Aircraft Structures Lab- I

AIRCRAFT STRUCTURES LAB – I

EXPERIMENT NO. 1

DETERMINATION OF YOUNGS MODULUS OF STEEL

USING MECHANICAL EXTENSOMETER

AIM

To verify Hooke‟s Law for steel specimen under tension test.

To find Young‟s Modulus for steel

To draw stress – strain diagram up to proportional limit

THEORY

Hooke‟s Law states that “within the limits of elasticity the strain produced is

proportional to the applied stress.

Let the applied tensile load on the specimen be P (N).

& the area of cross section of specimen be A (mm2)

Then the normal stress σ = P / A N / mm2

Let the gauge length of the specimen be L

& the elongation due to the load P be Δ L

Then the normal strain = Δ L / L

By Hooke‟s Law σ

= E

Where E is a constant of proportionality, termed as Young‟s Modulus or Modulus of

elasticity of the material.

If the plot of the stress Vs. strain is straight line, the Hooke‟s Law is verified.

APPARATUS REQUIRED

U.T.M., Double dial gauge extensometer, Vernier caliper and tensile test specimen

KNOWLEDGE OF THE INSTRUMENT

A Double dial gauge extensometer is a mechanical one to measure the strain in a

specimen that undergoes deformation.

Many extensometer utilize the dial indicators directly for strain measurement, as

illustrated in Fig.1

Such extensometers usually employ two or more dial indicators mounted in a frame,

which is attached to the test piece. A second frame is fixed at a set gauge length and their

relative motion is measured as strain. The spring loaded frames are usually secured to the

specimen through pointed screws or “knife edge” contacts. Reasonable accuracy in measuring

unit strains can be obtained using proper dial gauges.

PROCEDURE:

PRESENTATION OF DATA

1. Extensometer – Double Dial Gauges:

Gauge Length = mm

Value of each division = mm

2. Specimen

Material:

Cross-section: Rectangular – Width - w = mm

Thickness - t = mm

Area - A = wxt = mm2.

Circular – Diameter - d = mm

Area - d2 / 4 = mm

2.

RESULTS & CONCLUSIONS

A graph is plotted between stress and strain values at different values of loads.

Young‟s Modulus for steel, is found by measuring the slope of the stress – strain

diagram.

ASSESSMENT QUESTIONS

1. What is ASTM?

2. What is gauge length?

3. What are the mechanical properties that can be obtained from a typical tension test?

4. Define resilience and how will you measure it?

5. What are the advantages and limitations of Double dial gauge extensometer?

6. Draw typical stress strain diagram for cast iron for tensile and compressive loads.

EXPERIMENT NO. 2

DETERMINATION OF YOUNGS MODULUS OF ALUMINIUM

USING ELECTRICAL EXTENSOMETER

AIM

To verify Hooke‟s Law for Aluminium specimen under tension test.

To find Young‟s Modulus for Aluminium

To draw stress – strain diagram up to proportional limit

THEORY

Hooke‟s Law states that “within the limits of elasticity the strain produced is

proportional to the applied stress.

Let the applied tensile load on the specimen be P (N).

& the area of cross section of specimen be A (mm2)

Then the normal stress σ = P / A N / mm2.

The change in length per unit length, which is defined as strain , is measured by using

electrical resistance type strain gauges along with strain indicator.

By Hooke‟s Law σ

= E

Where E is a constant of proportionality, termed as Young‟s Modulus or Modulus of

elasticity of the material.

If the plot of the stress Vs. strain is straight line, the Hooke‟s Law is verified.

APPARATUS REQUIRED

U.T.M., strain gauges, strain indicator, specimen.

ELETRICAL STRAIN GAUGES:

An electrical resistance wire strain gauge is composed of a grid of fine wire (about

0.025 mm in diameter) laid in a preferential direction and bonded between two sheets of very

thin paper or plastic. The gauge can also be made of thin foil or a semi conducting material.

The gauge is cemented to the specimen at a particular point of interest.

