AE 362 – SPRING 2018

Experiment 1

EXPERIMENTAL STRESS ANALYSIS OF A SYMMETRIC WING

(due May 21st Monday)

Experiment report has to be prepared by groups of two people. Three people groups will

not be accepted. If you wish you can do the experiment by yourself. You need to submit

the reports in pdf to ODTUCLASS. Experiment reports will be submitted to turnitin

system to check for overlaps, direct copies etc. so do prepare your report yourself !

1. INTRODUCTION

Experiment is about strain measurement and accompanying stress calculation for a wing

structure which is loaded at the tip of the wing by a point force. This way you will have

chance to perform strain measurement on a lifting surface, learn how to calculate strain

induced from voltage readings which are read off the Wheatstone bridge and carry out

experimental stress analysis. Figure 1 shows the wing structure which is used as the test setup.

Figures 2-4 show the positions of the calibrated strain gages which are installed on the wing

structure. Wing structure is loaded from the wing tip by a load cell which applies and

measures the force applied to the wing structure. Figure 5 shows the load application points

on the front and rear spar and the load cell which is adjusted to load the wing from the front

spar location. The test set-up will be introduced in detail by the assistants during the test.

Test data will be collected by groups of 6 people. However, experiment groups will consist of

2 students. Experiment reports will be prepared by groups which have two students. Test

times will be adjusted according to the free times of the students during the week.

This document explains the format of the experiment report and explains the detailed

assignments. As Figures 2-4 show, there are 12 strain gages installed on the wing structure.

These strain gages are denoted by letters A-L. Strain gages EDC, HGF and IJK are in 45o

rosette configuration.

Strain gage A: placed on the upper flange of the front spar (inner face). It is in line with the

spar axis.

Strain gage B: placed on the lower flange of the front spar (inner face). It is in line with the

spar axis.

Strain gages EDC: placed on the web of the front spar (inner face). They are in 45o rosette

configuration.

Strain gages HGF: placed on the upper skin of the wing (inner face). They are in 45o rosette

configuration.

Strain gages IJK: placed on the lower skin of the wing (inner face). They are in 45o rosette

configuration.

Strain gage L: placed on the web of the rear spar (inner face). It is placed at the center of the

rear spar and perpendicular to the spar axis.

Figure 6 shows the dimensions of the wing structure, positions of the spars and strain gages

on the wing.

Figure 1. Wing structure test setup

Figure 2. Internal structural lay-out of the wing structure strain gage placements-1

Figure 3. Internal structural lay-out of the wing structure strain gage placements-2

Figure 4. Airfoil Strain Gage Orientation

Figure 5. Front and rear spar load application positions

Figure 6. Cross-section of the wing and spar positions (all dimensions are in mm)

Wing root

Wing tip

Leading

edge Trailing

edge

Connector of

the strain gages

Rear spar

Front spar

Strain gages are connected to Wheatstone bridge circuits which are placed in a control box.

Figure 7 shows the Wheatstone bridge of each strain gage. In Fig. 7, Rg corresponds to the

strain gage and R1-R3 are fixed resistances of 350 Ohm. The nominal value of Rg is also 350

Ohm but as the strain gage is loaded, Rg increases or decreases depending on the tensile or

compressive elongation.

Figure 8 shows the strain bridge controller which has Wheatstone bridge for each strain gage.

As Fig. 8 shows, the upper panel meter measures the load in terms of Pound force and bottom

panel meter shows the unloaded and loaded voltages across terminals B and D. So, for each

strain gage Vout=VB-VD is measured before and after loading.

Figure 7. Wheatstone bridge circuit (Vin=15000 milivolts)

Figure 8. Strain bridge control box

Bottom Panel Meter:

Displays the unloaded and

loaded output voltages of

Wheatstone bridge of each

strain gage (in milivolts)

Top Panel Meter:

Displays amount of load

applied to the structure

through Load Cell

Point Load Applicator.

Channel Knob:

Allows display of each

strain gage voltage

individually.

2. ASSIGNMENT 1

The strain values of each strain gage is calculated by the strain calculator which is linked in

this document. This calculator calculates the strain at the strain gage location by the following

relation.

GF

R/R gg (1)

where GF: is the gage factor. For the strain gages use 2.02.

gR : is the change in the resistance of the strain gage (either increase or decrease) due to

loading.

The change in the resistance of the strain gage can also be expressed in terms of voltage

difference and the above relation (1) can be put in the form given by (2). Prepare an excel

sheet (see Fig. 10) which calculates the strains based on Equation (2). That sheet will be your

strain calculator.

R

R

V*GF

V

21

4

(2)

where

unloadedin

out

Loadedin

outR

V

V

V

VV

where outV is shown in Fig.7 and it is equal to VB - VD. outV is what is read from lower panel

of the the strain bridge controller (Fig. 8). outV is in milivolts.

