aircraft structures lab ii manual for auc r2008.pdf

8/10/2019 Aircraft Structures Lab II Manual for AUC R2008.pdf

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Dhanalakshmi Srinivasan Engineering College, Perambalur 621 212. AUC R2008

Gurunath KAE 2305 Aircraft Structures Laboratory II | 1

Aircraft Structures Laboratory II

List of Experiments

1.

Unsymmetrical Bending of Beams.

2.

Shear Centre Location for Open Sections.

3. Shear Centre Location for Closed Sections.

4. Constant Strength Beam.

5. Beam with Combined Loading.

6. Structural Behaviour of a Semi-Tension Field Beam (Wagner Beam).

7. Determination of Natural Frequencies of Cantilever Beams.

8. Stresses in Circular Discs using Photo elastic Techniques


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AIM:To determine the principal axes of an unsymmetrical section.

THEORY:

The well-known flexure formula = based on the elementary theory of bendingof beams assumes that the load is always applied through one of the principal axes of the

section. Actually, even if the applied load passes through the centroid and/or the shear centre

of the section, the plane of bending and the plane of loading need not necessarily are the same.

Therefore, a knowledge of the location of the principal axes is required for the determination

of the stress distribution in beams (of any arbitrary cross section) using flexure formula. Thedetermination of the principal axes experimentally is described here.

If Ix, Iyand Ixyare the moments and product of inertia of any section about an arbitrary

orthogonal centroidal axes OX and OY then the inclination of one of the principal axes toOX is given by 2 = () Eqn (1)

The experimental determination of the principal axes of a given section is based on the

fact that when the load passes through the shear centre and is in the direction of one of the

principal axes of the section, the entire section under the load deflects in the direction of theload only.

APPARATUS REQUIRED:

A thin uniform cantilever Z section as shown in figure. At the free end extension

pieces are attached on either side of the web to facilitate vertical loading.

Two dial gauges (to be mounted vertically and horizontally as in figure). This enables

the determination of displacements u and v.

Two hooks are attached to the extension pieces to apply the vertical load WV.

A string and pulley arrangement to apply the horizontal load WH.

A steel support structure to mount the channel section as cantilever.

FORMULA USED:

1. Theoretical calculation

2 = 2( )Where, Inclination of one of the principal axes

Moment about X axis

Moment about Y axis Product of inertia

Exercise No.: 01

Unsymmetrical Bending of BeamsDate:


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TABULATION:

WV = Height, h = Breadth, b = Thickness, t =

Sl. No.Horizontal Load

WH

Dial gauge readings

Remarks

u v

01

02

03

04

05

06

07

08

09

10

11


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2. Experimental calculation

=tan Where,

Vertical load of weight

Horizontal load of weightPROCEDURE:

1. Mount two dial gauges on the tip section to measure the horizontal and vertical

deflections of a point on it.

2. Apply the vertical load WV(about 2.4 kg, including two hooks of each 200 gm).

3. Read u and v the horizontal and vertical deflections respectively, at the chosen point.

4. Increase the load WH in steps of about 300 gm (for the first case 100 gm + 200 gm

hook) from zero to a maximum of about 3 kg noting down in each case the values of u

and v. Repeat the procedure and check for consistency in measurements.

5.

Plot the graphs vs and find the intersection of this curve with a straight linethrough the origin at 45. (Note: The X and Y scales must be chosen to be same for the

graph).

6. Calculate the inclination of one of the principal axes to the web as = t a n where WV and WHcorrespond to the point of intersection.

7.

Calculate the inclination using Eqn (1).

RESULT:

Thus the principal axis of an unsymmetrical section has been determined.


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Wa Wb

Dial gauge Dial gauge

Wa + Wb = WV

Determination of Shear Center


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TABULATION:

Length, L = Height, h = Breadth, b = Thickness, t =

WV = (Wa+ Wb) Distance between the two hook sections (AB) =

Sl. No. Wa Wb

Dial gauge readings

(d1-d2)

=

d1 d2

01

02

03

04

05

06

07

08

09

10

11


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3. Now remove one load piece from the hook at A and place another hook at B. This

means that the total vertical load on this section remains 2 kg. Record the dial gauge

readings.

4.

Transfer carefully all the load pieces and finally the hook one by one to the other hook

noting each time the dial gauge readings. This procedure ensures that while the

magnitude of the resultant vertical force remains the same its line of action shifts by aknown amount along AB every time a load piece is shifted. Calculate the distance e

of the line of action from the web thus: = 5.

