 5.54
0 2× 10 6 6× 10 8× 10 10× 10 6 12× 10 14× 10 16× 10 6 18× 10 20× 10 20.8× 10 6 21.6× 10 22.4× 10 6 23.2× 10 24× 10 24.8× 10 6 25.6× 10 26.4× 10 27.2× 10 6 28× 10 28.8× 10 6 29.6× 10 30.3× 10
0 0.76× 10 9 1.91× 10 2.35× 10 2.78× 10 9 3.14× 10 3.48× 10 3.79× 10 9 4.07× 10 4.33× 10 4.44× 10 9 4.52× 10 4.65× 10 9 4.75× 10 4.82× 10 4.88× 10 9 4.98× 10 5.10× 10 5.15× 10 9 5.24× 10 5.35× 10 9 5.40× 10 5.47× 10
0 3.79× 10 6 9.55× 10 11.76× 10 13.89× 10 6 15.71× 10 17.41× 10 18.96× 10 6 20.36× 10 21.65× 10 22.22× 10 6 22.59× 10 23.24× 10 6 23.77× 10 24.10× 10 24.41× 10 6 24.90× 10 25.48× 10 25.76× 10 6 26.22× 10 26.77× 10 6 27.01× 10 27.33× 10
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Perpendicular to Grains: Initial thickness = 5cm Final thickness = 3.605cm
SR NO 1 2 3 4 5 6 7 8 9 10 11 12
LOAD (KN) 0 5 10 15 20 25 30 32 34 36 38 38.5
D.G READING 200 211 219 227 238 268 350 319 439 484 535 555
DEFLECTION %STRAIN (m) 0 0 0.000279 0.558 0.000483 0.966 0.000686 1.372 0.000965 1.930 0.00173 3.460 0.00381 7.620 0.00483 9.660 0.00607 12.14 0.00721 14.42 0.00851 17.02 0.00902 18.04
STRESS 0 2× 10 4× 10 6× 10 8× 10 10× 10 12× 10 12.8× 10 13.6× 10 14.4× 10 15.2× 10 15.4× 10
E (Pa) 0 0.358× 10 0.414× 10 0.437× 10 0.414× 10 0.289× 10 0.157× 10 0.132× 10 0.112× 10 0.100× 10 0.089× 10 0.085× 10
K (Pa) 0 0.018× 10 0.021× 10 21.87× 10 20.37× 10 14.45× 10 7.87× 10 6.62× 10 5.6× 10 5.0× 10 4.5× 10 4.3× 10
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Job # 6 To find the hardness value of a given steel sample using Rockwell Hardness testing machine Objective: To determine the hardness of the given sample to get an idea about the strength of the material
Equipment: Rockwell Hardness testing machine Steel specimen Indenter
a) Steel ball indenter b) Diamond cone indenter
Related Theory: Hardness: “Hardness is a measure of resistance of material against abrasion, scratching, indentation and punching.” There are so many ways of determining hardness of the materials like Moh scale of hardness. But this method is valid in geology and not in the mechanics. We perform so many types of tests on the materials to determine their hardness value but these values are not comparable with one another. Generally there are two types of approach. i. ii.
National Approach (having no mathematical/numerical approach) Empirical Approach (having no mathematical/numerical approach) The other two methods for testing hardness are as follows:
i. ii.
Brinell Hardness Test Vickers’s Hardness Test The values of these three test are not comparable with each other. Hardness assists us in quality control of material.
Indenter: “The element producing indentation is known as indenter.” In Rockwell hardness test we use two types of indenters:
1. Diamond cone indenter It is harder and is used for the harder materials.
2. Steel ball indenter It is relatively softer and is usually used for the soft materials. 21
Procedure: 1) Raise the specimen till it touches the underside of indenter and the pointer of the dial gauge is at initial position. 2) Apply a minor load for 10 – 15 seconds. 3) Then apply a major load 4) There will be a certain impression on the surface of the material. 5) Remove the major load and note the hardness value from the dial gauge of the machine.
e = Permanent increase in depth due to major load E = constant, depending upon the form of indenter
Rockwell Hardness Scale: Scale
Indenter
Miner Load
Major Load
Total Load
Value of E
A
Diamond cone
10
50
60
100
B
1/16” Steel Ball
10
90
100
130
C
Diamond cone
10
140
150
100
Observations and calculations: Sr No
specimen
Type of indenter
scale
1 2 3 1 2 3
Mild carbon steel
1/16” dia steel ball
B
High carbon steel
Diamond cone
C
Load Minor 10 10 10 10 10 10
Major 90 90 90 140 140 140
Hardness No HR 93.5 B HR 93 B HR 93 B HR 46 C HR 44.5 C HR 43.5 C
Mean Hardness HR 93 B
HR 45 C
Advantages: Test can be performed in only two to three minutes Sample can be used again
Precautions: No two values should be taken close to each other (on surface of material) The values should not be taken very close to the edge of material
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Job # 07 To perform Charpy’s impact test on given steel samples a) In Bending b) In Tension Objective: To measure the strength or response of material against impact loading
Equipment: Charpy’s impact testing machine Steel samples for tension and bending test
Related Theory: Types of loading: i.
Point load: It is a load which is localized to a specific location on a structure. It is also known as concentrated load.
ii.
Uniformly distributed load A load applied to a structure that is evenly distributed across the area where it is maintained. For example a lay-in ceiling tile…
iii.
Uniformly varying load It is a load which is varying uniformly (increasing or decreasing) from one side to the other of the beam. It is denoted by a triangle.