STRAIN INDICATOR

When the specimen is loaded, the resulting deformations produce a change in the

diameter and length of the wires or the thickness and length of the foils in the grid of the gage,

which in turn changes the gauge ohmic resistance. Proper instrumentation permits this

resistance change to be precisely determined, and suitable calibration of the gauge enable the

resistance change to be converted to strain.

PROCEDURE:


Specimen

Material:

Cross-section: Rectangular – Width - w = mm

Thickness - t = mm

Area - A = wxt = mm2.

Circular – Diameter - d = mm

Area - d2 / 4 = mm

2.

Sl.No. Load P (N) Stress (N / mm2) Strain (mm / mm)

RESULTS & CONCLUSION

A graph is plotted between stress and strain for different values of loads.

Young‟s Modulus for aluminium, is found by measuring the slope of the Stress- strain

diagram.


1. What are the different types of strain gauges?

2. List down the materials that are used for strain gauges?

3. What is Wheatstone bridge?

4. What are active and dummy gauges?

5. What are the advantages and limitations of the strain gauge technique?

6. How will you increase the sensitivity of a Wheatstone bridge?

EXPERIMENT NO. 3

DEFLECTION OF CANTILEVER BEAM

GENERAL OBJECTIVE

To determine the deflections at various points of beams with different types of supports

using dial gauges.

SPECIFIC OBJECTIVE

To determine the deflections at various locations in a cantilever beam.

To compare the results with theoretical calculations.

To draw deflection curve.

NEED AND SCOPE OF THE EXPERIMENT

This experiment is for obtaining deflection of a cantilever beams, subjected to lateral

loads, by using dial gauges. Experimental results obtained from such simple tests are compared

with theoretical calculations.


The apparatus required are mechanical dial gauges, screw-gauge, Vernier caliper, steel

and wooden beam specimen.

Dial indicators are smaller indicating devices containing a graduated dial scale along

with gear and pinion or level magnification system. When dial indicator is used as essential

part in the mechanism of any set – up for „comparison‟ measurement purpose, it is referred to

as dial gauge.

WORKING MECHANISM OF DIAL INDICATOR

The necessary high magnification ratio in this instrument is achieved by the use of gear

and pinion arrangement by arranging the gear train in a manner similar to a clock movement.

There is a plunger, which is a perfect sliding fit in its own bearings. This carries a rack, which

accurately meshes with a pinion, A shown in the figure. The rotation of the plunger about its

own axis is prevented by a pin attached to it, which to it, which is located in a slot in a rack

guide G. In order to keep the plunger in an extended or normal position a light coil spring S is

employed. The spring exerts a pressure of approximately 60z. A small movement of the

contact point causes the rack to turn to the pinion. A with which it is meshed. A large gear B is

attached to the same spindle as pinion A. The gear B is attached to the same spindle as pinion

A. The gear B is further meshed with a pinion C, which thus magnifies the movement of pinion

A. Attached to the second pinion C is another gear D which meshes with a third pinion E

mounted on the same spindle as the indicator pointer. The overall magnification of final pinion

is this (TD / TE) x (TB / Te) where TB, Te etc., represent the number of teeth of gears B and C

respectively. This magnification is further enlarged at the tip of the pointer by an amount

dependent upon its length. The overall magnification for any dial gauge may be thus calculated

by measuring the distance between divisions on the scale and dividing this dimension by the

equivalent movement of the measuring plunger.

If the pointer makes more than one revolution, a revolution counter is also incorporated

which will correctly indicate the number of revolutions made by the main printer and thus

enable a complete reading to be made when the gauge is used for direct measurement.

s

A

B

C

D

E

F

G

S

H

RACK

BUCK

LUG

STEM

PLUNGER

CONTACT POINT

BEZEL

BEZEL

CLAMP

PROCEDURE:


Young‟s Modulus of the beam material E =

Area Moment of Inertia of the beam I =

Length of the beam L =

Sl.No. Load (N)

Deflections (mm)

Experimental Theoretical

Location

1

Location

2

Location

3

Location

1

Location

2

Location

3

1.

2.

3.

4.

RESULTS

(i) The deflections at various locations of the beam are measured.

(ii) The values are compared with theoretical calculations.

(iii) The deflection curves are plotted.