For every load case calculate the algebraic difference between the dial gauge readings

as the measure of the angle of twist suffered by the section.6. Plot against e and obtain the meeting point of curve (a straight line in this case) with

the e-axis (i.e., the twist of the section is zero for this location of the resultant vertical

load). This determines the shear centre.

Theoretical location of the shear centre = +* Though a nominal value of 2 kg for the total load is suggested it can be less. In that event the

number of readings taken will reduce proportionately.

GRAPH:

Plot e versus (d1-d2) curve and determine where this meets the e axis and locate the

shear centre.

PRECAUTIONS:

I. For the section supplied there are limits on the maximum value of loads to obtain

acceptable experimental results. Beyond these the section could undergo excessive

permanent deformation and damage the beam forever. Do not therefore exceed the

suggested values for the loads.

II. The dial gauges must be mounted firmly. Every time before taking the readings tap the

set up (not the gauges) gently several times until the reading pointers on the gauges

settle down and do not shift any further. This shift happens due to both backlash and

slippages at the points of contact between the dial gauges and the sheet surfaces andcan induce errors if not taken care of. Repeat the experiments with identical settings

several times to ensure consistency in the readings.

RESULT:

The shear centre obtained experimentally is compared with the theoretical value.


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Wa Wb

Dial gauge Dial gauge

Determination of Shear Center- Closed section


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AIM:

To determine the shear centre of a closed section.

THEORY:

For any unsymmetrical section there exists a point at which any vertical force does not

produce a twist of that section. This point is known as shear centre.

The location of this shear centre is important in the design of beams of closed sections

when they should bend without twisting. The shear centre is important in the case of a closed

section like an aircraft wing, where the lift produces a torque about the shear centre. Similarly

the wing strut of a semi cantilever wing is a closed tube of aerofoil s ection. A thin walled D

section with its web vertical has a horizontal axis of symmetry and the shear centre lies on it.

The aim of the experiment is to determine its location on this axis if the applied shear to the tip

section is vertical (i.e., along the direction of one of the principal axes of the section) and passes

through the shear centre tip, all other sections of the beam do not twist.

APPARATUS REQUIRED:

A thin uniform cantilever beam of D section as shown in the figure. At the free end

extension pieces are attached on either side of the web to facilitate vertical loading.

Two dial gauges are mounted firmly on this section, a known distance apart, over the

top flange. This enables the determination of the twist, if any, experienced by thesection.

A steel support structure to mount the channel section as cantilever.

Two loading hooks each weighing about 200 gm.

PROCEDURE:

1. Mount two dial gauges on the flange at a known distance apart at the free and of the

beam. Set the dial gauge readings to zero.

2. Place a total of, say two kilograms load at A (loading hook and nine load pieces will

make up this value). Note the dial gauge readings (nominally, hooks also weigh a 200

gm each).3. Now remove one load piece from the hook at A and place another hook at B. This

means that the total vertical load on this section remains 2 kg. Record the dial gauge

readings.

4. Transfer carefully all the load pieces and finally the hook one by one to the other hook

noting each time the dial gauge readings. This procedure ensures that while the

magnitude of the resultant vertical force remains the same its line of action shifts by a

known amount along AB every time a load piece is shifted. Calculate the distance e

of the line of action from the web thus:

=

5.

For every load case calculate the algebraic difference between the dial gauge readingsas the measure of the angle of twist suffered by the section.

Exercise No.: 03

Shear Centre of Closed SectionsDate:


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6. Plot against e and obtain the meeting point of curve (a straight line in this case) withthe e-axis (i.e., the twist of the section is zero for this location of the resultant vertical

load). This determines the shear centre.

* Though a nominal value of 2 kg for the total load is suggested it can be less. In that event thenumber of readings taken will reduce proportionately.

GRAPH:

Plot e vs (d1-d2) curve and determine where this meets the e axis and locate the shear

centre.

PRECAUTIONS:

I. For the section supplied there are limits on the maximum value of loads to obtain

acceptable experimental results. Beyond these the section could undergo excessivepermanent deformation and damage the beam forever. Do not therefore exceed the

suggested values for the loads.

II. The dial gauges must be mounted firmly. Every time before taking the readings tap the

set up (not the gauges) gently several times until the reading pointers on the gauges

settle down and do not shift any further. This shift happens due to both backlash and

slippages at the points of contact between the dial gauges and the sheet surfaces and

can induce errors if not taken care of. Repeat the experiments with identical settings

several times to ensure consistency in the readings.

