structures lab finl copy
TRANSCRIPT
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 1
Experiment – 1
Deflection of a Simply Supported Beam
Aim: To determine the deflection of a simply supported beam.
Apparatus: Beam Test Set-Up with Load cells, steel scale, caliper, flat
beam, load indicator and dial gauge.
Scale
Gear box
Pointer
Hand wheel
Load
Loadindicator
Simply supportedbeam
Dialgauge
Fig. 1: Schematic layout of a beam setup Theory:
A beam shown in fig-2 shows the section which is simply supported at
the ends and is subjected to bending about its major axis with a concentrated
load anywhere in the beam. The beam is provided with strain gauge, the
deflection of the beam can be determined whenever the load is applied on
the beam. Strain gauge values may be noted for several further works
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 2
.
Deflections are given by following expressions; students may derive these
expressions using Unit Load Method or Castigliano`s Theorem.
Yx = W b [ (L2 –b
2) x –x
3] /(6 E I L) for 0<x<a
Yx = W b [ X3 – L/b (x-a)
3 - (L
2-b
2) x ] /(6 E I L) for a < x <L
Where,
W is the load placed at a distance `a` from the left support in Newton
L = span of the beam in mm
Yx = deflection at any point distance x from left end
I = moment of inertia of the beam in mm4 (Ixx)
E= Young’s modulus in N/mm2
Procedure:
Find the moment of inertia of beam from the following expression:
(1/12) b1 d1 3, where b1 is width of beam and d1 is depth.
Place the beam supporting from two wedge supports. The load position can
be varied. Set the load cell to read zero in the absence of load. Set the
deflection gauge to read zero in the absence of load.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 3
Load the beam with 0.25 Kg. Note deflections before and after the load point
through deflection gauge. Increase the load to 1.5 Kg and repeat the
experiment.
Find the deflections from the formula and verify.
Tabular column
Load
(N)
Ixx
mm4
L
mm
a
mm
b
mm
x
mm
Theoretical
value mm
Experimental
value mm
CAUTION : NEVER EXCEED 3 Kg LOAD ON THE BEAM
Conclusion: Deflection for three different loads for simply supported beam
is calculated and also verified by experimental values. The mean deflection
is ------units.
Example:
Determine the deflection of a simply supported beam loaded with W
=50,000 Newton, Young’s Modulus E =2 x105 N/mm
2; Second moment of
Inertia Ixx =7332.9x 104
mm4; & the load is placed at a distance a = 4800mm;
and the span of the beam L = 60000mm. Find the deflection at x =3000mm
from the left end.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 4
Yx = W b [ (L2 –b
2) X –X
3] /(6 E I L)
= 50000 x 1200x [ (60002 - 1200
2) 3000 -3000
3] /(6x2.0x10
5x 7332.9
x 104
x 6000)
Yx = 8.714 mm
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 5
Experiment – 2
Verification of Maxwell’s Reciprocal Theorem
Aim: To verify the Maxwell’s theorem for the structures system
Apparatus: Beam Test Set-Up with Load cells, steel scale, caliper, flat
beam, load indicator and dial gauge.
Scale
Gear box
Pointer
Hand wheel
Load
Loadindicator
Simply supportedbeam
Dialgauge
Fig. 3: Schematic layout of a beam setup
Theory:
The displacement at point i, in a linear elastic structure, due to
concentrated load at point j is equal to the displacement at point j due to a
concentrated load of same magnitude at point i.
The displacement at each point will be measured in the direction of the
concentrated load at that point. The only other restrictions on this statement,
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 6
in addition to the structure being linear elastic and stable, is that the
displacement at either point must be consistent with the type of load at that
point. If the load at a point is a concentrated force, then the displacement at
that point will be a translation, while if the load is moment, then the
displacement will be rotation. The displacement at any point will be in the
same direction as the load at that point and its positive direction will be in
the same direction as the load.
This theorem often referred to as Maxwell’s reciprocal displacement
theorem.
This can be proved through Unit Load Method i.e.; the deflection at A due
to unit load at B is equal to deflection at B due to unit load at A.
δ = ∫ M m dx / EI
where,
M = Bending Moment at any point x due to external load
m= Bending Moment at any point x due to unit load applied at the point
where deflection is required
let, mxA = Bending Moment at any point x due to unit load at A
mxB = Bending Moment at any point x due to unit load at B
When unit load (external load) is applied at A, M=mxA
To find deflection at B due to unit load at A, apply unit load at B
Then m=mxB
Hence, δBA = ∫ M m dx / EI δ = ∫ mxA mxB dx / EI ------(1)
Similarly, when unit load (external load) is applied at B, M=mxB
To find deflection at A, then m=mxA
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 7
Hence
δAB = ∫ M m dx / EI = ∫ mxA mxB dx / EI ------------------(2)
Comparing eqn. (1) and eqn. (2)
δAB = δBA-------------------------------------------------------------------------------------------- (3)
The external load (W) can be taken as a multiple with unit load, therefore
this load W will appear as multiple with mxA in eqn. (1) & as multiple with
mxB in eqn. (2). Thereby resulting in
W δAB = W δBA------------------------------------------------------ (4)
A beam shown in figure below which is simply supported at the ends
and is subjected to bending about its major axis with a concentrated load
anywhere in the beam.
Deflections δx at any distance `x` from left support are given by following
expressions; reference may be made to experiment no. 1.