ASSESSMENT QUESITONS

1. What are the advantages of dial gauges?

2. What are the limitations of dial gauges?

3. What are the tip deflections for a cantilever beam of length L and rigidity EI subjected to,

a) a tip load P.

b) a uniformly distributed load Q.

c) a concentrated load at mid span.

4. How will you measure the rotation at the tip of the cantilever?

5. Explain various methods to obtain the deflection of a beam.

EXPERIMENT NO. 4

DEFLECTION OF SIMPLY SUPPORTED BEAM

GENERAL OBJECTIVE

To determine the deflection of a simply supported beam using Dial gauges.

(i) To determine the deflection of a simply supported beam at various locations

(ii) To compare the deflection values with the theoretical calculations.

(iii) To draw the deflection curves.


The apparatus required are mechanical dial gauges, screw – gauge, vernier calipers,

beams and mounting frame.


Young‟s Modulus of the beam material E =

Area Moment of Inertia of the beam I =

Length of the beam L =

Sl.No. Load (N)

Deflections (mm)


Location

1

Location

2

Location

3

Location

1

Location

2

Location

3

1.

2.

3.

4.

PROCEDURE

RESULTS

(i) The deflections at various locations of the beam are measured

(ii) The values are compared with theoretical calculations.

(iii) The deflection curves with theoretical and experimental values are plotted.


1. Write down the equation for the deflection curve of a simply supported beam

subjected to a concentrated load at the mind span of the beam.

2. Write the expressions for deflection at the midpoint and slope at the supports of a

simply beam subjected to

(i) Uniformly distributed load

(ii) Concentrated load at mid span

3. What is a conjugate beam?

4. What is contraflexsure?

5. Obtain the relationship among the shear force, bending moment and the loading in a

beam.

EXPERIMENT NO. 5

VERIFICATION OF MAXWELL’S RECIPROCAL THEOREM

AIM

To verify Maxwell‟s Reciprocal Theorem for a Cantilever and Simply Supported

Beams.

THEORY

Consider a beam shown in Fig.1 and select two points 1 and 2 anywhere in the beam.

Apply a load W at station 1.

The work done by this load W over the displacement 11 at station 1 = W 11

11

Now without removing the load W at station 1, apply another load of the same

magnitude W at station 2.

Then the work done by this load W at stations 2 and 1

= W 22 + W 12

Then total W.D. by both the loads acting at 1 and 2

W.D. Total = W 11 + W 22 + W 12

Now change the order of the loading. First, apply the load W at station 2.

Then work done by this load over the displacement at 2.

= W 22

(2) (1)

W

(2) (1)

W W

Now without removing the load from 2, apply another load of the same magnitude W at

station 1.

Then the work done by this load W at stations 1 and 2 = W 11 + W21

Then the total W.D by both the loads acting at 1 & 2

W.D. Total = W 22 + W 11 + W 21

The total work done by both the loads does not change when the sequence of

application of loads is changed.

By equating the total work done, we obtain

= W 11 + W 22 + W 12 = W 22 + W 11 + W 21

12 = 21

That is the deflection at station 1 due to load at station 2 is equal to the deflection at

station 2 due to the same load at station 1. = W 22 + W 11 + W 21

Hence Maxwell‟s Reciprocal Theorem is verified.

APPARATUS REQUIRED

Dial Gauges, weights, meter scale, cantilever and simply supported beam specimens.

(2) (1) W

W (2) W (1)

PROCEDURE


A – CANTILEVER BEAM

SPECIMEN – Mild Steel Length = 60 cm.

Load (N) Deflection j

Station i

Deflections (mm)

1 2

1 11 21

2 12 22

B – SIMPLE SUPPORTED BEAM

Load (N) Deflection j

Station i

Deflections (mm)

1 2

1 11 21

2 12 22

RESULTS AND CONCLUSIONS

Maxwell‟s reciprocal theorem is verified.


1. State Betti‟s Theorem.

2. State Maxwell‟s reciprocal theorem.

3. What are the assumptions made in deriving Betti‟s Theorem?

EXPERIMENT NO. 6

VERIFICATION OF PRINCIPLE OF SUPER POSITION

AIM

To verify the principle of superposition using a cantilever beam.