RESULT:

The shear centre obtained experimentally is compared with the theoretical value.


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Constant Strength Beam


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AIM:

To determine the stress at various locations along the length of a constant strength beamto show that they are equal and compare with theoretical values.

THEORY:

The aerospace structures engineer is constantly searching for types of structures which

will save structural weight and still provide a structure which is satisfactory from a fabrication

and economic standpoint. One such structure is constant strength beam. A beam in which

section modules varies along the length of the beam in the same proportion as the bending

moment is known as constant strength beam. In this case the maximum stress remains constant

along the length of the beam.

bwidth of the beamLlength of the beamh depth of the beam

Section modulus, = =

= =

Let the width of the beam be constant and the depth varies. Then

= = 6 = 6 = = .. Eqn (1)

APPARATUS REQUIRED:

A constant strength beam in which the depth varies as in Eqn (1) and made of

aluminium. Strain gauges, strain indicator and weights with hook.

PROCEDURE:

The constant strength beam is fixed as a cantilever strain gauges are fixed near the root,

at and . The strain gauges are fixed both on the top and bottom surfaces at each location

to increase the circuit sensitivity of the strain gauge circuit. Hence half bridge used in the strain

indicator to measure the strain at each location (strain = strain meter reading x 2). The beam

loaded gradually in steps of 2 kg up to 10 kg by placing the weights slowly in the hook near

the tip of the cantilever (loading hook weight 0.25 kg is to be added). The strain gauge readings

are noted for every 2 kg at locations A, B, C and tabulated as given below.

Strain gauge resistance = 350 ohm

Gauge factor = 2Youngs modulus, E = 70 GPa

Exercise No.: 04

Constant Strength BeamDate:


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TABULATION:

Sl. No. Weight(Kg) = (MPa) = (MPa) = (MPa)01

02

03

04

05


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THEORETICAL CALCULATION

At point A:

Distance of point A from loading point =

Depth of the beam =

Width of the beam =

Moment of inertia =

Moment =

= =At point B:

Distance of point B from loading point =

Depth of the beam =

Width of the beam =

Moment of inertia =

Moment =

=

=

At point C:

Distance of point C from loading point =

Depth of the beam =

Width of the beam =

Moment of inertia =

Moment =

= =

RESULT:

The experimental values of the stress are compared with the theoretical values.


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TABULATIONS:

Youngs modulus of the tube =

Outside diameter of the tube =

Thickness of the tube =

Length of the tube =

Strain gauge resistance =

Gauge factor =

Distance of the strain gauges near root from tip =

Distance of the strain gauges at the middle from tip =

Distance from the centre of the tube to the centre of the hook =

Weight of the hook =

Sl. No. Weight(Kg)

01

02

03

04

05


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tan2= = (4)Where,

Principal angle

APPARATUS REQUIRED:

Hollow circular shaft fixed as a cantilever, weight hanger with slotted weights, strain

gauges, connecting wires, strain indicator and micrometre.

PROCEDURE:

Two strain gauges are fixed near the root of the tube fixed as a cantilever, one on the

top fibre and the other at the bottom to measure the bending strain. Another strain gauge is

fixed at the same location on the neutral axis at 45 to measure the shear strain. Similarly three

more strain gauges are fixed at the middle of the length to verify the result at various locations

of the tube. The strain gauges on the top and bottom of the tube are connected to half bridge

circuit in the strain indicator to increase the circuit sensitivity, since the tension and

compression get added up. The strain gauge at 45 is connected to the quarter bridge of the

strain indicator to measure the shear strain. The outside diameter of the tube is measured using

vernier callipers. Weights are added to the hook attached to the lever in steps of 2 kg and the

strain gauge readings are noted from the strain indicator for each load. From the strains the

bending stress, shear stress are calculated and hence principal stresses and principal angle are

calculated. These values are compared with theoretical values.

NOTE:

For half bridge the strain readings are multiplied by 2 and for Quarter Bridge by 4 to

get the actual strains.

RESULT:

Bending stress at the root (A) =

Shear stress at (B) =

Experimental:

Principal stresses at the root =

Principal angle at the root =

Theoretical:

Principal stresses at the root =

Principal angle at the root =


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Wagner Beam


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AIM:To investigate and study the behaviour of a semi-tension field beam.