δx = W b [ (L2 –b
2) x –x
3] /(6 E I L) for 0<x<a
δx = W b [ X3 – L/b (x-a)
3 - (L
2-b
2) x ] /(6 E I L) for a < x <L
Where,
W is the load placed at a distance `a` from the left support in Newton
b=distance of load from right side support
L = span of the beam in mm
Yx = deflection at any point distance x from left end
I = moment of inertia of the beam in mm4 (Ixx)
E= Young`s modulus in N/mm2
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 8
The Maxwell’s Reciprocal Displacement theorem is very useful in the
analysis of statistically indeterminate structures for evaluating the flexibility
coefficients.
The displacement relationship can be expressed at point i and j
δ i,B =f i,j W--------------------------------------------------- (5)
δ j,A =f j,i W--------------------------------------------------- (6)
Where, f i,j is the displacement at point i due to a unit load at point j and f
j,i is the displacement at point j due to a unit load at point i. If we now
substitute these expressions in Betti`s (Maxwell-Betti) law and cancel out
the term W on each side, we obtain
f i,j = f j,i
δ21 δ11
P
Fig-4: Simply supported Beam loaded at position 1 & 2
δ12 δ22
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 9
The theorem can be restated as the displacement at point i, in an elastic
structure, due to a unit load at point j is equal to the displacement at point j
due to unit load at point i.
Procedure:
Find the moment of inertia of beam from the following expression:
(1/12) b1 d1 3
where b1 is width of beam and d1 is depth. Place the beam supporting from
two wedge supports. The load position can be varied. Set the load cell to
read zero in the absence of load. Set the deflection gauge to read zero in the
absence of load.
Load the beam with 0.25 Kg. Note deflections at any point through
deflection gauge. Interchange the load location with the point of deflection
measurement and repeat the readings. Increase the load to 1.5 Kg and repeat
the experiment. Find the deflections from the formula and verify.
CAUTION: NEVER EXCEED 3 Kg LOAD ON THE BEAM .
Tabular column
Load
(N)
Ixx
mm4
L
mm
a
mm
b
mm
x
mm
Theoretical
value mm
δBA or δAB
Experimental
value mm
δBA or δAB
Conclusions: Maxwell’s reciprocal theorem is verified from the results i.e,
δ21=δ12. Deflection at 1, 2 are equal with interchange of loads (same
magnitude and direction).
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 10
Experiment – 3
Determination of Young’s Modulus using strain gauges
Aim: To determine the Young’s modulus of a simply supported beam or a
cantilever beam.
Apparatus: Beam Test Set-Up with load cells, Cantilever beam with
calibrated rosette strain gauge, strain measuring equipment and load
indicator.
Gear box
Strainindicator Load
indicator
Pointer
Scale
Load
Hand wheel
Cantileverbeam
straingauge
c1 c2 c3
c2
c1
c3
Strain guagearrangement
Fig. 5: Schematic layout of beam setup for Young’s modulus determination
Theory:
A beam shown in fig-4 shows the section which is simply supported at
the ends and is subjected to bending about its major axis with a concentrated
load anywhere in the beam. The beam is provided with strain gauge, the
deflection of the beam can be determined wherever the load is applied on to
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 11
the beam. An available cantilever beam can also be utilized for this
experiment.
The strain gauge is at a fixed position in the beam and load position
can be varied. A strain gauge is mounted on a free surface, which in
general, is in a state of plane stress where the state of stress is with regards to
a specific xy rectangular rosette. Consider the three element rectangular
rosette shown in fig-6, which provides normal strain components in three
directions spaced at angles of 450. If a xy coordinate system is assumed to
coincide with the gauge A and C then εx= εA and εy= εc. Gauge B provides
information necessary to determine γxy. Once εx, εy and γxy are known, then
Hooke’s law can be used to determine σx, σy, and τxy. However in this case
the requirement is to determine Young`s Modulus (E), which can be
determined from equation (1) below.
)()1( 2 yxx v
v
Eεεσ +
−= ; )(
)1( 2 xyy vv
Eεεσ +
−= ;
xyxyv
Eγτ
)1(2 +=
εx = εA; εy = εc; γxy = 2 εB - εA -εc ;
Sl.No Load (N)
εA εB εC εx εy γxy ν=εy/εx
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 12
M/I = σ/y --------------------------------------------------------------------------1
also
Shear Modulus xy
yxG
γ
τ=
------------------------------------------------2
Young’s Modulus E = 2G (1+ν) ------------------------------------------------3
Procedure: Mount the cantilever beam at the left support of beam test set-
up. Connect the strain gauges wires with the strain measuring equipment.
Use the following color codes
εA Red wires ch1
εB Yellow wires ch3
εc Black wires ch2
Set the load cell to read `zero` value in the absence of load. Set the three
strains to read `zero` in the absence of load. Now Load the beam with 0.25
Kg at some point and record the strains in three directions. Record the load
value at the load cell.
Repeat the experiment with load value of 1Kg. Compute the values of
Poisson’s ratio from:
ν=εy/εx
CAUTION: NEVER EXCEED 3 Kg LOAD ON THE BEAM
Tabular Column:
Sl.No Load
(N) εA
εB εC εx εy γxy ν=εy/εx
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 13
Find Young `s modulus through formulas above.
Conclusion: Young’s modulus for cantilever beam with point load is
evaluated as ------Units.
Example:
Sl No. Load
(N) εA εB εC εx εy γxy ν=εy/εx
1 10N 92µ 46µ -18µ 92µ -18µ 18µ 0.1957
2 20N 64µ 304µ -18µ 64µ -18µ 14µ 0.2188
3 30N 37µ 19µ -10µ 37µ -10µ 11µ 0.2973
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 14
Experiment – 4
Poisson`s ratio (ν) Determination
Aim: To determine the Poisson’s ratio of cantilever beam.
Apparatus: Beam Test Set-Up with load cells, Cantilever beam with
calibrated rosette strain gauge, strain measuring equipment and load
indicator.