Vinput= 15000 milivolts.

In assignment 1, students are expected to derive the simplified equation (2) which gives the

strain over a strain gage for a quarter bridge (one strain gage and three fixed resistances). EE

309 knowledge is enough to carry out the derivation. In this part you are expected to make

the derivation and verify one of your test results by the strain calculator.

Hints: Note that gR is a very small change of the resistance and nominal value of Rg is

approximately same as the fixed resistances which are 350 Ohm. And, if the resistance of the

strain gage in the unloaded state is Rg, then in the loaded state it is Rg+ gR . Express gR

/Rg in terms of VR and use (1) to derive (2). Calculate VB-VD as VB-VA-(VD-VA) and

proceed.

3. ASSIGNMENT 2-Front Spar Loading

Step1: Prepare the wing for the test. (To save time wing structure will be made ready

beforehand )

Before the test, in order to prevent the sag of the wing due to its own weight, lift the free end

of the wing and crank the load cell to the point of application so that it just touches the wing

bottom. This state will be taken as the unloaded state of the strain gages. Try to bring the load

cell reading to about 10 lb. Take the unloaded voltage readings from the lower panel of the

control box by changing the channels from A to L. While taking the readings, after you

change the channels wait for some time until the voltage reading stabilizes, and record the

voltage values which are in milivolts.

Figure 9. Removing the sag of the wing and positioning the load cell

Step2: Load the wing structure by a force of 50 lb (222.4 N) through the front spar as shown

in Fig. 5. Record all the strain data from each channel (A-L). You should bring the load to 60

lb so that the difference will be 50 lb. While taking the readings, after you change the

channels wait for some time until the voltage reading stabilizes and record the voltage values,

which are in milivolts.

Step 3: Enter the unloaded and loaded strain values in the respective fields in the strain

calculator that you will create in MS Excel Sheet. Once all the readings are entered, record the

strain values of the strain gages A-L.

Figure 10. Strain calculator – MS Excel Sheet

Step 4: Determine the axial stresses at the strain gage locations A (upper flange of front spar),

B (lower flange of front spar) and L (middle of web of rear spar). Comment on their signs and

magnitudes. Do they make sense?

Step 5:

Determine the strains yx , and the shear strain xy at the strain gage locations on the

upper and lower skin (45o rosette configuration). x and y directions to be used for the

strain gages on the upper and lower skin are shown in Fig. 11, along with the positive

sense of the angle . Wing is made of Al alloy 2024-T3 which has Young’s modulus

of 73.1 GPa and Poisson’s ratio 0.33. Determine stresses yx , and the shear stress

xy at the strain gage locations on the upper and lower skin. Note that you have to use

2D plane stress stress-strain relations to determine the stresses. Look at your

elasticity book.

Determine the shear flow and its direction on the upper or lower skin strain gage

locations. (Show the direction of shear stress on the front face of the wing section. Use

the below figure or draw your own figure).

Does the direction of shear strain (or shear flow) make sense? Draw a small stress

element in x-y coordinate system, show the direction of the shear strain xy on this

stress element taken at the edge of the front face. Make sure that the sign of the shear

strain is correct with respect to the x-y axis that is established An example is given

below.

Direction check of the shear strain: By looking at the magnitude and direction of the

diagonal strains (that you measured during the test; for instance K and I shown

below ) comment if the direction of shear strain, that you have obtained by referencing

the x-y coordinate system, is correct or not.

Determine the principal strains/stresses and maximum shear strain/stress and their

directions at the 45o strain rosette locations on the upper and lower skin. Note that you

have to use 2D plane stress stress-strain relations to determine the principal stresses

from principal strains. Or you can determine principal stresses from x-y normal and

shear strains. Look at your elasticity book. Show the principal stresses on

representative stress elements placed on the upper and lower skin of the wing. Draw

the stress element by referencing the x-y coordinate system. Do the directions of the

principal stresses makes sense? Make comment.

x

y

x = J

y

xy

K

I

Figure 11. x and y directions to be used for the strain gages on the upper and lower skin

Step 6:

Determine the strains yx , and the shear strain xy at the strain gage location on the

web of the front spar. x and y directions to be used for the strain gages on the upper

and lower skin are shown in Fig. 12. The wing is made of Al alloy 2024-T3 which has

Young’s modulus of 73.1 GPa and Poisson’s ratio 0.33. Determine stresses yx , and

the shear stress xy at the strain gage locations on the web of front spar. Note that you

have to use 2D plane stress stress-strain relations to determine the principal stresses

from principal strains. Or you can determine principal stresses from x-y normal and

shear strains. Look at your elasticity book. Show the principal stresses on

representative stress elements placed on the web of the front spar of the wing. Draw

the stress element by referencing the x-y coordinate system. Do the directions of the

principal stresses makes sense? Make comment.