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iv.
Haphazard load It is a load which has different intensities at different points of the beam.
Haphazard Load
v.
vi.
vii.
Dead load A load which keeps on placed at the same place without changing its position. Like the load of chairs and table in the class room etc. Live load A load which keeps on moving from one point of the beam to the other point is known as the live load. For example load of a car or the load of a human being/animal. Impact Load: “The load which is applies momentarily is known as impact load.” “High intensity load applied for a short time like hammering, slapping etc.”
Modulus of toughness: “Energy stored per unit volume is known as modulus of toughness.”
Modulus of toughness =
Procedure: 1) First of all raise the liver of the machine. 2) Then release the liver and it will swing freely. 3) Note the angular measurement from the free swinging of the liver. Take this value of the angle as θ1. Now place the specimen in the machine. Raise liver again and release it. The liver will strike against the specimen. The height after placing the specimen will be decreased and the angle which will now be noted will be known as θ2. 9) From this ∆E will be calculated. 10) By dividing ∆E from V we will get modulus of toughness. 4) 5) 6) 7) 8)
Mechanism: ∆E = energy utilized to break the material ∆E = E1 + E2 E1 = mgh1 = mg {ho + R Sin ( θ1 – 90)}
R θ
h2
1
θ2
h1
E2 = mgh2 = mg {ho + R Sin (θ2 – 90)} 24
∆E = mg [{ho + R Sin (θ1 – 90)} - {ho + R Sin (θ2 – 90)}] ∆E = mg {ho + R Sin (θ1 – 90) - ho - R Sin (θ2 – 90)} ∆E = mg {R Sin (θ1 – 90) - R Sin (θ2 – 90)} ∆E = mg (R Cos θ2 - R Cos θ1) ∆E = mg R (Cos θ2 - Cos θ1)
Modulus of toughness =
Observations and Calculations: Mass = m = 22.9 Kg Radius = R = 0.7 m -1 Gravitational acceleration = g = 9.81 m s
Calculations for Bending Test: 3
Volume of Sample = 0.335 in = 0.00000548966644 θ1 = 136o θ2= 107o We know that: ∆E = mg R (Cos θ2 - Cos θ1) Putting the values: o
o
∆E = 0.0229 × 9.81 × 0.7 (Cos 107 - Cos 136 ) ∆E = 0.0671 joule
Modulus of toughness =
Modulus of toughness = 12.23K Pa
Calculations for Tension Test: 3
Volume of Sample = 0.25 in = 0.000004096766 θ1 = 139o θ2= 62o We know that: ∆E = mg R (Cos θ2 - Cos θ1) Putting the values: o
o
∆E = 0.0229 × 9.81 × 0.7 (Cos 62 - Cos 139 ) ∆E = 0.193 joule
25
Modulus of toughness =
Modulus of toughness = 46.9 K
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Job # 08 To find the flexural strength of a wooden sample Objective: To find modulus of rupture, wooden behavior in bending and effect of two point loading
Equipment:
10 Ton Buckton Universal Testing Machine Wooden beam Deflection gauges Steel ruler
Related Theory: Isotropic material: Isotropy is uniformity in all directions; it is derived from the Greek iso (equal) and tropos (direction). Shear Force (V): A force which is applied parallel to the sections is known as Shear force.
Shear strain (ɣ): The distortion produced by shear stress on an element or rectangular block is shown in the diagram. The shear strain is ɣ and can be measured as the change in right angle. It is measured in radians and is dimensionless quantity.
Shear stress (Tau)
The intensity of the internal resistance when the applied force is parallel to the section being sheared is called Shear Stress.
Types of shear: 3. Direct shear One way shear or single shear
One way shear is a shear in which there is only one plane of failure.
Stress = σ
=
27
Failure plane
P
P
Two way shear Two way shear or double shear is a shear in which there are two planes of failure.
Stress = σ
=
Failure planes
P/2
P
P/2
4. Punching shear The shear in which some part of same body slides is known is called as punching shear.
Bending Moment: A bending moment exists in a structural element when a moment is applied to the element so that the element bends.
Procedure: 1) 2) 3) 4)
We take a given wooden sample and take the measurement of its dimensions. Then this material is placed under the two point loading under the Universal Testing Machine. The three gauges are placed under the beam and their first readings are noted. The load is then increased by 0.1 ton at each successive reading and the measurements of the deflections gauges are noted. 5) As the beam breaks from the center, the maximum breaking load is noted. 6) Now calculations are made and the values of modulus of Rupture and modulus of Elasticity are
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calculated and a graph is drawn between load and deflection.
Observations and calculations:
12000
10000
8000
) n o t w e 6000 N ( d a o L
Load
4000
2000
0 0
1
2
3
4
5
6
Deflection (m.m.)
(Graph of Load and deflection)
Calculations: a = 150 mm = 0.150m l = 500 mm = 0.500m b = 50mm = 0.050m h = 50 mm = 0.050m Breaking Load = 1.25 Tons = 12262.5 N 2
Modulus of Rupture = f = 3.P.a / b.h 2
Modulus of Elasticity = E = 3a.l / 4 .bh
3
Form the Graph: Pˈ / d = 2,000 N / mm = 2,000,000 N / m Modulus of rupture = 44.1MPa Modulus of Elasticity = 9 MPa Comments
This experiment is utterly useful in understanding the behavior of wood beams under the action of load and a graphical representation of elongation with the increase of load can be seen which 29