Theory: A cantilever beam is subjected to bending about its major axis with
a concentrated load anywhere in the beam. The beam is provided with
rosette strain gauge.
A calibrated strain gauge rosette is fixed at a location with-in the span
of the beam, and load position can be varied. Calibration has been done to
read strains in microns (µ). Consider the three element rectangular rosette
shown in fig-7, which provides normal strain components in three directions
spaced at angles of 450. If an xy co-ordinate system is assumed to coincide
with the gauge A and C then εx= εA and εy= εc.
Gauge B provides information necessary to determine shear strain
(γxy). Once εx, εy and γxy are known, then Hooke’s law can be used to
determine σx, σy, and τxy. Subsequently principal stresses can be determined.
Poisson’s ratio ( ν ) can be determined from:
ν=εy/εx
Fig. 7
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 15
)()1( 2 yxx v
v
Eεεσ +
−= ; )(
)1( 2 xyy vv
Eεεσ +
−= ;
xyxyv
Eγτ
)1(2 +=
εx = εA; εy = εc ; γxy = 2 εB - εA -εc
Principal stress axes:
Principal stress axes is located with the angle θ according to :
tan 2θ = (2 εB - εA -εc) / (εA -εc)
Principal Stresses are given by following expressions:
σ1 = A + √ B2 + C
2 , σ2 = A - √ B2 + C
2
τmax = ( σ1- σ2 )/ 2 =√ B2 + C
2
Where, A= (σx+ σy)/2 , B = (σx - σy)/2 and C = τxy
E= Young’s modulus in N/mm2
Strains are in microns
Procedure: Mount the cantilever beam at the left support of beam test set-
up. Connect the strain gauges wires with the strain measuring equipment.
Use the following color codes
εA Red wires channel 1
εB Yellow wires channel 3
εc Black wires channel 2
Set the load cell to read `zero` value in the absence of load. Set the three
strains to read `zero` in the absence of load. Now Load the beam with 0.25
Kg at some point and record the strains in three directions. Record the load
value at the load cell.
Repeat the experiment with load value of 1.5 Kg. Compute the values of
Poisson’s ratio from: νννν=εεεεy/εεεεx
CAUTION: NEVER EXCEED 3 Kg LOAD ON THE BEAM.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 16
Students may determine stresses using formulas above. MATLAB program
is provided at the end of this manual to compute stresses from given strain
data.
Tabular Column:
Sl.No Load
(N) εA
εB εC εx εy γxy
ν=εy/εx
Conclusion: Poisson’s ratios for three different loads are evaluated and
mean Poisson’s ratio for a cantilever beam is=-------
Example: A typical data is shown for the purpose of computing shear strain
and Poisson’s ratio is given below.
Sl.No load εA εB εC εx εy γxy ν=εy/εx
1 10N 92µ 46µ -18µ 92µ -18µ 18µ 0.1957
2 20N 64µ 304µ -18µ 64µ -18µ 14µ 0.2188
3 30N 37µ 19µ -10µ 37µ -10µ 11µ 0.2973
Example: A typical data is shown for the purpose of computing stresses,
principal stresses, and planes of principal stresses.
Sl
No εA εB εC
σx
Mpa σy Mpa
τxy
Mpa
Principle
stress
σ1 Mpa
Principle
Stress
σ2 Mpa
1 200µ 900µ 1000µ 105.58 230.09 46.69 342.04 -6.371
Normal, shear stress,& principal stress
Angle of principal
stress
Sl
No σx
Mpa
σy
Mpa
τxy
Mpa
σ1
Mpa
σ2
Mpa θ1 θ2
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 17
1 5.6787 0.8159 0.3879 6.8156 -0.242 64.65 -86.00
2 12.064 1.1000 0.9842 13.299 -0.651 51.45 -85.62
3 17.944 1.2762 1.5695 19.347 -1.273 41.80 -85.04
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 18
Experiment - 5
Buckling Load of Slender Eccentric Columns and Construction of
South Well plot
Aim: Practical columns have some imperfections in the form of initial
curvature and the buckling of loads of such struts is of real practical value.
The experiment aims at measuring the buckling loads of columns and
construction of South Well Plot. The imperfection amounts to initial
curvature, which shows up in this plot.
Apparatus: WAGNER beam set-up, hinged supports, load cells, Long
column with initial curvature, mounted dial for deflection measurements.
Support
Gear box Hand wheel
Load
Loadindicator
Dialindicator
Eccentricloading
Column
Fig. 8: WAGNER beam set-up for buckling load
Theory: Consider a pin ended strut AB of length L, whose centroidal longitudinal
axis is initially curved as shown in fig (9). Under the application of the end
load P, the strut will have some additional lateral displacement y at any
section.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 19
In this case, bending moment at any point is proportional to the change in
curvature of the column from its initial bent position y- δ0. The equation for
curvature of column is as follows.
M =P(y+y0) = - EI d2y/dx
2 … (1)
P/EI =k2
0
22
2
2
ykykdx
yd−=+ … (2)
Assuming initial curvature (yo) to be sinusoidal, satisfying the equation
)/sin(00 Lxy πδ= … (3)
Where δ0 equals to the initial displacement at the centre of the strut
The general solution of this differential equation is
Y
P
y
P
δ0
Fig-9
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 20
)/sin(/
sincos222
0
2
LxkL
kkxBkxAy π
πδ
−++= … (4)
If the ends are hinged, for the end conditions, then:
y=0 at x =0 and x =L
This results in values of constants: A=B=0.