THEORY:

The development of a structure in which buckling of the web is permitted with the shear

loads being carried by diagonal tension stresses in the web is a striking example of the departure

of the design of aerospace structures from the standard structural design methods in other fields

of structures, such as beam design for bridges and buildings. The first study and research on

this new type of structural design involving diagonal semi-tension field action in beam webs

done by Wagner and hence Wagner beam.

As thin sheets are weak in compressions, the webs of the Wagner beam will buckle at

a low value of the applied vertical load. The phenomena of buckling may be observed by

nothing the wrinkles that appear on the thin sheet. As the applied load is further increased, the

stress in the compression direction does not increase, however the stress increase in the tension

direction. This method of carrying the shear load permits the design of relatively thin webs

because of high allowable stresses in tension.

According to the theory developed by Wagner, the diagonal tensile stress t in thethin

web is given by the expression

= ............... Eqn (1)Where,W Shear loadd Distance between the CG of the flangest Thickness of the web Angle at which wrinkling occurs

tan = + +

............... Eqn (2)Where,

b Distance between stiffenersAF Area of flangeAS Area of stiffener

Exercise No.: 06

Structural Behaviour of a Semi-Tension Field BeamDate:


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Stress in the Flange = ............ Eqn (3)Stress in the stiffener

=

tan ............ Eqn (4)

APPARATUS REQUIRED:

A stiffened thin-webbed cantilever beam held in a suitable frame, strain gauges, strain

indicator, hydraulic jack, load cell and load indicator.

PROCEDURE:

The wrinkling angle is calculated using the Eqn (1) and a strain gauge is fixed at this

angle in the web. Strain gauges are also fixed on the flanges and a stiffener to measure their

respective stresses. The load is applied gradually in steps of 100 kg using the hydraulic jack.

For each load the load indicator reading, strain indicator reading corresponding to each straingauge is noted. Precaution is taken so that the beam does not undergo any permanent

deformation. Hence the beam is not loaded up to wrinkling load. The readings are tabulated as

given below

The strain gauges are connected in Quarter Bridge and hence the strain indicator

readings are to be multiplied by 4 to obtain the actual strain.

RESULT:

t, F and S values are calculated theoretically using Eqns (1),(3) and (4) andcompared with the experimental values given in the table.


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Fig. 7.1.A cantilever beam

Fig. 7.2.The cantilever beam under free vibration

Fig. 7.1 shows of a cantilever beam with rectangular cross section, which can besubjected to bending vibration by giving a small initial displacement at the free end; and

Fig. 7.2 depicts of cantilever beam under the free vibration.


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Fig. 7.3.The first three undamped natural frequencies and mode shape of cantilever beam


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We have following boundary conditions for a cantilever beam.

= 0, =0, = 0

= , =0, = 0For a uniform beam under free vibration from equation (1), we get

= 0where,

=

The mode shapes for a continuous cantilever beam is given as

= {sin s in hsin s in h cos cos hcos cos h}where,

=1,2,3 = A closed form of the circular natural frequency, from above equation of motionand boundary conditions can be written as,

= where,

=1.875,4.694,7.885

RESULT:

First Natural Frequency Second Natural Frequency Third Natural Frequency

= = =


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Fig. 8.1.Disk in compression

Fig. 8.2.Stress distribution along horizontal diameter


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AIM:To obtain the stresses in circular discs and beams using photo elastic techniques.

THEORY:

A common calibration specimen is the circular disk of diameter D and thickness loaded in diametral compression (Fig. 8.1).

The horizontal and vertical normal stresses along the x axis are principal stresses

because the shear stress

vanishes due to symmetry about the x axis. Also,

is positive,

while is negative. We therefore take = and = so as to render 0. Fromtheory of elasticity, the solutions for the normal stresses along the horizontal diameter are (afterDally and Riley 1991).

= 2 1

1

= 6

1 1 13

1

where

= = 2 These stresses are plotted in Fig. 8.2. Along the horizontal diameter, the maximum

difference occurs at the centre, that is, at = 0. At this point, = 8

Combining this result with the basic photo elastic relation gives

= = 8or

= 8 Notice that the specimen thickness does not appear in this equation. The reason is

that the relative retardation is proportional to, but for a given force P, the stresses areinversely proportional to. The net effect is a result forthat is independent of.

Exercise No.: 08

Stresses in Circular Discs using Photo elastic TechniquesDate:


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Fig. 8.3.Light-field isochromatics in a diametrally loaded circular disk.

Fig. 8.4.Enhanced image using only the green component of the light used in Fig. 8.3.


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aircraft structures lab ii manual for auc r2008.pdf

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