Determine the shear flow and its direction on the web of front spar. (Show the

direction of shear stress on the front face of the wing section. Use the below figure or

draw your own figure)

x y +

Figure 12. x and y directions to be used for the strain gages web of front spar

Step 7: Determine the bending stresses at the strain gage locations A,B, HGF and IJK by

assuming that wing is a cantilevered beam under tip loading through the front spar location.

Use symmetric beam bending formula (since wing is symmetric) to determine the bending

stresses at A, B, HGF and IJK. However note that the wing has short aspect ratio and the

location of the strain gages are close to the support location. In addition, front spar loading

will also induce torsion which will also create axial stresses in the strain gage locations since

the gages are not far away from the restraint end. So, beam assumption is not very accurate.

Therefore, do not expect to get close results with the experimental results. Experimental

results are more reliable since no assumption is made. One has to perform a detailed finite

element analysis to compare finite element results with the experimental results. However, by

making beam assumption and determining bending stresses at A, B, HGF and IJK we can get

an idea about the order of magnitude of the stresses, like if they are in the order of 10 MPa, 20

MPa, 50 MPa, 1-3 MPa etc.

To use the symmetric beam bending formula, first you have to determine the moment of the

inertia of the wing section by referencing Figure 6. Take the skin and webs into account in

calculating the moment of inertia of the wing section. You can approximate curved panels as

straight panels, some of which are shown below.

Note that thickness of rear spar flange is 1.59 mm, and thickness of the front spar flange is 1.7

mm. These values are also the thicknesses of the webs and the wing skin has a thickness of

0.64 mm. Therefore, structural idealization that we have used in the class is not suitable here

x

y

+

since spar flanges are very thin. In addition, as discussed above, the particular wing has low

aspect ratio and strain gages are considerably close to the restraint end.

In this step, students are expected to compare the experimentally determined axial (x direction)

stresses at strain gage locations A,B, HGF and IJK and compare them with the axial stresses

due to bending determined by the simple beam bending formula. Make the comparison in

terms orders of magnitude of the stress and sign of stresses (tensile and compressive).

In addition:

i- Compare the experimentally determined axial stress at A with the axial stress at HGF.

Which one is higher?

ii- Make the same comparison for the axial stress at A and at HGF which you have

determined from beam bending formula. Which one is higher?

iii- Is there a contradiction between your responses in i and ii such as:

axial stress at HGF (experimental) < axial stress at A (experimental)

axial stress at HGF (beam bending) > axial stress at A (beam bending)

If there is, comment on what could be the reason for this. Take a close look at the boundary

conditions (load application point and how the wing is fixed and comment on the

contradiction (if there is)

iv-Compare the axial stress (x direction stress) at strain gage location A

determined experimentally and calculated by the beam bending formula. Which one is

higher? Comment on the difference. What could be the reason for the difference?

Compare the axial stress at strain gage location G determined experimentally

and calculated by the beam bending formula. Which one is higher? Comment on the

difference. What could be the reason for the difference?

Step 8:

Draw the shear flow direction on the front spar web, upper skin and lower skin based on the

experimental results. (note that since we have rosette configuration strain gages on the front

spar web, upper and lower skin, we can determine shear strain only at these locations).

4. ASSIGNMENT 3-Rear Spar Loading

Repeat all steps of assignment 2 for loading through the rear spar.

5. ASSIGNMENT 4

Compare front and rear spar loadings.

-Which loading gives higher shear stress on wing skins? Does it make sense? Comment.

(Hint: Decide whether the shear center of the section is close to front and rear spar and make

your comment accordingly)

-Which loading gives higher normal stress on the flanges of the front spar? Does it make

sense? Comment.

-Which loading gives higher principal stress on the upper and lower skin of the wing? Does it

make sense? Comment.

Based on the comparison of the results you have obtained above which spar would be better

suited to mount the landing gear, from a load distribution point of view. Why?

6. REPORT FORMAT

Prepare your reports in the following format. Report should be typed, not hand-written.

DATE SUBMITTED:

TITLE OF THE DOCUMENT: Give an appropriate title

GROUP MEMBERS:

INTRODUCTION

Briefly introduce the experiment. Describe the test set-up. Use pictures as appropriate.

ASSIGNMENT 1

Summarize the derivation of the formula used in the strain calculator.

ASSIGNMENT 2 – Front spar loading

Report your responses Steps 1-8. Make clear headings and short explanations as to

what you are doing. If you use a book as reference indicate it by assiging a reference

number and list your references at the end of your report.

ASSIGNMENT 3 – Rear spar loading

Same as in assignment 2.

ASSIGNMENT 4 – Comparison of front and rear spar loading

Make your explanations about the questions asked in assignment 4 in this section.

CONCLUSION

Make a very brief summary of the objective of the test, what you have reported and

highlight conclusions that you think are important.