The resulting equation is as below:
−
=L
x
kL
ky
ππ
δsin
2
2
2
0
2
… (5)
Substituting Euler’s buckling load (Pe)
Pe =
and k 2 = P/EI
−=
L
x
P
Pey
πδsin
1
0 … (6)
for x=L/2, at center of column, the deflection at center yc
1
0
−=
P
Pey c
δ …(7)
The value Pe represents the buckling load for perfectly straight strut. In the
relation for deflection (y), the additional lateral displacement of the strut,
that the effect of end load P is to increase (y) by a factor 1/ (pe /p)-1; shown
by equation (6). When P approaches Pe, the additional displacement at mid
length of the strut is expressed by eqn. (7).
The load deflection relationship of eqn. (5) is the basis of South Well plot
technique for extrapolating for the elastic critical load from experimental
measurement.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 21
Pe
PPe
P
−=
10δ
δ … (8)
Rearranging the above equation we get
δ = (Pe / P) δ - δ0 … (9)
or
δ = (δ/ P) Pe - δ0
The linear relationship between δ/P and δ shown in figure below can be
experimentally determined. Thus if a straight line is drawn which best fits
the points determined from the experimental measurements of P and δ , the
reciprocal of the slope of this line gives an estimate of the magnitude of δ0 of
the initial curvature that can be determined from the intercept on the
horizontal axis.
δ
Fig.10: South Well
Plot
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 22
Procedure: Set up the two hinge supports on the WAGNER beam at the top
and bottom supports. Fix the column in the supports.
Set the load reading to zero in load cell. Determine the center of column. Set
–up the deflection dial gage for reading the column deflections at the center
of column. Set the deflection dial gage reading to zero.
Apply the vertical load in steps of 10 Kgs. each, in four steps (20Kg, 30Kg,
40Kg...) and record the deflections at each step of load.
Tabular Column:
Load (P)
N
Deflection (δ) mm δ/P
mm/N
Draw South Well Plot (δ/P vs δ ).
Determine the slope and estimate Pe. Find out the initial deflection of
column.
Conclusion: The buckling loads are computed for the column and the
SOUTHWELL plot is constructed. Slope is= --------- and Pe= ----------units.
CAUTION: NEVER EXCEED 100 Kg OF LOAD ON THE MILD
STEEL COLUMN AND 75Kg ON THE ALUMINIUM COLUMN.
Example: 1
A slender strut, 1800mm long, and of rectangular section 30mm x 12mm
transmits a longitudinal load P acting at the centre of each end. The strut was
slightly bent about its minor principal axis before loading. If the P is
increased form 500N to 1500N, the deflection at the middle of the length
increases by 4mm. Determine the amount of deflection before loading.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 23
Find also the total deflection and the maximum stress when P is 2000 N.
Take E = 2.15 x 105 N/mm
2.
I = 1/12 x 30 x 123
= 4320 mm4
Let Pe = Π2 EI /L
2 = Π2
2.15 x 105 x 4320 / (1800 X1800) =2830 N
Let δ1 be the central deflection when P =500 N and let δ2 be the central
deflection when P =1500 N
Substituting in 0δδ xPPe
Pec −
=
δ1 = 2830/ (2830-500) x δ0 … (1)
δ2 = 2830/ (2830-1500) x δ0 … (2)
from eqns.1 & 2
δδδδ0 = 4.381 mm
P =2000 N
δc = 2830/ (2830-2000) x 4.381 = 14.94 mm
A = 30 x 12 = 360mm2
Z = 1/6 x 30 x 122
Mc = P x δc = 2000 x 14.94 = 298880 N-mm
σ 0= P/A = 2000/360mm2
σb = Mc/Z = 29880/ 720 =41.5 N/mm2
σ max =σ0+ σb = 5.55 + 41.5 =47.05 N/mm2
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 24
Experiment - 6
Shear failure of Bolted and Riveted Joints
Aim: To determine the ultimate shear stress in a bolt.
Apparatus: WAGNER beam set-up, bolt for failure analysis, vernier caliper
and load indicator.
Support
Gear box Hand wheel
Load
Loadindicator
Single shear Double shear
Bolt
Load
P(vertical )N
P(vertical )N
Fig. 11: WAGNER beam set-up for shear failure of bolted joint
Theory: Riveted and bolted connections are common in structural
assemblies. Following are modes of failure in riveted joints:
� Tension failure in a plate
� Shearing failure across one or more planes of rivet
� Bearing failure between plate and the rivet
� Plate shear or shear out failure in the plate
In a riveted joint, the rivets may themselves fail in shear. The tendency is to
cut through the rivet across the section lying in the plane between the plates
it connects.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 25
If the load is transmitted through bearing between the plate and the shank of
the rivet producing shear in the rivet, the rivet is said to be in shear.
When the load is transmitted by shear in only one section of the rivet, the
rivet is said to be in single shear. When the loading of the rivet is such as to
have the load transmitted in two shear planes, the rivet is said to be in double
shear. When load is transmitted in more than two planes, the rivet is said to
be in multiple shear.
Rivets and bolts subjected to both shear and axial tension shall be so
proportioned that the calculated shear and axial tension do not exceed the
allowable stresses τ υf and σ tf and the flowing expression does not
exceed a specified value.
(τ υf ,cal / τ υf + σ tf,cal / σ tf )------------------------------------- (1)
Shearing failure of the rivet: In a riveted joint, the rivets may themselves fail
in shear. The tendency is to cut through the rivet across the section lying in
the plane between the plates it connects.
In analysing this possible manner of failure, one must always note whether a
rivet acts in single shear or double shear. In the latter case, the two cross-
sectional areas of the same rivet resist the applied force. The shearing stress
is assumed to be uniformly distributed over the cross-section of the rivet.