THEORY

Principle of superposition states that “Separate effects of various loads or strains on a

structure or a body, applied singly, can be superimposed or algebraically added to give the total

effects of all the loads, applied at the same time”.

This principle is applicable to most of the elastic deformation problems provided the

load-deformation relation is linear and deformation due to each load is too small to produce a

marked change in the geometry of the structure and the deflections measured in the same

direction in which the loads are applied.

The principle of superposition has wide applications in the analysis and design of

structures.

APPARATUS REQUIRED

Dial gauges, weights, meter scale, steel beam specimen.

1

2

+

3

+

= 3 2 1

PROCEDURE


A. CANTILEVER BEAM

Sl.No. Load P (N) Deflection (mm)

Station 1 Station 2 Station 3 Station 1 Station 2 Station 3

1 0 0 11 21 31

0 1 0 12 22 32

0 0 1 13 23 33

1 2 3

Total 1 1 1 1 2 3

B. SIMPLY SUPPORTED BEAM

Sl.No. Load P (N) Deflection (mm)

Station 1 Station 2 Station 3 Station 1 Station 2 Station 3

1 0 0 11 21 31

0 1 0 12 22 32

0 0 1 13 23 33

1 2 3

Total 1 1 1 1 2 3

RESULTS AND CONCLUSIONS

The principle of superposition is verified for a Cantilever and Simply Supported

Beams.


1. State the principle of superposition.

2. What are the applications of principle of superposition?

3. What are the limitations of the above theorem?

4. Find the mid-span deflection of a S.S.B. subjected to u.d.1. and a concentrated load at

the centre using the above theorem.

5. Find the tip deflection of a cantilever subjected to a concentrated load P at the tip and a

moment Mo (Clock-wise) at the mi

EXPERIMENT NO. 7

DETERMINATION OF FAILURE LOADS OF COLUMNS

AIM

To obtain the failure load for a column with different and conditions.

THEORY:

Slender long members under compression are referred as columns. They, at much

smaller load, buckle laterally and would collapse due to the phenomenon called structural

instability. The failures load is called the critical load or buckling load. It depends on the

flexural rigidity EI, length of the member and the support end conditions.

The governing differential equation for a member at the critical loading condition is

EI d2y / dx2 = -Mx. The solution for this equation will yield the critical load values as

Pcri = 2EI / ℓ2

for a pin-pin ends.

Pcri = 4 2 EI / ℓ2

for a fixed-fixed ends.

APPARATUS REQUIRED

Column Test Apparatus with load indicator, specimens made of different materials and

diameters.

KNOWLEDGE OF THE APPARATUS

The column test rig consisting of two vertical steel tubular members with cross heads at

the top and bottom. The cross heads have the provisions to change the support conditions. The

load is applied by means of a screw jack to the specimen which passes through a strain gauge

based load cell. The output of the strain gauge is calibrated against loads which will be

digitally displayed. A circular ring has also been provided at e middle of the specimen to

prevent undue lateral deflection of the column when buckling occurs.

PROCEDURE


Column Material :

Diameter :

Length :

I. Pin-Pin Column

Material Diameter

(mm)

Length

(mm)

Buckling load (N)

Theoretical Experimental

Stainless steel

Brass

Aluminium

II. Fixed-Fixed Column

Material Diameter

(mm)

Length

(mm)

Buckling load (N)

Theoretical Experimental

Stainless steel

Brass

Aluminium

RESULTS

The critical loads for different materials and end conditions have been obtained

experimentally and the values have been compared with the theoretical values.


1. Define tie, beam and column.

2. Explain how an ideal column fails.

3. Differentiate between long and short columns.

4. Define slenderness ratio and explain its usefulness in column design.

5. What is end fixity coefficient?

EXPERIMENT NO. 8

DETERMINATION OF COLUMN FAILURE LOAD USING

SOUTH WELL’S PLOT

AIM

To determine the failure load of a column using South Well‟s plot.

