Environmental Engineering Reference
In-Depth Information
Designing. the. shear. webs. (spars). that. carry. static. and. fatigue. loads. can.
minimize.the.wind.turbine.blade.thickness.shell.
Shear.webs.carry.the.bending.and.torsion.loads,.so.their.placements.can.be.
determined.by.analyzing.shear.stress.distributions.
2.9.2
Shear Web Analysis
The. differential. equation. that. determines. stress. function. F. for. the. leading.
and.trailing.wind.turbine.blade.is.shown.as:
4
2Q(
µ
s
+
µ
h
)y
1
G + G
∂
∂
2
F
x
1
∂
∂
F
y
2
Q
2(G + G
.
zy
zy
'(Y) + C
.
+
=
-
h
)I
s
h
2
s
h
2
s
h
s
G + G
(E + E )I
yz
yz
xz
xz
z
z
xz
x
z
.
.
.
.
.
(2.16)
where,
E
z
s
,. E
z
h
. are. the. modulus. of. normal. elasticity. for. skin. layers. (s). and. inner.
webs.(h);
G
xz
s
,. G
xz
h.
are. the. modulus. of. shear. stiffness. for. skin. layers. (s). and. inner.
webs.(h);
I.is.the.moment.of.inertia.for.skin.and.inner.webs.layers;
F.is.the.stress.function.that.is.acting.in.lexural.bending.and.twisting.of.the.
leading.and.trailing.edges.of.wind.turbine.blades;
μ
zy
s
.and.μ
zy
h
.are.Poisson's.ratio.for.skin.layers.and.inner.webs;
Q.represents.the.external.dynamic.load,.which.has.been.acted.upon.in.the.
center.of.the.point.of.hydrodynamic.stress.function;
φ'.is.the.derivative.of.proile.function;
C.is.a.constant.of.a.twist.determination.
If.the.lateral.surfaces.are.free.from.all.external.forces,.the.stress.function.
F.for.the.contour.will.be.equal.to.zero.and.all.cross.sections.will.satisfy.the.
boundary.conditions..From.Equation.(2.16),.the.values.of.the.stress.function.
F.along.the.boundary.can.be.calculated.for.all.cross.sections.
The.shear.stresses.for.the.skin.plates.can.be.found.using.Equation.(2.17).
=
∂
∂
F
y
-
Q
21
τ
xz
s
2
.
x - ( )
.
(2.17)
s
The.shear.stresses.for.inner.webs.(spars).can.be.found.using.Equation.2.17).
where:
F.is.a.stress.function,.φ(y).is.a.function.of.proile;
I
s
.and.I
h
.are.moments.of.inertia.for.skin.layers.and.inner.web.layers.
Now.follows:
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