Let Pus = pull required, per pitch length, for shear failure
fs = ultimate shear strength of the rivet material
d = gross diameter of the bolt
Resisting area of the rivet section = (π/4) d2 in single shear
and = 2 x (π/4) d2 in double shear
Pus = (π/4) d2 fs for single shear
Pus = 2x (π/4) d2 fs for double shear
Procedure:
� Set-up the WAGNER beam test set-up.
� Note the diameter of the bolt.
� Place a bolt in the slot.
� Set the load cell to read zero.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 26
� Apply the load gradually.
� Note the load reading at the point of shear failure of mild steel bolt.
� Change the loading for double shear and calculate the ultimate shear
stress from the formula below:
fs = Pus / [2x (π/4) d2
] ---------------------------------(2)
Conclusion: The ultimate shear stress for single shear= ----------units
The ultimate shear stress for double shear= ---------units.
CAUTION: NEVER EXCEED 3 TONS OF LOAD ON THE BEAM
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 27
Experiment - 7
Bending Modulus of a Sandwich Beam
Aim: To determine the Modulus in Bending of a cantilever sandwich
beam.
Apparatus: Beam Test Set-up, load cells, Sandwich Beam of symmetrical
section with strain gage installed, Strain measuring device.
Fig. 12 Sandwich beam
Theory: Beams that are made of more than one material are called
`composite beams`. Sandwich beam is one such example. It consists of
following:
� Two thin layers of strong material, called faces, placed at top and
bottom.
� Thick core, consisting of light weight, low strength material. The core
simply serves as a filler or spacer. Sandwich construction is used where
light weight combined with high strength and high stiffness is needed.
If both the materials are rigidly joined together, they will behave like a unit
piece and the bending will take place about the combined axis. Such
composite beams can be analysed by the same bending theory that is
applicable for beam of single material.
On the other hand, if both the materials have been simply placed one above
the other, they will bend about their respective axes. However, in both the
cases, the total amount of moment of resistance will be equal to the sum of
moments of resistance of individual sections.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 28
The position of neutral axis may not be the centroid of the section. The
criterion of strain compatibility has to be used, i.e. strain in two materials, at
a given vertical distance from the neutral axis, has to be same.
A cantilever sandwich beam provided with strain gauge can be used to
do experimental assessment of strains. The strain gauge is at a fixed position
in the beam and load position can be varied. A strain gauge is mounted on a
free surface, which in general, is in a state of plane stress where the state of
stress is with regards to a specific xy rectangular rosette. Consider the three
element rectangular rosette shown in fig-13, which provides normal strain
components in three directions spaced at angles of 450. If a xy coordinate
system is assumed to coincide with the gauge A and C then εx= εA and εy=
εc. Gauge B provides information necessary to determine γxy. Once εx, εy
and γxy are known, then Hooke’s law can be used to determine σx, σy, and
τxy. However in this case the requirement is to determine Modulus in
bending (E). An alternative approach is to measure deflection under load
condition.
Fig. 13
)()1( 2 yxx v
v
Eεεσ +
−= ; )(
)1( 2 xyy vv
Eεεσ +
−= ;
xyxyv
Eγτ
)1(2 +=
εx = εA; εy = εc; γxy = 2 εB - εA -εc;
Sl.No Load
(N) εA εB εC εx εy γxy
ν=εy/εx
Also, σx = M/Z , Z = I/ Y (1)
σ2 = (M - σ1 Z1 ) / Z2 (2)
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 29
σ2 = m σ1 , m = E2 / E1 (3)
Suffix `1` & `2` refer two different sections of beam
Procedure: Mount the cantilever beam at the left support of beam test set-
up. Connect the strain gauges wires with the strain measuring equipment.
Use the following color codes
εA Red wires channel1
εB Yellow wires channel3
εC Black wires channel2
Set the load cell to read `zero` value in the absence of load. Set the three
strains to read `zero` in the absence of load. Now Load the beam with 2.5 Kg
at some point and record the strains in three directions. Record the load
value at the load cell.
Repeat the experiment with load value of 5 Kg. Compute the values of
Poisson’s ratio from:
ν=εy/εx
Tabular Column:
Sl.No Load
(N)
εA
εB εC εx εy γxy
ν=εy/εx
Find Modulus in bending through formulas above.
Conclusion: Bending modulus of sandwich beam is= ---------units.
CAUTION: NEVER EXCEED 15 Kg LOAD ON THE BEAM.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 30
Experiment - 8
Verification of Superposition Theorem
Aim: To verify the theorem of superposition.
Apparatus: Beam Test Set-Up with multiple loading capability (atleast two
load points required), atleast two load cells, cantilever strain gauged beam,
strain measuring equipment.
Gear box
Strainindicator Load
indicator
Pointer
Scale
Load
Hand wheel
Cantileverbeam
straingauge
c1 c2 c3
c2
c1
c3
Strain guagearrangement
Fig. 14: Schematic layout of beam setup
Theory:
Many times, a structural member is subjected to a number of forces
acting not only at the ends, but also at the intermediate points along its
length. Such a member can be analyzed by the application of the principal of
superposition; the resulting strain will be equal to the algebraic sum of the
strains caused by individual forces acting along the length of member.
The strain gauge is at a fixed position in the beam and load position
can be varied. A strain gauge is mounted on a free surface, which in
general, is in a state of plane stress where the state of stress is with regards to
a specific xy rectangular rosette. Consider the three element rectangular
rosette shown in fig-2, which provides normal strain components in three
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 31
directions spaced at angles of 450. If a xy coordinate system is assumed to
coincide with the gauge A and C then εx= εA and εy= εc. Gauge B provides
information necessary to determine γxy.