THEORY

A long slender member under compression loses the stability when the load reaches the

buckling load. For ideal column at the time of buckling, the lateral deflection, mathematically,

becomes infinity R.V. South Well has suggested a method by which one can obtain

experimentally the critical load without actually making the column buckle.

This method is based on the assumption that the deflection of a column, under a load

that is below the critical value, is due to the initial curvature. The deflection at x = ℓ / 2 at

various stages of loading is given by

( /p) Pcri - = a1

Where P is the load at any instant,

the corresponding lateral deflection and

a1 a constant.

Plotting ( /p) Vs as a straight line, the inverse of the slope of the line gives the value

of the critical load.

/p

a1

PROCEDURE

APPARATUS REQUIRED

Column Test Apparatus with load indicator, specimens made of different materials and

diameters.

PRESENTATION DATA

Column Material :

Diameter :

Length :

End condition Pin-Pin column

Sl.No. Load (N) Deflection (mm) /p Critical load (N)


1.

2.

3.

RESULTS

The critical load has been obtaining experimentally and compared with theoretical

value.


1. What is a short column?

2. Write down a few short column formulae.

3. What is a beam column? Is principle of superposition valid for beam columns?

4. What is the characteristic equation for a column with one end fixed and the other the

other end pinned? Explain the method to obtain the critical load for that column.

5. Explain the energy method of obtaining critical load of a column.

EXPERIMENT NO.9

DETERMINATION OF FAILURE LOADS OF RIVETED JOINTS

AIM

To determine failure loads and study the corresponding failure modes of riveted joints.

THEORY

Joints are normally designed to transfer loads from one member to another through

welds, bolts and rivets.

Welded joints permanent one where as bolted joint is a temporary joint. The riveted one

is treated as a semi-permanent joint. Basically there are two types of riveted joints:

Lab joints wherein the rivets are under single shear

Butt joints with double straps in which they are under double shear. There could be multiple

rows of rivets which are of either chain type or zigzag type.

The riveted joints may fail in any one of the following modes:

1. Tension or tearing failure of the plates between the holes if the rivets are very close to

each other. (Fig. i)

2. Shearing failure of the plate between the edge of the plate and rivet hole, i.e., the hole is

too nearer to the edge. (Fig.ii)

3. Bearing failure of the plate, that is, the effect of rivet on the plate.

4. Crushing failure of the plate or the rivet. (Fig. iv)

5. Shearing failure of the rivet if the diameter of the rivet is smaller than the required

value. (Fig. iii)

DESIGN ANALYSIS OF A JOINT

The plate may failure by tension along the weakest section. Tearing resistance of a plate

between rivet holes P = (p-d) t t.

Where p = pitch of the riveted joint

d = diameter of the rivet

t = thickness of the plate

and t = tensile strength of the plate.

Shearing resistance of the plate

P = 2 et.

Where e = edge distance

t = thickness of the plate

= shear strength of the plate.

Bearing resistance of the plate

P = d.t. br

Where br = Bearing strength of the plate

Crushing resistance of the plate

P = d.t. cr

Where cr = Bearing strength of the plate

Shearing resistance of the rivet

For single shear P = d2 / 4.

(Lap joint)

And for double shear P = 2 d2 / 4.

Where = shearing strength of the rivet.

P i)

P ii)

P iii)

P iv)

P v)

APPARATUS REQUIRED

U.T.M., Specimens with lap and butt joints.


Loading range of the UTM =

Material of the rivet =

Material of the plate =

Yield strength of the plate

material =

Yield strength of the rivet

material =

Rivet diameter =

PRESENTATION OF RESULTS

Sl.No. Type of

joint

Rivet

diameter

(mm)

Plate

thickness

(mm)

Number of

rivets

Plate

width

Failure

mode

RESULTS AND CONCLUSION

The various failure modes of riveted joints were studied.


1. What are the different types of rivets used in aircraft practice? Sketch them.

2. Suggest some materials for aircraft rivets.

3. What are the advantages of riveting over welding techniques?

4. Where do you use bolted joints in an aircraft?

5. What type of riveted joints that are used in pressure vessels? Give reasons.

Aircraft Structures Lab- I

Documents

Transcript of Aircraft Structures Lab- I