Fig-15
εx = εA; εy = εc; γxy = 2 εB - εA -εc
Sl.No Load
(N) εA εB εC εx εy γxy
Procedure:
Mount the cantilever beam at the left support of beam test set-up. Connect
the strain gauges wires with the strain measuring equipment. Use the
following color codes:
εA Red wires channel1
εB Yellow wires channel3
εC Black wires channel2
Set the load cell to read `zero` value in the absence of load. Set the three
strains to read `zero` in the absence of load. Now Load the beam with 0.5 Kg
at some point from vertical and record the strains in three directions. Record
the load value at the load cell. Record the point of loading.
Remove this load.
Set the load cell to read `zero` value in the absence of load. Set the three
strains to read `zero` in the absence of load. Now Load the beam with load
load value of 1 Kg. from vertical at same point and record the strains in three
directions. Record the load value.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 32
Remove this load.
Set the load cell to read `zero` value in the absence of load. Set the three
strains to read `zero` in the absence of load. Now Load the beam with 1.5 Kg
at same point from vertical as done earlier.
Record the strains in three directions. Record the load values in the two load
cells. Record the vertical load position.
Compute the values of γxy from the formula:
γxy = 2 εB - εA -εc
CAUTION: NEVER EXCEED 3 Kg LOAD ON THE BEAM.
Tabular Column:
Table 1: Strains due to individual vertical loading
Sl.No Vertical
Load
(N)
Load
position
mm
εA
εB εC εx εy γxy
Table 2: Strains due to combined loading
Sl.No Vertical
Load
(N)
Vertical
Load
position
mm
εA
εB εC εx εy γxy
Add the values of strains in table 1 and compare with value in Table 2.
Conclusion: The strains obtained are compared between individual and
combined loading and hence the principle of superposition is verified.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 33
Experiment – 9
Vibration of Cantilever Beam
Objective: To determine the lateral or transverse vibration of a cantilever
beam when the beam is fixed at one end and free at the other end.
Introduction: A beam which is cantilevered of span L with uniform mass w/g per
unit run is shown in figure-1and fixed at one end. Assume a deflection
function and obtain the first approximation for the fundamental frequency
with the origin at the free end.
L is the span of the beam in mm
E is the Young’s Modulus of the beam in N/mm2
I =bd3/12 is the Moment of Inertia of the beam mm
4
w = Weight per unit length
g = Acceleration due to gravity
The fundamental frequency of the cantilever beam
ω2= 12.39 E I / wl
4
The natural frequency for the transverse vibration of a uniform beam fixed at
one end and free at the other end.
The four roots of the equation are:
β1 L= 1.8751
β2 L= 4.6941
β3 L= 7.8548
β4 L= 10.9955
Fig. 16: Cantilever beam
L
P
H
x
A B
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 34
4
22
AL
EInn
ρπω =
…. (1)
Example: Determine the three lowest natural frequency for the system
shown in fig-1
Given m=10kg,E=200x109 N/m2; ρ =7800 kg/m3 ; A =2.6 x 10-3 m2 ;
L=1m ; I= 4.7 x10-6
m4.
43
622
1106.27800
107.4102001
9
xxx
xxxn
−
−
= πω =215.3 φ2
φ1=1.423; φ2=4.113; φ3=7.192
ω1 = 486.1 rad/ s; ω2 = 3642 rad/s; ω3
= 1.114 x 10
4 rad/s.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 35
Experiment-10
Wagner Beam (Tension Field)
Objective: The objective of this experiment is to determine the constant k of the
Wagner beam.
Support
Gear box Hand wheel
Load
Strainindicator
Loadindicator
c1 c2 c3
c2 c3
c1
Strain guagearrangement
Wagner beam
Fig. 17: WAGNER beam set-up for tension field
Introduction: In the analysis of wing beams of airplanes, the designer is faced with several
problems which, in general are not present in civil engineering structural
design. The civil Engineer endeavors to make the web sheet of all beams
thick enough so that the web will not buckle before the design load is
reached on the structure.
Buckling is a case of failure and the shearing stress causing buckling
determines the allowable maximum shear that can be applied. The critical
buckling shear stress is given by
2
2
2
)1(12
−=
b
tEcr µ
πτ
…1
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 36
If the sheet is very thin, buckling stress given by equation (1) is extremely
low and, in the interest of making efficient use of all available material. The
aircraft engineer raises the question as to how much additional shear can be
carried by such a buckled plate before:
� Some portion of the sheet has a total stress equal to the yield point of
the material, thus giving rise to permanent deformations; or
� The ultimate strength is reached.
If now, we assume that the web plate in the beam is very thin, the above
discussion of the principal stress patterns takes on new significance. The
normal stresses, we see that one of them is a compressive stress against
which thin plates have a very low resistance. The tendency will then be for
the plate to buckles in a direction perpendicular to the compressive stress at
a value of the applied shear which becomes less and less as the web becomes
thinner and thinner, the limiting case being for a sheet of zero thickness.
In this case, the sheet buckles upon the application of a shear load and can
only resist shear by means of the tensile stresses at 45degresss. With such a
pattern, it is obvious that the tensile stresses will tend to pull the two beam
flanges together, thus necessitating vertical members to counteract this
tendency (as shown dotted in fig. 18).
Wagner assumes that the web buckles immediately upon the application of
shear load and that the only stresses resisting the shear forces are the tensile
stresses which act approximately 45 degrees.
Considering infinitely rigid parallel span flanges and vertical stiffners the
following equations for this limiting case is shown as below:
=
)2sin(
12
ασ
ht
Pt …2
Axial force in the tension flange:
)cot(2
αP
h
PxFt −= …3
Axial force in the compression flange
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 37
)cot(2
αP
h
PxFc −−= …4
Axial force in the vertical stiffeners
)tan(αh
dPFc −= …5
The limiting case of a web having no compressive strength has been treated
by Wagner and beams approximating this are known as Wagner beam.
The basic assumptions of this theory is that total shear force in the web
can be divided into a shear force carried by shear in the sheet and the
shear forced carried by diagonal tension;
ncrk )1(τ
τ−=
Fig.18: Wagner’s Beam Tension Field beam
0.2 0.2 0.2
0.1
5 KN
0.012
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 38
Fig.19
A strain gauge is mounted on a free surface, which in general, is in a state of
plane stress where the state of stress with regards to a specific xy rectangular
rosette since each gauge element provides only one piece of information, the
indicated normal strain at the point in direction of the gauge. Consider the
three element rectangular rosette shown in fig-20, which provides normal
strain components in three directions spaced at angles of 450.
If an xy coordinate system is assumed to coincide with the gauge A and C
then
εx= εA and εy= εc. Gauge B provides information necessary to determine γxy.
Once εx, εy and γxy are known, then Hooke’s law can be used to determine
σx, σy, and τxy.
25000
500 1000 500 1000 1000 1000 1000
325000
qs = 104 N/m
275000 25000
500 2000 500 1000 1000 1000 1000
250e06
N/m 0.5e06
N/m
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 39
Fig. 20
)()1(
2 yxx
Eυεε
µσ +
−= ; )(
)1(2 xyy
Eυεε
µσ +
−= ;
xyxy
Eγ
µτ
)1(2 +=
εx = εA; εy = εc; γxy = 2 εB - εA -εc;
Sl
No εA εB εC
σx
MPa
σy
MPa
τxy
MPa
σ1
MPa
σ2
MPa
1 200µ 900µ 1000µ 105.58 230.09 46.69
Example: 1
Apply a load of given intensity on the Wagner beam
Step: 1 Consider an axially loaded aluminium panel simply supported edges and
rivet lines .Each stringer has an area of 12mm x 8mm and E=0.588e11 N/m2
and determine the compressive load i) when the sheet first buckles ii)
Stringer stress is 58.84x106 N/mm2.
Critical Buckling Stress:
2
1
=b
tKEcσ
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 40
σc= 3.62 * 0.588 x 10 11
x (0.002/0.2)2 = 21.2856 x 10
6 N/m
2
A= 0.002 x 0.6 = 1.2 x 10-3
m2
P = A x σσσσc1 = 1.2 x 10-3
m2 x21.2856 x 10
6 N/m
2 = 25,542.72 N
Post Buckling Strenth:
uσE
0.85twe1 = we1= 0.85* 0.002√(0.5884e11/58.58e06 = 0.05374
m
A = (3.0*0.053774)* 0.002 = 6.4488 e-04 αm2;
P = 58.84e06 * 6.4488e-04 = 37945.05289 N
The ratio of Post buckling strength to critical buckling stress is 1.48.
Step: 2 Determination of k
E= 58.8e109 N/αm2; K= 5.34 (Simply supported beam) K= 10.38 (Fixed
end)
The ratio of longer dimension/ shorter dimension is called aspect ratio =2.0
ht
V=τ
= 50000/ 0.1* 0.002=250 e06 N/m2
2
=b
tKEcrτ =5.34 * 0.588 x 10
11 x (0.002/0.1)
2 = 125.5968 x 10
6
N/m2
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 41
)1(τ
τ crk −= = (1-125.5986e06/250e06) = 0.5024
Step 3: Schematic distribution of load
ht
Pσ s =
= 50000/(0.1*0.002) =250e06
N/m2
Assume buckling angle =450
(Normal Stress in Y-direction) yσ =sσ )tan(α = 250 e
06 tan (45) =250e
06
N/m2
(Normal Stress in x-direction) σx =sσ )cot(α = 250 e
06 cot (45) =250e
06 N/m2
=
)2sin(
12
ασ
ht
Pt = 2*50000*/(0.1*0.002)*(1/sin90) =500e
06
N/m2 ;( Tension in the beam at 45 degrees angle)
q s = σs * t = 250e06
* 0.002 = 0.5e06 N/m2; (Shear flow in the beam)
Fc_start = Ft_start = )cot(2
αP
h
PxFt −= = 0-50000/2*cot (45)
= 25000 N
Fc_end = Ft_end = )cot(2
αP
h
PxFt −= = (50000*0.6/0.1)-50000/2*cot
(45) = 325000,275000 N respectively. The stress distribution is shown in
figure.
Force in the vertical stiffener: )tan(αh
dPFc −=
= -50000*(0.2/0.1)*tan45 = - 0.100e06 N/m2
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 42
Appendix -1 Unsymmetrical bending of angle section
%function
[xbar,ybar,Ixx,Iyy,Ixy,Iuu,Ivv,Iuv,alpha_uv]=us_ang
le01(thick1,breadth1,thick2,breadth2,x1_bar,x2_bar,
y1_bar,y2_bar)
function
[xbar,ybar,Ixx,Iyy,Ixy,Iuu,Ivv,Iuv,alpha_uv]=us_ang
le01(thick1,breadth1,thick2,breadth2,x1_bar,x2_bar,
y1_bar,y2_bar)
area1=thick1*breadth1;
area2=thick2*breadth2;
total_area=area1+area2;
Nrx=area1*x1_bar+area2*x2_bar;
Nry=area1*y1_bar+area2*y2_bar;
xbar=Nrx/total_area;
ybar=Nry/total_area;
t1=1/12;
tx1=(xbar-x1_bar);
ty1=(ybar-y1_bar);
tx1_2=(xbar-x1_bar)*(xbar-x1_bar);
ty1_2=(ybar-y1_bar)*(ybar-y1_bar);
tx2=(xbar-x2_bar);
ty2=(ybar-y2_bar);
tx2_2=(xbar-x2_bar)*(xbar-x2_bar);
ty2_2=(ybar-y2_bar)*(ybar-y2_bar);
Ixx_1=t1*breadth1*thick1^3;
Iyy_1=t1*thick1*breadth1^3;
Ixy_1=area1*tx1*ty1;
Ixx_2=t1*breadth2*thick2^3;
Iyy_2=t1*thick2*breadth2^3;
Ixy_2=area2*tx2*ty2;
Ixx1=Ixx_1+area1*ty1_2;
Iyy1=Iyy_1+area1*tx1_2;
Ixx2=Ixx_2+area2*ty2_2;
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 43
Iyy2=Iyy_2+area2*tx2_2;
Ixx=Ixx1+Ixx2;
Iyy=Iyy1+Iyy2;
Ixy=Ixy_1+Ixy_2;
raddeg=180/pi;
tmpnr=Ixy;
tmpdr=(Iyy-Ixx)*0.5;
tmp=tmpnr/tmpdr;
alpha_uv=0.5*atan(tmp)*raddeg;
term1=0.5*(Ixx+Iyy);
term2=0.5*sqrt((Ixx-Iyy)*(Ixx-Iyy)+4.0*Ixy*Ixy);
Iuu=term1+term2;
Ivv=term1-term2;
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 44
Appendix-2
Rectangular strain rosette Compuation of stresses sig_x and sig_y and gamma_xy
ea=input('ea the strain in a-directon: \n')
eb=input('eb the strain in b-directon: \n')
ec=input('ec the strain in c-directon: \n')
%E=input('E the Youngs strain E=58.8e09 N/m2: \n')
%mu=input('mu the poissons ratio:(0.33) \n')
E=58.8e09;
mu=0.33;
ex=ea*10^-06
ey=ec*10^-06
exy=(2*eb-ec-ea)*10^-06
k1=E/(1-mu*mu);
sig_x=k1*(ex+mu*ey)
sig_y=k1*(ey+mu*ex)
tau_xy=0.5*(E/(1+mu))*exy
con1=(sig_x+sig_y);
con2=con1*con1;
con3=4*tau_xy*tau_xy;
sig_p1=0.5*(con1+sqrt(con2+con3))
sig_p2=0.5*(con1-sqrt(con2+con3))
theta_p1=atan((sig_p1-sig_x)/tau_xy)
theta_p2=atan((sig_p2-sig_x)/tau_xy)
thetp1=180/pi*theta_p1
thetp2=180/pi*theta_p2
valuexy=sig_x+sig_y
value12=sig_p1+sig_p2
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 45
Appendix -3 Flexibility matrix for cantilever beam %The program to compute the deflection and rotation of a cantilever beam % Def_x= P*x*x(3*L-x)/6EI Rotx=P*x(2*L-x)/2EI,where
x is from the fixed end;
x=1.5 %m;
L=3 %m;
E=2e08 %kN/m2;
I=1.70797e-4 %m4;
P=10 %kN
sd_x=0.05*x
sd_L=0.05*L
sd_E=0.05*E
sd_I=0.05*I
sd_P=0.15*P
u1=unifrnd(0,1,100000,1);
x1=norminv(u1).*sd_x+x;
const=P/(6*E*I);
x2=(3.*L-x1);
def_x=const*x2.*x1;
def_x1=def_x.*x1;
hist(def_x1)
mean_x1=mean(def_x1)
std_x1=std(def_x1)
median_x1=median(def_x1)
sk_x1=skewness(def_x1)
cov_x1=std_x1/mean_x1
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 46
VIVA QUESTIONS:
1. Explain Castigliano`s theorem and its verification through any
experimental set-up.
2. Explain Maxwell`s reciprocal theorem and its verification though
experiment.
3. What is Betti`s theorem?
4. Explain South well plot.
5. What are various modes of failures of riveted joints?
6. What is the value of maximum loading allowed in the existing
experimental beam test set-up?
7. What is the value of maximum loading allowed in the existing Wagner
beam set-up?
8. What is bending modulus?
9. What is a sandwich beam?
10. What is strain compatibility?
11. Explain unit load method for determining the deflection of beams.
12. How Young’s modulus and Poisson’s ratio can be determined from
beam test set-up?
13. Explain Superposition theorem.
14. What are mode shapes and types of modes in vibrations?
15. Define DOF.
16. What is a Rosette strain gauge?
17. Explain unsymmetrical bending of beams.
18. What is the purpose of Stiffeners, What is the purpose of Longirons?
19. What stresses are taken up by the web and the flange of the spars?
20. Explain how bending and torsion is taken up by the wing structure.
21. What is a torsion box?
22. Explain how bending and torsion is taken up by the fuselage structure.
23. What is shear center and how it can be determined through
experimental set-up?
24. What is Flexibility matrix?
25. What is Power Spectral Density?
26. What are Principal stress axes?
27. Define simple stress and simple strain.
28. Define plain stress, plain strain.
29. What is a stress Tensor? Stress at a point in a material will have how
many components? Segregate normal and shear components of stress
tensor.
AIRCRAFT STRUCTURES LAB (06AEL57)
===============================================================
=============================================================== DEPT. OF AERONAUTICAL ENGINEERING, DSCE 47
30. What is a Wagner Beam test set-up? What are Wagner assumptions?
31. Explain the Energy methods used for structural analysis.
32. Draw SFD and BMD for i) SSB with UDL ii) CB with UDL.
33. Draw the orthographic views of i) civil airframe ii) military airframe
(minimum 3 views i.e. front, top and side view).
34. Differentiate b/w i) stringer ii) spar and iii) longiron based on the type
of loading they undergo in general.
******